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    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 1.5.0, Dec 07 2006 )                                    */
    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       */
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    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 "stdimage.hxx"
    00044 #include "copyimage.hxx"
    00045 #include "transformimage.hxx"
    00046 #include "combineimages.hxx"
    00047 #include "numerictraits.hxx"
    00048 #include "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 namespace detail {
    01137
    01138 template <class T>
    01139 void
    01140 fourierTransformImpl(FFTWComplexImage::const_traverser sul,
    01141                      FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
    01142                      FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest, T sign)
    01143 {
    01144     int w = slr.x - sul.x;
    01145     int h = slr.y - sul.y;
    01146
    01147     FFTWComplexImage sworkImage, dworkImage;
    01148
    01149     fftw_complex * srcPtr = (fftw_complex *)(&*sul);
    01150     fftw_complex * destPtr = (fftw_complex *)(&*dul);
    01151
    01152     // test for right memory layout (fftw expects a 2*width*height floats array)
    01153     if (&(*(sul + Diff2D(w, 0))) != &(*(sul + Diff2D(0, 1))))
    01154     {
    01155         sworkImage.resize(w, h);
    01156         copyImage(srcIterRange(sul, slr, src), destImage(sworkImage));
    01157         srcPtr = (fftw_complex *)(&(*sworkImage.upperLeft()));
    01158     }
    01159     if (&(*(dul + Diff2D(w, 0))) != &(*(dul + Diff2D(0, 1))))
    01160     {
    01161         dworkImage.resize(w, h);
    01162         destPtr = (fftw_complex *)(&(*dworkImage.upperLeft()));
    01163     }
    01164
    01165     fftw_plan plan = fftw_plan_dft_2d(h, w, srcPtr, destPtr, sign, FFTW_ESTIMATE );
    01166     fftw_execute(plan);
    01167     fftw_destroy_plan(plan);
    01168
    01169     if (&(*(dul + Diff2D(w, 0))) != &(*(dul + Diff2D(0, 1))))
    01170     {
    01171         copyImage(srcImageRange(dworkImage), destIter(dul, dest));
    01172     }
    01173 }
    01174
    01175 } // namespace detail
    01176
    01177 /********************************************************/
    01178 /*                                                      */
    01179 /*                    fourierTrasform                   */
    01180 /*                                                      */
    01181 /********************************************************/
    01182
    01183 /** \brief Compute forward and inverse Fourier transforms.
    01184
    01185     In the forward direction, the input image may be scalar or complex, and the output image
    01186     is always complex. In the inverse direction, both input and output must be complex.
    01187
    01188     <b> Declarations:</b>
    01189
    01190     pass arguments explicitly:
    01191     \code
    01192     namespace vigra {
    01193         template <class SrcImageIterator, class SrcAccessor>
    01194         void fourierTransform(SrcImageIterator srcUpperLeft,
    01195                               SrcImageIterator srcLowerRight, SrcAccessor src,
    01196                               FFTWComplexImage::traverser destUpperLeft, FFTWComplexImage::Accessor dest);
    01197
    01198         void
    01199         fourierTransformInverse(FFTWComplexImage::const_traverser sul,
    01200                                 FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
    01201                                 FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
    01202     }
    01203     \endcode
    01204
    01205     use argument objects in conjunction with \ref ArgumentObjectFactories:
    01206     \code
    01207     namespace vigra {
    01208         template <class SrcImageIterator, class SrcAccessor>
    01209         void fourierTransform(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01210                               pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest);
    01211
    01212         void
    01213         fourierTransformInverse(triple<FFTWComplexImage::const_traverser,
    01214                                        FFTWComplexImage::const_traverser, FFTWComplexImage::ConstAccessor> src,
    01215                                 pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest);
    01216     }
    01217     \endcode
    01218
    01219     <b> Usage:</b>
    01220
    01221     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>"<br>
    01222     Namespace: vigra
    01223
    01224     \code
    01225     // compute complex Fourier transform of a real image
    01226     vigra::DImage src(w, h);
    01227     vigra::FFTWComplexImage fourier(w, h);
    01228
    01229     fourierTransform(srcImageRange(src), destImage(fourier));
    01230
    01231     // compute inverse Fourier transform
    01232     // note that both source and destination image must be of type vigra::FFTWComplexImage
    01233     vigra::FFTWComplexImage inverseFourier(w, h);
    01234
    01235     fourierTransform(srcImageRange(fourier), destImage(inverseFourier));
    01236     \endcode
    01237 */
    01238 inline void
    01239 fourierTransform(FFTWComplexImage::const_traverser sul,
    01240                  FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
    01241                  FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
    01242 {
    01243     detail::fourierTransformImpl(sul, slr, src, dul, dest, FFTW_FORWARD);
    01244 }
    01245
    01246 template <class SrcImageIterator, class SrcAccessor>
    01247 void fourierTransform(SrcImageIterator srcUpperLeft,
    01248                       SrcImageIterator srcLowerRight, SrcAccessor sa,
    01249                       FFTWComplexImage::traverser destUpperLeft, FFTWComplexImage::Accessor da)
    01250 {
    01251     // copy real input images into a complex one...
    01252     int w= srcLowerRight.x - srcUpperLeft.x;
    01253     int h= srcLowerRight.y - srcUpperLeft.y;
    01254
    01255     FFTWComplexImage workImage(w, h);
    01256     copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
    01257               destImage(workImage, FFTWWriteRealAccessor()));
    01258
    01259     // ...and call the complex -> complex version of the algorithm
    01260     FFTWComplexImage const & cworkImage = workImage;
    01261     fourierTransform(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
    01262                      destUpperLeft, da);
    01263 }
    01264
    01265 template <class SrcImageIterator, class SrcAccessor>
    01266 inline
    01267 void fourierTransform(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01268                       pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest)
    01269 {
    01270     fourierTransform(src.first, src.second, src.third, dest.first, dest.second);
    01271 }
    01272
    01273 inline void
    01274 fourierTransformInverse(FFTWComplexImage::const_traverser sul,
    01275                         FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
    01276                         FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
    01277 {
    01278     detail::fourierTransformImpl(sul, slr, src, dul, dest, FFTW_BACKWARD);
    01279 }
    01280
    01281 inline void
    01282 fourierTransformInverse(triple<FFTWComplexImage::const_traverser,
    01283                                FFTWComplexImage::const_traverser, FFTWComplexImage::ConstAccessor> src,
    01284                         pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest)
    01285 {
    01286     fourierTransformInverse(src.first, src.second, src.third, dest.first, dest.second);
    01287 }
    01288
    01289 /********************************************************/
    01290 /*                                                      */
    01291 /*                   applyFourierFilter                 */
    01292 /*                                                      */
    01293 /********************************************************/
    01294
    01295 /** \brief Apply a filter (defined in the frequency domain) to an image.
    01296
    01297     After transferring the image into the frequency domain, it is
    01298     multiplied pixel-wise with the filter and transformed back. The
    01299     result is put into the given destination image which must have the right size.
    01300     The result will be normalized to compensate for the two FFTs.
    01301
    01302     If the destination image is scalar, only the real part of the result image is
    01303     retained. In this case, you are responsible for choosing a filter image
    01304     which ensures a zero imaginary part of the result (e.g. use a real, even symmetric
    01305     filter image, or a purely imaginary, odd symmetric on).
    01306
    01307     The DC entry of the filter must be in the upper left, which is the
    01308     position where FFTW expects it (see \ref moveDCToUpperLeft()).
    01309
    01310     <b> Declarations:</b>
    01311
    01312     pass arguments explicitly:
    01313     \code
    01314     namespace vigra {
    01315         template <class SrcImageIterator, class SrcAccessor,
    01316                   class FilterImageIterator, class FilterAccessor,
    01317                   class DestImageIterator, class DestAccessor>
    01318         void applyFourierFilter(SrcImageIterator srcUpperLeft,
    01319                                 SrcImageIterator srcLowerRight, SrcAccessor sa,
    01320                                 FilterImageIterator filterUpperLeft, FilterAccessor fa,
    01321                                 DestImageIterator destUpperLeft, DestAccessor da);
    01322     }
    01323     \endcode
    01324
    01325     use argument objects in conjunction with \ref ArgumentObjectFactories:
    01326     \code
    01327     namespace vigra {
    01328         template <class SrcImageIterator, class SrcAccessor,
    01329                 class FilterImageIterator, class FilterAccessor,
    01330                 class DestImageIterator, class DestAccessor>
    01331         void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01332                                 pair<FilterImageIterator, FilterAccessor> filter,
    01333                                 pair<DestImageIterator, DestAccessor> dest);
    01334     }
    01335     \endcode
    01336
    01337     <b> Usage:</b>
    01338
    01339     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>"<br>
    01340     Namespace: vigra
    01341
    01342     \code
    01343     // create a Gaussian filter in Fourier space
    01344     vigra::FImage gaussFilter(w, h), filter(w, h);
    01345     for(int y=0; y<h; ++y)
    01346         for(int x=0; x<w; ++x)
    01347         {
    01348             xx = float(x - w / 2) / w;
    01349             yy = float(y - h / 2) / h;
    01350
    01351             gaussFilter(x,y) = std::exp(-(xx*xx + yy*yy) / 2.0 * scale);
    01352         }
    01353
    01354     // applyFourierFilter() expects the filter's DC in the upper left
    01355     moveDCToUpperLeft(srcImageRange(gaussFilter), destImage(filter));
    01356
    01357     vigra::FFTWComplexImage result(w, h);
    01358
    01359     vigra::applyFourierFilter(srcImageRange(image), srcImage(filter), result);
    01360     \endcode
    01361
    01362     For inspection of the result, \ref FFTWMagnitudeAccessor might be
    01363     useful. If you want to apply the same filter repeatedly, it may be more
    01364     efficient to use the FFTW functions directly with FFTW plans optimized
    01365     for good performance.
    01366 */
    01367 template <class SrcImageIterator, class SrcAccessor,
    01368           class FilterImageIterator, class FilterAccessor,
    01369           class DestImageIterator, class DestAccessor>
    01370 void applyFourierFilter(SrcImageIterator srcUpperLeft,
    01371                         SrcImageIterator srcLowerRight, SrcAccessor sa,
    01372                         FilterImageIterator filterUpperLeft, FilterAccessor fa,
    01373                         DestImageIterator destUpperLeft, DestAccessor da)
    01374 {
    01375     // copy real input images into a complex one...
    01376     int w= srcLowerRight.x - srcUpperLeft.x;
    01377     int h= srcLowerRight.y - srcUpperLeft.y;
    01378
    01379     FFTWComplexImage workImage(w, h);
    01380     copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
    01381               destImage(workImage, FFTWWriteRealAccessor()));
    01382
    01383     // ...and call the impl
    01384     FFTWComplexImage const & cworkImage = workImage;
    01385     applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
    01386                            filterUpperLeft, fa,
    01387                            destUpperLeft, da);
    01388 }
    01389
    01390 template <class FilterImageIterator, class FilterAccessor,
    01391           class DestImageIterator, class DestAccessor>
    01392 inline
    01393 void applyFourierFilter(
    01394     FFTWComplexImage::const_traverser srcUpperLeft,
    01395     FFTWComplexImage::const_traverser srcLowerRight,
    01396     FFTWComplexImage::ConstAccessor sa,
    01397     FilterImageIterator filterUpperLeft, FilterAccessor fa,
    01398     DestImageIterator destUpperLeft, DestAccessor da)
    01399 {
    01400     int w = srcLowerRight.x - srcUpperLeft.x;
    01401     int h = srcLowerRight.y - srcUpperLeft.y;
    01402
    01403     // test for right memory layout (fftw expects a 2*width*height floats array)
    01404     if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
    01405         applyFourierFilterImpl(srcUpperLeft, srcLowerRight, sa,
    01406                                filterUpperLeft, fa,
    01407                                destUpperLeft, da);
    01408     else
    01409     {
    01410         FFTWComplexImage workImage(w, h);
    01411         copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
    01412                   destImage(workImage));
    01413
    01414         FFTWComplexImage const & cworkImage = workImage;
    01415         applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
    01416                                filterUpperLeft, fa,
    01417                                destUpperLeft, da);
    01418     }
    01419 }
    01420
    01421 template <class SrcImageIterator, class SrcAccessor,
    01422           class FilterImageIterator, class FilterAccessor,
    01423           class DestImageIterator, class DestAccessor>
    01424 inline
    01425 void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01426                         pair<FilterImageIterator, FilterAccessor> filter,
    01427                         pair<DestImageIterator, DestAccessor> dest)
    01428 {
    01429     applyFourierFilter(src.first, src.second, src.third,
    01430                        filter.first, filter.second,
    01431                        dest.first, dest.second);
    01432 }
    01433
    01434 template <class FilterImageIterator, class FilterAccessor,
    01435           class DestImageIterator, class DestAccessor>
    01436 void applyFourierFilterImpl(
    01437     FFTWComplexImage::const_traverser srcUpperLeft,
    01438     FFTWComplexImage::const_traverser srcLowerRight,
    01439     FFTWComplexImage::ConstAccessor sa,
    01440     FilterImageIterator filterUpperLeft, FilterAccessor fa,
    01441     DestImageIterator destUpperLeft, DestAccessor da)
    01442 {
    01443     int w = srcLowerRight.x - srcUpperLeft.x;
    01444     int h = srcLowerRight.y - srcUpperLeft.y;
    01445
    01446     FFTWComplexImage complexResultImg(srcLowerRight - srcUpperLeft);
    01447
    01448     // FFT from srcImage to complexResultImg
    01449     fftw_plan forwardPlan=
    01450         fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
    01451                                (fftw_complex *)complexResultImg.begin(),
    01452                                FFTW_FORWARD, FFTW_ESTIMATE );
    01453     fftw_execute(forwardPlan);
    01454     fftw_destroy_plan(forwardPlan);
    01455
    01456     // convolve in freq. domain (in complexResultImg)
    01457     combineTwoImages(srcImageRange(complexResultImg), srcIter(filterUpperLeft, fa),
    01458                      destImage(complexResultImg), std::multiplies<FFTWComplex>());
    01459
    01460     // FFT back into spatial domain (inplace in complexResultImg)
    01461     fftw_plan backwardPlan=
    01462         fftw_plan_dft_2d(h, w, (fftw_complex *)complexResultImg.begin(),
    01463                                (fftw_complex *)complexResultImg.begin(),
    01464                                FFTW_BACKWARD, FFTW_ESTIMATE);
    01465     fftw_execute(backwardPlan);
    01466     fftw_destroy_plan(backwardPlan);
    01467
    01468     typedef typename
    01469         NumericTraits<typename DestAccessor::value_type>::isScalar
    01470         isScalarResult;
    01471
    01472     // normalization (after FFTs), maybe stripping imaginary part
    01473     applyFourierFilterImplNormalization(complexResultImg, destUpperLeft, da,
    01474                                         isScalarResult());
    01475 }
    01476
    01477 template <class DestImageIterator, class DestAccessor>
    01478 void applyFourierFilterImplNormalization(FFTWComplexImage const &srcImage,
    01479                                          DestImageIterator destUpperLeft,
    01480                                          DestAccessor da,
    01481                                          VigraFalseType)
    01482 {
    01483     double normFactor= 1.0/(srcImage.width() * srcImage.height());
    01484
    01485     for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
    01486     {
    01487         DestImageIterator dIt= destUpperLeft;
    01488         for(int x= 0; x< srcImage.width(); x++, dIt.x++)
    01489         {
    01490             da.setComponent(srcImage(x, y).re()*normFactor, dIt, 0);
    01491             da.setComponent(srcImage(x, y).im()*normFactor, dIt, 1);
    01492         }
    01493     }
    01494 }
    01495
    01496 inline
    01497 void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
    01498         FFTWComplexImage::traverser destUpperLeft,
    01499         FFTWComplexImage::Accessor da,
    01500         VigraFalseType)
    01501 {
    01502     transformImage(srcImageRange(srcImage), destIter(destUpperLeft, da),
    01503                    linearIntensityTransform<FFTWComplex>(1.0/(srcImage.width() * srcImage.height())));
    01504 }
    01505
    01506 template <class DestImageIterator, class DestAccessor>
    01507 void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
    01508                                          DestImageIterator destUpperLeft,
    01509                                          DestAccessor da,
    01510                                          VigraTrueType)
    01511 {
    01512     double normFactor= 1.0/(srcImage.width() * srcImage.height());
    01513
    01514     for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
    01515     {
    01516         DestImageIterator dIt= destUpperLeft;
    01517         for(int x= 0; x< srcImage.width(); x++, dIt.x++)
    01518             da.set(srcImage(x, y).re()*normFactor, dIt);
    01519     }
    01520 }
    01521
    01522 /**********************************************************/
    01523 /*                                                        */
    01524 /*                applyFourierFilterFamily                */
    01525 /*                                                        */
    01526 /**********************************************************/
    01527
    01528 /** \brief Apply an array of filters (defined in the frequency domain) to an image.
    01529
    01530     This provides the same functionality as \ref applyFourierFilter(),
    01531     but applying several filters at once allows to avoid
    01532     repeated Fourier transforms of the source image.
    01533
    01534     Filters and result images must be stored in \ref vigra::ImageArray data
    01535     structures. In contrast to \ref applyFourierFilter(), this function adjusts
    01536     the size of the result images and the the length of the array.
    01537
    01538     <b> Declarations:</b>
    01539
    01540     pass arguments explicitly:
    01541     \code
    01542     namespace vigra {
    01543         template <class SrcImageIterator, class SrcAccessor, class FilterType>
    01544         void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
    01545                                       SrcImageIterator srcLowerRight, SrcAccessor sa,
    01546                                       const ImageArray<FilterType> &filters,
    01547                                       ImageArray<FFTWComplexImage> &results)
    01548     }
    01549     \endcode
    01550
    01551     use argument objects in conjunction with \ref ArgumentObjectFactories:
    01552     \code
    01553     namespace vigra {
    01554         template <class SrcImageIterator, class SrcAccessor, class FilterType>
    01555         inline
    01556         void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01557                                       const ImageArray<FilterType> &filters,
    01558                                       ImageArray<FFTWComplexImage> &results)
    01559     }
    01560     \endcode
    01561
    01562     <b> Usage:</b>
    01563
    01564     <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>"<br>
    01565     Namespace: vigra
    01566
    01567     \code
    01568     // assuming the presence of a real-valued image named "image" to
    01569     // be filtered in this example
    01570
    01571     vigra::ImageArray<vigra::FImage> filters(16, image.size());
    01572
    01573     for (int i=0; i<filters.size(); i++)
    01574          // create some meaningful filters here
    01575          createMyFilterOfScale(i, destImage(filters[i]));
    01576
    01577     vigra::ImageArray<vigra::FFTWComplexImage> results();
    01578
    01579     vigra::applyFourierFilterFamily(srcImageRange(image), filters, results);
    01580     \endcode
    01581 */
    01582 template <class SrcImageIterator, class SrcAccessor,
    01583           class FilterType, class DestImage>
    01584 inline
    01585 void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
    01586                               const ImageArray<FilterType> &filters,
    01587                               ImageArray<DestImage> &results)
    01588 {
    01589     applyFourierFilterFamily(src.first, src.second, src.third,
    01590                              filters, results);
    01591 }
    01592
    01593 template <class SrcImageIterator, class SrcAccessor,
    01594           class FilterType, class DestImage>
    01595 void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
    01596                               SrcImageIterator srcLowerRight, SrcAccessor sa,
    01597                               const ImageArray<FilterType> &filters,
    01598                               ImageArray<DestImage> &results)
    01599 {
    01600     int w= srcLowerRight.x - srcUpperLeft.x;
    01601     int h= srcLowerRight.y - srcUpperLeft.y;
    01602
    01603     FFTWComplexImage workImage(w, h);
    01604     copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
    01605               destImage(workImage, FFTWWriteRealAccessor()));
    01606
    01607     FFTWComplexImage const & cworkImage = workImage;
    01608     applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
    01609                                  filters, results);
    01610 }
    01611
    01612 template <class FilterType, class DestImage>
    01613 inline
    01614 void applyFourierFilterFamily(
    01615     FFTWComplexImage::const_traverser srcUpperLeft,
    01616     FFTWComplexImage::const_traverser srcLowerRight,
    01617     FFTWComplexImage::ConstAccessor sa,
    01618     const ImageArray<FilterType> &filters,
    01619     ImageArray<DestImage> &results)
    01620 {
    01621     int w= srcLowerRight.x - srcUpperLeft.x;
    01622
    01623     // test for right memory layout (fftw expects a 2*width*height floats array)
    01624     if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
    01625         applyFourierFilterFamilyImpl(srcUpperLeft, srcLowerRight, sa,
    01626                                      filters, results);
    01627     else
    01628     {
    01629         int h = srcLowerRight.y - srcUpperLeft.y;
    01630         FFTWComplexImage workImage(w, h);
    01631         copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
    01632                   destImage(workImage));
    01633
    01634         FFTWComplexImage const & cworkImage = workImage;
    01635         applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
    01636                                      filters, results);
    01637     }
    01638 }
    01639
    01640 template <class FilterType, class DestImage>
    01641 void applyFourierFilterFamilyImpl(
    01642     FFTWComplexImage::const_traverser srcUpperLeft,
    01643     FFTWComplexImage::const_traverser srcLowerRight,
    01644     FFTWComplexImage::ConstAccessor sa,
    01645     const ImageArray<FilterType> &filters,
    01646     ImageArray<DestImage> &results)
    01647 {
    01648     // make sure the filter images have the right dimensions
    01649     vigra_precondition((srcLowerRight - srcUpperLeft) == filters.imageSize(),
    01650                        "applyFourierFilterFamily called with src image size != filters.imageSize()!");
    01651
    01652     // make sure the result image array has the right dimensions
    01653     results.resize(filters.size());
    01654     results.resizeImages(filters.imageSize());
    01655
    01656     // FFT from srcImage to freqImage
    01657     int w= srcLowerRight.x - srcUpperLeft.x;
    01658     int h= srcLowerRight.y - srcUpperLeft.y;
    01659
    01660     FFTWComplexImage freqImage(w, h);
    01661     FFTWComplexImage result(w, h);
    01662
    01663     fftw_plan forwardPlan=
    01664         fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
    01665                                (fftw_complex *)freqImage.begin(),
    01666                                FFTW_FORWARD, FFTW_ESTIMATE );
    01667     fftw_execute(forwardPlan);
    01668     fftw_destroy_plan(forwardPlan);
    01669
    01670     fftw_plan backwardPlan=
    01671         fftw_plan_dft_2d(h, w, (fftw_complex *)result.begin(),
    01672                                (fftw_complex *)result.begin(),
    01673                                FFTW_BACKWARD, FFTW_ESTIMATE );
    01674     typedef typename
    01675         NumericTraits<typename DestImage::Accessor::value_type>::isScalar
    01676         isScalarResult;
    01677
    01678     // convolve with filters in freq. domain
    01679     for (unsigned int i= 0;  i < filters.size(); i++)
    01680     {
    01681         combineTwoImages(srcImageRange(freqImage), srcImage(filters[i]),
    01682                          destImage(result), std::multiplies<FFTWComplex>());
    01683
    01684         // FFT back into spatial domain (inplace in destImage)
    01685         fftw_execute(backwardPlan);
    01686
    01687         // normalization (after FFTs), maybe stripping imaginary part
    01688         applyFourierFilterImplNormalization(result,
    01689                                             results[i].upperLeft(), results[i].accessor(),
    01690                                             isScalarResult());
    01691     }
    01692     fftw_destroy_plan(backwardPlan);
    01693 }
    01694
    01695 /********************************************************/
    01696 /*                                                      */
    01697 /*                fourierTransformReal                  */
    01698 /*                                                      */
    01699 /********************************************************/
    01700
    01701 /** \brief Real Fourier transforms for even and odd boundary conditions
    01702            (aka. cosine and sine transforms).
    01703
    01704
    01705     If the image is real and has even symmetry, its Fourier transform
    01706     is also real and has even symmetry. The Fourier transform of a real image with odd
    01707     symmetry is imaginary and has odd symmetry. In either case, only about a quarter
    01708     of the pixels need to be stored because the rest can be calculated from the symmetry
    01709     properties. This is especially useful, if the original image is implicitly assumed
    01710     to have reflective or anti-reflective boundary conditions. Then the "negative"
    01711     pixel locations are defined as
    01712
    01713     \code
    01714     even (reflective boundary conditions):      f[-x] = f[x]     (x = 1,...,N-1)
    01715     odd (anti-reflective boundary conditions):  f[-1] = 0
    01716                                                 f[-x] = -f[x-2]  (x = 2,...,N-1)
    01717     \endcode
    01718
    01719     end similar at the other boundary (see the FFTW documentation for details).
    01720     This has the advantage that more efficient Fourier transforms that use only
    01721     real numbers can be implemented. These are also known as cosine and sine transforms
    01722     respectively.
    01723
    01724     If you use the odd transform it is important to note that in the Fourier domain,
    01725     the DC component is always zero and is therefore dropped from the data structure.
    01726     This means that index 0 in an odd symmetric Fourier domain image refers to
    01727     the <i>first</i> harmonic. This is especially important if an image is first
    01728     cosine transformed (even symmetry), then in the Fourier domain multiplied
    01729     with an odd symmetric filter (e.g. a first derivative) and finally transformed
    01730     back to the spatial domain with a sine transform (odd symmetric). For this to work
    01731     properly the image must be shifted left or up by one pixel (depending on whether
    01732     the x- or y-axis is odd symmetric) before the inverse transform can be applied.
    01733     (see example below).
    01734
    01735     The real Fourier transform functions are named <tt>fourierTransformReal??</tt>
    01736     where the questions marks stand for either <tt>E</tt> or <tt>O</tt> indicating
    01737     whether the x- and y-axis is to be transformed using even or odd symmetry.
    01738     The same functions can be used for both the forward and inverse transforms,
    01739     only the normalization changes. For signal processing, the following
    01740     normalization factors are most appropriate:
    01741
    01742     \code
    01743                           forward             inverse
    01744     ------------------------------------------------------------
    01745     X even, Y even           1.0         4.0 * (w-1) * (h-1)
    01746     X even, Y odd           -1.0        -4.0 * (w-1) * (h+1)
    01747     X odd,  Y even          -1.0        -4.0 * (w+1) * (h-1)
    01748     X odd,  Y odd            1.0         4.0 * (w+1) * (h+1)
    01749     \endcode
    01750
    01751     where <tt>w</tt> and <tt>h</tt> denote the image width and height.
    01752
    01753     <b> Declarations:</b>
    01754
    01755     pass arguments explicitly:
    01756     \code
    01757     namespace vigra {
    01758         template <class SrcTraverser, class SrcAccessor,
    01759                   class DestTraverser, class DestAccessor>
    01760         void
    01761         fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01762                                DestTraverser dul, DestAccessor dest, fftw_real norm);
    01763
    01764         fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
    01765     }
    01766     \endcode
    01767
    01768
    01769     use argument objects in conjunction with \ref ArgumentObjectFactories:
    01770     \code
    01771     namespace vigra {
    01772         template <class SrcTraverser, class SrcAccessor,
    01773                   class DestTraverser, class DestAccessor>
    01774         void
    01775         fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01776                                pair<DestTraverser, DestAccessor> dest, fftw_real norm);
    01777
    01778         fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
    01779     }
    01780     \endcode
    01781
    01782     <b> Usage:</b>
    01783
    01784         <b>\#include</b> "<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>"<br>
    01785         Namespace: vigra
    01786
    01787     \code
    01788     vigra::FImage spatial(width,height), fourier(width,height);
    01789     ... // fill image with data
    01790
    01791     // forward cosine transform == reflective boundary conditions
    01792     fourierTransformRealEE(srcImageRange(spatial), destImage(fourier), (fftw_real)1.0);
    01793
    01794     // multiply with a first derivative of Gaussian in x-direction
    01795     for(int y = 0; y < height; ++y)
    01796     {
    01797         for(int x = 1; x < width; ++x)
    01798         {
    01799             double dx = x * M_PI / (width - 1);
    01800             double dy = y * M_PI / (height - 1);
    01801             fourier(x-1, y) = fourier(x, y) * dx * std::exp(-(dx*dx + dy*dy) * scale*scale / 2.0);
    01802         }
    01803         fourier(width-1, y) = 0.0;
    01804     }
    01805
    01806     // inverse transform -- odd symmetry in x-direction, even in y,
    01807     //                      due to symmetry of the filter
    01808     fourierTransformRealOE(srcImageRange(fourier), destImage(spatial),
    01809                            (fftw_real)-4.0 * (width+1) * (height-1));
    01810     \endcode
    01811 */
    01812 template <class SrcTraverser, class SrcAccessor,
    01813           class DestTraverser, class DestAccessor>
    01814 inline void
    01815 fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01816                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
    01817 {
    01818     fourierTransformRealEE(src.first, src.second, src.third,
    01819                                    dest.first, dest.second, norm);
    01820 }
    01821
    01822 template <class SrcTraverser, class SrcAccessor,
    01823           class DestTraverser, class DestAccessor>
    01824 inline void
    01825 fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01826                                DestTraverser dul, DestAccessor dest, fftw_real norm)
    01827 {
    01828     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01829                                       norm, FFTW_REDFT00, FFTW_REDFT00);
    01830 }
    01831
    01832 template <class DestTraverser, class DestAccessor>
    01833 inline void
    01834 fourierTransformRealEE(
    01835          FFTWRealImage::const_traverser sul,
    01836          FFTWRealImage::const_traverser slr,
    01837          FFTWRealImage::Accessor src,
    01838          DestTraverser dul, DestAccessor dest, fftw_real norm)
    01839 {
    01840     int w = slr.x - sul.x;
    01841
    01842     // test for right memory layout (fftw expects a width*height fftw_real array)
    01843     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
    01844         fourierTransformRealImpl(sul, slr, dul, dest,
    01845                                  norm, FFTW_REDFT00, FFTW_REDFT00);
    01846     else
    01847         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01848                                  norm, FFTW_REDFT00, FFTW_REDFT00);
    01849 }
    01850
    01851 /********************************************************************/
    01852
    01853 template <class SrcTraverser, class SrcAccessor,
    01854           class DestTraverser, class DestAccessor>
    01855 inline void
    01856 fourierTransformRealOE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01857                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
    01858 {
    01859     fourierTransformRealOE(src.first, src.second, src.third,
    01860                                    dest.first, dest.second, norm);
    01861 }
    01862
    01863 template <class SrcTraverser, class SrcAccessor,
    01864           class DestTraverser, class DestAccessor>
    01865 inline void
    01866 fourierTransformRealOE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01867                                DestTraverser dul, DestAccessor dest, fftw_real norm)
    01868 {
    01869     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01870                                       norm, FFTW_RODFT00, FFTW_REDFT00);
    01871 }
    01872
    01873 template <class DestTraverser, class DestAccessor>
    01874 inline void
    01875 fourierTransformRealOE(
    01876          FFTWRealImage::const_traverser sul,
    01877          FFTWRealImage::const_traverser slr,
    01878          FFTWRealImage::Accessor src,
    01879          DestTraverser dul, DestAccessor dest, fftw_real norm)
    01880 {
    01881     int w = slr.x - sul.x;
    01882
    01883     // test for right memory layout (fftw expects a width*height fftw_real array)
    01884     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
    01885         fourierTransformRealImpl(sul, slr, dul, dest,
    01886                                  norm, FFTW_RODFT00, FFTW_REDFT00);
    01887     else
    01888         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01889                                  norm, FFTW_RODFT00, FFTW_REDFT00);
    01890 }
    01891
    01892 /********************************************************************/
    01893
    01894 template <class SrcTraverser, class SrcAccessor,
    01895           class DestTraverser, class DestAccessor>
    01896 inline void
    01897 fourierTransformRealEO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01898                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
    01899 {
    01900     fourierTransformRealEO(src.first, src.second, src.third,
    01901                                    dest.first, dest.second, norm);
    01902 }
    01903
    01904 template <class SrcTraverser, class SrcAccessor,
    01905           class DestTraverser, class DestAccessor>
    01906 inline void
    01907 fourierTransformRealEO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01908                                DestTraverser dul, DestAccessor dest, fftw_real norm)
    01909 {
    01910     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01911                                       norm, FFTW_REDFT00, FFTW_RODFT00);
    01912 }
    01913
    01914 template <class DestTraverser, class DestAccessor>
    01915 inline void
    01916 fourierTransformRealEO(
    01917          FFTWRealImage::const_traverser sul,
    01918          FFTWRealImage::const_traverser slr,
    01919          FFTWRealImage::Accessor src,
    01920          DestTraverser dul, DestAccessor dest, fftw_real norm)
    01921 {
    01922     int w = slr.x - sul.x;
    01923
    01924     // test for right memory layout (fftw expects a width*height fftw_real array)
    01925     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
    01926         fourierTransformRealImpl(sul, slr, dul, dest,
    01927                                  norm, FFTW_REDFT00, FFTW_RODFT00);
    01928     else
    01929         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01930                                  norm, FFTW_REDFT00, FFTW_RODFT00);
    01931 }
    01932
    01933 /********************************************************************/
    01934
    01935 template <class SrcTraverser, class SrcAccessor,
    01936           class DestTraverser, class DestAccessor>
    01937 inline void
    01938 fourierTransformRealOO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
    01939                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
    01940 {
    01941     fourierTransformRealOO(src.first, src.second, src.third,
    01942                                    dest.first, dest.second, norm);
    01943 }
    01944
    01945 template <class SrcTraverser, class SrcAccessor,
    01946           class DestTraverser, class DestAccessor>
    01947 inline void
    01948 fourierTransformRealOO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01949                                DestTraverser dul, DestAccessor dest, fftw_real norm)
    01950 {
    01951     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01952                                       norm, FFTW_RODFT00, FFTW_RODFT00);
    01953 }
    01954
    01955 template <class DestTraverser, class DestAccessor>
    01956 inline void
    01957 fourierTransformRealOO(
    01958          FFTWRealImage::const_traverser sul,
    01959          FFTWRealImage::const_traverser slr,
    01960          FFTWRealImage::Accessor src,
    01961          DestTraverser dul, DestAccessor dest, fftw_real norm)
    01962 {
    01963     int w = slr.x - sul.x;
    01964
    01965     // test for right memory layout (fftw expects a width*height fftw_real array)
    01966     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
    01967         fourierTransformRealImpl(sul, slr, dul, dest,
    01968                                  norm, FFTW_RODFT00, FFTW_RODFT00);
    01969     else
    01970         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
    01971                                  norm, FFTW_RODFT00, FFTW_RODFT00);
    01972 }
    01973
    01974 /*******************************************************************/
    01975
    01976 template <class SrcTraverser, class SrcAccessor,
    01977           class DestTraverser, class DestAccessor>
    01978 void
    01979 fourierTransformRealWorkImageImpl(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
    01980                                   DestTraverser dul, DestAccessor dest,
    01981                                   fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
    01982 {
    01983     FFTWRealImage workImage(slr - sul);
    01984     copyImage(srcIterRange(sul, slr, src), destImage(workImage));
    01985     FFTWRealImage const & cworkImage = workImage;
    01986     fourierTransformRealImpl(cworkImage.upperLeft(), cworkImage.lowerRight(),
    01987                              dul, dest, norm, kindx, kindy);
    01988 }
    01989
    01990
    01991 template <class DestTraverser, class DestAccessor>
    01992 void
    01993 fourierTransformRealImpl(
    01994          FFTWRealImage::const_traverser sul,
    01995          FFTWRealImage::const_traverser slr,
    01996          DestTraverser dul, DestAccessor dest,
    01997          fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
    01998 {
    01999     int w = slr.x - sul.x;
    02000     int h = slr.y - sul.y;
    02001     BasicImage<fftw_real> res(w, h);
    02002
    02003     fftw_plan plan = fftw_plan_r2r_2d(h, w,
    02004                          (fftw_real *)&(*sul), (fftw_real *)res.begin(),
    02005                          kindy, kindx, FFTW_ESTIMATE);
    02006     fftw_execute(plan);
    02007     fftw_destroy_plan(plan);
    02008
    02009     if(norm != 1.0)
    02010         transformImage(srcImageRange(res), destIter(dul, dest),
    02011                        std::bind1st(std::multiplies<fftw_real>(), 1.0 / norm));
    02012     else
    02013         copyImage(srcImageRange(res), destIter(dul, dest));
    02014 }
    02015
    02016
    02017 //@}
    02018
    02019 } // namespace vigra
    02020
    02021 #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 1.5.0 (7 Dec 2006)