[ VIGRA Homepage | Class Index | Function Index | File Index | Main Page ]

| vigra/fftw3.hxx |
--- | --- | ---

    00001 /************************************************************************/
    00002 /*                                                                      */
    00003 /*               Copyright 1998-2004 by Ullrich Koethe                  */
    00004 /*       Cognitive Systems Group, University of Hamburg, Germany        */
    00005 /*                                                                      */
    00006 /*    This file is part of the VIGRA computer vision library.           */
    00007 /*    ( Version 1.4.0, Dec 21 2005 )                                    */
    00008 /*    The VIGRA Website is                                              */
    00009 /*        http://kogs-www.informatik.uni-hamburg.de/~koethe/vigra/      */
    00010 /*    Please direct questions, bug reports, and contributions to        */
    00011 /*        koethe@informatik.uni-hamburg.de          or                  */
    00012 /*        vigra@kogs1.informatik.uni-hamburg.de                         */
    00013 /*                                                                      */
    00014 /*    Permission is hereby granted, free of charge, to any person       */
    00015 /*    obtaining a copy of this software and associated documentation    */
    00016 /*    files (the "Software"), to deal in the Software without           */
    00017 /*    restriction, including without limitation the rights to use,      */
    00018 /*    copy, modify, merge, publish, distribute, sublicense, and/or      */
    00019 /*    sell copies of the Software, and to permit persons to whom the    */
    00020 /*    Software is furnished to do so, subject to the following          */
    00021 /*    conditions:                                                       */
    00022 /*                                                                      */
    00023 /*    The above copyright notice and this permission notice shall be    */
    00024 /*    included in all copies or substantial portions of the             */
    00025 /*    Software.                                                         */
    00026 /*                                                                      */
    00027 /*    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND    */
    00028 /*    EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES   */
    00029 /*    OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND          */
    00030 /*    NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT       */
    00031 /*    HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY,      */
    00032 /*    WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING      */
    00033 /*    FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR     */
    00034 /*    OTHER DEALINGS IN THE SOFTWARE.                                   */
    00035 /*                                                                      */
    00036 /************************************************************************/
    00037
    00038 #ifndef VIGRA_FFTW3_HXX
    00039 #define VIGRA_FFTW3_HXX
    00040
    00041 #include <cmath>
    00042 #include <functional>
    00043 #include "vigra/stdimage.hxx"
    00044 #include "vigra/copyimage.hxx"
    00045 #include "vigra/transformimage.hxx"
    00046 #include "vigra/combineimages.hxx"
    00047 #include "vigra/numerictraits.hxx"
    00048 #include "vigra/imagecontainer.hxx"
    00049 #include <fftw3.h>
    00050
    00051 namespace vigra {
    00052
    00053 typedef double fftw_real;
    00054
    00055 /********************************************************/
    00056 /*                                                      */
    00057 /*                    FFTWComplex                       */
    00058 /*                                                      */
    00059 /********************************************************/
    00060
    00061 /** \brief Wrapper class for the FFTW type '<TT>fftw_complex</TT>'.
    00062
    00063     This class provides constructors and other member functions
    00064     for the C struct '<TT>fftw_complex</TT>'. This struct is the basic
    00065     pixel type of the <a href="http://www.fftw.org/">FFTW Fast Fourier Transform</a>
    00066     library. It inherits the data members '<TT>re</TT>' and '<TT>im</TT>'
    00067     that denote the real and imaginary part of the number. In addition it
    00068     defines transformations to polar coordinates,
    00069     as well as \ref FFTWComplexOperators "arithmetic operators" and
    00070     \ref FFTWComplexAccessors "accessors".
    00071
    00072     FFTWComplex implements the concepts \ref AlgebraicField and
    00073     \ref DivisionAlgebra. The standard image types <tt>FFTWRealImage</tt>
    00074     and <tt>FFTWComplexImage</tt> are defined.
    00075
    00076     <b>See also:</b>
    00077     <ul>
    00078         <li> \ref FFTWComplexTraits
    00079         <li> \ref FFTWComplexOperators
    00080         <li> \ref FFTWComplexAccessors
    00081     </ul>
    00082
    00083     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00084     <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00085     Namespace: vigra
    00086 */
    00087 class FFTWComplex
    00088 {
    00089     fftw_complex data_;
    00090
    00091   public:
    00092         /** The complex' component type, as defined in '<TT>fftw3.h</TT>'
    00093         */
    00094     typedef fftw_real value_type;
    00095
    00096         /** reference type (result of operator[])
    00097         */
    00098     typedef fftw_real & reference;
    00099
    00100         /** const reference type (result of operator[] const)
    00101         */
    00102     typedef fftw_real const & const_reference;
    00103
    00104         /** iterator type (result of begin() )
    00105         */
    00106     typedef fftw_real * iterator;
    00107
    00108         /** const iterator type (result of begin() const)
    00109         */
    00110     typedef fftw_real const * const_iterator;
    00111
    00112         /** The norm type (result of magnitde())
    00113         */
    00114     typedef fftw_real NormType;
    00115
    00116         /** The squared norm type (result of squaredMagnitde())
    00117         */
    00118     typedef fftw_real SquaredNormType;
    00119
    00120         /** Construct from real and imaginary part.
    00121             Default: 0.
    00122         */
    00123     FFTWComplex(value_type const & re = 0.0, value_type const & im = 0.0)
    00124     {
    00125         data_[0] = re;
    00126         data_[1] = im;
    00127     }
    00128
    00129         /** Copy constructor.
    00130         */
    00131     FFTWComplex(FFTWComplex const & o)
    00132     {
    00133         data_[0] = o.data_[0];
    00134         data_[1] = o.data_[1];
    00135     }
    00136
    00137         /** Construct from plain <TT>fftw_complex</TT>.
    00138         */
    00139     FFTWComplex(fftw_complex const & o)
    00140     {
    00141         data_[0] = o[0];
    00142         data_[1] = o[1];
    00143     }
    00144
    00145         /** Construct from TinyVector.
    00146         */
    00147     template <class T>
    00148     FFTWComplex(TinyVector<T, 2> const & o)
    00149     {
    00150         data_[0] = o[0];
    00151         data_[1] = o[1];
    00152     }
    00153
    00154         /** Assignment.
    00155         */
    00156     FFTWComplex& operator=(FFTWComplex const & o)
    00157     {
    00158         data_[0] = o.data_[0];
    00159         data_[1] = o.data_[1];
    00160         return *this;
    00161     }
    00162
    00163         /** Assignment.
    00164         */
    00165     FFTWComplex& operator=(fftw_complex const & o)
    00166     {
    00167         data_[0] = o[0];
    00168         data_[1] = o[1];
    00169         return *this;
    00170     }
    00171
    00172         /** Assignment.
    00173         */
    00174     FFTWComplex& operator=(fftw_real const & o)
    00175     {
    00176         data_[0] = o;
    00177         data_[1] = 0.0;
    00178         return *this;
    00179     }
    00180
    00181         /** Assignment.
    00182         */
    00183     template <class T>
    00184     FFTWComplex& operator=(TinyVector<T, 2> const & o)
    00185     {
    00186         data_[0] = o[0];
    00187         data_[1] = o[1];
    00188         return *this;
    00189     }
    00190
    00191     reference re()
    00192         { return data_[0]; }
    00193
    00194     const_reference re() const
    00195         { return data_[0]; }
    00196
    00197     reference im()
    00198         { return data_[1]; }
    00199
    00200     const_reference im() const
    00201         { return data_[1]; }
    00202
    00203         /** Unary negation.
    00204         */
    00205     FFTWComplex operator-() const
    00206         { return FFTWComplex(-data_[0], -data_[1]); }
    00207
    00208         /** Squared magnitude x*conj(x)
    00209         */
    00210     SquaredNormType squaredMagnitude() const
    00211         { return data_[0]*data_[0]+data_[1]*data_[1]; }
    00212
    00213         /** Magnitude (length of radius vector).
    00214         */
    00215     NormType magnitude() const
    00216         { return VIGRA_CSTD::sqrt(squaredMagnitude()); }
    00217
    00218         /** Phase angle.
    00219         */
    00220     value_type phase() const
    00221         { return VIGRA_CSTD::atan2(data_[1], data_[0]); }
    00222
    00223         /** Access components as if number were a vector.
    00224         */
    00225     reference operator[](int i)
    00226         { return data_[i]; }
    00227
    00228         /** Read components as if number were a vector.
    00229         */
    00230     const_reference operator[](int i) const
    00231         { return data_[i]; }
    00232
    00233         /** Length of complex number (always 2).
    00234         */
    00235     int size() const
    00236         { return 2; }
    00237
    00238     iterator begin()
    00239         { return data_; }
    00240
    00241     iterator end()
    00242         { return data_ + 2; }
    00243
    00244     const_iterator begin() const
    00245         { return data_; }
    00246
    00247     const_iterator end() const
    00248         { return data_ + 2; }
    00249 };
    00250
    00251 /********************************************************/
    00252 /*                                                      */
    00253 /*                     FFTWComplexTraits                */
    00254 /*                                                      */
    00255 /********************************************************/
    00256
    00257 /** \page FFTWComplexTraits Numeric and Promote Traits of FFTWComplex
    00258
    00259     The numeric and promote traits for fftw_complex and FFTWComplex follow
    00260     the general specifications for \ref NumericPromotionTraits and
    00261     \ref AlgebraicField. They are explicitly specialized for the types
    00262     involved:
    00263
    00264     \code
    00265
    00266     template<>
    00267     struct NumericTraits<fftw_complex>
    00268     {
    00269         typedef fftw_complex Promote;
    00270         typedef fftw_complex RealPromote;
    00271         typedef fftw_complex ComplexPromote;
    00272         typedef fftw_real    ValueType;
    00273
    00274         typedef VigraFalseType isIntegral;
    00275         typedef VigraFalseType isScalar;
    00276         typedef VigraFalseType isOrdered;
    00277         typedef VigraTrueType  isComplex;
    00278
    00279         // etc.
    00280     };
    00281
    00282     template<>
    00283     struct NumericTraits<FFTWComplex>
    00284     {
    00285         typedef FFTWComplex Promote;
    00286         typedef FFTWComplex RealPromote;
    00287         typedef FFTWComplex ComplexPromote;
    00288         typedef fftw_real   ValueType;
    00289
    00290         typedef VigraFalseType isIntegral;
    00291         typedef VigraFalseType isScalar;
    00292         typedef VigraFalseType isOrdered;
    00293         typedef VigraTrueType  isComplex;
    00294
    00295         // etc.
    00296     };
    00297
    00298     template<>
    00299     struct NormTraits<fftw_complex>
    00300     {
    00301         typedef fftw_complex Type;
    00302         typedef fftw_real    SquaredNormType;
    00303         typedef fftw_real    NormType;
    00304     };
    00305
    00306     template<>
    00307     struct NormTraits<FFTWComplex>
    00308     {
    00309         typedef FFTWComplex Type;
    00310         typedef fftw_real   SquaredNormType;
    00311         typedef fftw_real   NormType;
    00312     };
    00313
    00314     template <>
    00315     struct PromoteTraits<fftw_complex, fftw_complex>
    00316     {
    00317         typedef fftw_complex Promote;
    00318     };
    00319
    00320     template <>
    00321     struct PromoteTraits<fftw_complex, double>
    00322     {
    00323         typedef fftw_complex Promote;
    00324     };
    00325
    00326     template <>
    00327     struct PromoteTraits<double, fftw_complex>
    00328     {
    00329         typedef fftw_complex Promote;
    00330     };
    00331
    00332     template <>
    00333     struct PromoteTraits<FFTWComplex, FFTWComplex>
    00334     {
    00335         typedef FFTWComplex Promote;
    00336     };
    00337
    00338     template <>
    00339     struct PromoteTraits<FFTWComplex, double>
    00340     {
    00341         typedef FFTWComplex Promote;
    00342     };
    00343
    00344     template <>
    00345     struct PromoteTraits<double, FFTWComplex>
    00346     {
    00347         typedef FFTWComplex Promote;
    00348     };
    00349     \endcode
    00350
    00351     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00352     <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00353     Namespace: vigra
    00354
    00355 */
    00356 template<>
    00357 struct NumericTraits<fftw_complex>
    00358 {
    00359     typedef fftw_complex Type;
    00360     typedef fftw_complex Promote;
    00361     typedef fftw_complex RealPromote;
    00362     typedef fftw_complex ComplexPromote;
    00363     typedef fftw_real    ValueType;
    00364
    00365     typedef VigraFalseType isIntegral;
    00366     typedef VigraFalseType isScalar;
    00367     typedef NumericTraits<fftw_real>::isSigned isSigned;
    00368     typedef VigraFalseType isOrdered;
    00369     typedef VigraTrueType  isComplex;
    00370
    00371     static FFTWComplex zero() { return FFTWComplex(0.0, 0.0); }
    00372     static FFTWComplex one() { return FFTWComplex(1.0, 0.0); }
    00373     static FFTWComplex nonZero() { return one(); }
    00374
    00375     static const Promote & toPromote(const Type & v) { return v; }
    00376     static const RealPromote & toRealPromote(const Type & v) { return v; }
    00377     static const Type & fromPromote(const Promote & v) { return v; }
    00378     static const Type & fromRealPromote(const RealPromote & v) { return v; }
    00379 };
    00380
    00381 template<>
    00382 struct NumericTraits<FFTWComplex>
    00383 {
    00384     typedef FFTWComplex Type;
    00385     typedef FFTWComplex Promote;
    00386     typedef FFTWComplex RealPromote;
    00387     typedef FFTWComplex ComplexPromote;
    00388     typedef fftw_real   ValueType;
    00389
    00390     typedef VigraFalseType isIntegral;
    00391     typedef VigraFalseType isScalar;
    00392     typedef NumericTraits<fftw_real>::isSigned isSigned;
    00393     typedef VigraFalseType isOrdered;
    00394     typedef VigraTrueType  isComplex;
    00395
    00396     static FFTWComplex zero() { return FFTWComplex(0.0, 0.0); }
    00397     static FFTWComplex one() { return FFTWComplex(1.0, 0.0); }
    00398     static FFTWComplex nonZero() { return one(); }
    00399
    00400     static const Promote & toPromote(const Type & v) { return v; }
    00401     static const RealPromote & toRealPromote(const Type & v) { return v; }
    00402     static const Type & fromPromote(const Promote & v) { return v; }
    00403     static const Type & fromRealPromote(const RealPromote & v) { return v; }
    00404 };
    00405
    00406 template<>
    00407 struct NormTraits<fftw_complex>
    00408 {
    00409     typedef fftw_complex Type;
    00410     typedef fftw_real    SquaredNormType;
    00411     typedef fftw_real    NormType;
    00412 };
    00413
    00414 template<>
    00415 struct NormTraits<FFTWComplex>
    00416 {
    00417     typedef FFTWComplex Type;
    00418     typedef fftw_real   SquaredNormType;
    00419     typedef fftw_real   NormType;
    00420 };
    00421
    00422 template <>
    00423 struct PromoteTraits<fftw_complex, fftw_complex>
    00424 {
    00425     typedef fftw_complex Promote;
    00426 };
    00427
    00428 template <>
    00429 struct PromoteTraits<fftw_complex, double>
    00430 {
    00431     typedef fftw_complex Promote;
    00432 };
    00433
    00434 template <>
    00435 struct PromoteTraits<double, fftw_complex>
    00436 {
    00437     typedef fftw_complex Promote;
    00438 };
    00439
    00440 template <>
    00441 struct PromoteTraits<FFTWComplex, FFTWComplex>
    00442 {
    00443     typedef FFTWComplex Promote;
    00444 };
    00445
    00446 template <>
    00447 struct PromoteTraits<FFTWComplex, double>
    00448 {
    00449     typedef FFTWComplex Promote;
    00450 };
    00451
    00452 template <>
    00453 struct PromoteTraits<double, FFTWComplex>
    00454 {
    00455     typedef FFTWComplex Promote;
    00456 };
    00457
    00458
    00459 /********************************************************/
    00460 /*                                                      */
    00461 /*                    FFTWComplex Operations            */
    00462 /*                                                      */
    00463 /********************************************************/
    00464
    00465 /** \addtogroup FFTWComplexOperators Functions for FFTWComplex
    00466
    00467     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00468     <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00469
    00470     These functions fulfill the requirements of an Algebraic Field.
    00471     Return types are determined according to \ref FFTWComplexTraits.
    00472
    00473     Namespace: vigra
    00474     <p>
    00475
    00476  */
    00477 //@{
    00478     /// equal
    00479 inline bool operator ==(FFTWComplex const &a, const FFTWComplex &b) {
    00480     return a.re() == b.re() && a.im() == b.im();
    00481 }
    00482
    00483     /// not equal
    00484 inline bool operator !=(FFTWComplex const &a, const FFTWComplex &b) {
    00485     return a.re() != b.re() || a.im() != b.im();
    00486 }
    00487
    00488     /// add-assignment
    00489 inline FFTWComplex &operator +=(FFTWComplex &a, const FFTWComplex &b) {
    00490     a.re() += b.re();
    00491     a.im() += b.im();
    00492     return a;
    00493 }
    00494
    00495     /// subtract-assignment
    00496 inline FFTWComplex &operator -=(FFTWComplex &a, const FFTWComplex &b) {
    00497     a.re() -= b.re();
    00498     a.im() -= b.im();
    00499     return a;
    00500 }
    00501
    00502     /// multiply-assignment
    00503 inline FFTWComplex &operator *=(FFTWComplex &a, const FFTWComplex &b) {
    00504     FFTWComplex::value_type t = a.re()*b.re()-a.im()*b.im();
    00505     a.im() = a.re()*b.im()+a.im()*b.re();
    00506     a.re() = t;
    00507     return a;
    00508 }
    00509
    00510     /// divide-assignment
    00511 inline FFTWComplex &operator /=(FFTWComplex &a, const FFTWComplex &b) {
    00512     FFTWComplex::value_type sm = b.squaredMagnitude();
    00513     FFTWComplex::value_type t = (a.re()*b.re()+a.im()*b.im())/sm;
    00514     a.im() = (b.re()*a.im()-a.re()*b.im())/sm;
    00515     a.re() = t;
    00516     return a;
    00517 }
    00518
    00519     /// multiply-assignment with scalar double
    00520 inline FFTWComplex &operator *=(FFTWComplex &a, const double &b) {
    00521     a.re() *= b;
    00522     a.im() *= b;
    00523     return a;
    00524 }
    00525
    00526     /// divide-assignment with scalar double
    00527 inline FFTWComplex &operator /=(FFTWComplex &a, const double &b) {
    00528     a.re() /= b;
    00529     a.im() /= b;
    00530     return a;
    00531 }
    00532
    00533     /// addition
    00534 inline FFTWComplex operator +(FFTWComplex a, const FFTWComplex &b) {
    00535     a += b;
    00536     return a;
    00537 }
    00538
    00539     /// subtraction
    00540 inline FFTWComplex operator -(FFTWComplex a, const FFTWComplex &b) {
    00541     a -= b;
    00542     return a;
    00543 }
    00544
    00545     /// multiplication
    00546 inline FFTWComplex operator *(FFTWComplex a, const FFTWComplex &b) {
    00547     a *= b;
    00548     return a;
    00549 }
    00550
    00551     /// right multiplication with scalar double
    00552 inline FFTWComplex operator *(FFTWComplex a, const double &b) {
    00553     a *= b;
    00554     return a;
    00555 }
    00556
    00557     /// left multiplication with scalar double
    00558 inline FFTWComplex operator *(const double &a, FFTWComplex b) {
    00559     b *= a;
    00560     return b;
    00561 }
    00562
    00563     /// division
    00564 inline FFTWComplex operator /(FFTWComplex a, const FFTWComplex &b) {
    00565     a /= b;
    00566     return a;
    00567 }
    00568
    00569     /// right division with scalar double
    00570 inline FFTWComplex operator /(FFTWComplex a, const double &b) {
    00571     a /= b;
    00572     return a;
    00573 }
    00574
    00575 using VIGRA_CSTD::abs;
    00576
    00577     /// absolute value (= magnitude)
    00578 inline FFTWComplex::value_type abs(const FFTWComplex &a)
    00579 {
    00580     return a.magnitude();
    00581 }
    00582
    00583     /// complex conjugate
    00584 inline FFTWComplex conj(const FFTWComplex &a)
    00585 {
    00586     return FFTWComplex(a.re(), -a.im());
    00587 }
    00588
    00589     /// norm (= magnitude)
    00590 inline FFTWComplex::NormType norm(const FFTWComplex &a)
    00591 {
    00592     return a.magnitude();
    00593 }
    00594
    00595     /// squared norm (= squared magnitude)
    00596 inline FFTWComplex::SquaredNormType squaredNorm(const FFTWComplex &a)
    00597 {
    00598     return a.squaredMagnitude();
    00599 }
    00600
    00601 //@}
    00602
    00603
    00604 /** \addtogroup StandardImageTypes
    00605 */
    00606 //@{
    00607
    00608 /********************************************************/
    00609 /*                                                      */
    00610 /*                      FFTWRealImage                   */
    00611 /*                                                      */
    00612 /********************************************************/
    00613
    00614     /** Float (<tt>fftw_real</tt>) image.
    00615
    00616         The type <tt>fftw_real</tt> is defined as <tt>double</tt> (in FFTW 2 it used to be
    00617         either <tt>float</tt> or <tt>double</tt>, as specified during compilation of FFTW).
    00618         FFTWRealImage uses \ref vigra::BasicImageIterator and \ref vigra::StandardAccessor and
    00619         their const counterparts to access the data.
    00620
    00621         <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00622         <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00623         Namespace: vigra
    00624     */
    00625 typedef BasicImage<fftw_real> FFTWRealImage;
    00626
    00627 /********************************************************/
    00628 /*                                                      */
    00629 /*                     FFTWComplexImage                 */
    00630 /*                                                      */
    00631 /********************************************************/
    00632
    00633 template<>
    00634 struct IteratorTraits<
    00635         BasicImageIterator<FFTWComplex, FFTWComplex **> >
    00636 {
    00637     typedef BasicImageIterator<FFTWComplex, FFTWComplex **>  Iterator;
    00638     typedef Iterator                             iterator;
    00639     typedef BasicImageIterator<FFTWComplex, FFTWComplex **>         mutable_iterator;
    00640     typedef ConstBasicImageIterator<FFTWComplex, FFTWComplex **>    const_iterator;
    00641     typedef iterator::iterator_category          iterator_category;
    00642     typedef iterator::value_type                 value_type;
    00643     typedef iterator::reference                  reference;
    00644     typedef iterator::index_reference            index_reference;
    00645     typedef iterator::pointer                    pointer;
    00646     typedef iterator::difference_type            difference_type;
    00647     typedef iterator::row_iterator               row_iterator;
    00648     typedef iterator::column_iterator            column_iterator;
    00649     typedef VectorAccessor<FFTWComplex>          default_accessor;
    00650     typedef VectorAccessor<FFTWComplex>          DefaultAccessor;
    00651     typedef VigraTrueType                        hasConstantStrides;
    00652 };
    00653
    00654 template<>
    00655 struct IteratorTraits<
    00656         ConstBasicImageIterator<FFTWComplex, FFTWComplex **> >
    00657 {
    00658     typedef ConstBasicImageIterator<FFTWComplex, FFTWComplex **>    Iterator;
    00659     typedef Iterator                             iterator;
    00660     typedef BasicImageIterator<FFTWComplex, FFTWComplex **>         mutable_iterator;
    00661     typedef ConstBasicImageIterator<FFTWComplex, FFTWComplex **>    const_iterator;
    00662     typedef iterator::iterator_category          iterator_category;
    00663     typedef iterator::value_type                 value_type;
    00664     typedef iterator::reference                  reference;
    00665     typedef iterator::index_reference            index_reference;
    00666     typedef iterator::pointer                    pointer;
    00667     typedef iterator::difference_type            difference_type;
    00668     typedef iterator::row_iterator               row_iterator;
    00669     typedef iterator::column_iterator            column_iterator;
    00670     typedef VectorAccessor<FFTWComplex>          default_accessor;
    00671     typedef VectorAccessor<FFTWComplex>          DefaultAccessor;
    00672     typedef VigraTrueType                        hasConstantStrides;
    00673 };
    00674
    00675     /** Complex (FFTWComplex) image.
    00676         It uses \ref vigra::BasicImageIterator and \ref vigra::StandardAccessor and
    00677         their const counterparts to access the data.
    00678
    00679         <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00680         <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00681         Namespace: vigra
    00682     */
    00683 typedef BasicImage<FFTWComplex> FFTWComplexImage;
    00684
    00685 //@}
    00686
    00687 /********************************************************/
    00688 /*                                                      */
    00689 /*                  FFTWComplex-Accessors               */
    00690 /*                                                      */
    00691 /********************************************************/
    00692
    00693 /** \addtogroup DataAccessors
    00694 */
    00695 //@{
    00696 /** \defgroup FFTWComplexAccessors Accessors for FFTWComplex
    00697
    00698     Encapsulate access to pixels of type FFTWComplex
    00699 */
    00700 //@{
    00701     /** Encapsulate access to the the real part of a complex number.
    00702
    00703     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00704     <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00705     Namespace: vigra
    00706     */
    00707 class FFTWRealAccessor
    00708 {
    00709   public:
    00710
    00711         /// The accessor's value type.
    00712     typedef fftw_real value_type;
    00713
    00714         /// Read real part at iterator position.
    00715     template <class ITERATOR>
    00716     value_type operator()(ITERATOR const & i) const {
    00717         return (*i).re();
    00718     }
    00719
    00720         /// Read real part at offset from iterator position.
    00721     template <class ITERATOR, class DIFFERENCE>
    00722     value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
    00723         return i[d].re();
    00724     }
    00725
    00726         /// Write real part at iterator position.
    00727     template <class ITERATOR>
    00728     void set(value_type const & v, ITERATOR const & i) const {
    00729         (*i).re()= v;
    00730     }
    00731
    00732         /// Write real part at offset from iterator position.
    00733     template <class ITERATOR, class DIFFERENCE>
    00734     void set(value_type const & v, ITERATOR const & i, DIFFERENCE d) const {
    00735         i[d].re()= v;
    00736     }
    00737 };
    00738
    00739     /** Encapsulate access to the the imaginary part of a complex number.
    00740
    00741     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00742     <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00743     Namespace: vigra
    00744     */
    00745 class FFTWImaginaryAccessor
    00746 {
    00747   public:
    00748         /// The accessor's value type.
    00749     typedef fftw_real value_type;
    00750
    00751         /// Read imaginary part at iterator position.
    00752     template <class ITERATOR>
    00753     value_type operator()(ITERATOR const & i) const {
    00754         return (*i).im();
    00755     }
    00756
    00757         /// Read imaginary part at offset from iterator position.
    00758     template <class ITERATOR, class DIFFERENCE>
    00759     value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
    00760         return i[d].im();
    00761     }
    00762
    00763         /// Write imaginary part at iterator position.
    00764     template <class ITERATOR>
    00765     void set(value_type const & v, ITERATOR const & i) const {
    00766         (*i).im()= v;
    00767     }
    00768
    00769         /// Write imaginary part at offset from iterator position.
    00770     template <class ITERATOR, class DIFFERENCE>
    00771     void set(value_type const & v, ITERATOR const & i, DIFFERENCE d) const {
    00772         i[d].im()= v;
    00773     }
    00774 };
    00775
    00776     /** Write a real number into a complex one. The imaginary part is set
    00777         to 0.
    00778
    00779     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00780     <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00781     Namespace: vigra
    00782     */
    00783 class FFTWWriteRealAccessor: public FFTWRealAccessor
    00784 {
    00785   public:
    00786         /// The accessor's value type.
    00787     typedef fftw_real value_type;
    00788
    00789         /** Write real number at iterator position. Set imaginary part
    00790             to 0.
    00791         */
    00792     template <class ITERATOR>
    00793     void set(value_type const & v, ITERATOR const & i) const {
    00794         (*i).re()= v;
    00795         (*i).im()= 0;
    00796     }
    00797
    00798         /** Write real number at offset from iterator position. Set imaginary part
    00799             to 0.
    00800         */
    00801     template <class ITERATOR, class DIFFERENCE>
    00802     void set(value_type const & v, ITERATOR const & i, DIFFERENCE d) const {
    00803         i[d].re()= v;
    00804         i[d].im()= 0;
    00805     }
    00806 };
    00807
    00808     /** Calculate magnitude of complex number on the fly.
    00809
    00810     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00811     <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00812     Namespace: vigra
    00813     */
    00814 class FFTWMagnitudeAccessor
    00815 {
    00816   public:
    00817         /// The accessor's value type.
    00818     typedef fftw_real value_type;
    00819
    00820         /// Read magnitude at iterator position.
    00821     template <class ITERATOR>
    00822     value_type operator()(ITERATOR const & i) const {
    00823         return (*i).magnitude();
    00824     }
    00825
    00826         /// Read magnitude at offset from iterator position.
    00827     template <class ITERATOR, class DIFFERENCE>
    00828     value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
    00829         return (i[d]).magnitude();
    00830     }
    00831 };
    00832
    00833     /** Calculate phase of complex number on the fly.
    00834
    00835     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>" (for FFTW 3) or<br>
    00836     <b>\#include</b> "<a href="fftw_8hxx-source.html">vigra/fftw.hxx</a>" (for deprecated FFTW 2)<br>
    00837     Namespace: vigra
    00838     */
    00839 class FFTWPhaseAccessor
    00840 {
    00841   public:
    00842         /// The accessor's value type.
    00843     typedef fftw_real value_type;
    00844
    00845         /// Read phase at iterator position.
    00846     template <class ITERATOR>
    00847     value_type operator()(ITERATOR const & i) const {
    00848         return (*i).phase();
    00849     }
    00850
    00851         /// Read phase at offset from iterator position.
    00852     template <class ITERATOR, class DIFFERENCE>
    00853     value_type operator()(ITERATOR const & i, DIFFERENCE d) const {
    00854         return (i[d]).phase();
    00855     }
    00856 };
    00857
    00858 //@}
    00859 //@}
    00860
    00861 /********************************************************/
    00862 /*                                                      */
    00863 /*                    Fourier Transform                 */
    00864 /*                                                      */
    00865 /********************************************************/
    00866
    00867 /** \addtogroup FourierTransform Fast Fourier Transform
    00868
    00869     This documentation describes the VIGRA interface to FFTW 3. There is also an
    00870     \link FourierTransformFFTW2 interface to the older version FFTW 2\endlink
    00871
    00872     VIGRA uses the <a href="http://www.fftw.org/">FFTW Fast Fourier
    00873     Transform</a> package to perform Fourier transformations. VIGRA
    00874     provides a wrapper for FFTW's complex number type (FFTWComplex),
    00875     but FFTW's functions are used verbatim. If the image is stored as
    00876     a FFTWComplexImage, the simplest call to an FFT function is like this:
    00877
    00878     \code
    00879     vigra::FFTWComplexImage spatial(width,height), fourier(width,height);
    00880     ... // fill image with data
    00881
    00882     // create a plan with estimated performance optimization
    00883     fftw_plan forwardPlan = fftw_plan_dft_2d(height, width,
    00884                                 (fftw_complex *)spatial.begin(), (fftw_complex *)fourier.begin(),
    00885                                 FFTW_FORWARD, FFTW_ESTIMATE );
    00886     // calculate FFT (this can be repeated as often as needed,
    00887     //                with fresh data written into the source array)
    00888     fftw_execute(forwardPlan);
    00889
    00890     // release the plan memory
    00891     fftw_destroy_plan(forwardPlan);
    00892
    00893     // likewise for the inverse transform
    00894     fftw_plan backwardPlan = fftw_plan_dft_2d(height, width,
    00895                                  (fftw_complex *)fourier.begin(), (fftw_complex *)spatial.begin(),
    00896                                  FFTW_BACKWARD, FFTW_ESTIMATE);
    00897     fftw_execute(backwardPlan);
    00898     fftw_destroy_plan(backwardPlan);
    00899
    00900     // do not forget to normalize the result according to the image size
    00901     transformImage(srcImageRange(spatial), destImage(spatial),
    00902                    std::bind1st(std::multiplies<FFTWComplex>(), 1.0 / width / height));
    00903     \endcode
    00904
    00905     Note that in the creation of a plan, the height must be given
    00906     first. Note also that <TT>spatial.begin()</TT> may only be passed
    00907     to <TT>fftw_plan_dft_2d</TT> if the transform shall be applied to the
    00908     entire image. When you want to restrict operation to an ROI, you
    00909     can create a copy of the ROI in an image of appropriate size, or
    00910     you may use the Guru interface to FFTW.
    00911
    00912     More information on using FFTW can be found <a href="http://www.fftw.org/doc/">here</a>.
    00913
    00914     FFTW produces fourier images that have the DC component (the
    00915     origin of the Fourier space) in the upper left corner. Often, one
    00916     wants the origin in the center of the image, so that frequencies
    00917     always increase towards the border of the image. This can be
    00918     achieved by calling \ref moveDCToCenter(). The inverse
    00919     transformation is done by \ref moveDCToUpperLeft().
    00920
    00921     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>"<br>
    00922     Namespace: vigra
    00923 */
    00924
    00925 /** \addtogroup FourierTransform
    00926 */
    00927 //@{
    00928
    00929 /********************************************************/
    00930 /*                                                      */
    00931 /*                     moveDCToCenter                   */
    00932 /*                                                      */
    00933 /********************************************************/
    00934
    00935 /** \brief Rearrange the quadrants of a Fourier image so that the origin is
    00936           in the image center.
    00937
    00938     FFTW produces fourier images where the DC component (origin of
    00939     fourier space) is located in the upper left corner of the
    00940     image. The quadrants are placed like this (using a 4x4 image for
    00941     example):
    00942
    00943     \code
    00944             DC 4 3 3
    00945              4 4 3 3
    00946              1 1 2 2
    00947              1 1 2 2
    00948     \endcode
    00949
    00950     After applying the function, the quadrants are at their usual places:
    00951
    00952     \code
    00953             2 2  1 1
    00954             2 2  1 1
    00955             3 3 DC 4
    00956             3 3  4 4
    00957     \endcode
    00958
    00959     This transformation can be reversed by \ref moveDCToUpperLeft().
    00960     Note that the transformation must not be executed in place - input
    00961     and output images must be different.
    00962
    00963     <b> Declarations:</b>
    00964
    00965     pass arguments explicitly:
    00966     \code
    00967     namespace vigra {
    00968         template <class SrcImageIterator, class SrcAccessor,
    00969           class DestImageIterator, class DestAccessor>
    00970         void moveDCToCenter(SrcImageIterator src_upperleft,
    00971                                SrcImageIterator src_lowerright, SrcAccessor sa,
    00972                                DestImageIterator dest_upperleft, DestAccessor da);
    00973     }
    00974     \endcode
    00975
    00976
    00977     use argument objects in conjunction with \ref ArgumentObjectFactories:
    00978     \code
    00979     namespace vigra {
    00980         template <class SrcImageIterator, class SrcAccessor,
    00981                   class DestImageIterator, class DestAccessor>
    00982         void moveDCToCenter(
    00983             triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    00984             pair<DestImageIterator, DestAccessor> dest);
    00985     }
    00986     \endcode
    00987
    00988     <b> Usage:</b>
    00989
    00990         <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>"<br>
    00991         Namespace: vigra
    00992
    00993     \code
    00994     vigra::FFTWComplexImage spatial(width,height), fourier(width,height);
    00995     ... // fill image with data
    00996
    00997     // create a plan with estimated performance optimization
    00998     fftw_plan forwardPlan = fftw_plan_dft_2d(height, width,
    00999                                 (fftw_complex *)spatial.begin(), (fftw_complex *)fourier.begin(),
    01000                                 FFTW_FORWARD, FFTW_ESTIMATE );
    01001     // calculate FFT
    01002     fftw_execute(forwardPlan);
    01003
    01004     vigra::FFTWComplexImage rearrangedFourier(width, height);
    01005     moveDCToCenter(srcImageRange(fourier), destImage(rearrangedFourier));
    01006
    01007     // delete the plan
    01008     fftw_destroy_plan(forwardPlan);
    01009     \endcode
    01010 */
    01011 template <class SrcImageIterator, class SrcAccessor,
    01012           class DestImageIterator, class DestAccessor>
    01013 void moveDCToCenter(SrcImageIterator src_upperleft,
    01014                                SrcImageIterator src_lowerright, SrcAccessor sa,
    01015                                DestImageIterator dest_upperleft, DestAccessor da)
    01016 {
    01017     int w= src_lowerright.x - src_upperleft.x;
    01018     int h= src_lowerright.y - src_upperleft.y;
    01019     int w1 = w/2;
    01020     int h1 = h/2;
    01021     int w2 = (w+1)/2;
    01022     int h2 = (h+1)/2;
    01023
    01024     // 2. Quadrant  zum 4.
    01025     copyImage(srcIterRange(src_upperleft,
    01026                            src_upperleft  + Diff2D(w2, h2), sa),
    01027               destIter    (dest_upperleft + Diff2D(w1, h1), da));
    01028
    01029     // 4. Quadrant zum 2.
    01030     copyImage(srcIterRange(src_upperleft + Diff2D(w2, h2),
    01031                            src_lowerright, sa),
    01032               destIter    (dest_upperleft, da));
    01033
    01034     // 1. Quadrant zum 3.
    01035     copyImage(srcIterRange(src_upperleft  + Diff2D(w2, 0),
    01036                            src_upperleft  + Diff2D(w,  h2), sa),
    01037               destIter    (dest_upperleft + Diff2D(0,  h1), da));
    01038
    01039     // 3. Quadrant zum 1.
    01040     copyImage(srcIterRange(src_upperleft  + Diff2D(0,  h2),
    01041                            src_upperleft  + Diff2D(w2, h), sa),
    01042               destIter    (dest_upperleft + Diff2D(w1, 0), da));
    01043 }
    01044
    01045 template <class SrcImageIterator, class SrcAccessor,
    01046           class DestImageIterator, class DestAccessor>
    01047 inline void moveDCToCenter(
    01048     triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01049     pair<DestImageIterator, DestAccessor> dest)
    01050 {
    01051     moveDCToCenter(src.first, src.second, src.third,
    01052                           dest.first, dest.second);
    01053 }
    01054
    01055 /********************************************************/
    01056 /*                                                      */
    01057 /*                   moveDCToUpperLeft                  */
    01058 /*                                                      */
    01059 /********************************************************/
    01060
    01061 /** \brief Rearrange the quadrants of a Fourier image so that the origin is
    01062           in the image's upper left.
    01063
    01064      This function is the inversion of \ref moveDCToCenter(). See there
    01065      for declarations and a usage example.
    01066
    01067     <b> Declarations:</b>
    01068
    01069     pass arguments explicitly:
    01070     \code
    01071     namespace vigra {
    01072         template <class SrcImageIterator, class SrcAccessor,
    01073           class DestImageIterator, class DestAccessor>
    01074         void moveDCToUpperLeft(SrcImageIterator src_upperleft,
    01075                                SrcImageIterator src_lowerright, SrcAccessor sa,
    01076                                DestImageIterator dest_upperleft, DestAccessor da);
    01077     }
    01078     \endcode
    01079
    01080
    01081     use argument objects in conjunction with \ref ArgumentObjectFactories:
    01082     \code
    01083     namespace vigra {
    01084         template <class SrcImageIterator, class SrcAccessor,
    01085                   class DestImageIterator, class DestAccessor>
    01086         void moveDCToUpperLeft(
    01087             triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01088             pair<DestImageIterator, DestAccessor> dest);
    01089     }
    01090     \endcode
    01091 */
    01092 template <class SrcImageIterator, class SrcAccessor,
    01093           class DestImageIterator, class DestAccessor>
    01094 void moveDCToUpperLeft(SrcImageIterator src_upperleft,
    01095                                SrcImageIterator src_lowerright, SrcAccessor sa,
    01096                                DestImageIterator dest_upperleft, DestAccessor da)
    01097 {
    01098     int w= src_lowerright.x - src_upperleft.x;
    01099     int h= src_lowerright.y - src_upperleft.y;
    01100     int w2 = w/2;
    01101     int h2 = h/2;
    01102     int w1 = (w+1)/2;
    01103     int h1 = (h+1)/2;
    01104
    01105     // 2. Quadrant  zum 4.
    01106     copyImage(srcIterRange(src_upperleft,
    01107                            src_upperleft  + Diff2D(w2, h2), sa),
    01108               destIter    (dest_upperleft + Diff2D(w1, h1), da));
    01109
    01110     // 4. Quadrant zum 2.
    01111     copyImage(srcIterRange(src_upperleft + Diff2D(w2, h2),
    01112                            src_lowerright, sa),
    01113               destIter    (dest_upperleft, da));
    01114
    01115     // 1. Quadrant zum 3.
    01116     copyImage(srcIterRange(src_upperleft  + Diff2D(w2, 0),
    01117                            src_upperleft  + Diff2D(w,  h2), sa),
    01118               destIter    (dest_upperleft + Diff2D(0,  h1), da));
    01119
    01120     // 3. Quadrant zum 1.
    01121     copyImage(srcIterRange(src_upperleft  + Diff2D(0,  h2),
    01122                            src_upperleft  + Diff2D(w2, h), sa),
    01123               destIter    (dest_upperleft + Diff2D(w1, 0), da));
    01124 }
    01125
    01126 template <class SrcImageIterator, class SrcAccessor,
    01127           class DestImageIterator, class DestAccessor>
    01128 inline void moveDCToUpperLeft(
    01129     triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01130     pair<DestImageIterator, DestAccessor> dest)
    01131 {
    01132     moveDCToUpperLeft(src.first, src.second, src.third,
    01133                                           dest.first, dest.second);
    01134 }
    01135
    01136 /********************************************************/
    01137 /*                                                      */
    01138 /*                   applyFourierFilter                 */
    01139 /*                                                      */
    01140 /********************************************************/
    01141
    01142 /** \brief Apply a filter (defined in the frequency domain) to an image.
    01143
    01144     After transferring the image into the frequency domain, it is
    01145     multiplied pixel-wise with the filter and transformed back. The
    01146     result is always put into the given FFTWComplexImage
    01147     <TT>destImg</TT> which must have the right size. Finally, the
    01148     result will be normalized to compensate for the two FFTs.
    01149
    01150     The input and filter images can be scalar images (more precisely,
    01151     <TT>SrcAccessor::value_type</TT> must be scalar) or
    01152     FFTWComplexImages (in this case, one conversion is saved).
    01153
    01154     The DC entry of the filter must be in the upper left, which is the
    01155     position where FFTW expects it (see \ref moveDCToUpperLeft()).
    01156
    01157     You can optionally pass two fftwnd_plans as last parameters, the
    01158     forward plan and the in-place backward plan. Both must have been
    01159     created for the right image size (see sample code).
    01160
    01161     <b> Declarations:</b>
    01162
    01163     pass arguments explicitly:
    01164     \code
    01165     namespace vigra {
    01166         template <class SrcImageIterator, class SrcAccessor,
    01167             class FilterImageIterator, class FilterAccessor>
    01168         void applyFourierFilter(SrcImageIterator srcUpperLeft,
    01169                                 SrcImageIterator srcLowerRight, SrcAccessor sa,
    01170                                 FilterImageIterator filterUpperLeft, FilterAccessor fa,
    01171                                 FFTWComplexImage & destImg)
    01172
    01173         template <class SrcImageIterator, class SrcAccessor,
    01174             class FilterImageIterator, class FilterAccessor>
    01175         void applyFourierFilter(SrcImageIterator srcUpperLeft,
    01176                                 SrcImageIterator srcLowerRight, SrcAccessor sa,
    01177                                 FilterImageIterator filterUpperLeft, FilterAccessor fa,
    01178                                 FFTWComplexImage & destImg,
    01179                                 const fftwnd_plan & forwardPlan, const fftwnd_plan & backwardPlan)
    01180     }
    01181     \endcode
    01182
    01183     use argument objects in conjunction with \ref ArgumentObjectFactories:
    01184     \code
    01185     namespace vigra {
    01186         template <class SrcImageIterator, class SrcAccessor,
    01187             class FilterImageIterator, class FilterAccessor>
    01188         inline
    01189         void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01190                                 pair<FilterImageIterator, FilterAccessor> filter,
    01191                                 FFTWComplexImage &destImg)
    01192
    01193         template <class SrcImageIterator, class SrcAccessor,
    01194             class FilterImageIterator, class FilterAccessor>
    01195         inline
    01196         void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01197                                 pair<FilterImageIterator, FilterAccessor> filter,
    01198                                 FFTWComplexImage &destImg,
    01199                                 const fftwnd_plan &forwardPlan, const fftwnd_plan &backwardPlan)
    01200     }
    01201     \endcode
    01202
    01203     <b> Usage:</b>
    01204
    01205     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>"<br>
    01206     Namespace: vigra
    01207
    01208     \code
    01209     // create a Gaussian filter in Fourier space
    01210     vigra::FImage gaussFilter(w, h), filter(w, h);
    01211     for(int y=0; y<h; ++y)
    01212         for(int x=0; x<w; ++x)
    01213         {
    01214             xx = float(x - w / 2) / w;
    01215             yy = float(y - h / 2) / h;
    01216
    01217             gaussFilter(x,y) = std::exp(-(xx*xx + yy*yy) / 2.0 * scale);
    01218         }
    01219
    01220     // applyFourierFilter() expects the filter's DC in the upper left
    01221     moveDCToUpperLeft(srcImageRange(gaussFilter), destImage(filter));
    01222
    01223     vigra::FFTWComplexImage result(w, h);
    01224
    01225     vigra::applyFourierFilter(srcImageRange(image), srcImage(filter), result);
    01226     \endcode
    01227
    01228     For inspection of the result, \ref FFTWMagnitudeAccessor might be
    01229     useful. If you want to apply the same filter repeatedly, it may be more
    01230     efficient to use the FFTW functions directly with FFTW plans optimized
    01231     for good performance.
    01232 */
    01233 template <class SrcImageIterator, class SrcAccessor,
    01234           class FilterImageIterator, class FilterAccessor,
    01235           class DestImageIterator, class DestAccessor>
    01236 inline
    01237 void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01238                         pair<FilterImageIterator, FilterAccessor> filter,
    01239                         pair<DestImageIterator, DestAccessor> dest)
    01240 {
    01241     applyFourierFilter(src.first, src.second, src.third,
    01242                        filter.first, filter.second,
    01243                        dest.first, dest.second);
    01244 }
    01245
    01246 template <class SrcImageIterator, class SrcAccessor,
    01247           class FilterImageIterator, class FilterAccessor,
    01248           class DestImageIterator, class DestAccessor>
    01249 void applyFourierFilter(SrcImageIterator srcUpperLeft,
    01250                         SrcImageIterator srcLowerRight, SrcAccessor sa,
    01251                         FilterImageIterator filterUpperLeft, FilterAccessor fa,
    01252                         DestImageIterator destUpperLeft, DestAccessor da)
    01253 {
    01254     // copy real input images into a complex one...
    01255     int w= srcLowerRight.x - srcUpperLeft.x;
    01256     int h= srcLowerRight.y - srcUpperLeft.y;
    01257
    01258     FFTWComplexImage workImage(w, h);
    01259     copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
    01260               destImage(workImage, FFTWWriteRealAccessor()));
    01261
    01262     // ...and call the impl
    01263     FFTWComplexImage const & cworkImage = workImage;
    01264     applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
    01265                            filterUpperLeft, fa,
    01266                            destUpperLeft, da);
    01267 }
    01268
    01269 template <class FilterImageIterator, class FilterAccessor,
    01270           class DestImageIterator, class DestAccessor>
    01271 inline
    01272 void applyFourierFilter(
    01273     FFTWComplexImage::const_traverser srcUpperLeft,
    01274     FFTWComplexImage::const_traverser srcLowerRight,
    01275     FFTWComplexImage::ConstAccessor sa,
    01276     FilterImageIterator filterUpperLeft, FilterAccessor fa,
    01277     DestImageIterator destUpperLeft, DestAccessor da)
    01278 {
    01279     int w = srcLowerRight.x - srcUpperLeft.x;
    01280     int h = srcLowerRight.y - srcUpperLeft.y;
    01281
    01282     // test for right memory layout (fftw expects a 2*width*height floats array)
    01283     if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
    01284         applyFourierFilterImpl(srcUpperLeft, srcLowerRight, sa,
    01285                                filterUpperLeft, fa,
    01286                                destUpperLeft, da);
    01287     else
    01288     {
    01289         FFTWComplexImage workImage(w, h);
    01290         copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
    01291                   destImage(workImage));
    01292
    01293         FFTWComplexImage const & cworkImage = workImage;
    01294         applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
    01295                                filterUpperLeft, fa,
    01296                                destUpperLeft, da);
    01297     }
    01298 }
    01299
    01300 template <class FilterImageIterator, class FilterAccessor,
    01301           class DestImageIterator, class DestAccessor>
    01302 void applyFourierFilterImpl(
    01303     FFTWComplexImage::const_traverser srcUpperLeft,
    01304     FFTWComplexImage::const_traverser srcLowerRight,
    01305     FFTWComplexImage::ConstAccessor sa,
    01306     FilterImageIterator filterUpperLeft, FilterAccessor fa,
    01307     DestImageIterator destUpperLeft, DestAccessor da)
    01308 {
    01309     int w = srcLowerRight.x - srcUpperLeft.x;
    01310     int h = srcLowerRight.y - srcUpperLeft.y;
    01311
    01312     FFTWComplexImage complexResultImg(srcLowerRight - srcUpperLeft);
    01313
    01314     // FFT from srcImage to complexResultImg
    01315     fftw_plan forwardPlan=
    01316         fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
    01317                                (fftw_complex *)complexResultImg.begin(),
    01318                                FFTW_FORWARD, FFTW_ESTIMATE );
    01319     fftw_execute(forwardPlan);
    01320     fftw_destroy_plan(forwardPlan);
    01321
    01322     // convolve in freq. domain (in complexResultImg)
    01323     combineTwoImages(srcImageRange(complexResultImg), srcIter(filterUpperLeft, fa),
    01324                      destImage(complexResultImg), std::multiplies<FFTWComplex>());
    01325
    01326     // FFT back into spatial domain (inplace in complexResultImg)
    01327     fftw_plan backwardPlan=
    01328         fftw_plan_dft_2d(h, w, (fftw_complex *)complexResultImg.begin(),
    01329                                (fftw_complex *)complexResultImg.begin(),
    01330                                FFTW_BACKWARD, FFTW_ESTIMATE);
    01331     fftw_execute(backwardPlan);
    01332     fftw_destroy_plan(backwardPlan);
    01333
    01334     typedef typename
    01335         NumericTraits<typename DestAccessor::value_type>::isScalar
    01336         isScalarResult;
    01337
    01338     // normalization (after FFTs), maybe stripping imaginary part
    01339     applyFourierFilterImplNormalization(complexResultImg, destUpperLeft, da,
    01340                                         isScalarResult());
    01341 }
    01342
    01343 template <class DestImageIterator, class DestAccessor>
    01344 void applyFourierFilterImplNormalization(FFTWComplexImage const &srcImage,
    01345                                          DestImageIterator destUpperLeft,
    01346                                          DestAccessor da,
    01347                                          VigraFalseType)
    01348 {
    01349     double normFactor= 1.0/(srcImage.width() * srcImage.height());
    01350
    01351     for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
    01352     {
    01353         DestImageIterator dIt= destUpperLeft;
    01354         for(int x= 0; x< srcImage.width(); x++, dIt.x++)
    01355         {
    01356             da.setComponent(srcImage(x, y).re()*normFactor, dIt, 0);
    01357             da.setComponent(srcImage(x, y).im()*normFactor, dIt, 1);
    01358         }
    01359     }
    01360 }
    01361
    01362 inline
    01363 void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
    01364         FFTWComplexImage::traverser destUpperLeft,
    01365         FFTWComplexImage::Accessor da,
    01366         VigraFalseType)
    01367 {
    01368     transformImage(srcImageRange(srcImage), destIter(destUpperLeft, da),
    01369                    linearIntensityTransform<FFTWComplex>(1.0/(srcImage.width() * srcImage.height())));
    01370 }
    01371
    01372 template <class DestImageIterator, class DestAccessor>
    01373 void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
    01374                                          DestImageIterator destUpperLeft,
    01375                                          DestAccessor da,
    01376                                          VigraTrueType)
    01377 {
    01378     double normFactor= 1.0/(srcImage.width() * srcImage.height());
    01379
    01380     for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
    01381     {
    01382         DestImageIterator dIt= destUpperLeft;
    01383         for(int x= 0; x< srcImage.width(); x++, dIt.x++)
    01384             da.set(srcImage(x, y).re()*normFactor, dIt);
    01385     }
    01386 }
    01387
    01388 /**********************************************************/
    01389 /*                                                        */
    01390 /*                applyFourierFilterFamily                */
    01391 /*                                                        */
    01392 /**********************************************************/
    01393
    01394 /** \brief Apply an array of filters (defined in the frequency domain) to an image.
    01395
    01396     This provides the same functionality as \ref applyFourierFilter(),
    01397     but applying several filters at once allows to avoid
    01398     repeated Fourier transforms of the source image.
    01399
    01400     Filters and result images must be stored in \ref vigra::ImageArray data
    01401     structures. In contrast to \ref applyFourierFilter(), this function adjusts
    01402     the size of the result images and the the length of the array.
    01403
    01404     <b> Declarations:</b>
    01405
    01406     pass arguments explicitly:
    01407     \code
    01408     namespace vigra {
    01409         template <class SrcImageIterator, class SrcAccessor, class FilterType>
    01410         void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
    01411                                       SrcImageIterator srcLowerRight, SrcAccessor sa,
    01412                                       const ImageArray<FilterType> &filters,
    01413                                       ImageArray<FFTWComplexImage> &results)
    01414     }
    01415     \endcode
    01416
    01417     use argument objects in conjunction with \ref ArgumentObjectFactories:
    01418     \code
    01419     namespace vigra {
    01420         template <class SrcImageIterator, class SrcAccessor, class FilterType>
    01421         inline
    01422         void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01423                                       const ImageArray<FilterType> &filters,
    01424                                       ImageArray<FFTWComplexImage> &results)
    01425     }
    01426     \endcode
    01427
    01428     <b> Usage:</b>
    01429
    01430     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>"<br>
    01431     Namespace: vigra
    01432
    01433     \code
    01434     // assuming the presence of a real-valued image named "image" to
    01435     // be filtered in this example
    01436
    01437     vigra::ImageArray<vigra::FImage> filters(16, image.size());
    01438
    01439     for (int i=0; i<filters.size(); i++)
    01440          // create some meaningful filters here
    01441          createMyFilterOfScale(i, destImage(filters[i]));
    01442
    01443     vigra::ImageArray<vigra::FFTWComplexImage> results();
    01444
    01445     vigra::applyFourierFilterFamily(srcImageRange(image), filters, results);
    01446     \endcode
    01447 */
    01448 template <class SrcImageIterator, class SrcAccessor,
    01449           class FilterType, class DestImage>
    01450 inline
    01451 void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01452                               const ImageArray<FilterType> &filters,
    01453                               ImageArray<DestImage> &results)
    01454 {
    01455     applyFourierFilterFamily(src.first, src.second, src.third,
    01456                              filters, results);
    01457 }
    01458
    01459 template <class SrcImageIterator, class SrcAccessor,
    01460           class FilterType, class DestImage>
    01461 void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
    01462                               SrcImageIterator srcLowerRight, SrcAccessor sa,
    01463                               const ImageArray<FilterType> &filters,
    01464                               ImageArray<DestImage> &results)
    01465 {
    01466     int w= srcLowerRight.x - srcUpperLeft.x;
    01467     int h= srcLowerRight.y - srcUpperLeft.y;
    01468
    01469     FFTWComplexImage workImage(w, h);
    01470     copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
    01471               destImage(workImage, FFTWWriteRealAccessor()));
    01472
    01473     FFTWComplexImage const & cworkImage = workImage;
    01474     applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
    01475                                  filters, results);
    01476 }
    01477
    01478 template <class FilterType, class DestImage>
    01479 inline
    01480 void applyFourierFilterFamily(
    01481     FFTWComplexImage::const_traverser srcUpperLeft,
    01482     FFTWComplexImage::const_traverser srcLowerRight,
    01483     FFTWComplexImage::ConstAccessor sa,
    01484     const ImageArray<FilterType> &filters,
    01485     ImageArray<DestImage> &results)
    01486 {
    01487     int w= srcLowerRight.x - srcUpperLeft.x;
    01488
    01489     // test for right memory layout (fftw expects a 2*width*height floats array)
    01490     if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
    01491         applyFourierFilterFamilyImpl(srcUpperLeft, srcLowerRight, sa,
    01492                                      filters, results);
    01493     else
    01494     {
    01495         int h = srcLowerRight.y - srcUpperLeft.y;
    01496         FFTWComplexImage workImage(w, h);
    01497         copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
    01498                   destImage(workImage));
    01499
    01500         FFTWComplexImage const & cworkImage = workImage;
    01501         applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
    01502                                      filters, results);
    01503     }
    01504 }
    01505
    01506 template <class FilterType, class DestImage>
    01507 void applyFourierFilterFamilyImpl(
    01508     FFTWComplexImage::const_traverser srcUpperLeft,
    01509     FFTWComplexImage::const_traverser srcLowerRight,
    01510     FFTWComplexImage::ConstAccessor sa,
    01511     const ImageArray<FilterType> &filters,
    01512     ImageArray<DestImage> &results)
    01513 {
    01514     // make sure the filter images have the right dimensions
    01515     vigra_precondition((srcLowerRight - srcUpperLeft) == filters.imageSize(),
    01516                        "applyFourierFilterFamily called with src image size != filters.imageSize()!");
    01517
    01518     // make sure the result image array has the right dimensions
    01519     results.resize(filters.size());
    01520     results.resizeImages(filters.imageSize());
    01521
    01522     // FFT from srcImage to freqImage
    01523     int w= srcLowerRight.x - srcUpperLeft.x;
    01524     int h= srcLowerRight.y - srcUpperLeft.y;
    01525
    01526     FFTWComplexImage freqImage(w, h);
    01527     FFTWComplexImage result(w, h);
    01528
    01529     fftw_plan forwardPlan=
    01530         fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
    01531                                (fftw_complex *)freqImage.begin(),
    01532                                FFTW_FORWARD, FFTW_ESTIMATE );
    01533     fftw_execute(forwardPlan);
    01534     fftw_destroy_plan(forwardPlan);
    01535
    01536     fftw_plan backwardPlan=
    01537         fftw_plan_dft_2d(h, w, (fftw_complex *)result.begin(),
    01538                                (fftw_complex *)result.begin(),
    01539                                FFTW_BACKWARD, FFTW_ESTIMATE );
    01540     typedef typename
    01541         NumericTraits<typename DestImage::Accessor::value_type>::isScalar
    01542         isScalarResult;
    01543
    01544     // convolve with filters in freq. domain
    01545     for (unsigned int i= 0;  i < filters.size(); i++)
    01546     {
    01547         combineTwoImages(srcImageRange(freqImage), srcImage(filters[i]),
    01548                          destImage(result), std::multiplies<FFTWComplex>());
    01549
    01550         // FFT back into spatial domain (inplace in destImage)
    01551         fftw_execute(backwardPlan);
    01552
    01553         // normalization (after FFTs), maybe stripping imaginary part
    01554         applyFourierFilterImplNormalization(result,
    01555                                             results[i].upperLeft(), results[i].accessor(),
    01556                                             isScalarResult());
    01557     }
    01558     fftw_destroy_plan(backwardPlan);
    01559 }
    01560
    01561 /********************************************************/
    01562 /*                                                      */
    01563 /*                fourierTransformReal                  */
    01564 /*                                                      */
    01565 /********************************************************/
    01566
    01567 /** \brief Real Fourier transforms for even and odd boundary conditions
    01568            (aka. cosine and sine transforms).
    01569
    01570
    01571     If the image is real and has even symmetry, its Fourier transform
    01572     is also real and has even symmetry. The Fourier transform of a real image with odd
    01573     symmetry is imaginary and has odd symmetry. In either case, only about a quarter
    01574     of the pixels need to be stored because the rest can be calculated from the symmetry
    01575     properties. This is especially useful, if the original image is implicitly assumed
    01576     to have reflective or anti-reflective boundary conditions. Then the "negative"
    01577     pixel locations are defined as
    01578
    01579     \code
    01580     even (reflective boundary conditions):      f[-x] = f[x]     (x = 1,...,N-1)
    01581     odd (anti-reflective boundary conditions):  f[-1] = 0
    01582                                                 f[-x] = -f[x-2]  (x = 2,...,N-1)
    01583     \endcode
    01584
    01585     end similar at the other boundary (see the FFTW documentation for details).
    01586     This has the advantage that more efficient Fourier transforms that use only
    01587     real numbers can be implemented. These are also known as cosine and sine transforms
    01588     respectively.
    01589
    01590     If you use the odd transform it is important to note that in the Fourier domain,
    01591     the DC component is always zero and is therefore dropped from the data structure.
    01592     This means that index 0 in an odd symmetric Fourier domain image refers to
    01593     the <i>first</i> harmonic. This is especially important if an image is first
    01594     cosine transformed (even symmetry), then in the Fourier domain multiplied
    01595     with an odd symmetric filter (e.g. a first derivative) and finally transformed
    01596     back to the spatial domain with a sine transform (odd symmetric). For this to work
    01597     properly the image must be shifted left or up by one pixel (depending on whether
    01598     the x- or y-axis is odd symmetric) before the inverse transform can be applied.
    01599     (see example below).
    01600
    01601     The real Fourier transform functions are named <tt>fourierTransformReal??</tt>
    01602     where the questions marks stand for either <tt>E</tt> or <tt>O</tt> indicating
    01603     whether the x- and y-axis is to be transformed using even or odd symmetry.
    01604     The same functions can be used for both the forward and inverse transforms,
    01605     only the normalization changes. For signal processing, the following
    01606     normalization factors are most appropriate:
    01607
    01608     \code
    01609                           forward             inverse
    01610     ------------------------------------------------------------
    01611     X even, Y even           1.0         4.0 * (w-1) * (h-1)
    01612     X even, Y odd           -1.0        -4.0 * (w-1) * (h+1)
    01613     X odd,  Y even          -1.0        -4.0 * (w+1) * (h-1)
    01614     X odd,  Y odd            1.0         4.0 * (w+1) * (h+1)
    01615     \endcode
    01616
    01617     where <tt>w</tt> and <tt>h</tt> denote the image width and height.
    01618
    01619     <b> Declarations:</b>
    01620
    01621     pass arguments explicitly:
    01622     \code
    01623     namespace vigra {
    01624         template <class SrcTraverser, class SrcAccessor,
    01625                   class DestTraverser, class DestAccessor>
    01626         void
    01627         fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01628                                DestTraverser dul, DestAccessor dest, fftw_real norm);
    01629
    01630         fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
    01631     }
    01632     \endcode
    01633
    01634
    01635     use argument objects in conjunction with \ref ArgumentObjectFactories:
    01636     \code
    01637     namespace vigra {
    01638         template <class SrcTraverser, class SrcAccessor,
    01639                   class DestTraverser, class DestAccessor>
    01640         void
    01641         fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01642                                pair<DestTraverser, DestAccessor> dest, fftw_real norm);
    01643
    01644         fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
    01645     }
    01646     \endcode
    01647
    01648     <b> Usage:</b>
    01649
    01650         <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>"<br>
    01651         Namespace: vigra
    01652
    01653     \code
    01654     vigra::FImage spatial(width,height), fourier(width,height);
    01655     ... // fill image with data
    01656
    01657     // forward cosine transform == reflective boundary conditions
    01658     fourierTransformRealEE(srcImageRange(spatial), destImage(fourier), (fftw_real)1.0);
    01659
    01660     // multiply with a first derivative of Gaussian in x-direction
    01661     for(int y = 0; y < height; ++y)
    01662     {
    01663         for(int x = 1; x < width; ++x)
    01664         {
    01665             double dx = x * M_PI / (width - 1);
    01666             double dy = y * M_PI / (height - 1);
    01667             fourier(x-1, y) = fourier(x, y) * dx * exp(-(dx*dx + dy*dy) * scale*scale / 2.0);
    01668         }
    01669         fourier(width-1, y) = 0.0;
    01670     }
    01671
    01672     // inverse transform -- odd symmetry in x-direction, even in y,
    01673     //                      due to symmetry of the filter
    01674     fourierTransformRealOE(srcImageRange(fourier), destImage(spatial),
    01675                            (fftw_real)-4.0 * (width+1) * (height-1));
    01676     \endcode
    01677 */
    01678 template <class SrcTraverser, class SrcAccessor,
    01679           class DestTraverser, class DestAccessor>
    01680 inline void
    01681 fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01682                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
    01683 {
    01684     fourierTransformRealEE(src.first, src.second, src.third,
    01685                                    dest.first, dest.second, norm);
    01686 }
    01687
    01688 template <class SrcTraverser, class SrcAccessor,
    01689           class DestTraverser, class DestAccessor>
    01690 inline void
    01691 fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01692                                DestTraverser dul, DestAccessor dest, fftw_real norm)
    01693 {
    01694     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01695                                       norm, FFTW_REDFT00, FFTW_REDFT00);
    01696 }
    01697
    01698 template <class DestTraverser, class DestAccessor>
    01699 inline void
    01700 fourierTransformRealEE(
    01701          FFTWRealImage::const_traverser sul,
    01702          FFTWRealImage::const_traverser slr,
    01703          FFTWRealImage::Accessor src,
    01704          DestTraverser dul, DestAccessor dest, fftw_real norm)
    01705 {
    01706     int w = slr.x - sul.x;
    01707
    01708     // test for right memory layout (fftw expects a width*height fftw_real array)
    01709     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
    01710         fourierTransformRealImpl(sul, slr, dul, dest,
    01711                                  norm, FFTW_REDFT00, FFTW_REDFT00);
    01712     else
    01713         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01714                                  norm, FFTW_REDFT00, FFTW_REDFT00);
    01715 }
    01716
    01717 /********************************************************************/
    01718
    01719 template <class SrcTraverser, class SrcAccessor,
    01720           class DestTraverser, class DestAccessor>
    01721 inline void
    01722 fourierTransformRealOE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01723                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
    01724 {
    01725     fourierTransformRealOE(src.first, src.second, src.third,
    01726                                    dest.first, dest.second, norm);
    01727 }
    01728
    01729 template <class SrcTraverser, class SrcAccessor,
    01730           class DestTraverser, class DestAccessor>
    01731 inline void
    01732 fourierTransformRealOE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01733                                DestTraverser dul, DestAccessor dest, fftw_real norm)
    01734 {
    01735     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01736                                       norm, FFTW_RODFT00, FFTW_REDFT00);
    01737 }
    01738
    01739 template <class DestTraverser, class DestAccessor>
    01740 inline void
    01741 fourierTransformRealOE(
    01742          FFTWRealImage::const_traverser sul,
    01743          FFTWRealImage::const_traverser slr,
    01744          FFTWRealImage::Accessor src,
    01745          DestTraverser dul, DestAccessor dest, fftw_real norm)
    01746 {
    01747     int w = slr.x - sul.x;
    01748
    01749     // test for right memory layout (fftw expects a width*height fftw_real array)
    01750     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
    01751         fourierTransformRealImpl(sul, slr, dul, dest,
    01752                                  norm, FFTW_RODFT00, FFTW_REDFT00);
    01753     else
    01754         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01755                                  norm, FFTW_RODFT00, FFTW_REDFT00);
    01756 }
    01757
    01758 /********************************************************************/
    01759
    01760 template <class SrcTraverser, class SrcAccessor,
    01761           class DestTraverser, class DestAccessor>
    01762 inline void
    01763 fourierTransformRealEO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01764                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
    01765 {
    01766     fourierTransformRealEO(src.first, src.second, src.third,
    01767                                    dest.first, dest.second, norm);
    01768 }
    01769
    01770 template <class SrcTraverser, class SrcAccessor,
    01771           class DestTraverser, class DestAccessor>
    01772 inline void
    01773 fourierTransformRealEO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01774                                DestTraverser dul, DestAccessor dest, fftw_real norm)
    01775 {
    01776     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01777                                       norm, FFTW_REDFT00, FFTW_RODFT00);
    01778 }
    01779
    01780 template <class DestTraverser, class DestAccessor>
    01781 inline void
    01782 fourierTransformRealEO(
    01783          FFTWRealImage::const_traverser sul,
    01784          FFTWRealImage::const_traverser slr,
    01785          FFTWRealImage::Accessor src,
    01786          DestTraverser dul, DestAccessor dest, fftw_real norm)
    01787 {
    01788     int w = slr.x - sul.x;
    01789
    01790     // test for right memory layout (fftw expects a width*height fftw_real array)
    01791     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
    01792         fourierTransformRealImpl(sul, slr, dul, dest,
    01793                                  norm, FFTW_REDFT00, FFTW_RODFT00);
    01794     else
    01795         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01796                                  norm, FFTW_REDFT00, FFTW_RODFT00);
    01797 }
    01798
    01799 /********************************************************************/
    01800
    01801 template <class SrcTraverser, class SrcAccessor,
    01802           class DestTraverser, class DestAccessor>
    01803 inline void
    01804 fourierTransformRealOO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01805                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
    01806 {
    01807     fourierTransformRealOO(src.first, src.second, src.third,
    01808                                    dest.first, dest.second, norm);
    01809 }
    01810
    01811 template <class SrcTraverser, class SrcAccessor,
    01812           class DestTraverser, class DestAccessor>
    01813 inline void
    01814 fourierTransformRealOO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01815                                DestTraverser dul, DestAccessor dest, fftw_real norm)
    01816 {
    01817     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01818                                       norm, FFTW_RODFT00, FFTW_RODFT00);
    01819 }
    01820
    01821 template <class DestTraverser, class DestAccessor>
    01822 inline void
    01823 fourierTransformRealOO(
    01824          FFTWRealImage::const_traverser sul,
    01825          FFTWRealImage::const_traverser slr,
    01826          FFTWRealImage::Accessor src,
    01827          DestTraverser dul, DestAccessor dest, fftw_real norm)
    01828 {
    01829     int w = slr.x - sul.x;
    01830
    01831     // test for right memory layout (fftw expects a width*height fftw_real array)
    01832     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
    01833         fourierTransformRealImpl(sul, slr, dul, dest,
    01834                                  norm, FFTW_RODFT00, FFTW_RODFT00);
    01835     else
    01836         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01837                                  norm, FFTW_RODFT00, FFTW_RODFT00);
    01838 }
    01839
    01840 /*******************************************************************/
    01841
    01842 template <class SrcTraverser, class SrcAccessor,
    01843           class DestTraverser, class DestAccessor>
    01844 void
    01845 fourierTransformRealWorkImageImpl(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01846                                   DestTraverser dul, DestAccessor dest,
    01847                                   fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
    01848 {
    01849     FFTWRealImage workImage(slr - sul);
    01850     copyImage(srcIterRange(sul, slr, src), destImage(workImage));
    01851     FFTWRealImage const & cworkImage = workImage;
    01852     fourierTransformRealImpl(cworkImage.upperLeft(), cworkImage.lowerRight(),
    01853                              dul, dest, norm, kindx, kindy);
    01854 }
    01855
    01856
    01857 template <class DestTraverser, class DestAccessor>
    01858 void
    01859 fourierTransformRealImpl(
    01860          FFTWRealImage::const_traverser sul,
    01861          FFTWRealImage::const_traverser slr,
    01862          DestTraverser dul, DestAccessor dest,
    01863          fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
    01864 {
    01865     int w = slr.x - sul.x;
    01866     int h = slr.y - sul.y;
    01867     BasicImage<fftw_real> res(w, h);
    01868
    01869     fftw_plan plan = fftw_plan_r2r_2d(h, w,
    01870                          (fftw_real *)&(*sul), (fftw_real *)res.begin(),
    01871                          kindy, kindx, FFTW_ESTIMATE);
    01872     fftw_execute(plan);
    01873     fftw_destroy_plan(plan);
    01874
    01875     if(norm != 1.0)
    01876         transformImage(srcImageRange(res), destIter(dul, dest),
    01877                        std::bind1st(std::multiplies<fftw_real>(), 1.0 / norm));
    01878     else
    01879         copyImage(srcImageRange(res), destIter(dul, dest));
    01880 }
    01881
    01882
    01883 //@}
    01884
    01885 } // namespace vigra
    01886
    01887 #endif // VIGRA_FFTW3_HXX

© Ullrich Köthe (koethe@informatik.uni-hamburg.de) Cognitive Systems Group, University of Hamburg, Germany | html generated using doxygen and Python VIGRA 1.4.0 (21 Dec 2005)