# CXCORE Reference Manual

- Basic Structures
- Operations on Arrays
  - Initialization
  - Accessing Elements and sub-Arrays
  - Copying and Filling
  - Transforms and Permutations
  - Arithmetic, Logic and Comparison
  - Statistics
  - Linear Algebra
  - Math Functions
  - Random Number Generation
  - Discrete Transforms
- Dynamic Structures
  - Memory Storages
  - Sequences
  - Sets
  - Graphs
  - Trees
- Drawing Functions
  - Curves and Shapes
  - Text
  - Point Sets and Contours
- Data Persistence and RTTI
  - File Storage
  - Writing Data
  - Reading Data
  - RTTI and Generic Functions
- Miscellaneous Functions
- Error Handling and System Functions
  - Error Handling
  - System Functions
- Alphabetical List of Functions
- List of Examples

# Basic Structures

### CvPoint

2D point with integer coordinates

        typedef struct CvPoint
        {
            int x; /* x-coordinate, usually zero-based */
            int y; /* y-coordinate, usually zero-based */
        }
        CvPoint;

        /* the constructor function */
        inline CvPoint cvPoint( int x, int y );

        /* conversion from CvPoint2D32f */
        inline CvPoint cvPointFrom32f( CvPoint2D32f point );

### CvPoint2D32f

2D point with floating-point coordinates

        typedef struct CvPoint2D32f
        {
            float x; /* x-coordinate, usually zero-based */
            float y; /* y-coordinate, usually zero-based */
        }
        CvPoint2D32f;

        /* the constructor function */
        inline CvPoint2D32f cvPoint2D32f( double x, double y );

        /* conversion from CvPoint */
        inline CvPoint2D32f cvPointTo32f( CvPoint point );

### CvPoint3D32f

3D point with floating-point coordinates

        typedef struct CvPoint3D32f
        {
            float x; /* x-coordinate, usually zero-based */
            float y; /* y-coordinate, usually zero-based */
            float z; /* z-coordinate, usually zero-based */
        }
        CvPoint3D32f;

        /* the constructor function */
        inline CvPoint3D32f cvPoint3D32f( double x, double y, double z );

### CvPoint2D64f

2D point with double precision floating-point coordinates

        typedef struct CvPoint2D64f
        {
            double x; /* x-coordinate, usually zero-based */
            double y; /* y-coordinate, usually zero-based */
        }
        CvPoint2D64f;

        /* the constructor function */
        inline CvPoint2D64f cvPoint2D64f( double x, double y );

        /* conversion from CvPoint */
        inline CvPoint2D64f cvPointTo64f( CvPoint point );

### CvPoint3D64f

3D point with double precision floating-point coordinates

        typedef struct CvPoint3D64f
        {
            double x; /* x-coordinate, usually zero-based */
            double y; /* y-coordinate, usually zero-based */
            double z; /* z-coordinate, usually zero-based */
        }
        CvPoint3D64f;

        /* the constructor function */
        inline CvPoint3D64f cvPoint3D64f( double x, double y, double z );

### CvSize

pixel-accurate size of a rectangle

        typedef struct CvSize
        {
            int width; /* width of the rectangle */
            int height; /* height of the rectangle */
        }
        CvSize;

        /* the constructor function */
        inline CvSize cvSize( int width, int height );

### CvSize2D32f

sub-pixel accurate size of a rectangle

        typedef struct CvSize2D32f
        {
            float width; /* width of the box */
            float height; /* height of the box */
        }
        CvSize2D32f;

        /* the constructor function */
        inline CvSize2D32f cvSize2D32f( double width, double height );

### CvRect

offset and size of a rectangle

        typedef struct CvRect
        {
            int x; /* x-coordinate of the left-most rectangle corner[s] */
            int y; /* y-coordinate of the top-most or bottom-most
                      rectangle corner[s] */
            int width; /* width of the rectangle */
            int height; /* height of the rectangle */
        }
        CvRect;

        /* the constructor function */
        inline CvRect cvRect( int x, int y, int width, int height );

### CvScalar

A container for 1-,2-,3- or 4-tuples of numbers

        typedef struct CvScalar
        {
            double val[4];
        }
        CvScalar;

        /* the constructor function: initializes val[0] with val0, val[1] with val1 etc. */
        inline CvScalar cvScalar( double val0, double val1=0,
                                  double val2=0, double val3=0 );
        /* the constructor function: initializes val[0]...val[3] with val0123 */
        inline CvScalar cvScalarAll( double val0123 );

        /* the constructor function: initializes val[0] with val0, val[1]...val[3] with zeros */
        inline CvScalar cvRealScalar( double val0 );

### CvTermCriteria

Termination criteria for iterative algorithms

    #define CV_TERMCRIT_ITER    1
    #define CV_TERMCRIT_NUMBER  CV_TERMCRIT_ITER
    #define CV_TERMCRIT_EPS     2

    typedef struct CvTermCriteria
    {
        int    type;  /* a combination of CV_TERMCRIT_ITER and CV_TERMCRIT_EPS */
        int    max_iter; /* maximum number of iterations */
        double epsilon; /* accuracy to achieve */
    }
    CvTermCriteria;

    /* the constructor function */
    inline  CvTermCriteria  cvTermCriteria( int type, int max_iter, double epsilon );

    /* check termination criteria and transform it so that type=CV_TERMCRIT_ITER+CV_TERMCRIT_EPS,
       and both max_iter and epsilon are valid */
    CvTermCriteria cvCheckTermCriteria( CvTermCriteria criteria,
                                        double default_eps,
                                        int default_max_iters );

### CvMat

Multi-channel matrix

        typedef struct CvMat
        {
            int type; /* CvMat signature (CV_MAT_MAGIC_VAL), element type and flags */
            int step; /* full row length in bytes */

            int* refcount; /* underlying data reference counter */

            union
            {
                uchar* ptr;
                short* s;
                int* i;
                float* fl;
                double* db;
            } data; /* data pointers */

        #ifdef __cplusplus
            union
            {
                int rows;
                int height;
            };

            union
            {
                int cols;
                int width;
            };
        #else
            int rows; /* number of rows */
            int cols; /* number of columns */
        #endif

        } CvMat;

### CvMatND

Multi-dimensional dense multi-channel array

        typedef struct CvMatND
        {
            int type; /* CvMatND signature (CV_MATND_MAGIC_VAL), element type and flags */
            int dims; /* number of array dimensions */

            int* refcount; /* underlying data reference counter */

            union
            {
                uchar* ptr;
                short* s;
                int* i;
                float* fl;
                double* db;
            } data; /* data pointers */

            /* pairs (number of elements, distance between elements in bytes) for
               every dimension */
            struct
            {
                int size;
                int step;
            }
            dim[CV_MAX_DIM];

        } CvMatND;

### CvSparseMat

Multi-dimensional sparse multi-channel array

        typedef struct CvSparseMat
        {
            int type; /* CvSparseMat signature (CV_SPARSE_MAT_MAGIC_VAL), element type and flags */
            int dims; /* number of dimensions */
            int* refcount; /* reference counter - not used */
            struct CvSet* heap; /* a pool of hashtable nodes */
            void** hashtable; /* hashtable: each entry has a list of nodes
                                 having the same "hashvalue modulo hashsize" */
            int hashsize; /* size of hashtable */
            int total; /* total number of sparse array nodes */
            int valoffset; /* value offset in bytes for the array nodes */
            int idxoffset; /* index offset in bytes for the array nodes */
            int size[CV_MAX_DIM]; /* arr of dimension sizes */

        } CvSparseMat;

### IplImage

IPL image header

        typedef struct _IplImage
        {
            int  nSize;         /* sizeof(IplImage) */
            int  ID;            /* version (=0)*/
            int  nChannels;     /* Most of OpenCV functions support 1,2,3 or 4 channels */
            int  alphaChannel;  /* ignored by OpenCV */
            int  depth;         /* pixel depth in bits: IPL_DEPTH_8U, IPL_DEPTH_8S, IPL_DEPTH_16U,
                                   IPL_DEPTH_16S, IPL_DEPTH_32S, IPL_DEPTH_32F and IPL_DEPTH_64F are supported */
            char colorModel[4]; /* ignored by OpenCV */
            char channelSeq[4]; /* ditto */
            int  dataOrder;     /* 0 - interleaved color channels, 1 - separate color channels.
                                   cvCreateImage can only create interleaved images */
            int  origin;        /* 0 - top-left origin,
                                   1 - bottom-left origin (Windows bitmaps style) */
            int  align;         /* Alignment of image rows (4 or 8).
                                   OpenCV ignores it and uses widthStep instead */
            int  width;         /* image width in pixels */
            int  height;        /* image height in pixels */
            struct _IplROI *roi;/* image ROI. when it is not NULL, this specifies image region to process */
            struct _IplImage *maskROI; /* must be NULL in OpenCV */
            void  *imageId;     /* ditto */
            struct _IplTileInfo *tileInfo; /* ditto */
            int  imageSize;     /* image data size in bytes
                                   (=image->height*image->widthStep
                                   in case of interleaved data)*/
            char *imageData;  /* pointer to aligned image data */
            int  widthStep;   /* size of aligned image row in bytes */
            int  BorderMode[4]; /* border completion mode, ignored by OpenCV */
            int  BorderConst[4]; /* ditto */
            char *imageDataOrigin; /* pointer to a very origin of image data
                                      (not necessarily aligned) -
                                      it is needed for correct image deallocation */
        }
        IplImage;

The structure `IplImage` came from Intel Image Processing Library where the format is native. OpenCV supports only a subset of possible `IplImage` formats:

- `alphaChannel` is ignored by OpenCV.
- `colorModel` and `channelSeq` are ignored by OpenCV. The single OpenCV function cvCvtColor working with color spaces takes the source and destination color spaces as a parameter.
- `dataOrder` must be IPL_DATA_ORDER_PIXEL (the color channels are interleaved), however selected channels of planar images can be processed as well if COI is set.
- `align` is ignored by OpenCV, while `widthStep` is used to access to subsequent image rows.
- `maskROI` is not supported. The function that can work with mask take it as a separate parameter. Also the mask in OpenCV is 8-bit, whereas in IPL it is 1-bit.
- `tileInfo` is not supported.
- `BorderMode` and `BorderConst` are not supported. Every OpenCV function working with a pixel neigborhood uses a single hard-coded border mode (most often, replication).

Besides the above restrictions, OpenCV handles ROI differently. It requires that the sizes or ROI sizes of all source and destination images match exactly (according to the operation, e.g. for cvPyrDown destination width(height) must be equal to source width(height) divided by 2 ±1), whereas IPL processes the intersection area - that is, the sizes or ROI sizes of all images may vary independently.

### CvArr

Arbitrary array

        typedef void CvArr;

The metatype `CvArr*` is used only as a function parameter to specify that the function accepts arrays of more than a single type, for example IplImage*, CvMat* or even CvSeq*. The particular array type is determined at runtime by analyzing the first 4 bytes of the header.

# Operations on Arrays

## Initialization

### CreateImage

Creates header and allocates data

    IplImage* cvCreateImage( CvSize size, int depth, int channels );

size
  Image width and height.
depth
  Bit depth of image elements. Can be one of:
  IPL_DEPTH_8U - unsigned 8-bit integers
  IPL_DEPTH_8S - signed 8-bit integers
  IPL_DEPTH_16U - unsigned 16-bit integers
  IPL_DEPTH_16S - signed 16-bit integers
  IPL_DEPTH_32S - signed 32-bit integers
  IPL_DEPTH_32F - single precision floating-point numbers
  IPL_DEPTH_64F - double precision floating-point numbers
channels
  Number of channels per element(pixel). Can be 1, 2, 3 or 4. The channels are interleaved, for example the usual data layout of a color image is:
  b0 g0 r0 b1 g1 r1 ...
  Although in general IPL image format can store non-interleaved images as well and some of OpenCV can process it, this function can create interleaved images only.

The function `cvCreateImage` creates the header and allocates data. This call is a shortened form of

        header = cvCreateImageHeader(size,depth,channels);
        cvCreateData(header);

### CreateImageHeader

Allocates, initializes, and returns structure IplImage

    IplImage* cvCreateImageHeader( CvSize size, int depth, int channels );

size
  Image width and height.
depth
  Image depth (see CreateImage).
channels
  Number of channels (see CreateImage).

The function `cvCreateImageHeader` allocates, initializes, and returns the structure `IplImage`. This call is an analogue of

      iplCreateImageHeader( channels, 0, depth,
                            channels == 1 ? "GRAY" : "RGB",
                            channels == 1 ? "GRAY" : channels == 3 ? "BGR" :
                            channels == 4 ? "BGRA" : "",
                            IPL_DATA_ORDER_PIXEL, IPL_ORIGIN_TL, 4,
                            size.width, size.height,
                            0,0,0,0);

though it does not use IPL functions by default (see also `CV_TURN_ON_IPL_COMPATIBILITY` macro)

### ReleaseImageHeader

Releases header

    void cvReleaseImageHeader( IplImage** image );

image
  Double pointer to the deallocated header.

The function `cvReleaseImageHeader` releases the header. This call is an analogue of

        if( image )
        {
            iplDeallocate( *image, IPL_IMAGE_HEADER | IPL_IMAGE_ROI );
            *image = 0;
        }

though it does not use IPL functions by default (see also `CV_TURN_ON_IPL_COMPATIBILITY`)

### ReleaseImage

Releases header and image data

    void cvReleaseImage( IplImage** image );

image
  Double pointer to the header of the deallocated image.

The function `cvReleaseImage` releases the header and the image data. This call is a shortened form of

        if( *image )
        {
            cvReleaseData( *image );
            cvReleaseImageHeader( image );
        }

### InitImageHeader

Initializes allocated by user image header

    IplImage* cvInitImageHeader( IplImage* image, CvSize size, int depth,
                                 int channels, int origin=0, int align=4 );

image
  Image header to initialize.
size
  Image width and height.
depth
  Image depth (see CreateImage).
channels
  Number of channels (see CreateImage).
origin
  `IPL_ORIGIN_TL` or `IPL_ORIGIN_BL`.
align
  Alignment for image rows, typically 4 or 8 bytes.

The function `cvInitImageHeader` initializes the image header structure, pointer to which is passed by the user, and returns the pointer.

### CloneImage

Makes a full copy of image

    IplImage* cvCloneImage( const IplImage* image );

image
  Original image.

The function `cvCloneImage` makes a full copy of the image including header, ROI and data

### SetImageCOI

Sets channel of interest to given value

    void cvSetImageCOI( IplImage* image, int coi );

image
  Image header.
coi
  Channel of interest.

The function `cvSetImageCOI` sets the channel of interest to a given value. Value 0 means that all channels are selected, 1 means that the first channel is selected etc. If ROI is `NULL` and `coi != 0`, ROI is allocated. Note that most of OpenCV functions do not support COI, so to process separate image/matrix channel one may copy (via cvCopy or cvSplit) the channel to separate image/matrix, process it and copy the result back (via cvCopy or cvCvtPlaneToPix) if need.

### GetImageCOI

Returns index of channel of interest

    int cvGetImageCOI( const IplImage* image );

image
  Image header.

The function `cvGetImageCOI` returns channel of interest of the image (it returns 0 if all the channels are selected).

### SetImageROI

Sets image ROI to given rectangle

    void cvSetImageROI( IplImage* image, CvRect rect );

image
  Image header.
rect
  ROI rectangle.

The function `cvSetImageROI` sets the image ROI to a given rectangle. If ROI is `NULL` and the value of the parameter `rect` is not equal to the whole image, ROI is allocated. Unlike COI, most of OpenCV functions do support ROI and treat it in a way as it would be a separate image (for example, all the pixel coordinates are counted from top-left or bottom-left (depending on the image origin) corner of ROI)

### ResetImageROI

Releases image ROI

    void cvResetImageROI( IplImage* image );

image
  Image header.

The function `cvResetImageROI` releases image ROI. After that the whole image is considered selected. The similar result can be achieved by

    cvSetImageROI( image, cvRect( 0, 0, image->width, image->height ));
    cvSetImageCOI( image, 0 );

But the latter variant does not deallocate `image->roi`.

### GetImageROI

Returns image ROI coordinates

    CvRect cvGetImageROI( const IplImage* image );

image
  Image header.

The function `cvGetImageROI` returns image ROI coordinates. The rectangle cvRect(0,0,image->width,image->height) is returned if there is no ROI

### CreateMat

Creates new matrix

    CvMat* cvCreateMat( int rows, int cols, int type );

rows
  Number of rows in the matrix.
cols
  Number of columns in the matrix.
type
  Type of the matrix elements. Usually it is specified in form `CV_<bit_depth>(S|U|F)C<number_of_channels>`, for example:
  `CV_8UC1` means an 8-bit unsigned single-channel matrix, `CV_32SC2` means a 32-bit signed matrix with two channels.

The function `cvCreateMat` allocates header for the new matrix and underlying data, and returns a pointer to the created matrix. It is a short form for:

        CvMat* mat = cvCreateMatHeader( rows, cols, type );
        cvCreateData( mat );

Matrices are stored row by row. All the rows are aligned by 4 bytes.

### CreateMatHeader

Creates new matrix header

    CvMat* cvCreateMatHeader( int rows, int cols, int type );

rows
  Number of rows in the matrix.
cols
  Number of columns in the matrix.
type
  Type of the matrix elements (see cvCreateMat).

The function `cvCreateMatHeader` allocates new matrix header and returns pointer to it. The matrix data can further be allocated using cvCreateData or set explicitly to user-allocated data via cvSetData.

### ReleaseMat

Deallocates matrix

    void cvReleaseMat( CvMat** mat );

mat
  Double pointer to the matrix.

The function `cvReleaseMat` decrements the matrix data reference counter and releases matrix header:

        if( *mat )
            cvDecRefData( *mat );
        cvFree( (void**)mat );

### InitMatHeader

Initializes matrix header

    CvMat* cvInitMatHeader( CvMat* mat, int rows, int cols, int type,
                            void* data=NULL, int step=CV_AUTOSTEP );

mat
  Pointer to the matrix header to be initialized.
rows
  Number of rows in the matrix.
cols
  Number of columns in the matrix.
type
  Type of the matrix elements.
data
  Optional data pointer assigned to the matrix header.
step
  Full row width in bytes of the data assigned. By default, the minimal possible step is used, i.e., no gaps is assumed between subsequent rows of the matrix.

The function `cvInitMatHeader` initializes already allocated CvMat structure. It can be used to process raw data with OpenCV matrix functions.

For example, the following code computes matrix product of two matrices, stored as ordinary arrays.

Calculating Product of Two Matrices

       double a[] = { 1, 2, 3, 4
                      5, 6, 7, 8,
                      9, 10, 11, 12 };

       double b[] = { 1, 5, 9,
                      2, 6, 10,
                      3, 7, 11,
                      4, 8, 12 };

       double c[9];
       CvMat Ma, Mb, Mc ;

       cvInitMatHeader( &Ma, 3, 4, CV_64FC1, a );
       cvInitMatHeader( &Mb, 4, 3, CV_64FC1, b );
       cvInitMatHeader( &Mc, 3, 3, CV_64FC1, c );

       cvMatMulAdd( &Ma, &Mb, 0, &Mc );
       // c array now contains product of a(3x4) and b(4x3) matrices

### Mat

Initializes matrix header (light-weight variant)

    CvMat cvMat( int rows, int cols, int type, void* data=NULL );

rows
  Number of rows in the matrix.
cols
  Number of columns in the matrix.
type
  Type of the matrix elements (see CreateMat).
data
  Optional data pointer assigned to the matrix header.

The function `cvMat` is a fast inline substitution for cvInitMatHeader. Namely, it is equivalent to:

         CvMat mat;
         cvInitMatHeader( &mat, rows, cols, type, data, CV_AUTOSTEP );

### CloneMat

Creates matrix copy

    CvMat* cvCloneMat( const CvMat* mat );

mat
  Input matrix.

The function `cvCloneMat` creates a copy of input matrix and returns the pointer to it.

### CreateMatND

Creates multi-dimensional dense array

    CvMatND* cvCreateMatND( int dims, const int* sizes, int type );

dims
  Number of array dimensions. It must not exceed CV_MAX_DIM (=32 by default, though it may be changed at build time)
sizes
  Array of dimension sizes.
type
  Type of array elements. The same as for CvMat

The function `cvCreateMatND` allocates header for multi-dimensional dense array and the underlying data, and returns pointer to the created array. It is a short form for:

        CvMatND* mat = cvCreateMatNDHeader( dims, sizes, type );
        cvCreateData( mat );

Array data is stored row by row. All the rows are aligned by 4 bytes.

### CreateMatNDHeader

Creates new matrix header

    CvMatND* cvCreateMatNDHeader( int dims, const int* sizes, int type );

dims
  Number of array dimensions.
sizes
  Array of dimension sizes.
type
  Type of array elements. The same as for CvMat

The function `cvCreateMatND` allocates header for multi-dimensional dense array. The array data can further be allocated using cvCreateData or set explicitly to user-allocated data via cvSetData.

### ReleaseMatND

Deallocates multi-dimensional array

    void cvReleaseMatND( CvMatND** mat );

mat
  Double pointer to the array.

The function `cvReleaseMatND` decrements the array data reference counter and releases the array header:

        if( *mat )
            cvDecRefData( *mat );
        cvFree( (void**)mat );

### InitMatNDHeader

Initializes multi-dimensional array header

    CvMatND* cvInitMatNDHeader( CvMatND* mat, int dims, const int* sizes, int type, void* data=NULL );

mat
  Pointer to the array header to be initialized.
dims
  Number of array dimensions.
sizes
  Array of dimension sizes.
type
  Type of array elements. The same as for CvMat
data
  Optional data pointer assigned to the matrix header.

The function `cvInitMatNDHeader` initializes CvMatND structure allocated by the user.

### CloneMatND

Creates full copy of multi-dimensional array

    CvMatND* cvCloneMatND( const CvMatND* mat );

mat
  Input array.

The function `cvCloneMatND` creates a copy of input array and returns pointer to it.

### DecRefData

Decrements array data reference counter

    void cvDecRefData( CvArr* arr );

arr
  array header.

The function `cvDecRefData` decrements CvMat or CvMatND data reference counter if the reference counter pointer is not NULL and deallocates the data if the counter reaches zero. In the current implementation the reference counter is not NULL only if the data was allocated using cvCreateData function, in other cases such as:
external data was assigned to the header using cvSetData
the matrix header presents a part of a larger matrix or image
the matrix header was converted from image or n-dimensional matrix header
the reference counter is set to NULL and thus it is not decremented. Whenever the data is deallocated or not, the data pointer and reference counter pointers are cleared by the function.

### IncRefData

Increments array data reference counter

    int cvIncRefData( CvArr* arr );

arr
  array header.

The function `cvIncRefData` increments CvMat or CvMatND data reference counter and returns the new counter value if the reference counter pointer is not NULL, otherwise it returns zero.

### CreateData

Allocates array data

    void cvCreateData( CvArr* arr );

arr
  Array header.

The function `cvCreateData` allocates image, matrix or multi-dimensional array data. Note that in case of matrix types OpenCV allocation functions are used and in case of IplImage they are used too unless `CV_TURN_ON_IPL_COMPATIBILITY` was called. In the latter case IPL functions are used to allocate the data

### ReleaseData

Releases array data

    void cvReleaseData( CvArr* arr );

arr
  Array header

The function `cvReleaseData` releases the array data. In case of CvMat or CvMatND it simply calls cvDecRefData(), that is the function can not deallocate external data. See also the note to cvCreateData.

### SetData

Assigns user data to the array header

    void cvSetData( CvArr* arr, void* data, int step );

arr
  Array header.
data
  User data.
step
  Full row length in bytes.

The function `cvSetData` assigns user data to the array header. Header should be initialized before using cvCreate*Header, cvInit*Header or cvMat (in case of matrix) function.

### GetRawData

Retrieves low-level information about the array

    void cvGetRawData( const CvArr* arr, uchar** data,
                       int* step=NULL, CvSize* roi_size=NULL );

arr
  Array header.
data
  Output pointer to the whole image origin or ROI origin if ROI is set.
step
  Output full row length in bytes.
roi_size
  Output ROI size.

The function `cvGetRawData` fills output variables with low-level information about the array data. All output parameters are optional, so some of the pointers may be set to `NULL`. If the array is `IplImage` with ROI set, parameters of ROI are returned.

The following example shows how to get access to array elements using this function.

Using GetRawData to calculate absolute value of elements of a single-channel floating-point array.

        float* data;
        int step;

        CvSize size;
        int x, y;

        cvGetRawData( array, (uchar**)&data, &step, &size );
        step /= sizeof(data[0]);

        for( y = 0; y < size.height; y++, data += step )
            for( x = 0; x < size.width; x++ )
                data[x] = (float)fabs(data[x]);

### GetMat

Returns matrix header for arbitrary array

    CvMat* cvGetMat( const CvArr* arr, CvMat* header, int* coi=NULL, int allowND=0 );

arr
  Input array.
header
  Pointer to CvMat structure used as a temporary buffer.
coi
  Optional output parameter for storing COI.
allowND
  If non-zero, the function accepts multi-dimensional dense arrays (CvMatND*) and returns 2D (if CvMatND has two dimensions) or 1D matrix (when CvMatND has 1 dimension or more than 2 dimensions). The array must be continuous.

The function `cvGetMat` returns matrix header for the input array that can be matrix - CvMat, image - `IplImage` or multi-dimensional dense array - CvMatND* (latter case is allowed only if `allowND != 0`) . In the case of matrix the function simply returns the input pointer. In the case of `IplImage*` or CvMatND* it initializes `header` structure with parameters of the current image ROI and returns pointer to this temporary structure. Because COI is not supported by CvMat, it is returned separately.

The function provides an easy way to handle both types of array - `IplImage` and CvMat -, using the same code. Reverse transform from CvMat to `IplImage` can be done using cvGetImage function.

Input array must have underlying data allocated or attached, otherwise the function fails.

If the input array is `IplImage` with planar data layout and COI set, the function returns pointer to the selected plane and COI = 0. It enables per-plane processing of multi-channel images with planar data layout using OpenCV functions.

### GetImage

Returns image header for arbitrary array

    IplImage* cvGetImage( const CvArr* arr, IplImage* image_header );

arr
  Input array.
image_header
  Pointer to `IplImage` structure used as a temporary buffer.

The function `cvGetImage` returns image header for the input array that can be matrix - CvMat*, or image - `IplImage*`. In the case of image the function simply returns the input pointer. In the case of CvMat* it initializes `image_header` structure with parameters of the input matrix. Note that if we transform `IplImage` to CvMat and then transform CvMat back to IplImage, we can get different headers if the ROI is set, and thus some IPL functions that calculate image stride from its width and align may fail on the resultant image.

### CreateSparseMat

Creates sparse array

    CvSparseMat* cvCreateSparseMat( int dims, const int* sizes, int type );

dims
  Number of array dimensions. As opposite to the dense matrix, the number of dimensions is practically unlimited (up to 216).
sizes
  Array of dimension sizes.
type
  Type of array elements. The same as for CvMat

The function `cvCreateSparseMat` allocates multi-dimensional sparse array. Initially the array contain no elements, that is cvGet*D or cvGetReal*D return zero for every index

### ReleaseSparseMat

Deallocates sparse array

    void cvReleaseSparseMat( CvSparseMat** mat );

mat
  Double pointer to the array.

The function `cvReleaseSparseMat` releases the sparse array and clears the array pointer upon exit

### CloneSparseMat

Creates full copy of sparse array

    CvSparseMat* cvCloneSparseMat( const CvSparseMat* mat );

mat
  Input array.

The function `cvCloneSparseMat` creates a copy of the input array and returns pointer to the copy.

## Accessing Elements and sub-Arrays

### GetSubRect

Returns matrix header corresponding to the rectangular sub-array of input image or matrix

    CvMat* cvGetSubRect( const CvArr* arr, CvMat* submat, CvRect rect );

arr
  Input array.
submat
  Pointer to the resultant sub-array header.
rect
  Zero-based coordinates of the rectangle of interest.

The function `cvGetSubRect` returns header, corresponding to a specified rectangle of the input array. In other words, it allows the user to treat a rectangular part of input array as a stand-alone array. ROI is taken into account by the function so the sub-array of ROI is actually extracted.

### GetRow, GetRows

Returns array row or row span

    CvMat* cvGetRow( const CvArr* arr, CvMat* submat, int row );
    CvMat* cvGetRows( const CvArr* arr, CvMat* submat, int start_row, int end_row, int delta_row=1 );

arr
  Input array.
submat
  Pointer to the resulting sub-array header.
row
  Zero-based index of the selected row.
start_row
  Zero-based index of the starting row (inclusive) of the span.
end_row
  Zero-based index of the ending row (exclusive) of the span.
delta_row
  Index step in the row span. That is, the function extracts every `delta_row`-th row from `start_row` and up to (but not including) `end_row`.

The functions `GetRow` and `GetRows` return the header, corresponding to a specified row/row span of the input array. Note that `GetRow` is a shortcut for cvGetRows:

    cvGetRow( arr, submat, row ) ~ cvGetRows( arr, submat, row, row + 1, 1 );

### GetCol, GetCols

Returns array column or column span

    CvMat* cvGetCol( const CvArr* arr, CvMat* submat, int col );
    CvMat* cvGetCols( const CvArr* arr, CvMat* submat, int start_col, int end_col );

arr
  Input array.
submat
  Pointer to the resulting sub-array header.
col
  Zero-based index of the selected column.
start_col
  Zero-based index of the starting column (inclusive) of the span.
end_col
  Zero-based index of the ending column (exclusive) of the span.

The functions `GetCol` and `GetCols` return the header, corresponding to a specified column/column span of the input array. Note that `GetCol` is a shortcut for cvGetCols:

    cvGetCol( arr, submat, col ); // ~ cvGetCols( arr, submat, col, col + 1 );

### GetDiag

Returns one of array diagonals

    CvMat* cvGetDiag( const CvArr* arr, CvMat* submat, int diag=0 );

arr
  Input array.
submat
  Pointer to the resulting sub-array header.
diag
  Array diagonal. Zero corresponds to the main diagonal, -1 corresponds to the diagonal above the main etc., 1 corresponds to the diagonal below the main etc.

The function `cvGetDiag` returns the header, corresponding to a specified diagonal of the input array.

### GetSize

Returns size of matrix or image ROI

    CvSize cvGetSize( const CvArr* arr );

arr
  array header.

The function `cvGetSize` returns number of rows (CvSize::height) and number of columns (CvSize::width) of the input matrix or image. In case of image the size of ROI is returned.

### InitSparseMatIterator

Initializes sparse array elements iterator

    CvSparseNode* cvInitSparseMatIterator( const CvSparseMat* mat,
                                           CvSparseMatIterator* mat_iterator );

mat
  Input array.
mat_iterator
  Initialized iterator.

The function `cvInitSparseMatIterator` initializes iterator of sparse array elements and returns pointer to the first element, or NULL if the array is empty.

### GetNextSparseNode

Initializes sparse array elements iterator

    CvSparseNode* cvGetNextSparseNode( CvSparseMatIterator* mat_iterator );

mat_iterator
  Sparse array iterator.

The function `cvGetNextSparseNode` moves iterator to the next sparse matrix element and returns pointer to it. In the current version there is no any particular order of the elements, because they are stored in hash table. The sample below demonstrates how to iterate through the sparse matrix:

Using cvInitSparseMatIterator and cvGetNextSparseNode to calculate sum of floating-point sparse array.

        double sum;
        int i, dims = cvGetDims( array );
        CvSparseMatIterator mat_iterator;
        CvSparseNode* node = cvInitSparseMatIterator( array, &mat_iterator );

        for( ; node != 0; node = cvGetNextSparseNode( &mat_iterator ))
        {
            const int* idx = CV_NODE_IDX( array, node ); /* get pointer to the element indices */
            float val = *(float*)CV_NODE_VAL( array, node ); /* get value of the element
                                                              (assume that the type is CV_32FC1) */
            printf( "(" );
            for( i = 0; i < dims; i++ )
                printf( "%4d%s", idx[i], i < dims - 1 "," : "): " );
            printf( "%g\n", val );

            sum += val;
        }

        printf( "\nTotal sum = %g\n", sum );

### GetElemType

Returns type of array elements

    int cvGetElemType( const CvArr* arr );

arr
  Input array.

The functions `GetElemType` returns type of the array elements as it is described in cvCreateMat discussion:

    CV_8UC1 ... CV_64FC4

### GetDims, GetDimSize

Return number of array dimensions and their sizes or the size of particular dimension

    int cvGetDims( const CvArr* arr, int* sizes=NULL );
    int cvGetDimSize( const CvArr* arr, int index );

arr
  Input array.
sizes
  Optional output vector of the array dimension sizes. For 2d arrays the number of rows (height) goes first, number of columns (width) next.
index
  Zero-based dimension index (for matrices 0 means number of rows, 1 means number of columns; for images 0 means height, 1 means width).

The function `cvGetDims` returns number of array dimensions and their sizes. In case of `IplImage` or CvMat it always returns 2 regardless of number of image/matrix rows. The function `cvGetDimSize` returns the particular dimension size (number of elements per that dimension). For example, the following code calculates total number of array elements in two ways:

    // via cvGetDims()
    int sizes[CV_MAX_DIM];
    int i, total = 1;
    int dims = cvGetDims( arr, size );
    for( i = 0; i < dims; i++ )
        total *= sizes[i];

    // via cvGetDims() and cvGetDimSize()
    int i, total = 1;
    int dims = cvGetDims( arr );
    for( i = 0; i < dims; i++ )
        total *= cvGetDimsSize( arr, i );

### Ptr*D

Return pointer to the particular array element

    uchar* cvPtr1D( const CvArr* arr, int idx0, int* type=NULL );
    uchar* cvPtr2D( const CvArr* arr, int idx0, int idx1, int* type=NULL );
    uchar* cvPtr3D( const CvArr* arr, int idx0, int idx1, int idx2, int* type=NULL );
    uchar* cvPtrND( const CvArr* arr, const int* idx, int* type=NULL, int create_node=1, unsigned* precalc_hashval=NULL );

arr
  Input array.
idx0
  The first zero-based component of the element index
idx1
  The second zero-based component of the element index
idx2
  The third zero-based component of the element index
idx
  Array of the element indices
type
  Optional output parameter: type of matrix elements
create_node
  Optional input parameter for sparse matrices. Non-zero value of the parameter means that the requested element is created if it does not exist already.
precalc_hashval
  Optional input parameter for sparse matrices. If the pointer is not NULL, the function does not recalculate the node hash value, but takes it from the specified location. It is useful for speeding up pair-wise operations (TODO: provide an example)

The functions `>cvPtr*D` return pointer to the particular array element. Number of array dimension should match to the number of indices passed to the function except for `cvPtr1D` function that can be used for sequential access to 1D, 2D or nD dense arrays.

The functions can be used for sparse arrays as well - if the requested node does not exist they create it and set it to zero.

All these as well as other functions accessing array elements (cvGet*D, cvGetReal*D, cvSet*D, cvSetReal*D) raise an error in case if the element index is out of range.

### Get*D

Return the particular array element

    CvScalar cvGet1D( const CvArr* arr, int idx0 );
    CvScalar cvGet2D( const CvArr* arr, int idx0, int idx1 );
    CvScalar cvGet3D( const CvArr* arr, int idx0, int idx1, int idx2 );
    CvScalar cvGetND( const CvArr* arr, const int* idx );

arr
  Input array.
idx0
  The first zero-based component of the element index
idx1
  The second zero-based component of the element index
idx2
  The third zero-based component of the element index
idx
  Array of the element indices

The functions `cvGet*D` return the particular array element. In case of sparse array the functions return 0 if the requested node does not exist (no new node is created by the functions)

### GetReal*D

Return the particular element of single-channel array

    double cvGetReal1D( const CvArr* arr, int idx0 );
    double cvGetReal2D( const CvArr* arr, int idx0, int idx1 );
    double cvGetReal3D( const CvArr* arr, int idx0, int idx1, int idx2 );
    double cvGetRealND( const CvArr* arr, const int* idx );

arr
  Input array. Must have a single channel.
idx0
  The first zero-based component of the element index
idx1
  The second zero-based component of the element index
idx2
  The third zero-based component of the element index
idx
  Array of the element indices

The functions `cvGetReal*D` return the particular element of single-channel array. If the array has multiple channels, runtime error is raised. Note that cvGet*D function can be used safely for both single-channel and multiple-channel arrays though they are a bit slower.

In case of sparse array the functions return 0 if the requested node does not exist (no new node is created by the functions)

### mGet

Return the particular element of single-channel floating-point matrix

    double cvmGet( const CvMat* mat, int row, int col );

mat
  Input matrix.
row
  The zero-based index of row.
col
  The zero-based index of column.

The function `cvmGet` is a fast replacement for cvGetReal2D in case of single-channel floating-point matrices. It is faster because it is inline, it does less checks for array type and array element type and it checks for the row and column ranges only in debug mode.

### Set*D

Change the particular array element

    void cvSet1D( CvArr* arr, int idx0, CvScalar value );
    void cvSet2D( CvArr* arr, int idx0, int idx1, CvScalar value );
    void cvSet3D( CvArr* arr, int idx0, int idx1, int idx2, CvScalar value );
    void cvSetND( CvArr* arr, const int* idx, CvScalar value );

arr
  Input array.
idx0
  The first zero-based component of the element index
idx1
  The second zero-based component of the element index
idx2
  The third zero-based component of the element index
idx
  Array of the element indices
value
  The assigned value

The functions `cvSet*D` assign the new value to the particular element of array. In case of sparse array the functions create the node if it does not exist yet

### SetReal*D

Change the particular array element

    void cvSetReal1D( CvArr* arr, int idx0, double value );
    void cvSetReal2D( CvArr* arr, int idx0, int idx1, double value );
    void cvSetReal3D( CvArr* arr, int idx0, int idx1, int idx2, double value );
    void cvSetRealND( CvArr* arr, const int* idx, double value );

arr
  Input array.
idx0
  The first zero-based component of the element index
idx1
  The second zero-based component of the element index
idx2
  The third zero-based component of the element index
idx
  Array of the element indices
value
  The assigned value

The functions `cvSetReal*D` assign the new value to the particular element of single-channel array. If the array has multiple channels, runtime error is raised. Note that cvSet*D function can be used safely for both single-channel and multiple-channel arrays though they are a bit slower.

In case of sparse array the functions create the node if it does not exist yet

### mSet

Return the particular element of single-channel floating-point matrix

    void cvmSet( CvMat* mat, int row, int col, double value );

mat
  The matrix.
row
  The zero-based index of row.
col
  The zero-based index of column.
value
  The new value of the matrix element

The function `cvmSet` is a fast replacement for cvSetReal2D in case of single-channel floating-point matrices. It is faster because it is inline, it does less checks for array type and array element type and it checks for the row and column ranges only in debug mode.

### ClearND

Clears the particular array element

    void cvClearND( CvArr* arr, const int* idx );

arr
  Input array.
idx
  Array of the element indices

The function cvClearND clears (sets to zero) the particular element of dense array or deletes the element of sparse array. If the element does not exists, the function does nothing.

## Copying and Filling

### Copy

Copies one array to another

    void cvCopy( const CvArr* src, CvArr* dst, const CvArr* mask=NULL );

src
  The source array.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvCopy` copies selected elements from input array to output array:

dst(I)=src(I) if mask(I)!=0.

If any of the passed arrays is of `IplImage` type, then its ROI and COI fields are used. Both arrays must have the same type, the same number of dimensions and the same size. The function can also copy sparse arrays (mask is not supported in this case).

### Set

Sets every element of array to given value

    void cvSet( CvArr* arr, CvScalar value, const CvArr* mask=NULL );

arr
  The destination array.
value
  Fill value.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvSet` copies scalar `value` to every selected element of the destination array:

    arr(I)=value if mask(I)!=0

If array `arr` is of `IplImage` type, then is ROI used, but COI must not be set.

### SetZero

Clears the array

    void cvSetZero( CvArr* arr );
    #define cvZero cvSetZero

arr
  array to be cleared.

The function `cvSetZero` clears the array. In case of dense arrays (CvMat, CvMatND or IplImage) cvZero(array) is equivalent to cvSet(array,cvScalarAll(0),0), in case of sparse arrays all the elements are removed.

### SetIdentity

Initializes scaled identity matrix

    void cvSetIdentity( CvArr* mat, CvScalar value=cvRealScalar(1) );

arr
  The matrix to initialize (not necesserily square).
value
  The value to assign to the diagonal elements.

The function `cvSetIdentity` initializes scaled identity matrix:

    arr(i,j)=value if i=j,
           0 otherwise

### Range

Fills matrix with given range of numbers

    void cvRange( CvArr* mat, double start, double end );

mat
  The matrix to initialize. It should be single-channel 32-bit, integer or floating-point.
start
  The lower inclusive boundary of the range.
end
  The upper exclusive boundary of the range.

The function `cvRange` initializes the matrix as following:

    arr(i,j)=(end-start)*(i*cols(arr)+j)/(cols(arr)*rows(arr))

For example, the following code will initilize 1D vector with subsequent integer numbers.

    CvMat* A = cvCreateMat( 1, 10, CV_32S );
    cvRange( A, 0, A->cols ); // A will be initialized as [0,1,2,3,4,5,6,7,8,9]

## Transforms and Permutations

### Reshape

Changes shape of matrix/image without copying data

    CvMat* cvReshape( const CvArr* arr, CvMat* header, int new_cn, int new_rows=0 );

arr
  Input array.
header
  Output header to be filled.
new_cn
  New number of channels. `new_cn = 0` means that number of channels remains unchanged.
new_rows
  New number of rows. `new_rows = 0` means that number of rows remains unchanged unless it needs to be changed according to `new_cn` value. destination array to be changed.

The function `cvReshape` initializes CvMat header so that it points to the same data as the original array but has different shape - different number of channels, different number of rows or both.

For example, the following code creates one image buffer and two image headers, first is for 320x240x3 image and the second is for 960x240x1 image:

    IplImage* color_img = cvCreateImage( cvSize(320,240), IPL_DEPTH_8U, 3 );
    CvMat gray_mat_hdr;
    IplImage gray_img_hdr, *gray_img;
    cvReshape( color_img, &gray_mat_hdr, 1 );
    gray_img = cvGetImage( &gray_mat_hdr, &gray_img_hdr );

And the next example converts 3x3 matrix to a single 1x9 vector

    CvMat* mat = cvCreateMat( 3, 3, CV_32F );
    CvMat row_header, *row;
    row = cvReshape( mat, &row_header, 0, 1 );

### ReshapeMatND

Changes shape of multi-dimensional array w/o copying data

    CvArr* cvReshapeMatND( const CvArr* arr,
                           int sizeof_header, CvArr* header,
                           int new_cn, int new_dims, int* new_sizes );

    #define cvReshapeND( arr, header, new_cn, new_dims, new_sizes )   \
          cvReshapeMatND( (arr), sizeof(*(header)), (header),         \
                          (new_cn), (new_dims), (new_sizes))

arr
  Input array.
sizeof_header
  Size of output header to distinguish between IplImage, CvMat and CvMatND output headers.
header
  Output header to be filled.
new_cn
  New number of channels. `new_cn = 0` means that number of channels remains unchanged.
new_dims
  New number of dimensions. `new_dims = 0` means that number of dimensions remains the same.
new_sizes
  Array of new dimension sizes. Only `new_dims-1` values are used, because the total number of elements must remain the same. Thus, if `new_dims = 1`, `new_sizes` array is not used

The function `cvReshapeMatND` is an advanced version of cvReshape that can work with multi-dimensional arrays as well (though, it can work with ordinary images and matrices) and change the number of dimensions. Below are the two samples from the cvReshape description rewritten using cvReshapeMatND:

    IplImage* color_img = cvCreateImage( cvSize(320,240), IPL_DEPTH_8U, 3 );
    IplImage gray_img_hdr, *gray_img;
    gray_img = (IplImage*)cvReshapeND( color_img, &gray_img_hdr, 1, 0, 0 );

    ...

    /* second example is modified to convert 2x2x2 array to 8x1 vector */
    int size[] = { 2, 2, 2 };
    CvMatND* mat = cvCreateMatND( 3, size, CV_32F );
    CvMat row_header, *row;
    row = cvReshapeND( mat, &row_header, 0, 1, 0 );

### Repeat

Fill destination array with tiled source array

    void cvRepeat( const CvArr* src, CvArr* dst );

src
  Source array, image or matrix.
dst
  Destination array, image or matrix.

The function `cvRepeat` fills the destination array with source array tiled:

    dst(i,j)=src(i mod rows(src), j mod cols(src))

So the destination array may be as larger as well as smaller than the source array.

### Flip

Flip a 2D array around vertical, horizontall or both axises

    void  cvFlip( const CvArr* src, CvArr* dst=NULL, int flip_mode=0);
    #define cvMirror cvFlip

src
  Source array.
dst
  Destination array. If `dst = NULL` the flipping is done inplace.
flip_mode
  Specifies how to flip the array.
  flip_mode = 0 means flipping around x-axis, flip_mode > 0 (e.g. 1) means flipping around y-axis and flip_mode < 0 (e.g. -1) means flipping around both axises. See also the discussion below for the formulas

The function `cvFlip` flips the array in one of different 3 ways (row and column indices are 0-based):

    dst(i,j)=src(rows(src)-i-1,j) if flip_mode = 0

    dst(i,j)=src(i,cols(src1)-j-1) if flip_mode > 0

    dst(i,j)=src(rows(src)-i-1,cols(src)-j-1) if flip_mode < 0

The example cenaria of the function use are:

- vertical flipping of the image (flip_mode > 0) to switch between top-left and bottom-left image origin, which is typical operation in video processing under Win32 systems.
- horizontal flipping of the image with subsequent horizontal shift and absolute difference calculation to check for a vertical-axis symmetry (flip_mode > 0)
- simultaneous horizontal and vertical flipping of the image with subsequent shift and absolute difference calculation to check for a central symmetry (flip_mode < 0)
- reversing the order of 1d point arrays(flip_mode > 0)

### Split

Divides multi-channel array into several single-channel arrays or extracts a single channel from the array

    void cvSplit( const CvArr* src, CvArr* dst0, CvArr* dst1,
                  CvArr* dst2, CvArr* dst3 );
    #define cvCvtPixToPlane cvSplit

src
  Source array.
dst0...dst3
  Destination channels.

The function `cvSplit` divides a multi-channel array into separate single-channel arrays. Two modes are available for the operation. If the source array has N channels then if the first N destination channels are not NULL, all they are extracted from the source array, otherwise if only a single destination channel of the first N is not NULL, this particular channel is extracted, otherwise an error is raised. Rest of destination channels (beyond the first N) must always be NULL. For IplImage cvCopy with COI set can be also used to extract a single channel from the image.

### Merge

Composes multi-channel array from several single-channel arrays or inserts a single channel into the array

    void cvMerge( const CvArr* src0, const CvArr* src1,
                  const CvArr* src2, const CvArr* src3, CvArr* dst );
    #define cvCvtPlaneToPix cvMerge

src0... src3
  Input channels.
dst
  Destination array.

The function `cvMerge` is the opposite to the previous. If the destination array has N channels then if the first N input channels are not NULL, all they are copied to the destination array, otherwise if only a single source channel of the first N is not NULL, this particular channel is copied into the destination array, otherwise an error is raised. Rest of source channels (beyond the first N) must always be NULL. For IplImage cvCopy with COI set can be also used to insert a single channel into the image.

### MixChannels

Copies several channels from input arrays to certain channels of output arrays

    void cvMixChannels( const CvArr** src, int src_count,
                        CvArr** dst, int dst_count,
                        const int* from_to, int pair_count );

src
  The array of input arrays.
src_count
  The number of input arrays.
dst
  The array of output arrays.
dst_count
  The number of output arrays.
from_to
  The array of pairs of indices of the planes copied. `from_to[k*2]` is the 0-based index of the input plane, and `from_to[k*2+1]` is the index of the output plane, where the continuous numbering of the planes over all the input and over all the output arrays is used. When `from_to[k*2]` is negative, the corresponding output plane is filled with 0's.
pair_count
  The number of pairs in `from_to`, or the number of the planes copied.

The function `cvMixChannels` is a generalized form of cvSplit and cvMerge and some forms of cvCvtColor. It can be used to change the order of the planes, add/remove alpha channel, extract or insert a single plane or multiple planes etc. Below is the example, how to split 4-channel RGBA image into 3-channel BGR (i.e. with R&B swapped) and separate alpha channel images:

        CvMat* rgba = cvCreateMat( 100, 100, CV_8UC4 );
        CvMat* bgr = cvCreateMat( rgba->rows, rgba->cols, CV_8UC3 );
        CvMat* alpha = cvCreateMat( rgba->rows, rgba->cols, CV_8UC1 );
        CvArr* out[] = { bgr, alpha };
        int from_to[] = { 0, 2, 1, 1, 2, 0, 3, 3 };
        cvSet( rgba, cvScalar(1,2,3,4) );
        cvMixChannels( (const CvArr**)&rgba, 1, out, 2, from_to, 4 );

### RandShuffle

Randomly shuffles the array elements

    void cvRandShuffle( CvArr* mat, CvRNG* rng, double iter_factor=1. );

mat
  The input/output matrix. It is shuffled in-place.
rng
  The Random Number Generator used to shuffle the elements. When the pointer is NULL, a temporary RNG will be created and used.
iter_factor
  The relative parameter that characterizes intensity of the shuffling performed. See the description below.

The function `cvRandShuffle` shuffles the matrix by swapping randomly chosen pairs of the matrix elements on each iteration (where each element may contain several components in case of multi-channel arrays). The number of iterations (i.e. pairs swapped) is `round(iter_factor*rows(mat)*cols(mat))`, so `iter_factor=0` means that no shuffling is done, `iter_factor=1` means that the function swaps `rows(mat)*cols(mat)` random pairs etc.

## Arithmetic, Logic and Comparison

### LUT

Performs look-up table transform of array

    void cvLUT( const CvArr* src, CvArr* dst, const CvArr* lut );

src
  Source array of 8-bit elements.
dst
  Destination array of arbitrary depth and of the same number of channels as the source array.
lut
  Look-up table of 256 elements; should have the same depth as the destination array. In case of multi-channel source and destination arrays, the table should either have a single-channel (in this case the same table is used for all channels), or the same number of channels as the source/destination array.

The function `cvLUT` fills the destination array with values from the look-up table. Indices of the entries are taken from the source array. That is, the function processes each element of `src` as following:

    dst(I)=lut[src(I)+DELTA]

where `DELTA=0` if `src` has depth `CV_8U`, and `DELTA=128` if `src` has depth `CV_8S`.

### ConvertScale

Converts one array to another with optional linear transformation

    void cvConvertScale( const CvArr* src, CvArr* dst, double scale=1, double shift=0 );

    #define cvCvtScale cvConvertScale
    #define cvScale  cvConvertScale
    #define cvConvert( src, dst )  cvConvertScale( (src), (dst), 1, 0 )

src
  Source array.
dst
  Destination array.
scale
  Scale factor.
shift
  Value added to the scaled source array elements.

The function `cvConvertScale` has several different purposes and thus has several synonyms. It copies one array to another with optional scaling, which is performed first, and/or optional type conversion, performed after:

    dst(I)=src(I)*scale + (shift,shift,...)

All the channels of multi-channel arrays are processed independently.

The type conversion is done with rounding and saturation, that is if a result of scaling + conversion can not be represented exactly by a value of destination array element type, it is set to the nearest representable value on the real axis.

In case of `scale=1, shift=0` no prescaling is done. This is a specially optimized case and it has the appropriate cvConvert synonym. If source and destination array types have equal types, this is also a special case that can be used to scale and shift a matrix or an image and that fits to cvScale synonym.

### ConvertScaleAbs

Converts input array elements to 8-bit unsigned integer another with optional linear transformation

    void cvConvertScaleAbs( const CvArr* src, CvArr* dst, double scale=1, double shift=0 );
    #define cvCvtScaleAbs cvConvertScaleAbs

src
  Source array.
dst
  Destination array (should have 8u depth).
scale
  ScaleAbs factor.
shift
  Value added to the scaled source array elements.

The function `cvConvertScaleAbs` is similar to the previous one, but it stores absolute values of the conversion results:

    dst(I)=abs(src(I)*scale + (shift,shift,...))

The function supports only destination arrays of 8u (8-bit unsigned integers) type, for other types the function can be emulated by combination of cvConvertScale and cvAbs functions.

### Add

Computes per-element sum of two arrays

    void cvAdd( const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvAdd` adds one array to another one:

    dst(I)=src1(I)+src2(I) if mask(I)!=0

All the arrays must have the same type, except the mask, and the same size (or ROI size)

### AddS

Computes sum of array and scalar

    void cvAddS( const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL );

src
  The source array.
value
  Added scalar.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvAddS` adds scalar `value` to every element in the source array `src1` and stores the result in `dst`

    dst(I)=src(I)+value if mask(I)!=0

All the arrays must have the same type, except the mask, and the same size (or ROI size)

### AddWeighted

Computes weighted sum of two arrays

    void  cvAddWeighted( const CvArr* src1, double alpha,
                         const CvArr* src2, double beta,
                         double gamma, CvArr* dst );

src1
  The first source array.
alpha
  Weight of the first array elements.
src2
  The second source array.
beta
  Weight of the second array elements.
dst
  The destination array.
gamma
  Scalar, added to each sum.

The function `cvAddWeighted` calculated weighted sum of two arrays as following:

    dst(I)=src1(I)*alpha+src2(I)*beta+gamma

All the arrays must have the same type and the same size (or ROI size)

### Sub

Computes per-element difference between two arrays

    void cvSub( const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvSub` subtracts one array from another one:

    dst(I)=src1(I)-src2(I) if mask(I)!=0

All the arrays must have the same type, except the mask, and the same size (or ROI size)

### SubS

Computes difference between array and scalar

    void cvSubS( const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL );

src
  The source array.
value
  Subtracted scalar.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvSubS` subtracts a scalar from every element of the source array:

    dst(I)=src(I)-value if mask(I)!=0

All the arrays must have the same type, except the mask, and the same size (or ROI size)

### SubRS

Computes difference between scalar and array

    void cvSubRS( const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL );

src
  The first source array.
value
  Scalar to subtract from.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvSubRS` subtracts every element of source array from a scalar:

    dst(I)=value-src(I) if mask(I)!=0

All the arrays must have the same type, except the mask, and the same size (or ROI size)

### Mul

Calculates per-element product of two arrays

    void cvMul( const CvArr* src1, const CvArr* src2, CvArr* dst, double scale=1 );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array.
scale
  Optional scale factor

The function `cvMul` calculates per-element product of two arrays:

    dst(I)=scale•src1(I)•src2(I)

All the arrays must have the same type, and the same size (or ROI size)

### Div

Performs per-element division of two arrays

    void cvDiv( const CvArr* src1, const CvArr* src2, CvArr* dst, double scale=1 );

src1
  The first source array. If the pointer is NULL, the array is assumed to be all 1’s.
src2
  The second source array.
dst
  The destination array.
scale
  Optional scale factor

The function `cvDiv` divides one array by another:

    dst(I)=scale•src1(I)/src2(I), if src1!=NULL
    dst(I)=scale/src2(I),      if src1=NULL

All the arrays must have the same type, and the same size (or ROI size)

### And

Calculates per-element bit-wise conjunction of two arrays

    void cvAnd( const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvAnd` calculates per-element bit-wise logical conjunction of two arrays:

    dst(I)=src1(I)&src2(I) if mask(I)!=0

In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size

### AndS

Calculates per-element bit-wise conjunction of array and scalar

    void cvAndS( const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL );

src
  The source array.
value
  Scalar to use in the operation.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function AndS calculates per-element bit-wise conjunction of array and scalar:

    dst(I)=src(I)&value if mask(I)!=0

Prior to the actual operation the scalar is converted to the same type as the arrays. In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size

The following sample demonstrates how to calculate absolute value of floating-point array elements by clearing the most-significant bit:

    float a[] = { -1, 2, -3, 4, -5, 6, -7, 8, -9 };
    CvMat A = cvMat( 3, 3, CV_32F, &a );
    int i, abs_mask = 0x7fffffff;
    cvAndS( &A, cvRealScalar(*(float*)&abs_mask), &A, 0 );
    for( i = 0; i < 9; i++ )
        printf("%.1f ", a[i] );

The code should print:

    1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0

### Or

Calculates per-element bit-wise disjunction of two arrays

    void cvOr( const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvOr` calculates per-element bit-wise disjunction of two arrays:

    dst(I)=src1(I)|src2(I)

In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size

### OrS

Calculates per-element bit-wise disjunction of array and scalar

    void cvOrS( const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL );

src1
  The source array.
value
  Scalar to use in the operation.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function OrS calculates per-element bit-wise disjunction of array and scalar:

    dst(I)=src(I)|value if mask(I)!=0

Prior to the actual operation the scalar is converted to the same type as the arrays. In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size

### Xor

Performs per-element bit-wise "exclusive or" operation on two arrays

    void cvXor( const CvArr* src1, const CvArr* src2, CvArr* dst, const CvArr* mask=NULL );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function `cvXor` calculates per-element bit-wise logical conjunction of two arrays:

    dst(I)=src1(I)^src2(I) if mask(I)!=0

In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size

### XorS

Performs per-element bit-wise "exclusive or" operation on array and scalar

    void cvXorS( const CvArr* src, CvScalar value, CvArr* dst, const CvArr* mask=NULL );

src
  The source array.
value
  Scalar to use in the operation.
dst
  The destination array.
mask
  Operation mask, 8-bit single channel array; specifies elements of destination array to be changed.

The function XorS calculates per-element bit-wise conjunction of array and scalar:

    dst(I)=src(I)^value if mask(I)!=0

Prior to the actual operation the scalar is converted to the same type as the arrays. In the case of floating-point arrays their bit representations are used for the operation. All the arrays must have the same type, except the mask, and the same size

The following sample demonstrates how to conjugate complex vector by switching the most-significant bit of imaging part:

    float a[] = { 1, 0, 0, 1, -1, 0, 0, -1 }; /* 1, j, -1, -j */
    CvMat A = cvMat( 4, 1, CV_32FC2, &a );
    int i, neg_mask = 0x80000000;
    cvXorS( &A, cvScalar( 0, *(float*)&neg_mask, 0, 0 ), &A, 0 );
    for( i = 0; i < 4; i++ )
        printf("(%.1f, %.1f) ", a[i*2], a[i*2+1] );

The code should print:

    (1.0,0.0) (0.0,-1.0) (-1.0,0.0) (0.0,1.0)

### Not

Performs per-element bit-wise inversion of array elements

    void cvNot( const CvArr* src, CvArr* dst );

src1
  The source array.
dst
  The destination array.

The function Not inverses every bit of every array element:

    dst(I)=~src(I)

### Cmp

Performs per-element comparison of two arrays

    void cvCmp( const CvArr* src1, const CvArr* src2, CvArr* dst, int cmp_op );

src1
  The first source array.
src2
  The second source array. Both source array must have a single channel.
dst
  The destination array, must have 8u or 8s type.
cmp_op
  The flag specifying the relation between the elements to be checked:
  CV_CMP_EQ - src1(I) "equal to" src2(I)
  CV_CMP_GT - src1(I) "greater than" src2(I)
  CV_CMP_GE - src1(I) "greater or equal" src2(I)
  CV_CMP_LT - src1(I) "less than" src2(I)
  CV_CMP_LE - src1(I) "less or equal" src2(I)
  CV_CMP_NE - src1(I) "not equal to" src2(I)

The function `cvCmp` compares the corresponding elements of two arrays and fills the destination mask array:

    dst(I)=src1(I) op src2(I),

where `op` is '=', '>', '>=', '<', '<=' or '!='.

`dst(I)` is set to 0xff (all '1'-bits) if the particular relation between the elements is true and 0 otherwise. All the arrays must have the same type, except the destination, and the same size (or ROI size)

### CmpS

Performs per-element comparison of array and scalar

    void cvCmpS( const CvArr* src, double value, CvArr* dst, int cmp_op );

src
  The source array, must have a single channel.
value
  The scalar value to compare each array element with.
dst
  The destination array, must have 8u or 8s type.
cmp_op
  The flag specifying the relation between the elements to be checked:
  CV_CMP_EQ - src1(I) "equal to" value
  CV_CMP_GT - src1(I) "greater than" value
  CV_CMP_GE - src1(I) "greater or equal" value
  CV_CMP_LT - src1(I) "less than" value
  CV_CMP_LE - src1(I) "less or equal" value
  CV_CMP_NE - src1(I) "not equal" value

The function `cvCmpS` compares the corresponding elements of array and scalar and fills the destination mask array:

    dst(I)=src(I) op scalar,

where `op` is '=', '>', '>=', '<', '<=' or '!='.

`dst(I)` is set to 0xff (all '1'-bits) if the particular relation between the elements is true and 0 otherwise. All the arrays must have the same size (or ROI size)

### InRange

Checks that array elements lie between elements of two other arrays

    void cvInRange( const CvArr* src, const CvArr* lower, const CvArr* upper, CvArr* dst );

src
  The first source array.
lower
  The inclusive lower boundary array.
upper
  The exclusive upper boundary array.
dst
  The destination array, must have 8u or 8s type.

The function `cvInRange` does the range check for every element of the input array:

    dst(I)=lower(I)0 <= src(I)0 < upper(I)0

for single-channel arrays,

    dst(I)=lower(I)0 <= src(I)0 < upper(I)0 &&
         lower(I)1 <= src(I)1 < upper(I)1

for two-channel arrays etc.

`dst(I)` is set to 0xff (all '1'-bits) if `src(I)` is within the range and 0 otherwise. All the arrays must have the same type, except the destination, and the same size (or ROI size)

### InRangeS

Checks that array elements lie between two scalars

    void cvInRangeS( const CvArr* src, CvScalar lower, CvScalar upper, CvArr* dst );

src
  The first source array.
lower
  The inclusive lower boundary.
upper
  The exclusive upper boundary.
dst
  The destination array, must have 8u or 8s type.

The function `cvInRangeS` does the range check for every element of the input array:

    dst(I)=lower0 <= src(I)0 < upper0

for a single-channel array,

    dst(I)=lower0 <= src(I)0 < upper0 &&
         lower1 <= src(I)1 < upper1

for a two-channel array etc.

`dst(I)` is set to 0xff (all '1'-bits) if `src(I)` is within the range and 0 otherwise. All the arrays must have the same size (or ROI size)

### Max

Finds per-element maximum of two arrays

    void cvMax( const CvArr* src1, const CvArr* src2, CvArr* dst );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array.

The function `cvMax` calculates per-element maximum of two arrays:

    dst(I)=max(src1(I), src2(I))

All the arrays must have a single channel, the same data type and the same size (or ROI size).

### MaxS

Finds per-element maximum of array and scalar

    void cvMaxS( const CvArr* src, double value, CvArr* dst );

src
  The first source array.
value
  The scalar value.
dst
  The destination array.

The function `cvMaxS` calculates per-element maximum of array and scalar:

    dst(I)=max(src(I), value)

All the arrays must have a single channel, the same data type and the same size (or ROI size).

### Min

Finds per-element minimum of two arrays

    void cvMin( const CvArr* src1, const CvArr* src2, CvArr* dst );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array.

The function `cvMin` calculates per-element minimum of two arrays:

    dst(I)=min(src1(I),src2(I))

All the arrays must have a single channel, the same data type and the same size (or ROI size).

### MinS

Finds per-element minimum of array and scalar

    void cvMinS( const CvArr* src, double value, CvArr* dst );

src
  The first source array.
value
  The scalar value.
dst
  The destination array.

The function `cvMinS` calculates minimum of array and scalar:

    dst(I)=min(src(I), value)

All the arrays must have a single channel, the same data type and the same size (or ROI size).

### AbsDiff

Calculates absolute difference between two arrays

    void cvAbsDiff( const CvArr* src1, const CvArr* src2, CvArr* dst );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array.

The function `cvAbsDiff` calculates absolute difference between two arrays.

    dst(I)c = abs(src1(I)c - src2(I)c).

All the arrays must have the same data type and the same size (or ROI size).

### AbsDiffS

Calculates absolute difference between array and scalar

    void cvAbsDiffS( const CvArr* src, CvArr* dst, CvScalar value );
    #define cvAbs(src, dst) cvAbsDiffS(src, dst, cvScalarAll(0))

src
  The source array.
dst
  The destination array.
value
  The scalar.

The function `cvAbsDiffS` calculates absolute difference between array and scalar.

    dst(I)c = abs(src(I)c - valuec).

All the arrays must have the same data type and the same size (or ROI size).

## Statistics

### CountNonZero

Counts non-zero array elements

    int cvCountNonZero( const CvArr* arr );

arr
  The array, must be single-channel array or multi-channel image with COI set.

The function `cvCountNonZero` returns the number of non-zero elements in src1:

    result = sumI arr(I)!=0

In case of `IplImage` both ROI and COI are supported.

### Sum

Summarizes array elements

    CvScalar cvSum( const CvArr* arr );

arr
  The array.

The function `cvSum` calculates sum `S` of array elements, independently for each channel:

    Sc = sumI arr(I)c

If the array is `IplImage` and COI is set, the function processes the selected channel only and stores the sum to the first scalar component (S0).

### Avg

Calculates average (mean) of array elements

    CvScalar cvAvg( const CvArr* arr, const CvArr* mask=NULL );

arr
  The array.
mask
  The optional operation mask.

The function `cvAvg` calculates the average value `M` of array elements, independently for each channel:

    N = sumI mask(I)!=0

    Mc = 1/N • sumI,mask(I)!=0 arr(I)c

If the array is `IplImage` and COI is set, the function processes the selected channel only and stores the average to the first scalar component (S0).

### AvgSdv

Calculates average (mean) of array elements

    void cvAvgSdv( const CvArr* arr, CvScalar* mean, CvScalar* std_dev, const CvArr* mask=NULL );

arr
  The array.
mean
  Pointer to the mean value, may be NULL if it is not needed.
std_dev
  Pointer to the standard deviation.
mask
  The optional operation mask.

The function `cvAvgSdv` calculates the average value and standard deviation of array elements, independently for each channel:

    N = sumI mask(I)!=0

    meanc = 1/N • sumI,mask(I)!=0 arr(I)c

    std_devc = sqrt(1/N • sumI,mask(I)!=0 (arr(I)c - Mc)2)

If the array is `IplImage` and COI is set, the function processes the selected channel only and stores the average and standard deviation to the first compoenents of output scalars (M0 and S0).

### MinMaxLoc

Finds global minimum and maximum in array or subarray

    void cvMinMaxLoc( const CvArr* arr, double* min_val, double* max_val,
                      CvPoint* min_loc=NULL, CvPoint* max_loc=NULL, const CvArr* mask=NULL );

arr
  The source array, single-channel or multi-channel with COI set.
min_val
  Pointer to returned minimum value.
max_val
  Pointer to returned maximum value.
min_loc
  Pointer to returned minimum location.
max_loc
  Pointer to returned maximum location.
mask
  The optional mask that is used to select a subarray.

The function `MinMaxLoc` finds minimum and maximum element values and their positions. The extremums are searched over the whole array, selected `ROI` (in case of `IplImage`) or, if `mask` is not `NULL`, in the specified array region. If the array has more than one channel, it must be `IplImage` with `COI` set. In case if multi-dimensional arrays `min_loc->x` and `max_loc->x` will contain raw (linear) positions of the extremums.

### Norm

Calculates absolute array norm, absolute difference norm or relative difference norm

    double cvNorm( const CvArr* arr1, const CvArr* arr2=NULL, int norm_type=CV_L2, const CvArr* mask=NULL );

arr1
  The first source image.
arr2
  The second source image. If it is NULL, the absolute norm of `arr1` is calculated, otherwise absolute or relative norm of `arr1`-`arr2` is calculated.
normType
  Type of norm, see the discussion.
mask
  The optional operation mask.

The function `cvNorm` calculates the absolute norm of `arr1` if `arr2` is NULL:

    norm = ||arr1||C = maxI abs(arr1(I)),  if normType = CV_C

    norm = ||arr1||L1 = sumI abs(arr1(I)),  if normType = CV_L1

    norm = ||arr1||L2 = sqrt( sumI arr1(I)2),  if normType = CV_L2

And the function calculates absolute or relative difference norm if `arr2` is not NULL:

    norm = ||arr1-arr2||C = maxI abs(arr1(I)-arr2(I)),  if normType = CV_C

    norm = ||arr1-arr2||L1 = sumI abs(arr1(I)-arr2(I)),  if normType = CV_L1

    norm = ||arr1-arr2||L2 = sqrt( sumI (arr1(I)-arr2(I))2 ),  if normType = CV_L2

    or

    norm = ||arr1-arr2||C/||arr2||C, if normType = CV_RELATIVE_C

    norm = ||arr1-arr2||L1/||arr2||L1, if normType = CV_RELATIVE_L1

    norm = ||arr1-arr2||L2/||arr2||L2, if normType = CV_RELATIVE_L2

The function`Norm` returns the calculated norm. The multiple-channel array are treated as single-channel, that is, the results for all channels are combined.

### Reduce

Reduces matrix to a vector

    void cvReduce( const CvArr* src, CvArr* dst, int op=CV_REDUCE_SUM );

src
  The input matrix.
dst
  The output single-row/single-column vector that accumulates somehow all the matrix rows/columns.
dim
  The dimension index along which the matrix is reduce. 0 means that the matrix is reduced to a single row, 1 means that the matrix is reduced to a single column. -1 means that the dimension is chosen automatically by analysing the `dst` size.
op
  The reduction operation. It can take of the following values:
  `CV_REDUCE_SUM` - the output is the sum of all the matrix rows/columns.
  `CV_REDUCE_AVG` - the output is the mean vector of all the matrix rows/columns.
  `CV_REDUCE_MAX` - the output is the maximum (column/row-wise) of all the matrix rows/columns.
  `CV_REDUCE_MIN` - the output is the minimum (column/row-wise) of all the matrix rows/columns.

The function `cvReduce` reduces matrix to a vector by treating the matrix rows/columns as a set of 1D vectors and performing the specified operation on the vectors until a single row/column is obtained. For example, the function can be used to compute horizontal and vertical projections of an raster image. In case of `CV_REDUCE_SUM` and `CV_REDUCE_AVG` the output may have a larger element bit-depth to preserve accuracy. And multi-channel arrays are also supported in these two reduction modes.

## Linear Algebra

### DotProduct

Calculates dot product of two arrays in Euclidian metrics

    double cvDotProduct( const CvArr* src1, const CvArr* src2 );

src1
  The first source array.
src2
  The second source array.

The function `cvDotProduct` calculates and returns the Euclidean dot product of two arrays.

    src1•src2 = sumI(src1(I)*src2(I))

In case of multiple channel arrays the results for all channels are accumulated. In particular, `cvDotProduct(a,a)`, where `a` is a complex vector, will return `||a||2`. The function can process multi-dimensional arrays, row by row, layer by layer and so on.

### Normalize

Normalizes array to a certain norm or value range

    void cvNormalize( const CvArr* src, CvArr* dst,
                      double a=1, double b=0, int norm_type=CV_L2,
                      const CvArr* mask=NULL );

src
  The input array.
dst
  The output array; in-place operation is supported.
a
  The minimum/maximum value of the output array or the norm of output array.
b
  The maximum/minimum value of the output array.
norm_type
  The normalization type. It can take one of the following values:
  `CV_C` - the C-norm (maximum of absolute values) of the array is normalized.
  `CV_L1` - the L1-norm (sum of absolute values) of the array is normalized.
  `CV_L2` - the (Euclidian) L2-norm of the array is normalized.
  `CV_MINMAX` - the array values are scaled and shifted to the specified range.
mask
  The operation mask. Makes the function consider and normalize only certain array elements.

The function `cvNormalize` normalizes the input array so that it's norm or value range takes the certain value(s).

When `norm_type==CV_MINMAX`:

        dst(i,j)=(src(i,j)-min(src))*(b'-a')/(max(src)-min(src)) + a',  if mask(i,j)!=0
        dst(i,j)=src(i,j)  otherwise

where `b'=MAX(a,b)`, `a'=MIN(a,b)`;
`min(src)` and `max(src)` are the global minimum and maximum, respectively, of the input array, computed over the whole array or the specified subset of it.

When `norm_type!=CV_MINMAX`:

        dst(i,j)=src(i,j)*a/cvNorm(src,0,norm_type,mask), if mask(i,j)!=0
        dst(i,j)=src(i,j)  otherwise

Here is the short example:

    float v[3] = { 1, 2, 3 };
    CvMat V = cvMat( 1, 3, CV_32F, v );

    // make vector v unit-length;
    // equivalent to
    //   for(int i=0;i<3;i++) v[i]/=sqrt(v[0]*v[0]+v[1]*v[1]+v[2]*v[2]);
    cvNormalize( &V, &V );

### CrossProduct

Calculates cross product of two 3D vectors

    void cvCrossProduct( const CvArr* src1, const CvArr* src2, CvArr* dst );

src1
  The first source vector.
src2
  The second source vector.
dst
  The destination vector.

The function `cvCrossProduct` calculates the cross product of two 3D vectors:

    dst = src1 × src2, (dst1 = src12src23 - src13src22 , dst2 = src13src21 - src11src23 , dst3 = src11src22 - src12src21).

### ScaleAdd

Calculates sum of scaled array and another array

    void cvScaleAdd( const CvArr* src1, CvScalar scale, const CvArr* src2, CvArr* dst );
    #define cvMulAddS cvScaleAdd

src1
  The first source array.
scale
  Scale factor for the first array.
src2
  The second source array.
dst
  The destination array

The function `cvScaleAdd` calculates sum of scaled array and another array:

    dst(I)=src1(I)*scale + src2(I)

All array parameters should have the same type and the same size.

### GEMM

Performs generalized matrix multiplication

    void  cvGEMM( const CvArr* src1, const CvArr* src2, double alpha,
                  const CvArr* src3, double beta, CvArr* dst, int tABC=0 );
    #define cvMatMulAdd( src1, src2, src3, dst ) cvGEMM( src1, src2, 1, src3, 1, dst, 0 )
    #define cvMatMul( src1, src2, dst ) cvMatMulAdd( src1, src2, 0, dst )

src1
  The first source array.
src2
  The second source array.
src3
  The third source array (shift). Can be NULL, if there is no shift.
dst
  The destination array.
tABC
  The operation flags that can be 0 or combination of the following values:
  CV_GEMM_A_T - transpose src1
  CV_GEMM_B_T - transpose src2
  CV_GEMM_C_T - transpose src3
  for example, CV_GEMM_A_T+CV_GEMM_C_T corresponds to

      alpha*src1T*src2 + beta*srcT

The function `cvGEMM` performs generalized matrix multiplication:

    dst = alpha*op(src1)*op(src2) + beta*op(src3), where op(X) is X or XT

All the matrices should have the same data type and the coordinated sizes. Real or complex floating-point matrices are supported

### Transform

Performs matrix transform of every array element

    void cvTransform( const CvArr* src, CvArr* dst, const CvMat* transmat, const CvMat* shiftvec=NULL );

src
  The first source array.
dst
  The destination array.
transmat
  Transformation matrix.
shiftvec
  Optional shift vector.

The function `cvTransform` performs matrix transformation of every element of array `src` and stores the results in `dst`:

    dst(I)=transmat*src(I) + shiftvec   or   dst(I)k=sumj(transmat(k,j)*src(I)j) + shiftvec(k)

That is every element of `N`-channel array `src` is considered as `N`-element vector, which is transformed using matrix `M`×`N` matrix `transmat` and shift vector `shiftvec` into an element of `M`-channel array `dst`. There is an option to embedd `shiftvec` into `transmat`. In this case `transmat` should be `M`×`N+1` matrix and the right-most column is treated as the shift vector.

Both source and destination arrays should have the same depth and the same size or selected ROI size. `transmat` and `shiftvec` should be real floating-point matrices.

The function may be used for geometrical transformation of `N`D point set, arbitrary linear color space transformation, shuffling the channels etc.

### PerspectiveTransform

Performs perspective matrix transform of vector array

    void cvPerspectiveTransform( const CvArr* src, CvArr* dst, const CvMat* mat );

src
  The source three-channel floating-point array.
dst
  The destination three-channel floating-point array.
mat
  3×3 or 4×4 transformation matrix.

The function `cvPerspectiveTransform` transforms every element of `src` (by treating it as 2D or 3D vector) in the following way:

    (x, y, z) -> (x’/w, y’/w, z’/w) or
    (x, y) -> (x’/w, y’/w),

    where
    (x’, y’, z’, w’) = mat4x4*(x, y, z, 1) or
    (x’, y’, w’) = mat3x3*(x, y, 1)

    and w = w’   if w’!=0,
            inf  otherwise

### MulTransposed

Calculates product of array and transposed array

    void cvMulTransposed( const CvArr* src, CvArr* dst, int order, const CvArr* delta=NULL );

src
  The source matrix.
dst
  The destination matrix.
order
  Order of multipliers.
delta
  An optional array, subtracted from `src` before multiplication.

The function `cvMulTransposed` calculates the product of src and its transposition.

The function evaluates

    dst=(src-delta)*(src-delta)T

if order=0, and

    dst=(src-delta)T*(src-delta)

otherwise.

### Trace

Returns trace of matrix

    CvScalar cvTrace( const CvArr* mat );

mat
  The source matrix.

The function `cvTrace` returns sum of diagonal elements of the matrix `src1`.

    tr(src1)=sumimat(i,i)

### Transpose

Transposes matrix

    void cvTranspose( const CvArr* src, CvArr* dst );
    #define cvT cvTranspose

src
  The source matrix.
dst
  The destination matrix.

The function `cvTranspose` transposes matrix `src1`:

    dst(i,j)=src(j,i)

Note that no complex conjugation is done in case of complex matrix. Conjugation should be done separately: look at the sample code in cvXorS for example

### Det

Returns determinant of matrix

    double cvDet( const CvArr* mat );

mat
  The source matrix.

The function `cvDet` returns determinant of the square matrix `mat`. The direct method is used for small matrices and Gaussian elimination is used for larger matrices. For symmetric positive-determined matrices it is also possible to run SVD with `U=V=NULL` and then calculate determinant as a product of the diagonal elements of `W`

### Invert

Finds inverse or pseudo-inverse of matrix

    double cvInvert( const CvArr* src, CvArr* dst, int method=CV_LU );
    #define cvInv cvInvert

src
  The source matrix.
dst
  The destination matrix.
method
  Inversion method:
  CV_LU - Gaussian elimination with optimal pivot element chose
  CV_SVD - Singular value decomposition (SVD) method
  CV_SVD_SYM - SVD method for a symmetric positively-defined matrix

The function `cvInvert` inverts matrix `src1` and stores the result in `src2`

In case of `LU` method the function returns `src1` determinant (src1 must be square). If it is 0, the matrix is not inverted and `src2` is filled with zeros.

In case of `SVD` methods the function returns the inversed condition number of `src1` (ratio of the smallest singular value to the largest singular value) and 0 if `src1` is all zeros. The SVD methods calculate a pseudo-inverse matrix if `src1` is singular

### Solve

Solves linear system or least-squares problem

    int cvSolve( const CvArr* A, const CvArr* B, CvArr* X, int method=CV_LU );

A
  The source matrix.
B
  The right-hand part of the linear system.
X
  The output solution.
method
  The solution (matrix inversion) method:
  CV_LU - Gaussian elimination with optimal pivot element chose
  CV_SVD - Singular value decomposition (SVD) method
  CV_SVD_SYM - SVD method for a symmetric positively-defined matrix.

The function `cvSolve` solves linear system or least-squares problem (the latter is possible with SVD methods):

    dst = arg minX||A*X-B||

If `CV_LU` method is used, the function returns 1 if `src1` is non-singular and 0 otherwise, in the latter case `dst` is not valid

### SVD

Performs singular value decomposition of real floating-point matrix

    void cvSVD( CvArr* A, CvArr* W, CvArr* U=NULL, CvArr* V=NULL, int flags=0 );

A
  Source `M`×`N` matrix.
W
  Resulting singular value matrix (`M`×`N` or `N`×`N`) or vector (`N`×`1`).
U
  Optional left orthogonal matrix (`M`×`M` or `M`×`N`). If CV_SVD_U_T is specified, the number of rows and columns in the sentence above should be swapped.
V
  Optional right orthogonal matrix (`N`×`N`)
flags
  Operation flags; can be 0 or combination of the following values:
  - `CV_SVD_MODIFY_A` enables modification of matrix `src1` during the operation. It speeds up the processing.
  - `CV_SVD_U_T` means that the tranposed matrix `U` is returned. Specifying the flag speeds up the processing.
  - `CV_SVD_V_T` means that the tranposed matrix `V` is returned. Specifying the flag speeds up the processing.

The function `cvSVD` decomposes matrix `A` into a product of a diagonal matrix and two orthogonal matrices:

    A=U*W*VT

Where `W` is diagonal matrix of singular values that can be coded as a 1D vector of singular values and `U` and `V`. All the singular values are non-negative and sorted (together with `U` and and `V` columns) in descenting order.

SVD algorithm is numerically robust and its typical applications include:

- accurate eigenvalue problem solution when matrix `A` is square, symmetric and positively defined matrix, for example, when it is a covariation matrix. `W` in this case will be a vector of eigen values, and `U`=`V` is matrix of eigen vectors (thus, only one of `U` or `V` needs to be calculated if the eigen vectors are required)
- accurate solution of poor-conditioned linear systems
- least-squares solution of overdetermined linear systems. This and previous is done by cvSolve function with `CV_SVD` method
- accurate calculation of different matrix characteristics such as rank (number of non-zero singular values), condition number (ratio of the largest singular value to the smallest one), determinant (absolute value of determinant is equal to the product of singular values). All the things listed in this item do not require calculation of `U` and `V` matrices.

### SVBkSb

Performs singular value back substitution

    void  cvSVBkSb( const CvArr* W, const CvArr* U, const CvArr* V,
                    const CvArr* B, CvArr* X, int flags );

W
  Matrix or vector of singular values.
U
  Left orthogonal matrix (tranposed, perhaps)
V
  Right orthogonal matrix (tranposed, perhaps)
B
  The matrix to multiply the pseudo-inverse of the original matrix `A` by. This is the optional parameter. If it is omitted then it is assumed to be an identity matrix of an appropriate size (So `X` will be the reconstructed pseudo-inverse of `A`).
X
  The destination matrix: result of back substitution.
flags
  Operation flags, should match exactly to the `flags` passed to cvSVD.

The function `cvSVBkSb` calculates back substitution for decomposed matrix `A` (see cvSVD description) and matrix `B`:

    X=V*W-1*UT*B

Where

    W-1(i,i)=1/W(i,i) if W(i,i) > epsilon•sumiW(i,i),
                        0        otherwise

And `epsilon` is a small number that depends on the matrix data type.

This function together with cvSVD is used inside cvInvert and cvSolve, and the possible reason to use these (svd & bksb) "low-level" function is to avoid temporary matrices allocation inside the high-level counterparts (inv & solve).

### EigenVV

Computes eigenvalues and eigenvectors of symmetric matrix

    void cvEigenVV( CvArr* mat, CvArr* evects, CvArr* evals, double eps=0 );

mat
  The input symmetric square matrix. It is modified during the processing.
evects
  The output matrix of eigenvectors, stored as a subsequent rows.
evals
  The output vector of eigenvalues, stored in the descenting order (order of eigenvalues and eigenvectors is syncronized, of course).
eps
  Accuracy of diagonalization (typically, DBL_EPSILON=≈10-15 is enough).

The function `cvEigenVV` computes the eigenvalues and eigenvectors of the matrix `A`:

    mat*evects(i,:)' = evals(i)*evects(i,:)' (in MATLAB notation)

The contents of matrix `A` is destroyed by the function.

Currently the function is slower than cvSVD yet less accurate, so if `A` is known to be positively-defined (for example, it is a covariation matrix), it is recommended to use cvSVD to find eigenvalues and eigenvectors of `A`, especially if eigenvectors are not required. That is, instead of

    cvEigenVV(mat, eigenvals, eigenvects);

call

    cvSVD(mat, eigenvals, eigenvects, 0, CV_SVD_U_T + CV_SVD_MODIFY_A);

### CalcCovarMatrix

Calculates covariation matrix of the set of vectors

    void cvCalcCovarMatrix( const CvArr** vects, int count, CvArr* cov_mat, CvArr* avg, int flags );

vects
  The input vectors. They all must have the same type and the same size. The vectors do not have to be 1D, they can be 2D (e.g. images) etc.
count
  The number of input vectors.
cov_mat
  The output covariation matrix that should be floating-point and square.
avg
  The input or output (depending on the flags) array - the mean (average) vector of the input vectors.
flags
  The operation flags, a combination of the following values:
  `CV_COVAR_SCRAMBLED` - the output covaration matrix is calculated as:
  `scale*[vects[0]-avg,vects[1]-avg,...]T*[vects[0]-avg,vects[1]-avg,...]`,
  that is, the covariation matrix is `count`×`count`. Such an unusual covariation matrix is used for fast PCA of a set of very large vectors (see, for example, EigenFaces technique for face recognition). Eigenvalues of this "scrambled" matrix will match to the eigenvalues of the true covariation matrix and the "true" eigenvectors can be easily calculated from the eigenvectors of the "scrambled" covariation matrix.
  `CV_COVAR_NORMAL` - the output covaration matrix is calculated as:
  `scale*[vects[0]-avg,vects[1]-avg,...]*[vects[0]-avg,vects[1]-avg,...]T`,
  that is, `cov_mat` will be a usual covariation matrix with the same linear size as the total number of elements in every input vector. One and only one of `CV_COVAR_SCRAMBLED` and `CV_COVAR_NORMAL` must be specified
  `CV_COVAR_USE_AVG` - if the flag is specified, the function does not calculate `avg` from the input vectors, but, instead, uses the passed `avg` vector. This is useful if `avg` has been already calculated somehow, or if the covariation matrix is calculated by parts - in this case, `avg` is not a mean vector of the input sub-set of vectors, but rather the mean vector of the whole set.
  `CV_COVAR_SCALE` - if the flag is specified, the covariation matrix is scaled by the number of input vectors. `CV_COVAR_ROWS` - Means that all the input vectors are stored as rows of a single matrix, `vects[0]`. `count` is ignored in this case, and `avg` should be a single-row vector of an appropriate size. `CV_COVAR_COLS` - Means that all the input vectors are stored as columns of a single matrix, `vects[0]`. `count` is ignored in this case, and `avg` should be a single-column vector of an appropriate size.

The function `cvCalcCovarMatrix` calculates the covariation matrix and, optionally, mean vector of the set of input vectors. The function can be used for PCA, for comparing vectors using Mahalanobis distance etc.

### Mahalonobis

Calculates Mahalonobis distance between two vectors

    double cvMahalanobis( const CvArr* vec1, const CvArr* vec2, CvArr* mat );

vec1
  The first 1D source vector.
vec2
  The second 1D source vector.
mat
  The inverse covariation matrix.

The function `cvMahalonobis` calculates the weighted distance between two vectors and returns it:

    d(vec1,vec2)=sqrt( sumi,j {mat(i,j)*(vec1(i)-vec2(i))*(vec1(j)-vec2(j))} )

The covariation matrix may be calculated using cvCalcCovarMatrix function and further inverted using cvInvert function (CV_SVD method is the preffered one, because the matrix might be singular).

### CalcPCA

Performs Principal Component Analysis of a vector set

    void cvCalcPCA( const CvArr* data, CvArr* avg,
                    CvArr* eigenvalues, CvArr* eigenvectors, int flags );

data
  The input data; each vector is either a single row (`CV_PCA_DATA_AS_ROW`) or a single column (`CV_PCA_DATA_AS_COL`).
avg
  The mean (average) vector, computed inside the function or provided by user.
eigenvalues
  The output eigenvalues of covariation matrix.
eigenvectors
  The output eigenvectors of covariation matrix (i.e. principal components); one vector per row.
flags
  The operation flags, a combination of the following values:
  `CV_PCA_DATA_AS_ROW` - the vectors are stored as rows (i.e. all the components of a certain vector are stored continously)
  `CV_PCA_DATA_AS_COL` - the vectors are stored as columns (i.e. values of a certain vector component are stored continuously)
  (the above two flags are mutually exclusive)
  `CV_PCA_USE_AVG` - use pre-computed average vector

The function `cvCalcPCA` performs PCA analysis of the vector set. First, it uses cvCalcCovarMatrix to compute covariation matrix and then it finds its eigenvalues and eigenvectors. The output number of eigenvalues/eigenvectors should be less than or equal to `MIN(rows(data),cols(data))`.

### ProjectPCA

Projects vectors to the specified subspace

    void cvProjectPCA( const CvArr* data, const CvArr* avg,
                       const CvArr* eigenvectors, CvArr* result )

data
  The input data; each vector is either a single row or a single column.
avg
  The mean (average) vector. If it is a single-row vector, it means that the input vectors are stored as rows of `data`; otherwise, it should be a single-column vector, then the vectors are stored as columns of `data`.
eigenvectors
  The eigenvectors (principal components); one vector per row.
result
  The output matrix of decomposition coefficients. The number of rows must be the same as the number of vectors, the number of columns must be less than or equal to the number of rows in `eigenvectors`. That it is less, the input vectors are projected into subspace of the first `cols(result)` principal components.

The function `cvProjectPCA` projects input vectors to the subspace represented by the orthonormal basis (`eigenvectors`). Before computing the dot products, `avg` vector is subtracted from the input vectors:

    result(i,:)=(data(i,:)-avg)*eigenvectors' // for CV_PCA_DATA_AS_ROW layout.

### BackProjectPCA

Reconstructs the original vectors from the projection coefficients

    void cvBackProjectPCA( const CvArr* proj, const CvArr* avg,
                           const CvArr* eigenvects, CvArr* result );

proj
  The input data; in the same format as `result` in cvProjectPCA.
avg
  The mean (average) vector. If it is a single-row vector, it means that the output vectors are stored as rows of `result`; otherwise, it should be a single-column vector, then the vectors are stored as columns of `result`.
eigenvectors
  The eigenvectors (principal components); one vector per row.
result
  The output matrix of reconstructed vectors.

The function `cvBackProjectPCA` reconstructs the vectors from the projection coefficients:

    result(i,:)=proj(i,:)*eigenvectors + avg // for CV_PCA_DATA_AS_ROW layout.

## Math Functions

### Round, Floor, Ceil

Converts floating-point number to integer

    int cvRound( double value );
    int cvFloor( double value );
    int cvCeil( double value );

value
  The input floating-point value

The functions `cvRound, cvFloor` and `cvCeil` convert input floating-point number to integer using one of the rounding modes. `cvRound` returns the nearest integer value to the argument. `cvFloor` returns the maximum integer value that is not larger than the argument. `cvCeil` returns the minimum integer value that is not smaller than the argument. On some architectures the functions work much faster than the standard cast operations in C. If absolute value of the argument is greater than 231, the result is not determined. Special values (±Inf, NaN) are not handled.

### Sqrt

Calculates square root

    float cvSqrt( float value );

value
  The input floating-point value

The function `cvSqrt` calculates square root of the argument. If the argument is negative, the result is not determined.

### InvSqrt

Calculates inverse square root

    float cvInvSqrt( float value );

value
  The input floating-point value

The function `cvInvSqrt` calculates inverse square root of the argument, and normally it is faster than `1./sqrt(value)`. If the argument is zero or negative, the result is not determined. Special values (±Inf, NaN) are not handled.

### Cbrt

Calculates cubic root

    float cvCbrt( float value );

value
  The input floating-point value

The function `cvCbrt` calculates cubic root of the argument, and normally it is faster than `pow(value,1./3)`. Besides, negative arguments are handled properly. Special values (±Inf, NaN) are not handled.

### FastArctan

Calculates angle of 2D vector

    float cvFastArctan( float y, float x );

x
  x-coordinate of 2D vector
y
  y-coordinate of 2D vector

The function `cvFastArctan` calculates full-range angle of input 2D vector. The angle is measured in degrees and varies from 0° to 360°. The accuracy is ~0.1°

### IsNaN

Determines if the argument is Not A Number

    int cvIsNaN( double value );

value
  The input floating-point value

The function `cvIsNaN` returns 1 if the argument is Not A Number (as defined by IEEE754 standard), 0 otherwise.

### IsInf

Determines if the argument is Infinity

    int cvIsInf( double value );

value
  The input floating-point value

The function `cvIsInf` returns 1 if the argument is ±Infinity (as defined by IEEE754 standard), 0 otherwise.

### CartToPolar

Calculates magnitude and/or angle of 2d vectors

    void cvCartToPolar( const CvArr* x, const CvArr* y, CvArr* magnitude,
                        CvArr* angle=NULL, int angle_in_degrees=0 );

x
  The array of x-coordinates
y
  The array of y-coordinates
magnitude
  The destination array of magnitudes, may be set to NULL if it is not needed
angle
  The destination array of angles, may be set to NULL if it is not needed. The angles are measured in radians (0..2π) or in degrees (0..360°).
angle_in_degrees
  The flag indicating whether the angles are measured in radians, which is default mode, or in degrees.

The function `cvCartToPolar` calculates either magnitude, angle, or both of every 2d vector `(x(I),y(I))`:

    magnitude(I)=sqrt( x(I)2+y(I)2 ),
    angle(I)=atan( y(I)/x(I) )

The angles are calculated with ≈0.1° accuracy. For (0,0) point the angle is set to 0.

### PolarToCart

Calculates cartesian coordinates of 2d vectors represented in polar form

    void cvPolarToCart( const CvArr* magnitude, const CvArr* angle,
                        CvArr* x, CvArr* y, int angle_in_degrees=0 );

magnitude
  The array of magnitudes. If it is NULL, the magnitudes are assumed all 1’s.
angle
  The array of angles, whether in radians or degrees.
x
  The destination array of x-coordinates, may be set to NULL if it is not needed.
y
  The destination array of y-coordinates, mau be set to NULL if it is not needed.
angle_in_degrees
  The flag indicating whether the angles are measured in radians, which is default mode, or in degrees.

The function `cvPolarToCart` calculates either x-coodinate, y-coordinate or both of every vector `magnitude(I)*exp(angle(I)*j), j=sqrt(-1)`:

    x(I)=magnitude(I)*cos(angle(I)),
    y(I)=magnitude(I)*sin(angle(I))

### Pow

Raises every array element to power

    void cvPow( const CvArr* src, CvArr* dst, double power );

src
  The source array.
dst
  The destination array, should be the same type as the source.
power
  The exponent of power.

The function `cvPow` raises every element of input array to `p`:

    dst(I)=src(I)p, if p is integer
    dst(I)=abs(src(I))p, otherwise

That is, for non-integer power exponent the absolute values of input array elements are used. However, it is possible to get true values for negative values using some extra operations, as the following sample, computing cube root of array elements, shows:

    CvSize size = cvGetSize(src);
    CvMat* mask = cvCreateMat( size.height, size.width, CV_8UC1 );
    cvCmpS( src, 0, mask, CV_CMP_LT ); /* find negative elements */
    cvPow( src, dst, 1./3 );
    cvSubRS( dst, cvScalarAll(0), dst, mask ); /* negate the results of negative inputs */
    cvReleaseMat( &mask );

For some values of `power`, such as integer values, 0.5 and -0.5, specialized faster algorithms are used.

### Exp

Calculates exponent of every array element

    void cvExp( const CvArr* src, CvArr* dst );

src
  The source array.
dst
  The destination array, it should have `double` type or the same type as the source.

The function `cvExp` calculates exponent of every element of input array:

    dst(I)=exp(src(I))

Maximum relative error is ≈7e-6. Currently, the function converts denormalized values to zeros on output.

### Log

Calculates natural logarithm of every array element absolute value

    void cvLog( const CvArr* src, CvArr* dst );

src
  The source array.
dst
  The destination array, it should have `double` type or the same type as the source.

The function `cvLog` calculates natural logarithm of absolute value of every element of input array:

    dst(I)=log(abs(src(I))), src(I)!=0
    dst(I)=C,  src(I)=0

Where `C` is large negative number (≈-700 in the current implementation)

### SolveCubic

Finds real roots of a cubic equation

    int cvSolveCubic( const CvMat* coeffs, CvMat* roots );

coeffs
  The equation coefficients, array of 3 or 4 elements.
roots
  The output array of real roots. Should have 3 elements.

The function `cvSolveCubic` finds real roots of a cubic equation:

    coeffs[0]*x3 + coeffs[1]*x2 + coeffs[2]*x + coeffs[3] = 0
    (if coeffs is 4-element vector)

    or

    x3 + coeffs[0]*x2 + coeffs[1]*x + coeffs[2] = 0
    (if coeffs is 3-element vector)

The function returns the number of real roots found. The roots are stored to `root` array, which is padded with zeros if there is only one root.

## Random Number Generation

### RNG

Initializes random number generator state

    CvRNG cvRNG( int64 seed=-1 );

seed
  64-bit value used to initiate a random sequence.

The function `cvRNG` initializes random number generator and returns the state. Pointer to the state can be then passed to cvRandInt, cvRandReal and cvRandArr functions. In the current implementation a multiply-with-carry generator is used.

### RandArr

Fills array with random numbers and updates the RNG state

    void cvRandArr( CvRNG* rng, CvArr* arr, int dist_type, CvScalar param1, CvScalar param2 );

rng
  RNG state initialized by cvRNG.
arr
  The destination array.
dist_type
  Distribution type:
  CV_RAND_UNI - uniform distribution
  CV_RAND_NORMAL - normal or Gaussian distribution
param1
  The first parameter of distribution. In case of uniform distribution it is the inclusive lower boundary of random numbers range. In case of normal distribution it is the mean value of random numbers.
param2
  The second parameter of distribution. In case of uniform distribution it is the exclusive upper boundary of random numbers range. In case of normal distribution it is the standard deviation of random numbers.

The function `cvRandArr` fills the destination array with uniformly or normally distributed random numbers. In the sample below the function is used to add a few normally distributed floating-point numbers to random locations within a 2d array

    /* let noisy_screen be the floating-point 2d array that is to be "crapped" */
    CvRNG rng_state = cvRNG(0xffffffff);
    int i, pointCount = 1000;
    /* allocate the array of coordinates of points */
    CvMat* locations = cvCreateMat( pointCount, 1, CV_32SC2 );
    /* arr of random point values */
    CvMat* values = cvCreateMat( pointCount, 1, CV_32FC1 );
    CvSize size = cvGetSize( noisy_screen );

    cvRandInit( &rng_state,
                0, 1, /* use dummy parameters now and adjust them further */
                0xffffffff /* just use a fixed seed here */,
                CV_RAND_UNI /* specify uniform type */ );

    /* initialize the locations */
    cvRandArr( &rng_state, locations, CV_RAND_UNI, cvScalar(0,0,0,0), cvScalar(size.width,size.height,0,0) );

    /* modify RNG to make it produce normally distributed values */
    rng_state.disttype = CV_RAND_NORMAL;
    cvRandSetRange( &rng_state,
                    30 /* deviation */,
                    100 /* average point brightness */,
                    -1 /* initialize all the dimensions */ );
    /* generate values */
    cvRandArr( &rng_state, values, CV_RAND_NORMAL,
               cvRealScalar(100), // average intensity
               cvRealScalar(30) // deviation of the intensity
               );

    /* set the points */
    for( i = 0; i < pointCount; i++ )
    {
        CvPoint pt = *(CvPoint*)cvPtr1D( locations, i, 0 );
        float value = *(float*)cvPtr1D( values, i, 0 );
        *((float*)cvPtr2D( noisy_screen, pt.y, pt.x, 0 )) += value;
    }

    /* not to forget to release the temporary arrays */
    cvReleaseMat( &locations );
    cvReleaseMat( &values );

    /* RNG state does not need to be deallocated */

### RandInt

Returns 32-bit unsigned integer and updates RNG

    unsigned cvRandInt( CvRNG* rng );

rng
  RNG state initialized by `RandInit` and, optionally, customized by `RandSetRange` (though, the latter function does not affect on the discussed function outcome).

The function `cvRandInt` returns uniformly-distributed random 32-bit unsigned integer and updates RNG state. It is similar to rand() function from C runtime library, but it always generates 32-bit number whereas rand() returns a number in between 0 and `RAND_MAX` which is 2**16 or 2**32, depending on the platform.

The function is useful for generating scalar random numbers, such as points, patch sizes, table indices etc, where integer numbers of a certain range can be generated using modulo operation and floating-point numbers can be generated by scaling to 0..1 of any other specific range. Here is the example from the previous function discussion rewritten using cvRandInt:

    /* the input and the task is the same as in the previous sample. */
    CvRNG rng_state = cvRNG(0xffffffff);
    int i, pointCount = 1000;
    /* ... - no arrays are allocated here */
    CvSize size = cvGetSize( noisy_screen );
    /* make a buffer for normally distributed numbers to reduce call overhead */
    #define bufferSize 16
    float normalValueBuffer[bufferSize];
    CvMat normalValueMat = cvMat( bufferSize, 1, CV_32F, normalValueBuffer );
    int valuesLeft = 0;

    for( i = 0; i < pointCount; i++ )
    {
        CvPoint pt;
        /* generate random point */
        pt.x = cvRandInt( &rng_state ) % size.width;
        pt.y = cvRandInt( &rng_state ) % size.height;

        if( valuesLeft <= 0 )
        {
            /* fulfill the buffer with normally distributed numbers if the buffer is empty */
            cvRandArr( &rng_state, &normalValueMat, CV_RAND_NORMAL, cvRealScalar(100), cvRealScalar(30) );
            valuesLeft = bufferSize;
        }
        *((float*)cvPtr2D( noisy_screen, pt.y, pt.x, 0 ) = normalValueBuffer[--valuesLeft];
    }

    /* there is no need to deallocate normalValueMat because we have
    both the matrix header and the data on stack. It is a common and efficient
    practice of working with small, fixed-size matrices */

### RandReal

Returns floating-point random number and updates RNG

    double cvRandReal( CvRNG* rng );

rng
  RNG state initialized by cvRNG.

The function `cvRandReal` returns uniformly-distributed random floating-point number from 0..1 range (1 is not included).

## Discrete Transforms

### DFT

Performs forward or inverse Discrete Fourier transform of 1D or 2D floating-point array

    #define CV_DXT_FORWARD  0
    #define CV_DXT_INVERSE  1
    #define CV_DXT_SCALE    2
    #define CV_DXT_ROWS     4
    #define CV_DXT_INV_SCALE (CV_DXT_SCALE|CV_DXT_INVERSE)
    #define CV_DXT_INVERSE_SCALE CV_DXT_INV_SCALE

    void cvDFT( const CvArr* src, CvArr* dst, int flags, int nonzero_rows=0 );

src
  Source array, real or complex.
dst
  Destination array of the same size and same type as the source.
flags
  Transformation flags, a combination of the following values:
  `CV_DXT_FORWARD` - do forward 1D or 2D transform. The result is not scaled.
  `CV_DXT_INVERSE` - do inverse 1D or 2D transform. The result is not scaled. `CV_DXT_FORWARD` and `CV_DXT_INVERSE` are mutually exclusive, of course.
  `CV_DXT_SCALE` - scale the result: divide it by the number of array elements. Usually, it is combined with `CV_DXT_INVERSE`, and one may use a shortcut `CV_DXT_INV_SCALE`.
  `CV_DXT_ROWS` - do forward or inverse transform of every individual row of the input matrix. This flag allows user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms etc.
nonzero_rows
  Number of nonzero rows to in the source array (in case of forward 2d transform), or a number of rows of interest in the destination array (in case of inverse 2d transform). If the value is negative, zero, or greater than the total number of rows, it is ignored. The parameter can be used to speed up 2d convolution/correlation when computing them via DFT. See the sample below.

The function `cvDFT` performs forward or inverse transform of 1D or 2D floating-point array:

    Forward Fourier transform of 1D vector of N elements:
    y = F(N)•x, where F(N)jk=exp(-i•2Pi•j•k/N), i=sqrt(-1)

    Inverse Fourier transform of 1D vector of N elements:
    x'= (F(N))-1•y = conj(F(N))•y
    x = (1/N)•x

    Forward Fourier transform of 2D vector of M×N elements:
    Y = F(M)•X•F(N)

    Inverse Fourier transform of 2D vector of M×N elements:
    X'= conj(F(M))•Y•conj(F(N))
    X = (1/(M•N))•X'

In case of real (single-channel) data, the packed format, borrowed from IPL, is used to to represent a result of forward Fourier transform or input for inverse Fourier transform:

    Re Y0,0      Re Y0,1    Im Y0,1    Re Y0,2     Im Y0,2  ...  Re Y0,N/2-1   Im Y0,N/2-1  Re Y0,N/2
    Re Y1,0      Re Y1,1    Im Y1,1    Re Y1,2     Im Y1,2  ...  Re Y1,N/2-1   Im Y1,N/2-1  Re Y1,N/2
    Im Y1,0      Re Y2,1    Im Y2,1    Re Y2,2     Im Y2,2  ...  Re Y2,N/2-1   Im Y2,N/2-1  Im Y2,N/2
    ............................................................................................
    Re YM/2-1,0   Re YM-3,1   Im YM-3,1  Re YM-3,2   Im YM-3,2 ...  Re YM-3,N/2-1  Im YM-3,N/2-1 Re YM-3,N/2
    Im YM/2-1,0   Re YM-2,1   Im YM-2,1  Re YM-2,2   Im YM-2,2 ...  Re YM-2,N/2-1  Im YM-2,N/2-1 Im YM-2,N/2
    Re YM/2,0    Re YM-1,1   Im YM-1,1  Re YM-1,2   Im YM-1,2  ... Re YM-1,N/2-1  Im YM-1,N/2-1 Im YM-1,N/2

Note: the last column is present if `N` is even, the last row is present if `M` is even.

In case of 1D real transform the result looks like the first row of the above matrix

Computing 2D Convolution using DFT

       CvMat* A = cvCreateMat( M1, N1, CV_32F );
       CvMat* B = cvCreateMat( M2, N2, A->type );

       // it is also possible to have only abs(M2-M1)+1×abs(N2-N1)+1
       // part of the full convolution result
       CvMat* conv = cvCreateMat( A->rows + B->rows - 1, A->cols + B->cols - 1, A->type );

       // initialize A and B
       ...

       int dft_M = cvGetOptimalDFTSize( A->rows + B->rows - 1 );
       int dft_N = cvGetOptimalDFTSize( A->cols + B->cols - 1 );

       CvMat* dft_A = cvCreateMat( dft_M, dft_N, A->type );
       CvMat* dft_B = cvCreateMat( dft_M, dft_N, B->type );
       CvMat tmp;

       // copy A to dft_A and pad dft_A with zeros
       cvGetSubRect( dft_A, &tmp, cvRect(0,0,A->cols,A->rows));
       cvCopy( A, &tmp );
       cvGetSubRect( dft_A, &tmp, cvRect(A->cols,0,dft_A->cols - A->cols,A->rows));
       cvZero( &tmp );
       // no need to pad bottom part of dft_A with zeros because of
       // use nonzero_rows parameter in cvDFT() call below

       cvDFT( dft_A, dft_A, CV_DXT_FORWARD, A->rows );

       // repeat the same with the second array
       cvGetSubRect( dft_B, &tmp, cvRect(0,0,B->cols,B->rows));
       cvCopy( B, &tmp );
       cvGetSubRect( dft_B, &tmp, cvRect(B->cols,0,dft_B->cols - B->cols,B->rows));
       cvZero( &tmp );
       // no need to pad bottom part of dft_B with zeros because of
       // use nonzero_rows parameter in cvDFT() call below

       cvDFT( dft_B, dft_B, CV_DXT_FORWBRD, B->rows );

       cvMulSpectrums( dft_A, dft_B, dft_A, 0 /* or CV_DXT_MUL_CONJ to get correlation
                                                 rather than convolution */ );

       cvDFT( dft_A, dft_A, CV_DXT_INV_SCALE, conv->rows ); // calculate only the top part
       cvGetSubRect( dft_A, &tmp, cvRect(0,0,conv->cols,conv->rows) );

       cvCopy( &tmp, conv );

### GetOptimalDFTSize

Returns optimal DFT size for given vector size

    int cvGetOptimalDFTSize( int size0 );

size0
  Vector size.

The function `cvGetOptimalDFTSize` returns the minimum number `N` that is greater to equal to `size0`, such that DFT of a vector of size `N` can be computed fast. In the current implementation `N=2p×3q×5r` for some `p, q, r`.

The function returns a negative number if `size0` is too large (very close to `INT_MAX`)

### MulSpectrums

Performs per-element multiplication of two Fourier spectrums

    void cvMulSpectrums( const CvArr* src1, const CvArr* src2, CvArr* dst, int flags );

src1
  The first source array.
src2
  The second source array.
dst
  The destination array of the same type and the same size of the sources.
flags
  A combination of the following values:
  `CV_DXT_ROWS` - treat each row of the arrays as a separate spectrum (see cvDFT parameters description).
  `CV_DXT_MUL_CONJ` - conjugate the second source array before the multiplication.

The function `cvMulSpectrums` performs per-element multiplication of the two CCS-packed or complex matrices that are results of real or complex Fourier transform.

The function, together with cvDFT, may be used to calculate convolution of two arrays fast.

### DCT

Performs forward or inverse Discrete Cosine transform of 1D or 2D floating-point array

    #define CV_DXT_FORWARD  0
    #define CV_DXT_INVERSE  1
    #define CV_DXT_ROWS     4

    void cvDCT( const CvArr* src, CvArr* dst, int flags );

src
  Source array, real 1D or 2D array.
dst
  Destination array of the same size and same type as the source.
flags
  Transformation flags, a combination of the following values:
  `CV_DXT_FORWARD` - do forward 1D or 2D transform.
  `CV_DXT_INVERSE` - do inverse 1D or 2D transform.
  `CV_DXT_ROWS` - do forward or inverse transform of every individual row of the input matrix. This flag allows user to transform multiple vectors simultaneously and can be used to decrease the overhead (which is sometimes several times larger than the processing itself), to do 3D and higher-dimensional transforms etc.

The function `cvDCT` performs forward or inverse transform of 1D or 2D floating-point array:

    Forward Cosine transform of 1D vector of N elements:
    y = C(N)•x, where C(N)jk=sqrt((j==0?1:2)/N)•cos(Pi•(2k+1)•j/N)

    Inverse Cosine transform of 1D vector of N elements:
    x = (C(N))-1•y = (C(N))T•y

    Forward Cosine transform of 2D vector of M×N elements:
    Y = (C(M))•X•(C(N))T

    Inverse Cosine transform of 2D vector of M×N elements:
    X = (C(M))T•Y•C(N)

# Dynamic Structures

## Memory Storages

### CvMemStorage

Growing memory storage

    typedef struct CvMemStorage
    {
        struct CvMemBlock* bottom;/* first allocated block */
        struct CvMemBlock* top; /* the current memory block - top of the stack */
        struct CvMemStorage* parent; /* borrows new blocks from */
        int block_size; /* block size */
        int free_space; /* free space in the top block (in bytes) */
    } CvMemStorage;

Memory storage is a low-level structure used to store dynamically growing data structures such as sequences, contours, graphs, subdivisions etc. It is organized as a list of memory blocks of equal size - `bottom` field is the beginning of the list of blocks and `top` is the currently used block, but not necessarily the last block of the list. All blocks between `bottom` and `top`, not including the latter, are considered fully ocupied; and all blocks between `top` and the last block, not including `top`, are considered free and `top` block itself is partly ocupied - `free_space` contains the number of free bytes left in the end of `top`.

New memory buffer that may be allocated explicitly by cvMemStorageAlloc function or implicitly by higher-level functions, such as cvSeqPush, cvGraphAddEdge etc., `always` starts in the end of the current block if it fits there. After allocation `free_space` is decremented by the size of the allocated buffer plus some padding to keep the proper alignment. When the allocated buffer does not fit into the available part of `top`, the next storage block from the list is taken as `top` and `free_space` is reset to the whole block size prior to the allocation.

If there is no more free blocks, a new block is allocated (or borrowed from parent, see cvCreateChildMemStorage) and added to the end of list. Thus, the storage behaves as a stack with `bottom` indicating bottom of the stack and the pair (`top`, `free_space`) indicating top of the stack. The stack top may be saved via cvSaveMemStoragePos, restored via cvRestoreMemStoragePos or reset via cvClearStorage.

### CvMemBlock

Memory storage block

    typedef struct CvMemBlock
    {
        struct CvMemBlock* prev;
        struct CvMemBlock* next;
    } CvMemBlock;

The structure CvMemBlock represents a single block of memory storage. Actual data of the memory blocks follows the header, that is, the `i-th` byte of the memory block can be retrieved with the expression `((char*)(mem_block_ptr+1))[i]`. However, normally there is no need to access the storage structure fields directly.

### CvMemStoragePos

Memory storage position

    typedef struct CvMemStoragePos
    {
        CvMemBlock* top;
        int free_space;
    } CvMemStoragePos;

The structure described below stores the position of the stack top that can be saved via cvSaveMemStoragePos and restored via cvRestoreMemStoragePos.

### CreateMemStorage

Creates memory storage

    CvMemStorage* cvCreateMemStorage( int block_size=0 );

block_size
  Size of the storage blocks in bytes. If it is 0, the block size is set to default value - currently it is ≈64K.

The function `cvCreateMemStorage` creates a memory storage and returns pointer to it. Initially the storage is empty. All fields of the header, except the `block_size`, are set to 0.

### CreateChildMemStorage

Creates child memory storage

    CvMemStorage* cvCreateChildMemStorage( CvMemStorage* parent );

parent
  Parent memory storage.

The function `cvCreateChildMemStorage` creates a child memory storage that is similar to simple memory storage except for the differences in the memory allocation/deallocation mechanism. When a child storage needs a new block to add to the block list, it tries to get this block from the parent. The first unoccupied parent block available is taken and excluded from the parent block list. If no blocks are available, the parent either allocates a block or borrows one from its own parent, if any. In other words, the chain, or a more complex structure, of memory storages where every storage is a child/parent of another is possible. When a child storage is released or even cleared, it returns all blocks to the parent. In other aspects, the child storage is the same as the simple storage.

The children storages are useful in the following situation. Imagine that user needs to process dynamical data resided in some storage and put the result back to the same storage. With the simplest approach, when temporary data is resided in the same storage as the input and output data, the storage will look as following after processing:

Dynamic data processing without using child storage

That is, garbage appears in the middle of the storage. However, if one creates a child memory storage in the beginning of the processing, writes temporary data there and releases the child storage in the end, no garbage will appear in the source/destination storage:

Dynamic data processing using a child storage

### ReleaseMemStorage

Releases memory storage

    void cvReleaseMemStorage( CvMemStorage** storage );

storage
  Pointer to the released storage.

The function `cvReleaseMemStorage` deallocates all storage memory blocks or returns them to the parent, if any. Then it deallocates the storage header and clears the pointer to the storage. All children of the storage must be released before the parent is released.

### ClearMemStorage

Clears memory storage

    void cvClearMemStorage( CvMemStorage* storage );

storage
  Memory storage.

The function `cvClearMemStorage` resets the top (free space boundary) of the storage to the very beginning. This function does not deallocate any memory. If the storage has a parent, the function returns all blocks to the parent.

### MemStorageAlloc

Allocates memory buffer in the storage

    void* cvMemStorageAlloc( CvMemStorage* storage, size_t size );

storage
  Memory storage.
size
  Buffer size.

The function `cvMemStorageAlloc` allocates memory buffer in the storage. The buffer size must not exceed the storage block size, otherwise runtime error is raised. The buffer address is aligned by `CV_STRUCT_ALIGN` (=`sizeof(double)` for the moment) bytes.

### MemStorageAllocString

Allocates text string in the storage

    typedef struct CvString
    {
        int len;
        char* ptr;
    }
    CvString;

    CvString cvMemStorageAllocString( CvMemStorage* storage, const char* ptr, int len=-1 );

storage
  Memory storage.
ptr
  The string.
len
  Length of the string (not counting the ending '\0'). If the parameter is negative, the function computes the length.

The function `cvMemStorageAllocString` creates copy of the string in the memory storage. It returns the structure that contains user-passed or computed length of the string and pointer to the copied string.

### SaveMemStoragePos

Saves memory storage position

    void cvSaveMemStoragePos( const CvMemStorage* storage, CvMemStoragePos* pos );

storage
  Memory storage.
pos
  The output position of the storage top.

The function `cvSaveMemStoragePos` saves the current position of the storage top to the parameter `pos`. The function `cvRestoreMemStoragePos` can further retrieve this position.

### RestoreMemStoragePos

Restores memory storage position

    void cvRestoreMemStoragePos( CvMemStorage* storage, CvMemStoragePos* pos );

storage
  Memory storage.
pos
  New storage top position.

The function `cvRestoreMemStoragePos` restores the position of the storage top from the parameter `pos`. This function and The function `cvClearMemStorage` are the only methods to release memory occupied in memory blocks. Note again that there is no way to free memory in the middle of the occupied part of the storage.

## Sequences

### CvSeq

Growable sequence of elements

    #define CV_SEQUENCE_FIELDS() \
        int flags; /* micsellaneous flags */ \
        int header_size; /* size of sequence header */ \
        struct CvSeq* h_prev; /* previous sequence */ \
        struct CvSeq* h_next; /* next sequence */ \
        struct CvSeq* v_prev; /* 2nd previous sequence */ \
        struct CvSeq* v_next; /* 2nd next sequence */ \
        int total; /* total number of elements */ \
        int elem_size;/* size of sequence element in bytes */ \
        char* block_max;/* maximal bound of the last block */ \
        char* ptr; /* current write pointer */ \
        int delta_elems; /* how many elements allocated when the sequence grows (sequence granularity) */ \
        CvMemStorage* storage; /* where the seq is stored */ \
        CvSeqBlock* free_blocks; /* free blocks list */ \
        CvSeqBlock* first; /* pointer to the first sequence block */

    typedef struct CvSeq
    {
        CV_SEQUENCE_FIELDS()
    } CvSeq;

The structure CvSeq is a base for all of OpenCV dynamic data structures.

Such an unusual definition via a helper macro simplifies the extension of the structure CvSeq with additional parameters. To extend CvSeq the user may define a new structure and put user-defined fields after all CvSeq fields that are included via the macro `CV_SEQUENCE_FIELDS()`.

There are two types of sequences - dense and sparse. Base type for dense sequences is CvSeq and such sequences are used to represent growable 1d arrays - vectors, stacks, queues, deques. They have no gaps in the middle - if an element is removed from the middle or inserted into the middle of the sequence the elements from the closer end are shifted. Sparse sequences have CvSet base class and they are discussed later in more details. They are sequences of nodes each of those may be either occupied or free as indicated by the node flag. Such sequences are used for unordered data structures such as sets of elements, graphs, hash tables etc.

The field `header_size` contains the actual size of the sequence header and should be greater or equal to `sizeof(CvSeq)`.

The fields `h_prev, h_next, v_prev, v_next` can be used to create hierarchical structures from separate sequences. The fields `h_prev` and `h_next` point to the previous and the next sequences on the same hierarchical level while the fields `v_prev` and `v_next` point to the previous and the next sequence in the vertical direction, that is, parent and its first child. But these are just names and the pointers can be used in a different way.

The field `first` points to the first sequence block, whose structure is described below.

The field `total` contains the actual number of dense sequence elements and number of allocated nodes in sparse sequence.

The field `flags`contain the particular dynamic type signature (`CV_SEQ_MAGIC_VAL` for dense sequences and `CV_SET_MAGIC_VAL` for sparse sequences) in the highest 16 bits and miscellaneous information about the sequence. The lowest `CV_SEQ_ELTYPE_BITS` bits contain the ID of the element type. Most of sequence processing functions do not use element type but element size stored in `elem_size`. If sequence contains the numeric data of one of CvMat type then the element type matches to the corresponding CvMat element type, e.g. CV_32SC2 may be used for sequence of 2D points, CV_32FC1 for sequences of floating-point values etc. `CV_SEQ_ELTYPE(seq_header_ptr)` macro retrieves the type of sequence elements. Processing function that work with numerical sequences check that `elem_size` is equal to the calculated from the type element size. Besides CvMat compatible types, there are few extra element types defined in cvtypes.h header:

Standard Types of Sequence Elements

        #define CV_SEQ_ELTYPE_POINT          CV_32SC2  /* (x,y) */
        #define CV_SEQ_ELTYPE_CODE           CV_8UC1   /* freeman code: 0..7 */
        #define CV_SEQ_ELTYPE_GENERIC        0 /* unspecified type of sequence elements */
        #define CV_SEQ_ELTYPE_PTR            CV_USRTYPE1 /* =6 */
        #define CV_SEQ_ELTYPE_PPOINT         CV_SEQ_ELTYPE_PTR  /* &elem: pointer to element of other sequence */
        #define CV_SEQ_ELTYPE_INDEX          CV_32SC1  /* #elem: index of element of some other sequence */
        #define CV_SEQ_ELTYPE_GRAPH_EDGE     CV_SEQ_ELTYPE_GENERIC  /* &next_o, &next_d, &vtx_o, &vtx_d */
        #define CV_SEQ_ELTYPE_GRAPH_VERTEX   CV_SEQ_ELTYPE_GENERIC  /* first_edge, &(x,y) */
        #define CV_SEQ_ELTYPE_TRIAN_ATR      CV_SEQ_ELTYPE_GENERIC  /* vertex of the binary tree   */
        #define CV_SEQ_ELTYPE_CONNECTED_COMP CV_SEQ_ELTYPE_GENERIC  /* connected component  */
        #define CV_SEQ_ELTYPE_POINT3D        CV_32FC3  /* (x,y,z)  */

The next `CV_SEQ_KIND_BITS` bits specify the kind of the sequence:

Standard Kinds of Sequences

        /* generic (unspecified) kind of sequence */
        #define CV_SEQ_KIND_GENERIC     (0 << CV_SEQ_ELTYPE_BITS)

        /* dense sequence suntypes */
        #define CV_SEQ_KIND_CURVE       (1 << CV_SEQ_ELTYPE_BITS)
        #define CV_SEQ_KIND_BIN_TREE    (2 << CV_SEQ_ELTYPE_BITS)

        /* sparse sequence (or set) subtypes */
        #define CV_SEQ_KIND_GRAPH       (3 << CV_SEQ_ELTYPE_BITS)
        #define CV_SEQ_KIND_SUBDIV2D    (4 << CV_SEQ_ELTYPE_BITS)

The remaining bits are used to identify different features specific to certain sequence kinds and element types. For example, curves made of points ( `CV_SEQ_KIND_CURVE|CV_SEQ_ELTYPE_POINT` ), together with the flag `CV_SEQ_FLAG_CLOSED` belong to the type `CV_SEQ_POLYGON` or, if other flags are used, to its subtype. Many contour processing functions check the type of the input sequence and report an error if they do not support this type. The file cvtypes.h stores the complete list of all supported predefined sequence types and helper macros designed to get the sequence type of other properties. Below follows the definition of the building block of sequences.

### CvSeqBlock

Continuous sequence block

    typedef struct CvSeqBlock
    {
        struct CvSeqBlock* prev; /* previous sequence block */
        struct CvSeqBlock* next; /* next sequence block */
        int start_index; /* index of the first element in the block +
        sequence->first->start_index */
        int count; /* number of elements in the block */
        char* data; /* pointer to the first element of the block */
    } CvSeqBlock;

Sequence blocks make up a circular double-linked list, so the pointers `prev` and `next` are never `NULL` and point to the previous and the next sequence blocks within the sequence. It means that `next` of the last block is the first block and `prev` of the first block is the last block. The fields `start_index` and `count` help to track the block location within the sequence. For example, if the sequence consists of 10 elements and splits into three blocks of 3, 5, and 2 elements, and the first block has the parameter `start_index = 2`, then pairs `(start_index, count)` for the sequence blocks are `(2,3), (5, 5)`, and `(10, 2)` correspondingly. The parameter `start_index` of the first block is usually `0` unless some elements have been inserted at the beginning of the sequence.

### CvSlice

A sequence slice

    typedef struct CvSlice
    {
        int start_index;
        int end_index;
    } CvSlice;

    inline CvSlice cvSlice( int start, int end );
    #define CV_WHOLE_SEQ_END_INDEX 0x3fffffff
    #define CV_WHOLE_SEQ  cvSlice(0, CV_WHOLE_SEQ_END_INDEX)

    /* calculates the sequence slice length */
    int cvSliceLength( CvSlice slice, const CvSeq* seq );

Some of functions that operate on sequences take `CvSlice slice` parameter that is often set to the whole sequence (CV_WHOLE_SEQ) by default. Either of the `start_index` and `end_index` may be negative or exceed the sequence length, `start_index` is inclusive, `end_index` is exclusive boundary. If they are equal, the slice is considered empty (i.e. contains no elements). Because sequences are treated as circular structures, the slice may select a few elements in the end of a sequence followed by a few elements in the beginning of the sequence, for example, `cvSlice(-2, 3)` in case of 10-element sequence will select 5-element slice, containing pre-last (8th), last (9th), the very first (0th), second (1th) and third (2nd) elements. The functions normalize the slice argument in the following way: first, cvSliceLength is called to determine the length of the slice, then, `start_index` of the slice is normalized similarly to the argument of cvGetSeqElem (i.e. negative indices are allowed). The actual slice to process starts at the normalized `start_index` and lasts cvSliceLength elements (again, assuming the sequence is a circular structure).

If a function does not take slice argument, but you want to process only a part of the sequence, the sub-sequence may be extracted using cvSeqSlice function, or stored as into a continuous buffer with cvCvtSeqToArray (optionally, followed by cvMakeSeqHeaderForArray.

### CreateSeq

Creates sequence

    CvSeq* cvCreateSeq( int seq_flags, int header_size,
                        int elem_size, CvMemStorage* storage );

seq_flags
  Flags of the created sequence. If the sequence is not passed to any function working with a specific type of sequences, the sequence value may be set to 0, otherwise the appropriate type must be selected from the list of predefined sequence types.
header_size
  Size of the sequence header; must be greater or equal to `sizeof(CvSeq)`. If a specific type or its extension is indicated, this type must fit the base type header.
elem_size
  Size of the sequence elements in bytes. The size must be consistent with the sequence type. For example, for a sequence of points to be created, the element type `CV_SEQ_ELTYPE_POINT` should be specified and the parameter `elem_size` must be equal to `sizeof(CvPoint)`.
storage
  Sequence location.

The function `cvCreateSeq` creates a sequence and returns the pointer to it. The function allocates the sequence header in the storage block as one continuous chunk and sets the structure fields `flags`, `elem_size`, `header_size` and `storage` to passed values, sets `delta_elems` to the default value (that may be reassigned using cvSetSeqBlockSize function), and clears other header fields, including the space after the first `sizeof(CvSeq)` bytes.

### SetSeqBlockSize

Sets up sequence block size

    void cvSetSeqBlockSize( CvSeq* seq, int delta_elems );

seq
  Sequence.
delta_elems
  Desirable sequence block size in elements.

The function `cvSetSeqBlockSize` affects memory allocation granularity. When the free space in the sequence buffers has run out, the function allocates the space for `delta_elems` sequence elements. If this block immediately follows the one previously allocated, the two blocks are concatenated, otherwise, a new sequence block is created. Therefore, the bigger the parameter is, the lower the possible sequence fragmentation, but the more space in the storage is wasted. When the sequence is created, the parameter `delta_elems` is set to the default value ≈1K. The function can be called any time after the sequence is created and affects future allocations. The function can modify the passed value of the parameter to meet the memory storage constraints.

### SeqPush

Adds element to sequence end

    char* cvSeqPush( CvSeq* seq, void* element=NULL );

seq
  Sequence.
element
  Added element.

The function `cvSeqPush` adds an element to the end of sequence and retuns pointer to the allocated element. If the input `element` is NULL, the function simply allocates a space for one more element.

The following code demonstrates how to create a new sequence using this function:

    CvMemStorage* storage = cvCreateMemStorage(0);
    CvSeq* seq = cvCreateSeq( CV_32SC1, /* sequence of integer elements */
                              sizeof(CvSeq), /* header size - no extra fields */
                              sizeof(int), /* element size */
                              storage /* the container storage */ );
    int i;
    for( i = 0; i < 100; i++ )
    {
        int* added = (int*)cvSeqPush( seq, &i );
        printf( "%d is added\n", *added );
    }

    ...
    /* release memory storage in the end */
    cvReleaseMemStorage( &storage );

The function `cvSeqPush` has O(1) complexity, but there is a faster method for writing large sequences (see cvStartWriteSeq and related functions).

### SeqPop

Removes element from sequence end

    void cvSeqPop( CvSeq* seq, void* element=NULL );

seq
  Sequence.
element
  Optional parameter. If the pointer is not zero, the function copies the removed element to this location.

The function `cvSeqPop` removes an element from the sequence. The function reports an error if the sequence is already empty. The function has O(1) complexity.

### SeqPushFront

Adds element to sequence beginning

    char* cvSeqPushFront( CvSeq* seq, void* element=NULL );

seq
  Sequence.
element
  Added element.

The function `cvSeqPushFront` is similar to cvSeqPush but it adds the new element to the beginning of the sequence. The function has O(1) complexity.

### SeqPopFront

Removes element from sequence beginning

    void cvSeqPopFront( CvSeq* seq, void* element=NULL );

seq
  Sequence.
element
  Optional parameter. If the pointer is not zero, the function copies the removed element to this location.

The function `cvSeqPopFront` removes an element from the beginning of the sequence. The function reports an error if the sequence is already empty. The function has O(1) complexity.

### SeqPushMulti

Pushes several elements to the either end of sequence

    void cvSeqPushMulti( CvSeq* seq, void* elements, int count, int in_front=0 );

seq
  Sequence.
elements
  Added elements.
count
  Number of elements to push.
in_front
  The flags specifying the modified sequence end:
  CV_BACK (=0) - the elements are added to the end of sequence
  CV_FRONT(!=0) - the elements are added to the beginning of sequence

The function `cvSeqPushMulti` adds several elements to either end of the sequence. The elements are added to the sequence in the same order as they are arranged in the input array but they can fall into different sequence blocks.

### SeqPopMulti

Removes several elements from the either end of sequence

    void cvSeqPopMulti( CvSeq* seq, void* elements, int count, int in_front=0 );

seq
  Sequence.
elements
  Removed elements.
count
  Number of elements to pop.
in_front
  The flags specifying the modified sequence end:
  CV_BACK (=0) - the elements are removed from the end of sequence
  CV_FRONT(!=0) - the elements are removed from the beginning of sequence

The function `cvSeqPopMulti` removes several elements from either end of the sequence. If the number of the elements to be removed exceeds the total number of elements in the sequence, the function removes as many elements as possible.

### SeqInsert

Inserts element in sequence middle

    char* cvSeqInsert( CvSeq* seq, int before_index, void* element=NULL );

seq
  Sequence.
before_index
  Index before which the element is inserted. Inserting before 0 (the minimal allowed value of the parameter) is equal to cvSeqPushFront and inserting before `seq->total` (the maximal allowed value of the parameter) is equal to cvSeqPush.
element
  Inserted element.

The function `cvSeqInsert` shifts the sequence elements from the inserted position to the nearest end of the sequence and copies the `element` content there if the pointer is not NULL. The function returns pointer to the inserted element.

### SeqRemove

Removes element from sequence middle

    void cvSeqRemove( CvSeq* seq, int index );

seq
  Sequence.
index
  Index of removed element.

The function `cvSeqRemove` removes elements with the given index. If the index is out of range the function reports an error. An attempt to remove an element from an empty sequence is a partitial case of this situation. The function removes an element by shifting the sequence elements between the nearest end of the sequence and the `index`-th position, not counting the latter.

### ClearSeq

Clears sequence

    void cvClearSeq( CvSeq* seq );

seq
  Sequence.

The function `cvClearSeq` removes all elements from the sequence. The function does not return the memory to the storage, but this memory is reused later when new elements are added to the sequence. This function time complexity is `O(1)`.

### GetSeqElem

Returns pointer to sequence element by its index

    char* cvGetSeqElem( const CvSeq* seq, int index );
    #define CV_GET_SEQ_ELEM( TYPE, seq, index )  (TYPE*)cvGetSeqElem( (CvSeq*)(seq), (index) )

seq
  Sequence.
index
  Index of element.

The function `cvGetSeqElem` finds the element with the given index in the sequence and returns the pointer to it. If the element is not found, the function returns 0. The function supports negative indices, where -1 stands for the last sequence element, -2 stands for the one before last, etc. If the sequence is most likely to consist of a single sequence block or the desired element is likely to be located in the first block, then the macro `CV_GET_SEQ_ELEM( elemType, seq, index )` should be used, where the parameter `elemType` is the type of sequence elements ( CvPoint for example), the parameter `seq` is a sequence, and the parameter `index` is the index of the desired element. The macro checks first whether the desired element belongs to the first block of the sequence and returns it if it does, otherwise the macro calls the main function `GetSeqElem`. Negative indices always cause the cvGetSeqElem call. The function has O(1) time complexity assuming that number of blocks is much smaller than the number of elements.

### SeqElemIdx

Returns index of concrete sequence element

    int cvSeqElemIdx( const CvSeq* seq, const void* element, CvSeqBlock** block=NULL );

seq
  Sequence.
element
  Pointer to the element within the sequence.
block
  Optional argument. If the pointer is not `NULL`, the address of the sequence block that contains the element is stored in this location.

The function `cvSeqElemIdx` returns the index of a sequence element or a negative number if the element is not found.

### CvtSeqToArray

Copies sequence to one continuous block of memory

    void* cvCvtSeqToArray( const CvSeq* seq, void* elements, CvSlice slice=CV_WHOLE_SEQ );

seq
  Sequence.
elements
  Pointer to the destination array that must be large enough. It should be a pointer to data, not a matrix header.
slice
  The sequence part to copy to the array.

The function `cvCvtSeqToArray` copies the entire sequence or subsequence to the specified buffer and returns the pointer to the buffer.

### MakeSeqHeaderForArray

Constructs sequence from array

    CvSeq* cvMakeSeqHeaderForArray( int seq_type, int header_size, int elem_size,
                                    void* elements, int total,
                                    CvSeq* seq, CvSeqBlock* block );

seq_type
  Type of the created sequence.
header_size
  Size of the header of the sequence. Parameter sequence must point to the structure of that size or greater size.
elem_size
  Size of the sequence element.
elements
  Elements that will form a sequence.
total
  Total number of elements in the sequence. The number of array elements must be equal to the value of this parameter.
seq
  Pointer to the local variable that is used as the sequence header.
block
  Pointer to the local variable that is the header of the single sequence block.

The function `cvMakeSeqHeaderForArray` initializes sequence header for array. The sequence header as well as the sequence block are allocated by the user (for example, on stack). No data is copied by the function. The resultant sequence will consists of a single block and have NULL storage pointer, thus, it is possible to read its elements, but the attempts to add elements to the sequence will raise an error in most cases.

### SeqSlice

Makes separate header for the sequence slice

    CvSeq* cvSeqSlice( const CvSeq* seq, CvSlice slice,
                       CvMemStorage* storage=NULL, int copy_data=0 );

seq
  Sequence.
slice
  The part of the sequence to extract.
storage
  The destination storage to keep the new sequence header and the copied data if any. If it is NULL, the function uses the storage containing the input sequence.
copy_data
  The flag that indicates whether to copy the elements of the extracted slice (`copy_data`!=0) or not (`copy_data`=0)

The function `cvSeqSlice` creates a sequence that represents the specified slice of the input sequence. The new sequence either shares the elements with the original sequence or has own copy of the elements. So if one needs to process a part of sequence but the processing function does not have a slice parameter, the required sub-sequence may be extracted using this function.

### CloneSeq

Creates a copy of sequence

    CvSeq* cvCloneSeq( const CvSeq* seq, CvMemStorage* storage=NULL );

seq
  Sequence.
storage
  The destination storage to keep the new sequence header and the copied data if any. If it is NULL, the function uses the storage containing the input sequence.

The function `cvCloneSeq` makes a complete copy of the input sequence and returns it. The call `cvCloneSeq( seq, storage )` is equivalent to `cvSeqSlice( seq, CV_WHOLE_SEQ, storage, 1 )`

### SeqRemoveSlice

Removes sequence slice

    void cvSeqRemoveSlice( CvSeq* seq, CvSlice slice );

seq
  Sequence.
slice
  The part of the sequence to remove.

The function `cvSeqRemoveSlice` removes slice from the sequence.

### SeqInsertSlice

Inserts array in the middle of sequence

    void cvSeqInsertSlice( CvSeq* seq, int before_index, const CvArr* from_arr );

seq
  Sequence.
slice
  The part of the sequence to remove.
from_arr
  The array to take elements from.

The function `cvSeqInsertSlice` inserts all `from_arr` array elements at the specified position of the sequence. The array `from_arr` can be a matrix or another sequence.

### SeqInvert

Reverses the order of sequence elements

    void cvSeqInvert( CvSeq* seq );

seq
  Sequence.

The function `cvSeqInvert` reverses the sequence in-place - makes the first element go last, the last element go first etc.

### SeqSort

Sorts sequence element using the specified comparison function

    /* a < b ? -1 : a > b ? 1 : 0 */
    typedef int (CV_CDECL* CvCmpFunc)(const void* a, const void* b, void* userdata);

    void cvSeqSort( CvSeq* seq, CvCmpFunc func, void* userdata=NULL );

seq
  The sequence to sort
func
  The comparison function that returns negative, zero or positive value depending on the elements relation (see the above declaration and the example below) - similar function is used by `qsort` from C runline except that in the latter `userdata` is not used
userdata
  The user parameter passed to the compasion function; helps to avoid global variables in some cases.

The function `cvSeqSort` sorts the sequence in-place using the specified criteria. Below is the example of the function use:

    /* Sort 2d points in top-to-bottom left-to-right order */
    static int cmp_func( const void* _a, const void* _b, void* userdata )
    {
        CvPoint* a = (CvPoint*)_a;
        CvPoint* b = (CvPoint*)_b;
        int y_diff = a->y - b->y;
        int x_diff = a->x - b->x;
        return y_diff ? y_diff : x_diff;
    }

    ...

    CvMemStorage* storage = cvCreateMemStorage(0);
    CvSeq* seq = cvCreateSeq( CV_32SC2, sizeof(CvSeq), sizeof(CvPoint), storage );
    int i;

    for( i = 0; i < 10; i++ )
    {
        CvPoint pt;
        pt.x = rand() % 1000;
        pt.y = rand() % 1000;
        cvSeqPush( seq, &pt );
    }

    cvSeqSort( seq, cmp_func, 0 /* userdata is not used here */ );

    /* print out the sorted sequence */
    for( i = 0; i < seq->total; i++ )
    {
        CvPoint* pt = (CvPoint*)cvSeqElem( seq, i );
        printf( "(%d,%d)\n", pt->x, pt->y );
    }

    cvReleaseMemStorage( &storage );

### SeqSearch

Searches element in sequence

    /* a < b ? -1 : a > b ? 1 : 0 */
    typedef int (CV_CDECL* CvCmpFunc)(const void* a, const void* b, void* userdata);

    char* cvSeqSearch( CvSeq* seq, const void* elem, CvCmpFunc func,
                       int is_sorted, int* elem_idx, void* userdata=NULL );

seq
  The sequence
elem
  The element to look for
func
  The comparison function that returns negative, zero or positive value depending on the elements relation (see also cvSeqSort).
is_sorted
  Whether the sequence is sorted or not.
elem_idx
  Output parameter; index of the found element.
userdata
  The user parameter passed to the compasion function; helps to avoid global variables in some cases.

The function `cvSeqSearch` searches the element in the sequence. If the sequence is sorted, binary O(log(N)) search is used, otherwise, a simple linear search is used. If the element is not found, the function returns NULL pointer and the index is set to the number of sequence elements if the linear search is used, and to the smallest index `i, seq(i)>elem`.

### StartAppendToSeq

Initializes process of writing data to sequence

    void cvStartAppendToSeq( CvSeq* seq, CvSeqWriter* writer );

seq
  Pointer to the sequence.
writer
  Writer state; initialized by the function.

The function `cvStartAppendToSeq` initializes the process of writing data to the sequence. Written elements are added to the end of the sequence by `CV_WRITE_SEQ_ELEM( written_elem, writer )` macro. Note that during the writing process other operations on the sequence may yield incorrect result or even corrupt the sequence (see description of cvFlushSeqWriter that helps to avoid some of these problems).

### StartWriteSeq

Creates new sequence and initializes writer for it

    void cvStartWriteSeq( int seq_flags, int header_size, int elem_size,
                          CvMemStorage* storage, CvSeqWriter* writer );

seq_flags
  Flags of the created sequence. If the sequence is not passed to any function working with a specific type of sequences, the sequence value may be equal to 0, otherwise the appropriate type must be selected from the list of predefined sequence types.
header_size
  Size of the sequence header. The parameter value may not be less than `sizeof(CvSeq)`. If a certain type or extension is specified, it must fit the base type header.
elem_size
  Size of the sequence elements in bytes; must be consistent with the sequence type. For example, if the sequence of points is created (element type `CV_SEQ_ELTYPE_POINT` ), then the parameter elem_size must be equal to `sizeof(CvPoint)`.
storage
  Sequence location.
writer
  Writer state; initialized by the function.

The function `cvStartWriteSeq` is a composition of cvCreateSeq and cvStartAppendToSeq. The pointer to the created sequence is stored at `writer->seq` and is also returned by cvEndWriteSeq function that should be called in the end.

### EndWriteSeq

Finishes process of writing sequence

    CvSeq* cvEndWriteSeq( CvSeqWriter* writer );

writer
  Writer state

The function `cvEndWriteSeq` finishes the writing process and returns the pointer to the written sequence. The function also truncates the last incomplete sequence block to return the remaining part of the block to the memory storage. After that the sequence can be read and modified safely.

### FlushSeqWriter

Updates sequence headers from the writer state

    void cvFlushSeqWriter( CvSeqWriter* writer );

writer
  Writer state

The function `cvFlushSeqWriter` is intended to enable the user to read sequence elements, whenever required, during the writing process, e.g., in order to check specific conditions. The function updates the sequence headers to make reading from the sequence possible. The writer is not closed, however, so that the writing process can be continued any time. In some algorithm requires often flush'es, consider using cvSeqPush instead.

### StartReadSeq

Initializes process of sequential reading from sequence

    void cvStartReadSeq( const CvSeq* seq, CvSeqReader* reader, int reverse=0 );

seq
  Sequence.
reader
  Reader state; initialized by the function.
reverse
  Determines the direction of the sequence traversal. If `reverse` is 0, the reader is positioned at the first sequence element, otherwise it is positioned at the last element.

The function `cvStartReadSeq` initializes the reader state. After that all the sequence elements from the first down to the last one can be read by subsequent calls of the macro `CV_READ_SEQ_ELEM( read_elem, reader )` in case of forward reading and by using `CV_REV_READ_SEQ_ELEM( read_elem, reader )` in case of reversed reading. Both macros put the sequence element to `read_elem` and move the reading pointer toward the next element. A circular structure of sequence blocks is used for the reading process, that is, after the last element has been read by the macro `CV_READ_SEQ_ELEM`, the first element is read when the macro is called again. The same applies to `CV_REV_READ_SEQ_ELEM` . There is no function to finish the reading process, since it neither changes the sequence nor creates any temporary buffers. The reader field `ptr` points to the current element of the sequence that is to be read next. The code below demonstrates how to use sequence writer and reader.

    CvMemStorage* storage = cvCreateMemStorage(0);
    CvSeq* seq = cvCreateSeq( CV_32SC1, sizeof(CvSeq), sizeof(int), storage );
    CvSeqWriter writer;
    CvSeqReader reader;
    int i;

    cvStartAppendToSeq( seq, &writer );
    for( i = 0; i < 10; i++ )
    {
        int val = rand()%100;
        CV_WRITE_SEQ_ELEM( val, writer );
        printf("%d is written\n", val );
    }
    cvEndWriteSeq( &writer );

    cvStartReadSeq( seq, &reader, 0 );
    for( i = 0; i < seq->total; i++ )
    {
        int val;
    #if 1
        CV_READ_SEQ_ELEM( val, reader );
        printf("%d is read\n", val );
    #else /* alternative way, that is prefferable if sequence elements are large,
             or their size/type is unknown at compile time */
        printf("%d is read\n", *(int*)reader.ptr );
        CV_NEXT_SEQ_ELEM( seq->elem_size, reader );
    #endif
    }
    ...

    cvReleaseStorage( &storage );

### GetSeqReaderPos

Returns the current reader position

    int cvGetSeqReaderPos( CvSeqReader* reader );

reader
  Reader state.

The function `cvGetSeqReaderPos` returns the current reader position (within 0 ... `reader->seq->total` - 1).

### SetSeqReaderPos

Moves the reader to specified position

    void cvSetSeqReaderPos( CvSeqReader* reader, int index, int is_relative=0 );

reader
  Reader state.
index
  The destination position. If the positioning mode is used (see the next parameter) the actual position will be `index` mod `reader->seq->total`.
is_relative
  If it is not zero, then `index` is a relative to the current position.

The function `cvSetSeqReaderPos` moves the read position to the absolute position or relative to the current position.

## Sets

### CvSet

Collection of nodes

        typedef struct CvSetElem
        {
            int flags; /* it is negative if the node is free and zero or positive otherwise */
            struct CvSetElem* next_free; /* if the node is free, the field is a
                                            pointer to next free node */
        }
        CvSetElem;

        #define CV_SET_FIELDS()    \
            CV_SEQUENCE_FIELDS()   /* inherits from CvSeq */ \
            struct CvSetElem* free_elems; /* list of free nodes */

        typedef struct CvSet
        {
            CV_SET_FIELDS()
        } CvSet;

The structure CvSet is a base for OpenCV sparse data structures.

As follows from the above declaration CvSet inherits from CvSeq and it adds `free_elems` field it to, which is a list of free nodes. Every set node, whether free or not, is the element of the underlying sequence. While there is no restrictions on elements of dense sequences, the set (and derived structures) elements must start with integer field and be able to fit CvSetElem structure, because these two fields (integer followed by the pointer) are required for organization of node set with the list of free nodes. If a node is free, `flags` field is negative (the most-significant bit, or MSB, of the field is set), and `next_free` points to the next free node (the first free node is referenced by `free_elems` field of CvSet). And if a node is occupied, `flags` field is positive and contains the node index that may be retrieved using (set_elem->flags & CV_SET_ELEM_IDX_MASK) expression, the rest of the node content is determined by the user. In particular, the occupied nodes are not linked as the free nodes are, so the second field can be used for such a link as well as for some different purpose. The macro `CV_IS_SET_ELEM(set_elem_ptr)` can be used to determined whether the specified node is occupied or not.

Initially the set and the list are empty. When a new node is requiested from the set, it is taken from the list of free nodes, which is updated then. If the list appears to be empty, a new sequence block is allocated and all the nodes within the block are joined in the list of free nodes. Thus, `total` field of the set is the total number of nodes both occupied and free. When an occupied node is released, it is added to the list of free nodes. The node released last will be occupied first.

In OpenCV CvSet is used for representing graphs (CvGraph), sparse multi-dimensional arrays (CvSparseMat), planar subdivisions (CvSubdiv2D) etc.

### CreateSet

Creates empty set

    CvSet* cvCreateSet( int set_flags, int header_size,
                        int elem_size, CvMemStorage* storage );

set_flags
  Type of the created set.
header_size
  Set header size; may not be less than `sizeof(CvSet)`.
elem_size
  Set element size; may not be less than CvSetElem.
storage
  Container for the set.

The function `cvCreateSet` creates an empty set with a specified header size and element size, and returns the pointer to the set. The function is just a thin layer on top of cvCreateSeq.

### SetAdd

Occupies a node in the set

    int cvSetAdd( CvSet* set_header, CvSetElem* elem=NULL, CvSetElem** inserted_elem=NULL );

set_header
  Set.
elem
  Optional input argument, inserted element. If not NULL, the function copies the data to the allocated node (The MSB of the first integer field is cleared after copying).
inserted_elem
  Optional output argument; the pointer to the allocated cell.

The function `cvSetAdd` allocates a new node, optionally copies input element data to it, and returns the pointer and the index to the node. The index value is taken from the lower bits of `flags` field of the node. The function has O(1) complexity, however there exists a faster function for allocating set nodes (see cvSetNew).

### SetRemove

Removes element from set

    void cvSetRemove( CvSet* set_header, int index );

set_header
  Set.
index
  Index of the removed element.

The function `cvSetRemove` removes an element with a specified index from the set. If the node at the specified location is not occupied the function does nothing. The function has O(1) complexity, however, cvSetRemoveByPtr provides yet faster way to remove a set element if it is located already.

### SetNew

Adds element to set (fast variant)

    CvSetElem* cvSetNew( CvSet* set_header );

set_header
  Set.

The function `cvSetNew` is inline light-weight variant of cvSetAdd. It occupies a new node and returns pointer to it rather than index.

### SetRemoveByPtr

Removes set element given its pointer

    void cvSetRemoveByPtr( CvSet* set_header, void* elem );

set_header
  Set.
elem
  Removed element.

The function `cvSetRemoveByPtr` is inline light-weight variant of cvSetRemove that takes element pointer. The function does not check whether the node is occupied or not - the user should take care of it.

### GetSetElem

Finds set element by its index

    CvSetElem* cvGetSetElem( const CvSet* set_header, int index );

set_header
  Set.
index
  Index of the set element within a sequence.

The function `cvGetSetElem` finds a set element by index. The function returns the pointer to it or 0 if the index is invalid or the corresponding node is free. The function supports negative indices as it uses cvGetSeqElem to locate the node.

### ClearSet

Clears set

    void cvClearSet( CvSet* set_header );

set_header
  Cleared set.

The function `cvClearSet` removes all elements from set. It has O(1) time complexity.

## Graphs

### CvGraph

Oriented or unoriented weigted graph

        #define CV_GRAPH_VERTEX_FIELDS()    \
            int flags; /* vertex flags */   \
            struct CvGraphEdge* first; /* the first incident edge */

        typedef struct CvGraphVtx
        {
            CV_GRAPH_VERTEX_FIELDS()
        }
        CvGraphVtx;

        #define CV_GRAPH_EDGE_FIELDS()      \
            int flags; /* edge flags */     \
            float weight; /* edge weight */ \
            struct CvGraphEdge* next[2]; /* the next edges in the incidence lists for staring (0) */ \
                                         /* and ending (1) vertices */ \
            struct CvGraphVtx* vtx[2]; /* the starting (0) and ending (1) vertices */

        typedef struct CvGraphEdge
        {
            CV_GRAPH_EDGE_FIELDS()
        }
        CvGraphEdge;

        #define  CV_GRAPH_FIELDS()                  \
            CV_SET_FIELDS() /* set of vertices */   \
            CvSet* edges;   /* set of edges */

        typedef struct CvGraph
        {
            CV_GRAPH_FIELDS()
        }
        CvGraph;

The structure CvGraph is a base for graphs used in OpenCV.

Graph structure inherits from CvSet - this part describes common graph properties and the graph vertices, and contains another set as a member - this part describes the graph edges.

The vertex, edge and the graph header structures are declared using the same technique as other extendible OpenCV structures - via macros, that simplifies extension and customization of the structures. While the vertex and edge structures do not inherit from CvSetElem explicitly, they satisfy both conditions on the set elements - have an integer field in the beginning and fit CvSetElem structure. The `flags` fields are used as for indicating occupied vertices and edges as well as for other purposes, for example, for graph traversal (see cvCreateGraphScanner et al.), so it is better not to use them directly.

The graph is represented as a set of edges each of whose has the list of incident edges. The incidence lists for different vertices are interleaved to avoid information duplication as much as posssible.

The graph may be oriented or unoriented. In the latter case there is no distiction between edge connecting vertex A with vertex B and the edge connecting vertex B with vertex A - only one of them can exist in the graph at the same moment and it represents both <A, B> and <B, A> edges..

### CreateGraph

Creates empty graph

    CvGraph* cvCreateGraph( int graph_flags, int header_size, int vtx_size,
                            int edge_size, CvMemStorage* storage );

graph_flags
  Type of the created graph. Usually, it is either `CV_SEQ_KIND_GRAPH` for generic unoriented graphs and `CV_SEQ_KIND_GRAPH | CV_GRAPH_FLAG_ORIENTED` for generic oriented graphs.
header_size
  Graph header size; may not be less than `sizeof(CvGraph).`
vtx_size
  Graph vertex size; the custom vertex structure must start with CvGraphVtx (use `CV_GRAPH_VERTEX_FIELDS()`)
edge_size
  Graph edge size; the custom edge structure must start with CvGraphEdge (use `CV_GRAPH_EDGE_FIELDS()`)
storage
  The graph container.

The function `cvCreateGraph` creates an empty graph and returns pointer to it.

### GraphAddVtx

Adds vertex to graph

    int cvGraphAddVtx( CvGraph* graph, const CvGraphVtx* vtx=NULL,
                       CvGraphVtx** inserted_vtx=NULL );

graph
  Graph.
vtx
  Optional input argument used to initialize the added vertex (only user-defined fields beyond `sizeof(CvGraphVtx)` are copied).
inserted_vertex
  Optional output argument. If not `NULL`, the address of the new vertex is written there.

The function `cvGraphAddVtx` adds a vertex to the graph and returns the vertex index.

### GraphRemoveVtx

Removes vertex from graph

    int cvGraphRemoveVtx( CvGraph* graph, int index );

graph
  Graph.
vtx_idx
  Index of the removed vertex.

The function `cvGraphRemoveAddVtx` removes a vertex from the graph together with all the edges incident to it. The function reports an error, if the input vertex does not belong to the graph. The return value is number of edges deleted, or -1 if the vertex does not belong to the graph.

### GraphRemoveVtxByPtr

Removes vertex from graph

    int cvGraphRemoveVtxByPtr( CvGraph* graph, CvGraphVtx* vtx );

graph
  Graph.
vtx
  Pointer to the removed vertex.

The function `cvGraphRemoveVtxByPtr` removes a vertex from the graph together with all the edges incident to it. The function reports an error, if the vertex does not belong to the graph. The return value is number of edges deleted, or -1 if the vertex does not belong to the graph.

### GetGraphVtx

Finds graph vertex by index

    CvGraphVtx* cvGetGraphVtx( CvGraph* graph, int vtx_idx );

graph
  Graph.
vtx_idx
  Index of the vertex.

The function `cvGetGraphVtx` finds the graph vertex by index and returns the pointer to it or NULL if the vertex does not belong to the graph.

### GraphVtxIdx

Returns index of graph vertex

    int cvGraphVtxIdx( CvGraph* graph, CvGraphVtx* vtx );

graph
  Graph.
vtx
  Pointer to the graph vertex.

The function `cvGraphVtxIdx` returns index of the graph vertex.

### GraphAddEdge

Adds edge to graph

    int cvGraphAddEdge( CvGraph* graph, int start_idx, int end_idx,
                        const CvGraphEdge* edge=NULL, CvGraphEdge** inserted_edge=NULL );

graph
  Graph.
start_idx
  Index of the starting vertex of the edge.
end_idx
  Index of the ending vertex of the edge. For unoriented graph the order of the vertex parameters does not matter.
edge
  Optional input parameter, initialization data for the edge.
inserted_edge
  Optional output parameter to contain the address of the inserted edge.

The function `cvGraphAddEdge` connects two specified vertices. The function returns 1 if the edge has been added successfully, 0 if the edge connecting the two vertices exists already and -1 if either of the vertices was not found, the starting and the ending vertex are the same or there is some other critical situation. In the latter case (i.e. when the result is negative) the function also reports an error by default.

### GraphAddEdgeByPtr

Adds edge to graph

    int cvGraphAddEdgeByPtr( CvGraph* graph, CvGraphVtx* start_vtx, CvGraphVtx* end_vtx,
                             const CvGraphEdge* edge=NULL, CvGraphEdge** inserted_edge=NULL );

graph
  Graph.
start_vtx
  Pointer to the starting vertex of the edge.
end_vtx
  Pointer to the ending vertex of the edge. For unoriented graph the order of the vertex parameters does not matter.
edge
  Optional input parameter, initialization data for the edge.
inserted_edge
  Optional output parameter to contain the address of the inserted edge within the edge set.

The function `cvGraphAddEdge` connects two specified vertices. The function returns 1 if the edge has been added successfully, 0 if the edge connecting the two vertices exists already and -1 if either of the vertices was not found, the starting and the ending vertex are the same or there is some other critical situation. In the latter case (i.e. when the result is negative) the function also reports an error by default.

### GraphRemoveEdge

Removes edge from graph

    void cvGraphRemoveEdge( CvGraph* graph, int start_idx, int end_idx );

graph
  Graph.
start_idx
  Index of the starting vertex of the edge.
end_idx
  Index of the ending vertex of the edge. For unoriented graph the order of the vertex parameters does not matter.

The function `cvGraphRemoveEdge` removes the edge connecting two specified vertices. If the vertices are not connected [in that order], the function does nothing.

### GraphRemoveEdgeByPtr

Removes edge from graph

    void cvGraphRemoveEdgeByPtr( CvGraph* graph, CvGraphVtx* start_vtx, CvGraphVtx* end_vtx );

graph
  Graph.
start_vtx
  Pointer to the starting vertex of the edge.
end_vtx
  Pointer to the ending vertex of the edge. For unoriented graph the order of the vertex parameters does not matter.

The function `cvGraphRemoveEdgeByPtr` removes the edge connecting two specified vertices. If the vertices are not connected [in that order], the function does nothing.

### FindGraphEdge

Finds edge in graph

    CvGraphEdge* cvFindGraphEdge( const CvGraph* graph, int start_idx, int end_idx );
    #define cvGraphFindEdge cvFindGraphEdge

graph
  Graph.
start_idx
  Index of the starting vertex of the edge.
end_idx
  Index of the ending vertex of the edge. For unoriented graph the order of the vertex parameters does not matter.

The function `cvFindGraphEdge` finds the graph edge connecting two specified vertices and returns pointer to it or NULL if the edge does not exists.

### FindGraphEdgeByPtr

Finds edge in graph

    CvGraphEdge* cvFindGraphEdgeByPtr( const CvGraph* graph, const CvGraphVtx* start_vtx,
                                       const CvGraphVtx* end_vtx );
    #define cvGraphFindEdgeByPtr cvFindGraphEdgeByPtr

graph
  Graph.
start_vtx
  Pointer to the starting vertex of the edge.
end_vtx
  Pointer to the ending vertex of the edge. For unoriented graph the order of the vertex parameters does not matter.

The function `cvFindGraphEdge` finds the graph edge connecting two specified vertices and returns pointer to it or NULL if the edge does not exists.

### GraphEdgeIdx

Returns index of graph edge

    int cvGraphEdgeIdx( CvGraph* graph, CvGraphEdge* edge );

graph
  Graph.
edge
  Pointer to the graph edge.

The function `cvGraphEdgeIdx` returns index of the graph edge.

### GraphVtxDegree

Counts edges indicent to the vertex

    int cvGraphVtxDegree( const CvGraph* graph, int vtx_idx );

graph
  Graph.
vtx
  Index of the graph vertex.

The function `cvGraphVtxDegree` returns the number of edges incident to the specified vertex, both incoming and outcoming. To count the edges, the following code is used:

        CvGraphEdge* edge = vertex->first; int count = 0;
        while( edge )
        {
            edge = CV_NEXT_GRAPH_EDGE( edge, vertex );
            count++;
        }

The macro `CV_NEXT_GRAPH_EDGE( edge, vertex )` returns the edge incident to `vertex` that follows after `edge`.

### GraphVtxDegreeByPtr

Finds edge in graph

    int cvGraphVtxDegreeByPtr( const CvGraph* graph, const CvGraphVtx* vtx );

graph
  Graph.
vtx
  Pointer to the graph vertex.

The function `cvGraphVtxDegree` returns the number of edges incident to the specified vertex, both incoming and outcoming.

### ClearGraph

Clears graph

    void cvClearGraph( CvGraph* graph );

graph
  Graph.

The function `cvClearGraph` removes all vertices and edges from the graph. The function has O(1) time complexity.

### CloneGraph

Clone graph

    CvGraph* cvCloneGraph( const CvGraph* graph, CvMemStorage* storage );

graph
  The graph to copy.
storage
  Container for the copy.

The function `cvCloneGraph` creates full copy of the graph. If the graph vertices or edges have pointers to some external data, it still be shared between the copies. The vertex and edge indices in the new graph may be different from the original, because the function defragments the vertex and edge sets.

### CvGraphScanner

Graph traversal state

        typedef struct CvGraphScanner
        {
            CvGraphVtx* vtx;       /* current graph vertex (or current edge origin) */
            CvGraphVtx* dst;       /* current graph edge destination vertex */
            CvGraphEdge* edge;     /* current edge */

            CvGraph* graph;        /* the graph */
            CvSeq*   stack;        /* the graph vertex stack */
            int      index;        /* the lower bound of certainly visited vertices */
            int      mask;         /* event mask */
        }
        CvGraphScanner;

The structure CvGraphScanner is used for depth-first graph traversal. See discussion of the functions below.

### CreateGraphScanner

Creates structure for depth-first graph traversal

    CvGraphScanner*  cvCreateGraphScanner( CvGraph* graph, CvGraphVtx* vtx=NULL,
                                           int mask=CV_GRAPH_ALL_ITEMS );

graph
  Graph.
vtx
  Initial vertex to start from. If NULL, the traversal starts from the first vertex (a vertex with the minimal index in the sequence of vertices).
mask
  Event mask indicating which events are interesting to the user (where cvNextGraphItem function returns control to the user) It can be `CV_GRAPH_ALL_ITEMS` (all events are interesting) or combination of the following flags:
  - CV_GRAPH_VERTEX - stop at the graph vertices visited for the first time
  - CV_GRAPH_TREE_EDGE - stop at tree edges (`tree edge` is the edge connecting the last visited vertex and the vertex to be visited next)
  - CV_GRAPH_BACK_EDGE - stop at back edges (`back edge` is an edge connecting the last visited vertex with some of its ancestors in the search tree)
  - CV_GRAPH_FORWARD_EDGE - stop at forward edges (`forward edge` is an edge conecting the last visited vertex with some of its descendants in the search tree). The `forward edges` are only possible during oriented graph traversal)
  - CV_GRAPH_CROSS_EDGE - stop at cross edges (`cross edge` is an edge connecting different search trees or branches of the same tree. The `cross edges` are only possible during oriented graphs traversal)
  - CV_GRAPH_ANY_EDGE - stop and any edge (`tree, back, forward` and `cross edges`)
  - CV_GRAPH_NEW_TREE - stop in the beginning of every new search tree. When the traversal procedure visits all vertices and edges reachible from the initial vertex (the visited vertices together with tree edges make up a tree), it searches for some unvisited vertex in the graph and resumes the traversal process from that vertex. Before starting a new tree (including the very first tree when `cvNextGraphItem` is called for the first time) it generates `CV_GRAPH_NEW_TREE` event.
    For unoriented graphs each search tree corresponds to a connected component of the graph.
  - CV_GRAPH_BACKTRACKING - stop at every already visited vertex during backtracking - returning to already visited vertexes of the traversal tree.

The function `cvCreateGraphScanner` creates structure for depth-first graph traversal/search. The initialized structure is used in cvNextGraphItem function - the incremental traversal procedure.

### NextGraphItem

Makes one or more steps of the graph traversal procedure

    int cvNextGraphItem( CvGraphScanner* scanner );

scanner
  Graph traversal state. It is updated by the function.

The function `cvNextGraphItem` traverses through the graph until an event interesting to the user (that is, an event, specified in the `mask` in cvCreateGraphScanner call) is met or the traversal is over. In the first case it returns one of the events, listed in the description of `mask` parameter above and with the next call it resumes the traversal. In the latter case it returns CV_GRAPH_OVER (-1). When the event is `CV_GRAPH_VERTEX`, or `CV_GRAPH_BACKTRACKING` or `CV_GRAPH_NEW_TREE`, the currently observed vertex is stored in `scanner->vtx`. And if the event is edge-related, the edge itself is stored at `scanner->edge`, the previously visited vertex - at `scanner->vtx` and the other ending vertex of the edge - at `scanner->dst`.

### ReleaseGraphScanner

Finishes graph traversal procedure

    void cvReleaseGraphScanner( CvGraphScanner** scanner );

scanner
  Double pointer to graph traverser.

The function `cvGraphScanner` finishes graph traversal procedure and releases the traverser state.

## Trees

### CV_TREE_NODE_FIELDS

Helper macro for a tree node type declaration

    #define CV_TREE_NODE_FIELDS(node_type)                          \
        int       flags;         /* micsellaneous flags */          \
        int       header_size;   /* size of sequence header */      \
        struct    node_type* h_prev; /* previous sequence */        \
        struct    node_type* h_next; /* next sequence */            \
        struct    node_type* v_prev; /* 2nd previous sequence */    \
        struct    node_type* v_next; /* 2nd next sequence */

The macro `CV_TREE_NODE_FIELDS()` is used to declare structures that can be organized into hierarchical strucutures (trees), such as CvSeq - the basic type for all dynamical structures. The trees made of nodes declared using this macro can be processed using the functions described below in this section.

### CvTreeNodeIterator

Opens existing or creates new file storage

    typedef struct CvTreeNodeIterator
    {
        const void* node;
        int level;
        int max_level;
    }
    CvTreeNodeIterator;

The structure CvTreeNodeIterator is used to traverse trees. The tree node declaration should start with `CV_TREE_NODE_FIELDS(...)` macro.

### InitTreeNodeIterator

Initializes tree node iterator

    void cvInitTreeNodeIterator( CvTreeNodeIterator* tree_iterator,
                                 const void* first, int max_level );

tree_iterator
  Tree iterator initialized by the function.
first
  The initial node to start traversing from.
max_level
  The maximal level of the tree (`first` node assumed to be at the first level) to traverse up to. For example, 1 means that only nodes at the same level as `first` should be visited, 2 means that the nodes on the same level as `first` and their direct children should be visited etc.

The function `cvInitTreeNodeIterator` initializes tree iterator. The tree is traversed in depth-first order.

### NextTreeNode

Returns the currently observed node and moves iterator toward the next node

    void* cvNextTreeNode( CvTreeNodeIterator* tree_iterator );

tree_iterator
  Tree iterator initialized by the function.

The function `cvNextTreeNode` returns the currently observed node and then updates the iterator - moves it toward the next node. In other words, the function behavior is similar to *p++ expression on usual C pointer or C++ collection iterator. The function returns NULL if there is no more nodes.

### PrevTreeNode

Returns the currently observed node and moves iterator toward the previous node

    void* cvPrevTreeNode( CvTreeNodeIterator* tree_iterator );

tree_iterator
  Tree iterator initialized by the function.

The function `cvPrevTreeNode` returns the currently observed node and then updates the iterator - moves it toward the previous node. In other words, the function behavior is similar to *p-- expression on usual C pointer or C++ collection iterator. The function returns NULL if there is no more nodes.

### TreeToNodeSeq

Gathers all node pointers to the single sequence

    CvSeq* cvTreeToNodeSeq( const void* first, int header_size, CvMemStorage* storage );

first
  The initial tree node.
header_size
  Header size of the created sequence (sizeof(CvSeq) is the most used value).
storage
  Container for the sequence.

The function `cvTreeToNodeSeq` puts pointers of all nodes reacheable from `first` to the single sequence. The pointers are written subsequently in the depth-first order.

### InsertNodeIntoTree

Adds new node to the tree

    void cvInsertNodeIntoTree( void* node, void* parent, void* frame );

node
  The inserted node.
parent
  The parent node that is already in the tree.
frame
  The top level node. If `parent` and `frame` are the same, `v_prev` field of `node` is set to NULL rather than `parent`.

The function `cvInsertNodeIntoTree` adds another node into tree. The function does not allocate any memory, it can only modify links of the tree nodes.

### RemoveNodeFromTree

Removes node from tree

    void cvRemoveNodeFromTree( void* node, void* frame );

node
  The removed node.
frame
  The top level node. If `node->v_prev = NULL` and `node->h_prev` is NULL (i.e. if `node` is the first child of `frame`), `frame->v_next` is set to `node->h_next` (i.e. the first child or frame is changed).

The function `cvRemoveNodeFromTree` removes node from tree. The function does not deallocate any memory, it can only modify links of the tree nodes.

# Drawing Functions

Drawing functions work with matrices/images or arbitrary depth. Antialiasing is implemented only for 8-bit images. All the functions include parameter color that means rgb value (that may be constructed with `CV_RGB` macro or `cvScalar` function) for color images and brightness for grayscale images.

If a drawn figure is partially or completely outside the image, it is clipped. For color images the order channel is: Blue Green Red ... If one needs a different channel order, it is possible to construct color via `cvScalar` with the particular channel order, or convert the image before and/or after drawing in it with cvCvtColor or cvTransform.

## Curves and Shapes

### CV_RGB

Constructs a color value

    #define CV_RGB( r, g, b )  cvScalar( (b), (g), (r) )

### Line

Draws a line segment connecting two points

    void cvLine( CvArr* img, CvPoint pt1, CvPoint pt2, CvScalar color,
                 int thickness=1, int line_type=8, int shift=0 );

img
  The image.
pt1
  First point of the line segment.
pt2
  Second point of the line segment.
color
  Line color.
thickness
  Line thickness.
line_type
  Type of the line:
  `8` (or `0`) - 8-connected line.
  `4` - 4-connected line.
  `CV_AA` - antialiased line.
shift
  Number of fractional bits in the point coordinates.

The function `cvLine` draws the line segment between `pt1` and `pt2` points in the image. The line is clipped by the image or ROI rectangle. For non-antialiased lines with integer coordinates the 8-connected or 4-connected Bresenham algorithm is used. Thick lines are drawn with rounding endings. Antialiased lines are drawn using Gaussian filtering. To specify the line color, the user may use the macro `CV_RGB( r, g, b )`.

### Rectangle

Draws simple, thick or filled rectangle

    void cvRectangle( CvArr* img, CvPoint pt1, CvPoint pt2, CvScalar color,
                      int thickness=1, int line_type=8, int shift=0 );

img
  Image.
pt1
  One of the rectangle vertices.
pt2
  Opposite rectangle vertex.
color
  Line color (RGB) or brightness (grayscale image).
thickness
  Thickness of lines that make up the rectangle. Negative values, e.g. CV_FILLED, make the function to draw a filled rectangle.
line_type
  Type of the line, see cvLine description.
shift
  Number of fractional bits in the point coordinates.

The function `cvRectangle` draws a rectangle with two opposite corners `pt1` and `pt2`.

### Circle

Draws a circle

    void cvCircle( CvArr* img, CvPoint center, int radius, CvScalar color,
                   int thickness=1, int line_type=8, int shift=0 );

img
  Image where the circle is drawn.
center
  Center of the circle.
radius
  Radius of the circle.
color
  Circle color.
thickness
  Thickness of the circle outline if positive, otherwise indicates that a filled circle has to be drawn.
line_type
  Type of the circle boundary, see cvLine description.
shift
  Number of fractional bits in the center coordinates and radius value.

The function `cvCircle` draws a simple or filled circle with given center and radius. The circle is clipped by ROI rectangle. To specify the circle color, the user may use the macro `CV_RGB ( r, g, b )`.

### Ellipse

Draws simple or thick elliptic arc or fills ellipse sector

    void cvEllipse( CvArr* img, CvPoint center, CvSize axes, double angle,
                    double start_angle, double end_angle, CvScalar color,
                    int thickness=1, int line_type=8, int shift=0 );

img
  Image.
center
  Center of the ellipse.
axes
  Length of the ellipse axes.
angle
  Rotation angle.
start_angle
  Starting angle of the elliptic arc.
end_angle
  Ending angle of the elliptic arc.
color
  Ellipse color.
thickness
  Thickness of the ellipse arc.
line_type
  Type of the ellipse boundary, see cvLine description.
shift
  Number of fractional bits in the center coordinates and axes' values.

The function `cvEllipse` draws a simple or thick elliptic arc or fills an ellipse sector. The arc is clipped by ROI rectangle. A piecewise-linear approximation is used for antialiased arcs and thick arcs. All the angles are given in degrees. The picture below explains the meaning of the parameters.

Parameters of Elliptic Arc

### EllipseBox

Draws simple or thick elliptic arc or fills ellipse sector

    void cvEllipseBox( CvArr* img, CvBox2D box, CvScalar color,
                       int thickness=1, int line_type=8, int shift=0 );

img
  Image.
box
  The enclosing box of the ellipse drawn
thickness
  Thickness of the ellipse boundary.
line_type
  Type of the ellipse boundary, see cvLine description.
shift
  Number of fractional bits in the box vertex coordinates.

The function `cvEllipseBox` draws a simple or thick ellipse outline, or fills an ellipse. The functions provides a convenient way to draw an ellipse approximating some shape; that is what cvCamShift and cvFitEllipse do. The ellipse drawn is clipped by ROI rectangle. A piecewise-linear approximation is used for antialiased arcs and thick arcs.

### FillPoly

Fills polygons interior

    void cvFillPoly( CvArr* img, CvPoint** pts, int* npts, int contours,
                     CvScalar color, int line_type=8, int shift=0 );

img
  Image.
pts
  Array of pointers to polygons.
npts
  Array of polygon vertex counters.
contours
  Number of contours that bind the filled region.
color
  Polygon color.
line_type
  Type of the polygon boundaries, see cvLine description.
shift
  Number of fractional bits in the vertex coordinates.

The function `cvFillPoly` fills an area bounded by several polygonal contours. The function fills complex areas, for example, areas with holes, contour self-intersection, etc.

### FillConvexPoly

Fills convex polygon

    void cvFillConvexPoly( CvArr* img, CvPoint* pts, int npts,
                           CvScalar color, int line_type=8, int shift=0 );

img
  Image.
pts
  Array of pointers to a single polygon.
npts
  Polygon vertex counter.
color
  Polygon color.
line_type
  Type of the polygon boundaries, see cvLine description.
shift
  Number of fractional bits in the vertex coordinates.

The function `cvFillConvexPoly` fills convex polygon interior. This function is much faster than The function `cvFillPoly` and can fill not only the convex polygons but any monotonic polygon, i.e. a polygon whose contour intersects every horizontal line (scan line) twice at the most.

### PolyLine

Draws simple or thick polygons

    void cvPolyLine( CvArr* img, CvPoint** pts, int* npts, int contours, int is_closed,
                     CvScalar color, int thickness=1, int line_type=8, int shift=0 );

img
  Image.
pts
  Array of pointers to polylines.
npts
  Array of polyline vertex counters.
contours
  Number of polyline contours.
is_closed
  Indicates whether the polylines must be drawn closed. If closed, the function draws the line from the last vertex of every contour to the first vertex.
color
  Polyline color.
thickness
  Thickness of the polyline edges.
line_type
  Type of the line segments, see cvLine description.
shift
  Number of fractional bits in the vertex coordinates.

The function `cvPolyLine` draws a single or multiple polygonal curves.

## Text

### InitFont

Initializes font structure

    void cvInitFont( CvFont* font, int font_face, double hscale,
                     double vscale, double shear=0,
                     int thickness=1, int line_type=8 );

font
  Pointer to the font structure initialized by the function.
font_face
  Font name identifier. Only a subset of Hershey fonts (http://sources.isc.org/utils/misc/hershey-font.txt) are supported now:
  `CV_FONT_HERSHEY_SIMPLEX` - normal size sans-serif font
  `CV_FONT_HERSHEY_PLAIN` - small size sans-serif font
  `CV_FONT_HERSHEY_DUPLEX` - normal size sans-serif font (more complex than `CV_FONT_HERSHEY_SIMPLEX`)
  `CV_FONT_HERSHEY_COMPLEX` - normal size serif font
  `CV_FONT_HERSHEY_TRIPLEX` - normal size serif font (more complex than `CV_FONT_HERSHEY_COMPLEX`)
  `CV_FONT_HERSHEY_COMPLEX_SMALL` - smaller version of `CV_FONT_HERSHEY_COMPLEX`
  `CV_FONT_HERSHEY_SCRIPT_SIMPLEX` - hand-writing style font
  `CV_FONT_HERSHEY_SCRIPT_COMPLEX` - more complex variant of `CV_FONT_HERSHEY_SCRIPT_SIMPLEX`
  The parameter can be composited from one of the values above and optional `CV_FONT_ITALIC` flag, that means italic or oblique font.
hscale
  Horizontal scale. If equal to `1.0f`, the characters have the original width depending on the font type. If equal to `0.5f`, the characters are of half the original width.
vscale
  Vertical scale. If equal to `1.0f`, the characters have the original height depending on the font type. If equal to `0.5f`, the characters are of half the original height.
shear
  Approximate tangent of the character slope relative to the vertical line. Zero value means a non-italic font, `1.0f` means `≈45°` slope, etc. thickness Thickness of lines composing letters outlines. The function `cvLine` is used for drawing letters.
thickness
  Thickness of the text strokes.
line_type
  Type of the strokes, see cvLine description.

The function `cvInitFont` initializes the font structure that can be passed to text rendering functions.

### PutText

Draws text string

    void cvPutText( CvArr* img, const char* text, CvPoint org, const CvFont* font, CvScalar color );

img
  Input image.
text
  String to print.
org
  Coordinates of the bottom-left corner of the first letter.
font
  Pointer to the font structure.
color
  Text color.

The function `cvPutText` renders the text in the image with the specified font and color. The printed text is clipped by ROI rectangle. Symbols that do not belong to the specified font are replaced with the rectangle symbol.

### GetTextSize

Retrieves width and height of text string

    void cvGetTextSize( const char* text_string, const CvFont* font, CvSize* text_size, int* baseline );

font
  Pointer to the font structure.
text_string
  Input string.
text_size
  Resultant size of the text string. Height of the text does not include the height of character parts that are below the baseline.
baseline
  y-coordinate of the baseline relatively to the bottom-most text point.

The function `cvGetTextSize` calculates the binding rectangle for the given text string when a specified font is used.

## Point Sets and Contours

### DrawContours

Draws contour outlines or interiors in the image

    void cvDrawContours( CvArr *img, CvSeq* contour,
                         CvScalar external_color, CvScalar hole_color,
                         int max_level, int thickness=1,
                         int line_type=8, CvPoint offset=cvPoint(0,0) );

img
  Image where the contours are to be drawn. Like in any other drawing function, the contours are clipped with the ROI.
contour
  Pointer to the first contour.
external_color
  Color of the external contours.
hole_color
  Color of internal contours (holes).
max_level
  Maximal level for drawn contours. If 0, only `contour` is drawn. If 1, the contour and all contours after it on the same level are drawn. If 2, all contours after and all contours one level below the contours are drawn, etc. If the value is negative, the function does not draw the contours following after `contour` but draws child contours of `contour` up to abs(`max_level`)-1 level.
thickness
  Thickness of lines the contours are drawn with. If it is negative (e.g. =CV_FILLED), the contour interiors are drawn.
line_type
  Type of the contour segments, see cvLine description.
offset
  Shift all the point coordinates by the specified value. It is useful in case if the contours retrived in some image ROI and then the ROI offset needs to be taken into account during the rendering.

The function `cvDrawContours` draws contour outlines in the image if `thickness`>=0 or fills area bounded by the contours if `thickness`<0.

#### Example. Connected component detection via contour functions

    #include "cv.h"
    #include "highgui.h"

    int main( int argc, char** argv )
    {
        IplImage* src;
        // the first command line parameter must be file name of binary (black-n-white) image
        if( argc == 2 && (src=cvLoadImage(argv[1], 0))!= 0)
        {
            IplImage* dst = cvCreateImage( cvGetSize(src), 8, 3 );
            CvMemStorage* storage = cvCreateMemStorage(0);
            CvSeq* contour = 0;

            cvThreshold( src, src, 1, 255, CV_THRESH_BINARY );
            cvNamedWindow( "Source", 1 );
            cvShowImage( "Source", src );

            cvFindContours( src, storage, &contour, sizeof(CvContour), CV_RETR_CCOMP, CV_CHAIN_APPROX_SIMPLE );
            cvZero( dst );

            for( ; contour != 0; contour = contour->h_next )
            {
                CvScalar color = CV_RGB( rand()&255, rand()&255, rand()&255 );
                /* replace CV_FILLED with 1 to see the outlines */
                cvDrawContours( dst, contour, color, color, -1, CV_FILLED, 8 );
            }

            cvNamedWindow( "Components", 1 );
            cvShowImage( "Components", dst );
            cvWaitKey(0);
        }
    }

Replace CV_FILLED with 1 in the sample below to see the contour outlines

### InitLineIterator

Initializes line iterator

    int cvInitLineIterator( const CvArr* image, CvPoint pt1, CvPoint pt2,
                            CvLineIterator* line_iterator, int connectivity=8,
                            int left_to_right=0 );

image
  Image to sample the line from.
pt1
  First ending point of the line segment.
pt2
  Second ending point of the line segment.
line_iterator
  Pointer to the line iterator state structure.
connectivity
  The scanned line connectivity, 4 or 8.
left_to_right
  The flag, indicating whether the line should be always scanned from the left-most point to the right-most out of `pt1` and `pt2` (`left_to_right≠0`), or it is scanned in the specified order, from `pt1` to `pt2` (`left_to_right=0`).

The function `cvInitLineIterator` initializes the line iterator and returns the number of pixels between two end points. Both points must be inside the image. After the iterator has been initialized, all the points on the raster line that connects the two ending points may be retrieved by successive calls of `CV_NEXT_LINE_POINT` point. The points on the line are calculated one by one using 4-connected or 8-connected Bresenham algorithm.

#### Example. Using line iterator to calculate sum of pixel values along the color line

        CvScalar sum_line_pixels( IplImage* image, CvPoint pt1, CvPoint pt2 )
        {
            CvLineIterator iterator;
            int blue_sum = 0, green_sum = 0, red_sum = 0;
            int count = cvInitLineIterator( image, pt1, pt2, &iterator, 8, 0 );

            for( int i = 0; i < count; i++ ){
                blue_sum += iterator.ptr[0];
                green_sum += iterator.ptr[1];
                red_sum += iterator.ptr[2];
                CV_NEXT_LINE_POINT(iterator);

                /* print the pixel coordinates: demonstrates how to calculate the coordinates */
                {
                int offset, x, y;
                /* assume that ROI is not set, otherwise need to take it into account. */
                offset = iterator.ptr - (uchar*)(image->imageData);
                y = offset/image->widthStep;
                x = (offset - y*image->widthStep)/(3*sizeof(uchar) /* size of pixel */);
                printf("(%d,%d)\n", x, y );
                }
            }
            return cvScalar( blue_sum, green_sum, red_sum );
        }

### ClipLine

Clips the line against the image rectangle

    int cvClipLine( CvSize img_size, CvPoint* pt1, CvPoint* pt2 );

img_size
  Size of the image.
pt1
  First ending point of the line segment. It is modified by the function.
pt2
  Second ending point of the line segment. It is modified by the function.

The function `cvClipLine` calculates a part of the line segment which is entirely in the image. It returns 0 if the line segment is completely outside the image and 1 otherwise.

### Ellipse2Poly

Approximates elliptic arc with polyline

    int cvEllipse2Poly( CvPoint center, CvSize axes,
                        int angle, int arc_start,
                        int arc_end, CvPoint* pts, int delta );

center
  Center of the arc.
axes
  Half-sizes of the arc. See cvEllipse.
angle
  Rotation angle of the ellipse in degrees. See cvEllipse.
start_angle
  Starting angle of the elliptic arc.
end_angle
  Ending angle of the elliptic arc.
pts
  The array of points, filled by the function.
delta
  Angle between the subsequent polyline vertices, approximation accuracy. So, the total number of output points will ceil((end_angle - start_angle)/delta) + 1 at max.

The function `cvEllipse2Poly` computes vertices of the polyline that approximates the specified elliptic arc. It is used by cvEllipse.

### ClipLine

CVAPI(int) cvEllipse2Poly( CvPoint center, CvSize axes, int angle, int arc_start, int arc_end, CvPoint * pts, int delta );

# Data Persistence and RTTI

## File Storage

### CvFileStorage

File Storage

        typedef struct CvFileStorage
        {
            ...       // hidden fields
        } CvFileStorage;

The structure CvFileStorage is "black box" representation of file storage that is associated with a file on disk. Several functions that are described below take `CvFileStorage` on input and allow user to save or to load hierarchical collections that consist of scalar values, standard CXCore objects (such as matrices, sequences, graphs) and user-defined objects.

CXCore can read and write data in XML (http://www.w3c.org/XML) or YAML (http://www.yaml.org) formats. Below is the example of 3×3 floating-point identity matrix `A`, stored in XML and YAML files using CXCore functions:

XML:

      <?xml version="1.0">
      <opencv_storage>
      <A type_id="opencv-matrix">
        <rows>3</rows>
        <cols>3</cols>
        <dt>f</dt>
        <data>1. 0. 0. 0. 1. 0. 0. 0. 1.</data>
      </A>
      </opencv_storage>

YAML:

      %YAML:1.0
      A: !!opencv-matrix
        rows: 3
        cols: 3
        dt: f
        data: [ 1., 0., 0., 0., 1., 0., 0., 0., 1.]

As it can be seen from the examples, XML uses nested tags to represent hierarchy, while YAML uses indentation for that purpose (similarly to Python programming language).

The same CXCore functions can read and write data in both formats, the particular format is determined by the extension of the opened file, .xml for XML files and .yml or .yaml for YAML.

### CvFileNode

File Storage Node

    /* file node type */
    #define CV_NODE_NONE        0
    #define CV_NODE_INT         1
    #define CV_NODE_INTEGER     CV_NODE_INT
    #define CV_NODE_REAL        2
    #define CV_NODE_FLOAT       CV_NODE_REAL
    #define CV_NODE_STR         3
    #define CV_NODE_STRING      CV_NODE_STR
    #define CV_NODE_REF         4 /* not used */
    #define CV_NODE_SEQ         5
    #define CV_NODE_MAP         6
    #define CV_NODE_TYPE_MASK   7

    /* optional flags */
    #define CV_NODE_USER        16
    #define CV_NODE_EMPTY       32
    #define CV_NODE_NAMED       64

    #define CV_NODE_TYPE(tag)  ((tag) & CV_NODE_TYPE_MASK)

    #define CV_NODE_IS_INT(tag)        (CV_NODE_TYPE(tag) == CV_NODE_INT)
    #define CV_NODE_IS_REAL(tag)       (CV_NODE_TYPE(tag) == CV_NODE_REAL)
    #define CV_NODE_IS_STRING(tag)     (CV_NODE_TYPE(tag) == CV_NODE_STRING)
    #define CV_NODE_IS_SEQ(tag)        (CV_NODE_TYPE(tag) == CV_NODE_SEQ)
    #define CV_NODE_IS_MAP(tag)        (CV_NODE_TYPE(tag) == CV_NODE_MAP)
    #define CV_NODE_IS_COLLECTION(tag) (CV_NODE_TYPE(tag) >= CV_NODE_SEQ)
    #define CV_NODE_IS_FLOW(tag)       (((tag) & CV_NODE_FLOW) != 0)
    #define CV_NODE_IS_EMPTY(tag)      (((tag) & CV_NODE_EMPTY) != 0)
    #define CV_NODE_IS_USER(tag)       (((tag) & CV_NODE_USER) != 0)
    #define CV_NODE_HAS_NAME(tag)      (((tag) & CV_NODE_NAMED) != 0)

    #define CV_NODE_SEQ_SIMPLE 256
    #define CV_NODE_SEQ_IS_SIMPLE(seq) (((seq)->flags & CV_NODE_SEQ_SIMPLE) != 0)

    typedef struct CvString
    {
        int len;
        char* ptr;
    }
    CvString;

    /* all the keys (names) of elements in the readed file storage
       are stored in the hash to speed up the lookup operations */
    typedef struct CvStringHashNode
    {
        unsigned hashval;
        CvString str;
        struct CvStringHashNode* next;
    }
    CvStringHashNode;

    /* basic element of the file storage - scalar or collection */
    typedef struct CvFileNode
    {
        int tag;
        struct CvTypeInfo* info; /* type information
                (only for user-defined object, for others it is 0) */
        union
        {
            double f; /* scalar floating-point number */
            int i;    /* scalar integer number */
            CvString str; /* text string */
            CvSeq* seq; /* sequence (ordered collection of file nodes) */
            struct CvMap* map; /* map (collection of named file nodes) */
        } data;
    }
    CvFileNode;

The structure is used only for retrieving data from file storage (i.e. for loading data from file). When data is written to file, it is done sequentially, with minimal buffering. No data is stored in the file storage.

In opposite, when data is read from file, the whole file is parsed and represented in memory as a tree. Every node of the tree is represented by CvFileNode. Type of the file node `N` can be retrieved as `CV_NODE_TYPE(N->tag)`. Some file nodes (leaves) are scalars: text strings, integer or floating-point numbers. Other file nodes are collections of file nodes, which can be scalars or collections in their turn. There are two types of collections: sequences and maps (we use YAML notation, however, the same is true for XML streams). Sequences (do not mix them with CvSeq) are ordered collections of unnamed file nodes, maps are unordered collections of named file nodes. Thus, elements of sequences are accessed by index (cvGetSeqElem), while elements of maps are accessed by name (cvGetFileNodeByName). The table below describes the different types of a file node:

Type | CV_NODE_TYPE(node->tag) | Value
Integer | CV_NODE_INT | node->data.i
Floating-point | CV_NODE_REAL | node->data.f
Text string | CV_NODE_STR | node->data.str.ptr
Sequence | CV_NODE_SEQ | node->data.seq
Map | CV_NODE_MAP | node->data.map*

*
  There is no need to access `map` field directly (BTW, `CvMap` is a hidden structure). The elements of the map can be retrieved with cvGetFileNodeByName function that takes pointer to the "map" file node.

A user (custom) object is instance of either one of standard CxCore types, such as CvMat, CvSeq etc., or any type registered with cvRegisterTypeInfo. Such an object is initially represented in file as a map (as shown in XML and YAML sample files above), after file storage has been opened and parsed. Then the object can be decoded (coverted to the native representation) by request - when user calls cvRead or cvReadByName function.

### CvAttrList

List of attributes

    typedef struct CvAttrList
    {
        const char** attr; /* NULL-terminated array of (attribute_name,attribute_value) pairs */
        struct CvAttrList* next; /* pointer to next chunk of the attributes list */
    }
    CvAttrList;

    /* initializes CvAttrList structure */
    inline CvAttrList cvAttrList( const char** attr=NULL, CvAttrList* next=NULL );

    /* returns attribute value or 0 (NULL) if there is no such attribute */
    const char* cvAttrValue( const CvAttrList* attr, const char* attr_name );

In the current implementation attributes are used to pass extra parameters when writing user objects (see cvWrite). XML attributes inside tags are not supported, besides the object type specification (`type_id` attribute).

### OpenFileStorage

Opens file storage for reading or writing data

    CvFileStorage* cvOpenFileStorage( const char* filename, CvMemStorage* memstorage, int flags );

filename
  Name of the file associated with the storage.
memstorage
  Memory storage used for temporary data and for storing dynamic structures, such as CvSeq or CvGraph. If it is NULL, a temporary memory storage is created and used.
flags
  Can be one of the following:
  `CV_STORAGE_READ` - the storage is open for reading
  `CV_STORAGE_WRITE` - the storage is open for writing

The function `cvOpenFileStorage` opens file storage for reading or writing data. In the latter case a new file is created or existing file is rewritten. Type of the read of written file is determined by the filename extension: `.xml` for XML, and `.yml` or `.yaml` for YAML. The function returns pointer to CvFileStorage structure.

### ReleaseFileStorage

Releases file storage

    void  cvReleaseFileStorage( CvFileStorage** fs );

fs
  Double pointer to the released file storage.

The function `cvReleaseFileStorage` closes the file associated with the storage and releases all the temporary structures. It must be called after all I/O operations with the storage are finished.

## Writing Data

### StartWriteStruct

Starts writing a new structure

    void  cvStartWriteStruct( CvFileStorage* fs, const char* name,
                              int struct_flags, const char* type_name=NULL,
                              CvAttrList attributes=cvAttrList());

fs
  File storage.
name
  Name of the written structure. The structure can be accessed by this name when the storage is read.
struct_flags
  A combination one of the following values:
  `CV_NODE_SEQ` - the written structure is a sequence (see discussion of CvFileStorage), that is, its elements do not have a name.
  `CV_NODE_MAP` - the written structure is a map (see discussion of CvFileStorage), that is, all its elements have names.
  One and only one of the two above flags must be specified
  `CV_NODE_FLOW` - the optional flag that has sense only for YAML streams. It means that the structure is written as a flow (not as a block), which is more compact. It is recommended to use this flag for structures or arrays whose elements are all scalars.
type_name
  Optional parameter - the object type name. In case of XML it is written as `type_id` attribute of the structure opening tag. In case of YAML it is written after a colon following the structure name (see the example in CvFileStorage description). Mainly it comes with user objects. When the storage is read, the encoded type name is used to determine the object type (see CvTypeInfo and cvFindTypeInfo).
attributes
  This parameter is not used in the current implementation.

The function `cvStartWriteStruct` starts writing a compound structure (collection) that can be a sequence or a map. After all the structure fields, which can be scalars or structures, are written, cvEndWriteStruct should be called. The function can be used to group some objects or to implement write function for a some user object (see CvTypeInfo).

### EndWriteStruct

Ends writing a structure

    void  cvEndWriteStruct( CvFileStorage* fs );

fs
  File storage.

The function `cvEndWriteStruct` finishes the currently written structure.

### WriteInt

Writes an integer value

    void  cvWriteInt( CvFileStorage* fs, const char* name, int value );

fs
  File storage.
name
  Name of the written value. Should be NULL if and only if the parent structure is a sequence.
value
  The written value.

The function `cvWriteInt` writes a single integer value (with or without a name) to the file storage.

### WriteReal

Writes a floating-point value

    void  cvWriteReal( CvFileStorage* fs, const char* name, double value );

fs
  File storage.
name
  Name of the written value. Should be NULL if and only if the parent structure is a sequence.
value
  The written value.

The function `cvWriteReal` writes a single floating-point value (with or without a name) to the file storage. The special values are encoded: NaN (Not A Number) as .NaN, ±Infinity as +.Inf (-.Inf).

The following example shows how to use the low-level writing functions to store custom structures, such as termination criteria, without registering a new type.

    void write_termcriteria( CvFileStorage* fs, const char* struct_name,
                             CvTermCriteria* termcrit )
    {
        cvStartWriteStruct( fs, struct_name, CV_NODE_MAP, NULL, cvAttrList(0,0));
        cvWriteComment( fs, "termination criteria", 1 ); // just a description
        if( termcrit->type & CV_TERMCRIT_ITER )
            cvWriteInteger( fs, "max_iterations", termcrit->max_iter );
        if( termcrit->type & CV_TERMCRIT_EPS )
            cvWriteReal( fs, "accuracy", termcrit->epsilon );
        cvEndWriteStruct( fs );
    }

### WriteString

Writes a text string

    void  cvWriteString( CvFileStorage* fs, const char* name,
                         const char* str, int quote=0 );

fs
  File storage.
name
  Name of the written string. Should be NULL if and only if the parent structure is a sequence.
str
  The written text string.
quote
  If non-zero, the written string is put in quotes, regardless of whether they are required or not. Otherwise, if the flag is zero, quotes are used only when they are required (e.g. when the string starts with a digit or contains spaces).

The function `cvWriteString` writes a text string to the file storage.

### WriteComment

Writes comment

    void  cvWriteComment( CvFileStorage* fs, const char* comment, int eol_comment );

fs
  File storage.
comment
  The written comment, single-line or multi-line.
eol_comment
  If non-zero, the function tries to put the comment in the end of current line. If the flag is zero, if the comment is multi-line, or if it does not fit in the end of the current line, the comment starts from a new line.

The function `cvWriteComment` writes a comment into the file storage. The comments are skipped when the storage is read, so they may be used only for debugging or descriptive purposes.

### StartNextStream

Starts the next stream

    void  cvStartNextStream( CvFileStorage* fs );

fs
  File storage.

The function `cvStartNextStream` starts the next stream in the file storage. Both YAML and XML supports multiple "streams". This is useful for concatenating files or for resuming the writing process.

### Write

Writes user object

    void  cvWrite( CvFileStorage* fs, const char* name,
                   const void* ptr, CvAttrList attributes=cvAttrList() );

fs
  File storage.
name
  Name, of the written object. Should be NULL if and only if the parent structure is a sequence.
ptr
  Pointer to the object.
attributes
  The attributes of the object. They are specific for each particular type (see the dicsussion).

The function `cvWrite` writes the object to file storage. First, the appropriate type info is found using cvTypeOf. Then, `write` method of the type info is called.

Attributes are used to customize the writing procedure. The standard types support the following attributes (all the `*dt` attributes have the same format as in cvWriteRawData):

CvSeq
  - `header_dt` - description of user fields of the sequence header that follow CvSeq, or CvChain (if the sequence is Freeman chain) or CvContour (if the sequence is a contour or point sequence)
  - `dt` - description of the sequence elements.
  - `recursive` - if the attribute is present and is not equal to "0" or "false", the whole tree of sequences (contours) is stored.
`CvGraph`
  - `header_dt` - description of user fields of the graph header that follow CvGraph;
  - `vertex_dt` - description of user fields of graph vertices
  - `edge_dt` - description of user fields of graph edges (note, that edge weight is always written, so there is no need to specify it explicitly)

Below is the code that creates the YAML file shown in `CvFileStorage` description:

    #include "cxcore.h"

    int main( int argc, char** argv )
    {
        CvMat* mat = cvCreateMat( 3, 3, CV_32F );
        CvFileStorage* fs = cvOpenFileStorage( "example.yml", 0, CV_STORAGE_WRITE );

        cvSetIdentity( mat );
        cvWrite( fs, "A", mat, cvAttrList(0,0) );

        cvReleaseFileStorage( &fs );
        cvReleaseMat( &mat );
        return 0;
    }

### WriteRawData

Writes multiple numbers

    void  cvWriteRawData( CvFileStorage* fs, const void* src,
                          int len, const char* dt );

fs
  File storage.
src
  Pointer to the written array
len
  Number of the array elements to write.
dt
  Specification of each array element that has the following format: `([count]{'u'|'c'|'w'|'s'|'i'|'f'|'d'})...`, where the characters correspond to fundamental C types:
  - 'u' - 8-bit unsigned number
  - 'c' - 8-bit signed number
  - 'w' - 16-bit unsigned number
  - 's' - 16-bit signed number
  - 'i' - 32-bit signed number
  - 'f' - single precision floating-point number
  - 'd' - double precision floating-point number
  - 'r' - pointer. 32 lower bits of it are written as a signed integer. The type can be used to store structures with links between the elements.
  `count` is the optional counter of values of the certain type. For example, `dt='2if'` means that each array element is a structure of 2 integers, followed by a single-precision floating-point number. The equivalent notations of the above specification are `'iif'`, `'2i1f'` etc. Other examples: `dt='u'` means that the array consists of bytes, `dt='2d'` - the array consists of pairs of double’s.

The function `cvWriteRawData` writes array, which elements consist of a single of multiple numbers. The function call can be replaced with a loop containing a few cvWriteInt and cvWriteReal calls, but a single call is more efficient. Note, that because none of the elements have a name, they should be written to a sequence rather than a map.

### WriteFileNode

Writes file node to another file storage

    void cvWriteFileNode( CvFileStorage* fs, const char* new_node_name,
                          const CvFileNode* node, int embed );

fs
  Destination file storage.
new_file_node
  New name of the file node in the destination file storage. To keep the existing name, use `cvGetFileNodeName(node)`.
node
  The written node
embed
  If the written node is a collection and this parameter is not zero, no extra level of hiararchy is created. Instead, all the elements of `node` are written into the currently written structure. Of course, map elements may be written only to map, and sequence elements may be written only to sequence.

The function `cvWriteFileNode` writes a copy of file node to file storage. The possible application of the function are: merging several file storages into one. Conversion between XML and YAML formats etc.

## Reading Data

Data are retrieved from file storage in 2 steps: first, the file node containing the requested data is found; then, data is extracted from the node manually or using custom `read` method.

### GetRootFileNode

Retrieves one of top-level nodes of the file storage

    CvFileNode* cvGetRootFileNode( const CvFileStorage* fs, int stream_index=0 );

fs
  File storage.
stream_index
  Zero-based index of the stream. See cvStartNextStream. In most cases, there is only one stream in the file, however there can be several.

The function `cvGetRootFileNode` returns one of top-level file nodes. The top-level nodes do not have a name, they correspond to the streams, that are stored one after another in the file storage. If the index is out of range, the function returns NULL pointer, so all the top-level nodes may be iterated by subsequent calls to the function with `stream_index=0,1,...`, until NULL pointer is returned. This function may be used as a base for recursive traversal of the file storage.

### GetFileNodeByName

Finds node in the map or file storage

    CvFileNode* cvGetFileNodeByName( const CvFileStorage* fs,
                                     const CvFileNode* map,
                                     const char* name );

fs
  File storage.
map
  The parent map. If it is NULL, the function searches in all the top-level nodes (streams), starting from the first one.
name
  The file node name.

The function `cvGetFileNodeByName` finds a file node by `name`. The node is searched either in `map` or, if the pointer is NULL, among the top-level file nodes of the storage. Using this function for maps and cvGetSeqElem (or sequence reader) for sequences, it is possible to nagivate through the file storage. To speed up multiple queries for a certain key (e.g. in case of array of structures) one may use a pair of cvGetHashedKey and cvGetFileNode.

### GetHashedKey

Returns a unique pointer for given name

    CvStringHashNode* cvGetHashedKey( CvFileStorage* fs, const char* name,
                                      int len=-1, int create_missing=0 );

fs
  File storage.
name
  Literal node name.
len
  Length of the name (if it is known apriori), or -1 if it needs to be calculated.
create_missing
  Flag that specifies, whether an absent key should be added into the hash table, or not.

The function `cvGetHashedKey` returns the unique pointer for each particular file node name. This pointer can be then passed to cvGetFileNode function that is faster than cvGetFileNodeByName because it compares text strings by comparing pointers rather than the strings' content.

Consider the following example: an array of points is encoded as a sequence of 2-entry maps, e.g.:

    %YAML:1.0
    points:
      - { x: 10, y: 10 }
      - { x: 20, y: 20 }
      - { x: 30, y: 30 }
      # ...

Then, it is possible to get hashed "x" and "y" pointers to speed up decoding of the points.

#### Example. Reading an array of structures from file storage

    #include "cxcore.h"

    int main( int argc, char** argv )
    {
        CvFileStorage* fs = cvOpenFileStorage( "points.yml", 0, CV_STORAGE_READ );
        CvStringHashNode* x_key = cvGetHashedNode( fs, "x", -1, 1 );
        CvStringHashNode* y_key = cvGetHashedNode( fs, "y", -1, 1 );
        CvFileNode* points = cvGetFileNodeByName( fs, 0, "points" );

        if( CV_NODE_IS_SEQ(points->tag) )
        {
            CvSeq* seq = points->data.seq;
            int i, total = seq->total;
            CvSeqReader reader;
            cvStartReadSeq( seq, &reader, 0 );
            for( i = 0; i < total; i++ )
            {
                CvFileNode* pt = (CvFileNode*)reader.ptr;
    #if 1 /* faster variant */
                CvFileNode* xnode = cvGetFileNode( fs, pt, x_key, 0 );
                CvFileNode* ynode = cvGetFileNode( fs, pt, y_key, 0 );
                assert( xnode && CV_NODE_IS_INT(xnode->tag) &&
                        ynode && CV_NODE_IS_INT(ynode->tag));
                int x = xnode->data.i; // or x = cvReadInt( xnode, 0 );
                int y = ynode->data.i; // or y = cvReadInt( ynode, 0 );
    #elif 1 /* slower variant; does not use x_key & y_key */
                CvFileNode* xnode = cvGetFileNodeByName( fs, pt, "x" );
                CvFileNode* ynode = cvGetFileNodeByName( fs, pt, "y" );
                assert( xnode && CV_NODE_IS_INT(xnode->tag) &&
                        ynode && CV_NODE_IS_INT(ynode->tag));
                int x = xnode->data.i; // or x = cvReadInt( xnode, 0 );
                int y = ynode->data.i; // or y = cvReadInt( ynode, 0 );
    #else /* the slowest yet the easiest to use variant */
                int x = cvReadIntByName( fs, pt, "x", 0 /* default value */ );
                int y = cvReadIntByName( fs, pt, "y", 0 /* default value */ );
    #endif
                CV_NEXT_SEQ_ELEM( seq->elem_size, reader );
                printf("%d: (%d, %d)\n", i, x, y );
            }
        }
        cvReleaseFileStorage( &fs );
        return 0;
    }

Please note that, whatever method of accessing map you are using, it is still much slower than using plain sequences, for example, in the above sample, it is more efficient to encode the points as pairs of integers in the single numeric sequence.

### GetFileNode

Finds node in the map or file storage

    CvFileNode* cvGetFileNode( CvFileStorage* fs, CvFileNode* map,
                               const CvStringHashNode* key, int create_missing=0 );

fs
  File storage.
map
  The parent map. If it is NULL, the function searches a top-level node. If both `map` and `key` are NULLs, the function returns the root file node - a map that contains top-level nodes.
key
  Unique pointer to the node name, retrieved with cvGetHashedKey.
create_missing
  Flag that specifies, whether an absent node should be added to the map, or not.

The function `cvGetFileNode` finds a file node. It is a faster version cvGetFileNodeByName (see cvGetHashedKey discussion). Also, the function can insert a new node, if it is not in the map yet (which is used by parsing functions).

### GetFileNodeName

Returns name of file node

    const char* cvGetFileNodeName( const CvFileNode* node );

node
  File node

The function `cvGetFileNodeName` returns name of the file node or NULL, if the file node does not have a name, or if `node` is `NULL`.

### ReadInt

Retrieves integer value from file node

    int cvReadInt( const CvFileNode* node, int default_value=0 );

node
  File node.
default_value
  The value that is returned if `node` is NULL.

The function `cvReadInt` returns integer that is represented by the file node. If the file node is NULL, `default_value` is returned (thus, it is convenient to call the function right after cvGetFileNode without checking for NULL pointer), otherwise if the file node has type `CV_NODE_INT`, then `node->data.i` is returned, otherwise if the file node has type `CV_NODE_REAL`, then `node->data.f` is converted to integer and returned, otherwise the result is not determined.

### ReadIntByName

Finds file node and returns its value

    int cvReadIntByName( const CvFileStorage* fs, const CvFileNode* map,
                         const char* name, int default_value=0 );

fs
  File storage.
map
  The parent map. If it is NULL, the function searches a top-level node.
name
  The node name.
default_value
  The value that is returned if the file node is not found.

The function `cvReadIntByName` is a simple superposition of cvGetFileNodeByName and cvReadInt.

### ReadReal

Retrieves floating-point value from file node

    double cvReadReal( const CvFileNode* node, double default_value=0. );

node
  File node.
default_value
  The value that is returned if `node` is NULL.

The function `cvReadReal` returns floating-point value that is represented by the file node. If the file node is NULL, `default_value` is returned (thus, it is convenient to call the function right after cvGetFileNode without checking for NULL pointer), otherwise if the file node has type `CV_NODE_REAL`, then `node->data.f` is returned, otherwise if the file node has type `CV_NODE_INT`, then `node->data.f` is converted to floating-point and returned, otherwise the result is not determined.

### ReadRealByName

Finds file node and returns its value

    double  cvReadRealByName( const CvFileStorage* fs, const CvFileNode* map,
                              const char* name, double default_value=0. );

fs
  File storage.
map
  The parent map. If it is NULL, the function searches a top-level node.
name
  The node name.
default_value
  The value that is returned if the file node is not found.

The function `cvReadRealByName` is a simple superposition of cvGetFileNodeByName and cvReadReal.

### ReadString

Retrieves text string from file node

    const char* cvReadString( const CvFileNode* node, const char* default_value=NULL );

node
  File node.
default_value
  The value that is returned if `node` is NULL.

The function `cvReadString` returns text string that is represented by the file node. If the file node is NULL, `default_value` is returned (thus, it is convenient to call the function right after cvGetFileNode without checking for NULL pointer), otherwise if the file node has type `CV_NODE_STR`, then `node->data.str.ptr` is returned, otherwise the result is not determined.

### ReadStringByName

Finds file node and returns its value

    const char* cvReadStringByName( const CvFileStorage* fs, const CvFileNode* map,
                                    const char* name, const char* default_value=NULL );

fs
  File storage.
map
  The parent map. If it is NULL, the function searches a top-level node.
name
  The node name.
default_value
  The value that is returned if the file node is not found.

The function `cvReadStringByName` is a simple superposition of cvGetFileNodeByName and cvReadString.

### Read

Decodes object and returns pointer to it

    void* cvRead( CvFileStorage* fs, CvFileNode* node,
                  CvAttrList* attributes=NULL );

fs
  File storage.
node
  The root object node.
attributes
  Unused parameter.

The function `cvRead` decodes user object (creates object in a native representation from the file storage subtree) and returns it. The object to be decoded must be an instance of registered type that supports `read` method (see CvTypeInfo). Type of the object is determined by the type name that is encoded in the file. If the object is dynamic structure, it is created either in memory storage, passed to cvOpenFileStorage or, if NULL pointer was passed, in temporary memory storage, which is release when cvReleaseFileStorage is called. Otherwise, if the object is not a dynamic structure, it is created in heap and should be released with a specialized function or using generic cvRelease.

### ReadByName

Finds object and decodes it

    void* cvReadByName( CvFileStorage* fs, const CvFileNode* map,
                        const char* name, CvAttrList* attributes=NULL );

fs
  File storage.
map
  The parent map. If it is NULL, the function searches a top-level node.
name
  The node name.
attributes
  Unused parameter.

The function `cvReadByName` is a simple superposition of cvGetFileNodeByName and cvRead.

### ReadRawData

Reads multiple numbers

    void cvReadRawData( const CvFileStorage* fs, const CvFileNode* src,
                        void* dst, const char* dt );

fs
  File storage.
src
  The file node (a sequence) to read numbers from.
dst
  Pointer to the destination array.
dt
  Specification of each array element. It has the same format as in cvWriteRawData.

The function `cvReadRawData` reads elements from a file node that represents a sequence of scalars

### StartReadRawData

Initializes file node sequence reader

    void cvStartReadRawData( const CvFileStorage* fs, const CvFileNode* src,
                             CvSeqReader* reader );

fs
  File storage.
src
  The file node (a sequence) to read numbers from.
reader
  Pointer to the sequence reader.

The function `cvStartReadRawData` initializes sequence reader to read data from file node. The initialized reader can be then passed to cvReadRawDataSlice.

### ReadRawDataSlice

Initializes file node sequence reader

    void cvReadRawDataSlice( const CvFileStorage* fs, CvSeqReader* reader,
                             int count, void* dst, const char* dt );

fs
  File storage.
reader
  The sequence reader. Initialize it with cvStartReadRawData.
count
  The number of elements to read.
dst
  Pointer to the destination array.
dt
  Specification of each array element. It has the same format as in cvWriteRawData.

The function `cvReadRawDataSlice` reads one or more elements from the file node, representing a sequence, to user-specified array. The total number of read sequence elements is a product of `total` and the number of components in each array element. For example, if `dt='2if'`, the function will read `total*3` sequence elements. As with any sequence, some parts of the file node sequence may be skipped or read repeatedly by repositioning the reader using cvSetSeqReaderPos.

## RTTI and Generic Functions

### CvTypeInfo

Type information

    typedef int (CV_CDECL *CvIsInstanceFunc)( const void* struct_ptr );
    typedef void (CV_CDECL *CvReleaseFunc)( void** struct_dblptr );
    typedef void* (CV_CDECL *CvReadFunc)( CvFileStorage* storage, CvFileNode* node );
    typedef void (CV_CDECL *CvWriteFunc)( CvFileStorage* storage,
                                          const char* name,
                                          const void* struct_ptr,
                                          CvAttrList attributes );
    typedef void* (CV_CDECL *CvCloneFunc)( const void* struct_ptr );

    typedef struct CvTypeInfo
    {
        int flags; /* not used */
        int header_size; /* sizeof(CvTypeInfo) */
        struct CvTypeInfo* prev; /* previous registered type in the list */
        struct CvTypeInfo* next; /* next registered type in the list */
        const char* type_name; /* type name, written to file storage */

        /* methods */
        CvIsInstanceFunc is_instance; /* checks if the passed object belongs to the type */
        CvReleaseFunc release; /* releases object (memory etc.) */
        CvReadFunc read; /* reads object from file storage */
        CvWriteFunc write; /* writes object to file storage */
        CvCloneFunc clone; /* creates a copy of the object */
    }
    CvTypeInfo;

The structure CvTypeInfo contains information about one of standard or user-defined types. Instances of the type may or may not contain pointer to the corresponding CvTypeInfo structure. In any case there is a way to find type info structure for given object - using cvTypeOf function. Aternatively, type info can be found by the type name using cvFindType, which is used when object is read from file storage. User can register a new type with cvRegisterType that adds the type information structure into the beginning of the type list - thus, it is possible to create specialized types from generic standard types and override the basic methods.

### RegisterType

Registers new type

    void cvRegisterType( const CvTypeInfo* info );

info
  Type info structure.

The function `cvRegisterType` registers a new type, which is described by `info`. The function creates a copy of the structure, so user should delete it after calling the function.

### UnregisterType

Unregisters the type

    void cvUnregisterType( const char* type_name );

type_name
  Name of the unregistered type.

The function `cvUnregisterType` unregisters the type with the specified name. If the name is unknown, it is possible to locate the type info by an instance of the type using cvTypeOf or by iterating the type list, starting from cvFirstType, and then call `cvUnregisterType(info->type_name)`.

### FirstType

Returns the beginning of type list

    CvTypeInfo* cvFirstType( void );

The function `cvFirstType` returns the first type of the list of registered types. Navigation through the list can be done via `prev` and `next` fields of CvTypeInfo structure.

### FindType

Finds type by its name

    CvTypeInfo* cvFindType( const char* type_name );

type_name
  Type name.

The function `cvFindType` finds a registered type by its name. It returns NULL, if there is no type with the specified name.

### TypeOf

Returns type of the object

    CvTypeInfo* cvTypeOf( const void* struct_ptr );

struct_ptr
  The object pointer.

The function `cvTypeOf` finds the type of given object. It iterates through the list of registered types and calls `is_instance` function/method of every type info structure with the object until one of them return non-zero or until the whole list has been traversed. In the latter case the function returns NULL.

### Release

Releases the object

    void cvRelease( void** struct_ptr );

struct_ptr
  Double pointer to the object.

The function `cvRelease` finds the type of given object and calls `release` with the double pointer.

### Clone

Makes a clone of the object

    void* cvClone( const void* struct_ptr );

struct_ptr
  The object to clone.

The function `cvClone` finds the type of given object and calls `clone` with the passed object.

### Save

Saves object to file

    void cvSave( const char* filename, const void* struct_ptr,
                 const char* name=NULL,
                 const char* comment=NULL,
                 CvAttrList attributes=cvAttrList());

filename
  File name.
struct_ptr
  Object to save.
name
  Optional object name. If it is NULL, the name will be formed from `filename`.
comment
  Optional comment to put in the beginning of the file.
attributes
  Optional attributes passed to cvWrite.

The function `cvSave` saves object to file. It provides a simple interface to cvWrite.

### Load

Loads object from file

    void* cvLoad( const char* filename, CvMemStorage* memstorage=NULL,
                  const char* name=NULL, const char** real_name=NULL );

filename
  File name.
memstorage
  Memory storage for dynamic structures, such as CvSeq or CvGraph. It is not used for matrices or images.
name
  Optional object name. If it is NULL, the first top-level object in the storage will be loaded.
real_name
  Optional output parameter that will contain name of the loaded object (useful if `name=NULL`).

The function `cvLoad` loads object from file. It provides a simple interface to cvRead. After object is loaded, the file storage is closed and all the temporary buffers are deleted. Thus, to load a dynamic structure, such as sequence, contour or graph, one should pass a valid destination memory storage to the function.

# Miscellaneous Functions

### CheckArr

Checks every element of input array for invalid values

    int  cvCheckArr( const CvArr* arr, int flags=0,
                     double min_val=0, double max_val=0);
    #define cvCheckArray cvCheckArr

arr
  The array to check.
flags
  The operation flags, 0 or combination of:
  `CV_CHECK_RANGE` - if set, the function checks that every value of array is within [minVal,maxVal) range, otherwise it just checks that every element is neigther NaN nor ±Infinity.
  `CV_CHECK_QUIET` - if set, the function does not raises an error if an element is invalid or out of range
min_val
  The inclusive lower boundary of valid values range. It is used only if `CV_CHECK_RANGE` is set.
max_val
  The exclusive upper boundary of valid values range. It is used only if `CV_CHECK_RANGE` is set.

The function `cvCheckArr` checks that every array element is neither NaN nor ±Infinity. If `CV_CHECK_RANGE` is set, it also checks that every element is greater than or equal to `minVal` and less than `maxVal`. The function returns nonzero if the check succeeded, i.e. all elements are valid and within the range, and zero otherwise. In the latter case if `CV_CHECK_QUIET` flag is not set, the function raises runtime error.

### KMeans2

Splits set of vectors by given number of clusters

    void cvKMeans2( const CvArr* samples, int cluster_count,
                    CvArr* labels, CvTermCriteria termcrit );

samples
  Floating-point matrix of input samples, one row per sample.
cluster_count
  Number of clusters to split the set by.
labels
  Output integer vector storing cluster indices for every sample.
termcrit
  Specifies maximum number of iterations and/or accuracy (distance the centers move by between the subsequent iterations).

The function `cvKMeans2` implements k-means algorithm that finds centers of `cluster_count` clusters and groups the input samples around the clusters. On output `labels(i)` contains a cluster index for sample stored in the i-th row of `samples` matrix.

#### Example. Clustering random samples of multi-gaussian distribution with k-means

    #include "cxcore.h"
    #include "highgui.h"

    void main( int argc, char** argv )
    {
        #define MAX_CLUSTERS 5
        CvScalar color_tab[MAX_CLUSTERS];
        IplImage* img = cvCreateImage( cvSize( 500, 500 ), 8, 3 );
        CvRNG rng = cvRNG(0xffffffff);

        color_tab[0] = CV_RGB(255,0,0);
        color_tab[1] = CV_RGB(0,255,0);
        color_tab[2] = CV_RGB(100,100,255);
        color_tab[3] = CV_RGB(255,0,255);
        color_tab[4] = CV_RGB(255,255,0);

        cvNamedWindow( "clusters", 1 );

        for(;;)
        {
            int k, cluster_count = cvRandInt(&rng)%MAX_CLUSTERS + 1;
            int i, sample_count = cvRandInt(&rng)%1000 + 1;
            CvMat* points = cvCreateMat( sample_count, 1, CV_32FC2 );
            CvMat* clusters = cvCreateMat( sample_count, 1, CV_32SC1 );

            /* generate random sample from multigaussian distribution */
            for( k = 0; k < cluster_count; k++ )
            {
                CvPoint center;
                CvMat point_chunk;
                center.x = cvRandInt(&rng)%img->width;
                center.y = cvRandInt(&rng)%img->height;
                cvGetRows( points, &point_chunk, k*sample_count/cluster_count,
                           k == cluster_count - 1 ? sample_count : (k+1)*sample_count/cluster_count );
                cvRandArr( &rng, &point_chunk, CV_RAND_NORMAL,
                           cvScalar(center.x,center.y,0,0),
                           cvScalar(img->width/6, img->height/6,0,0) );
            }

            /* shuffle samples */
            for( i = 0; i < sample_count/2; i++ )
            {
                CvPoint2D32f* pt1 = (CvPoint2D32f*)points->data.fl + cvRandInt(&rng)%sample_count;
                CvPoint2D32f* pt2 = (CvPoint2D32f*)points->data.fl + cvRandInt(&rng)%sample_count;
                CvPoint2D32f temp;
                CV_SWAP( *pt1, *pt2, temp );
            }

            cvKMeans2( points, cluster_count, clusters,
                       cvTermCriteria( CV_TERMCRIT_EPS+CV_TERMCRIT_ITER, 10, 1.0 ));

            cvZero( img );

            for( i = 0; i < sample_count; i++ )
            {
                CvPoint2D32f pt = ((CvPoint2D32f*)points->data.fl)[i];
                int cluster_idx = clusters->data.i[i];
                cvCircle( img, cvPointFrom32f(pt), 2, color_tab[cluster_idx], CV_FILLED );
            }

            cvReleaseMat( &points );
            cvReleaseMat( &clusters );

            cvShowImage( "clusters", img );

            int key = cvWaitKey(0);
            if( key == 27 ) // 'ESC'
                break;
        }
    }

### SeqPartition

Splits sequence into equivalency classes

    typedef int (CV_CDECL* CvCmpFunc)(const void* a, const void* b, void* userdata);
    int cvSeqPartition( const CvSeq* seq, CvMemStorage* storage, CvSeq** labels,
                        CvCmpFunc is_equal, void* userdata );

seq
  The sequence to partition.
storage
  The storage to store the sequence of equivalency classes. If it is NULL, the function uses `seq->storage` for output labels.
labels
  Ouput parameter. Double pointer to the sequence of 0-based labels of input sequence elements.
is_equal
  The relation function that should return non-zero if the two particular sequence elements are from the same class, and zero overwise. The partitioning algorithm uses transitive closure of the relation function as equivalency critria.
userdata
  Pointer that is transparently passed to the `is_equal` function.

The function `cvSeqPartition` implements quadratic algorithm for splitting a set into one or more classes of equivalency. The function returns the number of equivalency classes.

#### Example. Partitioning 2d point set.

    #include "cxcore.h"
    #include "highgui.h"
    #include <stdio.h>

    CvSeq* point_seq = 0;
    IplImage* canvas = 0;
    CvScalar* colors = 0;
    int pos = 10;

    int is_equal( const void* _a, const void* _b, void* userdata )
    {
        CvPoint a = *(const CvPoint*)_a;
        CvPoint b = *(const CvPoint*)_b;
        double threshold = *(double*)userdata;
        return (double)(a.x - b.x)*(a.x - b.x) + (double)(a.y - b.y)*(a.y - b.y) <= threshold;
    }

    void on_track( int pos )
    {
        CvSeq* labels = 0;
        double threshold = pos*pos;
        int i, class_count = cvSeqPartition( point_seq, 0, &labels, is_equal, &threshold );
        printf("%4d classes\n", class_count );
        cvZero( canvas );

        for( i = 0; i < labels->total; i++ )
        {
            CvPoint pt = *(CvPoint*)cvGetSeqElem( point_seq, i, 0 );
            CvScalar color = colors[*(int*)cvGetSeqElem( labels, i, 0 )];
            cvCircle( canvas, pt, 1, color, -1 );
        }

        cvShowImage( "points", canvas );
    }

    int main( int argc, char** argv )
    {
        CvMemStorage* storage = cvCreateMemStorage(0);
        point_seq = cvCreateSeq( CV_32SC2, sizeof(CvSeq), sizeof(CvPoint), storage );
        CvRNG rng = cvRNG(0xffffffff);

        int width = 500, height = 500;
        int i, count = 1000;
        canvas = cvCreateImage( cvSize(width,height), 8, 3 );

        colors = (CvScalar*)cvAlloc( count*sizeof(colors[0]) );
        for( i = 0; i < count; i++ )
        {
            CvPoint pt;
            int icolor;
            pt.x = cvRandInt( &rng ) % width;
            pt.y = cvRandInt( &rng ) % height;
            cvSeqPush( point_seq, &pt );
            icolor = cvRandInt( &rng ) | 0x00404040;
            colors[i] = CV_RGB(icolor & 255, (icolor >> 8)&255, (icolor >> 16)&255);
        }

        cvNamedWindow( "points", 1 );
        cvCreateTrackbar( "threshold", "points", &pos, 50, on_track );
        on_track(pos);
        cvWaitKey(0);
        return 0;
    }

# Error Handling and System Functions

## Error Handling

Error handling in OpenCV is similar to IPL (Image Processing Library). In case of error functions do not return the error code. Instead, they raise an error using CV_ERROR macro that calls cvError that, in its turn, sets the error status with cvSetErrStatus and calls a standard or user-defined error handler (that can display a message box, write to log etc., see cvRedirectError, cvNulDevReport, cvStdErrReport, cvGuiBoxReport). There is global variable, one per each program thread, that contains current error status (an integer value). The status can be retrieved with cvGetErrStatus function.

There are three modes of error handling (see cvSetErrMode and cvGetErrMode):

Leaf
  The program is terminated after error handler is called. This is the default value. It is useful for debugging, as the error is signalled immediately after it occurs. However, for production systems other two methods may be prefferable as they provide more control.
Parent
  The program is not terminated, but the error handler is called. The stack is unwinded (it is done w/o using C++ exception mechanism). User may check error code after calling CxCore function with cvGetErrStatus and react.
Silent
  Similar to Parent mode, but no error handler is called.

Actually, the semantics of Leaf and Parent modes is implemented by error handlers and the above description is true for cvNulDevReport, cvStdErrReport. cvGuiBoxReport behaves slightly differently, and some custom error handler may implement quite different semantics.

### ERROR Handling Macros

Macros for raising an error, checking for errors etc.

    /* special macros for enclosing processing statements within a function and separating
       them from prologue (resource initialization) and epilogue (guaranteed resource release) */
    #define __BEGIN__       {
    #define __END__         goto exit; exit: ; }
    /* proceeds to "resource release" stage */
    #define EXIT            goto exit

    /* Declares locally the function name for CV_ERROR() use */
    #define CV_FUNCNAME( Name )  \
        static char cvFuncName[] = Name

    /* Raises an error within the current context */
    #define CV_ERROR( Code, Msg )                                       \
    {                                                                   \
         cvError( (Code), cvFuncName, Msg, __FILE__, __LINE__ );        \
         EXIT;                                                          \
    }

    /* Checks status after calling CXCORE function */
    #define CV_CHECK()                                                  \
    {                                                                   \
        if( cvGetErrStatus() < 0 )                                   \
            CV_ERROR( CV_StsBackTrace, "Inner function failed." );      \
    }

    /* Provies shorthand for CXCORE function call and CV_CHECK() */
    #define CV_CALL( Statement )                                        \
    {                                                                   \
        Statement;                                                      \
        CV_CHECK();                                                     \
    }

    /* Checks some condition in both debug and release configurations */
    #define CV_ASSERT( Condition )                                          \
    {                                                                       \
        if( !(Condition) )                                                  \
            CV_ERROR( CV_StsInternal, "Assertion: " #Condition " failed" ); \
    }

    /* these macros are similar to their CV_... counterparts, but they
       do not need exit label nor cvFuncName to be defined */
    #define OPENCV_ERROR(status,func_name,err_msg) ...
    #define OPENCV_ERRCHK(func_name,err_msg) ...
    #define OPENCV_ASSERT(condition,func_name,err_msg) ...
    #define OPENCV_CALL(statement) ...

Instead of a discussion, here are the documented example of typical CXCORE function and the example of the function use.

#### Use of Error Handling Macros

    #include "cxcore.h"
    #include <stdio.h>

    void cvResizeDCT( CvMat* input_array, CvMat* output_array )
    {
        CvMat* temp_array = 0; // declare pointer that should be released anyway.

        CV_FUNCNAME( "cvResizeDCT" ); // declare cvFuncName

        __BEGIN__; // start processing. There may be some declarations just after this macro,
                   // but they couldn't be accessed from the epilogue.

        if( !CV_IS_MAT(input_array) || !CV_IS_MAT(output_array) )
            // use CV_ERROR() to raise an error
            CV_ERROR( CV_StsBadArg, "input_array or output_array are not valid matrices" );

        // some restrictions that are going to be removed later, may be checked with CV_ASSERT()
        CV_ASSERT( input_array->rows == 1 && output_array->rows == 1 );

        // use CV_CALL for safe function call
        CV_CALL( temp_array = cvCreateMat( input_array->rows, MAX(input_array->cols,output_array->cols),
                                           input_array->type ));

        if( output_array->cols > input_array->cols )
            CV_CALL( cvZero( temp_array ));

        temp_array->cols = input_array->cols;
        CV_CALL( cvDCT( input_array, temp_array, CV_DXT_FORWARD ));
        temp_array->cols = output_array->cols;
        CV_CALL( cvDCT( temp_array, output_array, CV_DXT_INVERSE ));
        CV_CALL( cvScale( output_array, output_array, 1./sqrt((double)input_array->cols*output_array->cols), 0 ));

        __END__; // finish processing. Epilogue follows after the macro.

        // release temp_array. If temp_array has not been allocated before an error occured, cvReleaseMat
        // takes care of it and does nothing in this case.
        cvReleaseMat( &temp_array );
    }

    int main( int argc, char** argv )
    {
        CvMat* src = cvCreateMat( 1, 512, CV_32F );
    #if 1 /* no errors */
        CvMat* dst = cvCreateMat( 1, 256, CV_32F );
    #else
        CvMat* dst = 0; /* test error processing mechanism */
    #endif
        cvSet( src, cvRealScalar(1.), 0 );
    #if 0 /* change 0 to 1 to suppress error handler invocation */
        cvSetErrMode( CV_ErrModeSilent );
    #endif
        cvResizeDCT( src, dst ); // if some error occurs, the message box will popup, or a message will be
                                 // written to log, or some user-defined processing will be done
        if( cvGetErrStatus() < 0 )
            printf("Some error occured" );
        else
            printf("Everything is OK" );
        return 0;
    }

### GetErrStatus

Returns the current error status

    int cvGetErrStatus( void );

The function `cvGetErrStatus` returns the current error status - the value set with the last cvSetErrStatus call. Note, that in Leaf mode the program terminates immediately after error occured, so to always get control after the function call, one should call cvSetErrMode and set Parent or Silent error mode.

### SetErrStatus

Sets the error status

    void cvSetErrStatus( int status );

status
  The error status.

The function `cvSetErrStatus` sets the error status to the specified value. Mostly, the function is used to reset the error status (set to it `CV_StsOk`) to recover after error. In other cases it is more natural to call cvError or CV_ERROR.

### GetErrMode

Returns the current error mode

    int cvGetErrMode( void );

The function `cvGetErrMode` returns the current error mode - the value set with the last cvSetErrMode call.

### SetErrMode

Sets the error mode

    #define CV_ErrModeLeaf    0
    #define CV_ErrModeParent  1
    #define CV_ErrModeSilent  2
    int cvSetErrMode( int mode );

mode
  The error mode.

The function `cvSetErrMode` sets the specified error mode. For description of different error modes see the beginning of the section.

### Error

Raises an error

    int cvError( int status, const char* func_name,
                 const char* err_msg, const char* file_name, int line );

status
  The error status.
func_name
  Name of the function where the error occured.
err_msg
  Additional information/diagnostics about the error.
file_name
  Name of the file where the error occured.
line
  Line number, where the error occured.

The function `cvError` sets the error status to the specified value (via cvSetErrStatus) and, if the error mode is not Silent, calls the error handler.

### ErrorStr

Returns textual description of error status code

    const char* cvErrorStr( int status );

status
  The error status.

The function `cvErrorStr` returns the textual description for the specified error status code. In case of unknown status the function returns NULL pointer.

### RedirectError

Sets a new error handler

    typedef int (CV_CDECL *CvErrorCallback)( int status, const char* func_name,
                        const char* err_msg, const char* file_name, int line );

    CvErrorCallback cvRedirectError( CvErrorCallback error_handler,
                                     void* userdata=NULL, void** prev_userdata=NULL );

error_handler
  The new error_handler.
userdata
  Arbitrary pointer that is transparetly passed to the error handler.
prev_userdata
  Pointer to the previously assigned user data pointer.

The function `cvRedirectError` sets a new error handler that can be one of standard handlers or a custom handler that has the certain interface. The handler takes the same parameters as cvError function. If the handler returns non-zero value, the program is terminated, otherwise, it continues. The error handler may check the current error mode with cvGetErrMode to make a decision.

### cvNulDevReport cvStdErrReport cvGuiBoxReport

Provide standard error handling

    int cvNulDevReport( int status, const char* func_name,
                        const char* err_msg, const char* file_name,
                        int line, void* userdata );

    int cvStdErrReport( int status, const char* func_name,
                        const char* err_msg, const char* file_name,
                        int line, void* userdata );

    int cvGuiBoxReport( int status, const char* func_name,
                        const char* err_msg, const char* file_name,
                        int line, void* userdata );

status
  The error status.
func_name
  Name of the function where the error occured.
err_msg
  Additional information/diagnostics about the error.
file_name
  Name of the file where the error occured.
line
  Line number, where the error occured.
userdata
  Pointer to the user data. Ignored by the standard handlers.

The functions `cvNullDevReport, cvStdErrReport` and `cvGuiBoxReport` provide standard error handling. `cvGuiBoxReport` is the default error handler on Win32 systems, `cvStdErrReport` - on other systems. `cvGuiBoxReport` pops up message box with the error description and suggest a few options. Below is the sample message box that may be recieved with the sample code above, if one introduce an error as described in the sample

#### Error Message Box

If the error handler is set `cvStdErrReport`, the above message will be printed to standard error output and program will be terminated or continued, depending on the current error mode.

#### Error Message printed to Standard Error Output (in Leaf mode)

    OpenCV ERROR: Bad argument (input_array or output_array are not valid matrices)
            in function cvResizeDCT, D:\User\VP\Projects\avl_proba\a.cpp(75)
    Terminating the application...

## System and Utility Functions

### Alloc

Allocates memory buffer

    void* cvAlloc( size_t size );

size
  Buffer size in bytes.

The function `cvAlloc` allocates `size` bytes and returns pointer to the allocated buffer. In case of error the function reports an error and returns NULL pointer. By default cvAlloc calls icvAlloc which itself calls malloc, however it is possible to assign user-defined memory allocation/deallocation functions using cvSetMemoryManager function.

### Free

Deallocates memory buffer

    void cvFree( T** ptr );

buffer
  Double pointer to released buffer.

The function `cvFree` deallocates memory buffer allocated by cvAlloc. It clears the pointer to buffer upon exit, that is why the double pointer is used. If *buffer is already NULL, the function does nothing

### GetTickCount

Returns number of tics

    int64 cvGetTickCount( void );

The function `cvGetTickCount` returns number of tics starting from some platform-dependent event (number of CPU ticks from the startup, number of milliseconds from 1970th year etc.). The function is useful for accurate measurement of a function/user-code execution time. To convert the number of tics to time units, use cvGetTickFrequency.

### GetTickFrequency

Returns number of tics per microsecond

    double cvGetTickFrequency( void );

The function `cvGetTickFrequency` returns number of tics per microsecond. Thus, the quotient of cvGetTickCount() and cvGetTickFrequency() will give a number of microseconds starting from the platform-dependent event.

### RegisterModule

Registers another module

    typedef struct CvPluginFuncInfo
    {
        void** func_addr;
        void* default_func_addr;
        const char* func_names;
        int search_modules;
        int loaded_from;
    }
    CvPluginFuncInfo;

    typedef struct CvModuleInfo
    {
        struct CvModuleInfo* next;
        const char* name;
        const char* version;
        CvPluginFuncInfo* func_tab;
    }
    CvModuleInfo;

    int cvRegisterModule( const CvModuleInfo* module_info );

module_info
  Information about the module.

The function `cvRegisterModule` adds module to the list of registered modules. After the module is registered, information about it can be retrieved using cvGetModuleInfo function. Also, the registered module makes full use of optimized plugins (IPP, MKL, ...), supported by CXCORE. CXCORE itself, CV (computer vision), CVAUX (auxilary computer vision) and HIGHGUI (visualization & image/video acquisition) are examples of modules. Registration is usually done then the shared library is loaded. See cxcore/src/cxswitcher.cpp and cv/src/cvswitcher.cpp for details, how registration is done and look at cxcore/src/cxswitcher.cpp, cxcore/src/_cxipp.h on how IPP and MKL are connected to the modules.

### GetModuleInfo

Retrieves information about the registered module(s) and plugins

    void  cvGetModuleInfo( const char* module_name,
                           const char** version,
                           const char** loaded_addon_plugins );

module_name
  Name of the module of interest, or NULL, which means all the modules.
version
  The output parameter. Information about the module(s), including version.
loaded_addon_plugins
  The list of names and versions of the optimized plugins that CXCORE was able to find and load.

The function `cvGetModuleInfo` returns information about one of or all of the registered modules. The returned information is stored inside the libraries, so user should not deallocate or modify the returned text strings.

### UseOptimized

Switches between optimized/non-optimized modes

    int cvUseOptimized( int on_off );

on_off
  Use optimized (<>0) or not (0).

The function `cvUseOptimized` switches between the mode, where only pure C implementations from cxcore, OpenCV etc. are used, and the mode, where IPP and MKL functions are used if available. When `cvUseOptimized(0)` is called, all the optimized libraries are unloaded. The function may be useful for debugging, IPP&MKL upgrade on the fly, online speed comparisons etc. It returns the number of optimized functions loaded. Note that by default the optimized plugins are loaded, so it is not necessary to call `cvUseOptimized(1)` in the beginning of the program (actually, it will only increase the startup time)

### SetMemoryManager

Assings custom/default memory managing functions

    typedef void* (CV_CDECL *CvAllocFunc)(size_t size, void* userdata);
    typedef int (CV_CDECL *CvFreeFunc)(void* pptr, void* userdata);

    void cvSetMemoryManager( CvAllocFunc alloc_func=NULL,
                             CvFreeFunc free_func=NULL,
                             void* userdata=NULL );

alloc_func
  Allocation function; the interface is similar to `malloc`, except that `userdata` may be used to determine the context.
free_func
  Deallocation function; the interface is similar to `free`.
userdata
  User data that is transparetly passed to the custom functions.

The function `cvSetMemoryManager` sets user-defined memory managment functions (substitutors for malloc and free) that will be called by cvAlloc, cvFree and higher-level functions (e.g. cvCreateImage). Note, that the function should be called when there is data allocated using cvAlloc. Also, to avoid infinite recursive calls, it is not allowed to call cvAlloc and cvFree from the custom allocation/deallocation functions.

If `alloc_func` and `free_func` pointers are `NULL`, the default memory managing functions are restored.

### SetIPLAllocators

Switches to IPL functions for image allocation/deallocation

    typedef IplImage* (CV_STDCALL* Cv_iplCreateImageHeader)
                                (int,int,int,char*,char*,int,int,int,int,int,
                                IplROI*,IplImage*,void*,IplTileInfo*);
    typedef void (CV_STDCALL* Cv_iplAllocateImageData)(IplImage*,int,int);
    typedef void (CV_STDCALL* Cv_iplDeallocate)(IplImage*,int);
    typedef IplROI* (CV_STDCALL* Cv_iplCreateROI)(int,int,int,int,int);
    typedef IplImage* (CV_STDCALL* Cv_iplCloneImage)(const IplImage*);

    void cvSetIPLAllocators( Cv_iplCreateImageHeader create_header,
                             Cv_iplAllocateImageData allocate_data,
                             Cv_iplDeallocate deallocate,
                             Cv_iplCreateROI create_roi,
                             Cv_iplCloneImage clone_image );

    #define CV_TURN_ON_IPL_COMPATIBILITY()                                  \
        cvSetIPLAllocators( iplCreateImageHeader, iplAllocateImage,         \
                            iplDeallocate, iplCreateROI, iplCloneImage )

create_header
  Pointer to iplCreateImageHeader.
allocate_data
  Pointer to iplAllocateImage.
deallocate
  Pointer to iplDeallocate.
create_roi
  Pointer to iplCreateROI.
clone_image
  Pointer to iplCloneImage.

The function `cvSetIPLAllocators` makes CXCORE to use IPL functions for image allocation/deallocation operations. For convenience, there is the wrapping macro `CV_TURN_ON_IPL_COMPATIBILITY`. The function is useful for applications where IPL and CXCORE/OpenCV are used together and still there are calls to `iplCreateImageHeader` etc. The function is not necessary if IPL is called only for data processing and all the allocation/deallocation is done by CXCORE, or if all the allocation/deallocation is done by IPL and some of OpenCV functions are used to process the data.

### GetNumThreads

Returns the current number of threads used

    int cvGetNumThreads(void);

The function `cvGetNumThreads` return the current number of threads that are used by parallelized (via OpenMP) OpenCV functions.

### SetNumThreads

Sets the number of threads

    void cvSetNumThreads( int threads=0 );

threads
  The number of threads.

The function `cvSetNumThreads` sets the number of threads that are used by parallelized OpenCV functions. When the argument is zero or negative, and at the beginning of the program, the number of threads is set to the number of processors in the system, as returned by the function `omp_get_num_procs()` from OpenMP runtime.

### GetThreadNum

Returns index of the current thread

    int cvGetThreadNum( void );

The function `cvGetThreadNum` returns the index, from 0 to cvGetNumThreads()-1, of the thread that called the function. It is a wrapper for the function `omp_get_thread_num()` from OpenMP runtime. The retrieved index may be used to access local-thread data inside the parallelized code fragments.

# Alphabetical List of Functions

### A

AbsDiff | AddWeighted | Avg
AbsDiffS | Alloc | AvgSdv
Add | And |
AddS | AndS |

### B

BackProjectPCA |  |

### C

CalcCovarMatrix | CloneGraph | CreateGraph
CalcPCA | CloneImage | CreateGraphScanner
CartToPolar | CloneMat | CreateImage
Cbrt | CloneMatND | CreateImageHeader
CheckArr | CloneSeq | CreateMat
Circle | CloneSparseMat | CreateMatHeader
ClearGraph | Cmp | CreateMatND
ClearMemStorage | CmpS | CreateMatNDHeader
ClearND | ConvertScale | CreateMemStorage
ClearSeq | ConvertScaleAbs | CreateSeq
ClearSet | Copy | CreateSet
ClipLine | CountNonZero | CreateSparseMat
ClipLine | CreateChildMemStorage | CrossProduct
Clone | CreateData | CvtSeqToArray

### D

DCT | Det | DrawContours
DFT | Div |
DecRefData | DotProduct |

### E

EigenVV | EllipseBox | Error
Ellipse | EndWriteSeq | ErrorStr
Ellipse2Poly | EndWriteStruct | Exp

### F

FastArctan | FindGraphEdgeByPtr | FlushSeqWriter
FillConvexPoly | FindType | Free
FillPoly | FirstType |
FindGraphEdge | Flip |

### G

GEMM | GetMat | GetTickCount
Get*D | GetModuleInfo | GetTickFrequency
GetCol | GetNextSparseNode | GraphAddEdge
GetDiag | GetNumThreads | GraphAddEdgeByPtr
GetDims | GetOptimalDFTSize | GraphAddVtx
GetElemType | GetRawData | GraphEdgeIdx
GetErrMode | GetReal*D | GraphRemoveEdge
GetErrStatus | GetRootFileNode | GraphRemoveEdgeByPtr
GetFileNode | GetRow | GraphRemoveVtx
GetFileNodeByName | GetSeqElem | GraphRemoveVtxByPtr
GetFileNodeName | GetSeqReaderPos | GraphVtxDegree
GetGraphVtx | GetSetElem | GraphVtxDegreeByPtr
GetHashedKey | GetSize | GraphVtxIdx
GetImage | GetSubRect | GuiBoxReport
GetImageCOI | GetTextSize | Get
GetImageROI | GetThreadNum |

### I

InRange | InitLineIterator | InsertNodeIntoTree
InRangeS | InitMatHeader | InvSqrt
IncRefData | InitMatNDHeader | Invert
InitFont | InitSparseMatIterator | IsInf
InitImageHeader | InitTreeNodeIterator | IsNaN

### K

KMeans2 |  |

### L

LUT | Load |
Line | Log |

### M

Mahalonobis | MemStorageAlloc | MinS
MakeSeqHeaderForArray | MemStorageAllocString | MixChannels
Mat | Merge | Mul
Max | Min | MulSpectrums
MaxS | MinMaxLoc | MulTransposed

### N

NextGraphItem | Norm | Not
NextTreeNode | Normalize | NulDevReport

### O

OpenFileStorage | Or | OrS

### P

PerspectiveTransform | Pow | Ptr*D
PolarToCart | PrevTreeNode | PutText
PolyLine | ProjectPCA |

### R

RNG | ReadRealByName | ReleaseImageHeader
RandArr | ReadString | ReleaseMat
RandInt | ReadStringByName | ReleaseMatND
RandReal | Rectangle | ReleaseMemStorage
RandShuffle | RedirectError | ReleaseSparseMat
Range | Reduce | RemoveNodeFromTree
Read | RegisterModule | Repeat
ReadByName | RegisterType | ResetImageROI
ReadInt | Release | Reshape
ReadIntByName | ReleaseData | ReshapeMatND
ReadRawData | ReleaseFileStorage | RestoreMemStoragePos
ReadRawDataSlice | ReleaseGraphScanner | Round
ReadReal | ReleaseImage |

### S

SVBkSb | SeqSlice | SetSeqReaderPos
SVD | SeqSort | SetZero
Save | Set | Solve
SaveMemStoragePos | Set*D | SolveCubic
ScaleAdd | SetAdd | Split
SeqElemIdx | SetData | Sqrt
SeqInsert | SetErrMode | StartAppendToSeq
SeqInsertSlice | SetErrStatus | StartNextStream
SeqInvert | SetIPLAllocators | StartReadRawData
SeqPartition | SetIdentity | StartReadSeq
SeqPop | SetImageCOI | StartWriteSeq
SeqPopFront | SetImageROI | StartWriteStruct
SeqPopMulti | SetMemoryManager | StdErrReport
SeqPush | SetNew | Sub
SeqPushFront | SetNumThreads | SubRS
SeqPushMulti | SetReal*D | SubS
SeqRemove | SetRemove | Sum
SeqRemoveSlice | SetRemoveByPtr | Set
SeqSearch | SetSeqBlockSize |

### T

Trace | Transpose | TypeOf
Transform | TreeToNodeSeq |

### U

UnregisterType | UseOptimized |

### W

Write | WriteInt | WriteString
WriteComment | WriteRawData |
WriteFileNode | WriteReal |

### X

Xor | XorS |

# List of Examples