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vigra/fftw3.hxx

00001 /************************************************************************/
00002 /*                                                                      */
00003 /*               Copyright 1998-2004 by Ullrich Koethe                  */
00004 /*       Cognitive Systems Group, University of Hamburg, Germany        */
00005 /*                                                                      */
00006 /*    This file is part of the VIGRA computer vision library.           */
00007 /*    ( Version 1.6.0, Aug 13 2008 )                                    */
00008 /*    The VIGRA Website is                                              */
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00010 /*    Please direct questions, bug reports, and contributions to        */
00011 /*        ullrich.koethe@iwr.uni-heidelberg.de    or                    */
00012 /*        vigra@informatik.uni-hamburg.de                               */
00013 /*                                                                      */
00014 /*    Permission is hereby granted, free of charge, to any person       */
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00021 /*    conditions:                                                       */
00022 /*                                                                      */
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00025 /*    Software.                                                         */
00026 /*                                                                      */
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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 version 3. The interface
00870     to the old FFTW version 2 (file "vigra/fftw.hxx") is deprecated.
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 doxygen_overloaded_function(template <...> void moveDCToCenter)
01012 
01013 template <class SrcImageIterator, class SrcAccessor,
01014           class DestImageIterator, class DestAccessor>
01015 void moveDCToCenter(SrcImageIterator src_upperleft,
01016                                SrcImageIterator src_lowerright, SrcAccessor sa,
01017                                DestImageIterator dest_upperleft, DestAccessor da)
01018 {
01019     int w= src_lowerright.x - src_upperleft.x;
01020     int h= src_lowerright.y - src_upperleft.y;
01021     int w1 = w/2;
01022     int h1 = h/2;
01023     int w2 = (w+1)/2;
01024     int h2 = (h+1)/2;
01025 
01026     // 2. Quadrant  zum 4.
01027     copyImage(srcIterRange(src_upperleft,
01028                            src_upperleft  + Diff2D(w2, h2), sa),
01029               destIter    (dest_upperleft + Diff2D(w1, h1), da));
01030 
01031     // 4. Quadrant zum 2.
01032     copyImage(srcIterRange(src_upperleft + Diff2D(w2, h2),
01033                            src_lowerright, sa),
01034               destIter    (dest_upperleft, da));
01035 
01036     // 1. Quadrant zum 3.
01037     copyImage(srcIterRange(src_upperleft  + Diff2D(w2, 0),
01038                            src_upperleft  + Diff2D(w,  h2), sa),
01039               destIter    (dest_upperleft + Diff2D(0,  h1), da));
01040 
01041     // 3. Quadrant zum 1.
01042     copyImage(srcIterRange(src_upperleft  + Diff2D(0,  h2),
01043                            src_upperleft  + Diff2D(w2, h), sa),
01044               destIter    (dest_upperleft + Diff2D(w1, 0), da));
01045 }
01046 
01047 template <class SrcImageIterator, class SrcAccessor,
01048           class DestImageIterator, class DestAccessor>
01049 inline void moveDCToCenter(
01050     triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
01051     pair<DestImageIterator, DestAccessor> dest)
01052 {
01053     moveDCToCenter(src.first, src.second, src.third,
01054                           dest.first, dest.second);
01055 }
01056 
01057 /********************************************************/
01058 /*                                                      */
01059 /*                   moveDCToUpperLeft                  */
01060 /*                                                      */
01061 /********************************************************/
01062 
01063 /** \brief Rearrange the quadrants of a Fourier image so that the origin is
01064           in the image's upper left.
01065 
01066      This function is the inversion of \ref moveDCToCenter(). See there
01067      for declarations and a usage example.
01068 
01069      <b> Declarations:</b>
01070 
01071      pass arguments explicitly:
01072      \code
01073         namespace vigra {
01074             template <class SrcImageIterator, class SrcAccessor,
01075                       class DestImageIterator, class DestAccessor>
01076             void moveDCToUpperLeft(SrcImageIterator src_upperleft,
01077                                    SrcImageIterator src_lowerright, SrcAccessor sa,
01078                                    DestImageIterator dest_upperleft, DestAccessor da);
01079         }
01080      \endcode
01081 
01082 
01083      use argument objects in conjunction with \ref ArgumentObjectFactories :
01084      \code
01085         namespace vigra {
01086             template <class SrcImageIterator, class SrcAccessor,
01087                       class DestImageIterator, class DestAccessor>
01088             void moveDCToUpperLeft(
01089                 triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
01090                 pair<DestImageIterator, DestAccessor> dest);
01091         }
01092      \endcode
01093 */
01094 doxygen_overloaded_function(template <...> void moveDCToUpperLeft)
01095 
01096 template <class SrcImageIterator, class SrcAccessor,
01097           class DestImageIterator, class DestAccessor>
01098 void moveDCToUpperLeft(SrcImageIterator src_upperleft,
01099                                SrcImageIterator src_lowerright, SrcAccessor sa,
01100                                DestImageIterator dest_upperleft, DestAccessor da)
01101 {
01102     int w= src_lowerright.x - src_upperleft.x;
01103     int h= src_lowerright.y - src_upperleft.y;
01104     int w2 = w/2;
01105     int h2 = h/2;
01106     int w1 = (w+1)/2;
01107     int h1 = (h+1)/2;
01108 
01109     // 2. Quadrant  zum 4.
01110     copyImage(srcIterRange(src_upperleft,
01111                            src_upperleft  + Diff2D(w2, h2), sa),
01112               destIter    (dest_upperleft + Diff2D(w1, h1), da));
01113 
01114     // 4. Quadrant zum 2.
01115     copyImage(srcIterRange(src_upperleft + Diff2D(w2, h2),
01116                            src_lowerright, sa),
01117               destIter    (dest_upperleft, da));
01118 
01119     // 1. Quadrant zum 3.
01120     copyImage(srcIterRange(src_upperleft  + Diff2D(w2, 0),
01121                            src_upperleft  + Diff2D(w,  h2), sa),
01122               destIter    (dest_upperleft + Diff2D(0,  h1), da));
01123 
01124     // 3. Quadrant zum 1.
01125     copyImage(srcIterRange(src_upperleft  + Diff2D(0,  h2),
01126                            src_upperleft  + Diff2D(w2, h), sa),
01127               destIter    (dest_upperleft + Diff2D(w1, 0), da));
01128 }
01129 
01130 template <class SrcImageIterator, class SrcAccessor,
01131           class DestImageIterator, class DestAccessor>
01132 inline void moveDCToUpperLeft(
01133     triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
01134     pair<DestImageIterator, DestAccessor> dest)
01135 {
01136     moveDCToUpperLeft(src.first, src.second, src.third,
01137                                           dest.first, dest.second);
01138 }
01139 
01140 namespace detail {
01141 
01142 template <class T>
01143 void
01144 fourierTransformImpl(FFTWComplexImage::const_traverser sul,
01145                      FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
01146                      FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest, T sign)
01147 {
01148     int w = slr.x - sul.x;
01149     int h = slr.y - sul.y;
01150 
01151     FFTWComplexImage sworkImage, dworkImage;
01152 
01153     fftw_complex * srcPtr = (fftw_complex *)(&*sul);
01154     fftw_complex * destPtr = (fftw_complex *)(&*dul);
01155 
01156     // test for right memory layout (fftw expects a 2*width*height floats array)
01157     if (&(*(sul + Diff2D(w, 0))) != &(*(sul + Diff2D(0, 1))))
01158     {
01159         sworkImage.resize(w, h);
01160         copyImage(srcIterRange(sul, slr, src), destImage(sworkImage));
01161         srcPtr = (fftw_complex *)(&(*sworkImage.upperLeft()));
01162     }
01163     if (&(*(dul + Diff2D(w, 0))) != &(*(dul + Diff2D(0, 1))))
01164     {
01165         dworkImage.resize(w, h);
01166         destPtr = (fftw_complex *)(&(*dworkImage.upperLeft()));
01167     }
01168 
01169     fftw_plan plan = fftw_plan_dft_2d(h, w, srcPtr, destPtr, sign, FFTW_ESTIMATE );
01170     fftw_execute(plan);
01171     fftw_destroy_plan(plan);
01172 
01173     if (&(*(dul + Diff2D(w, 0))) != &(*(dul + Diff2D(0, 1))))
01174     {
01175         copyImage(srcImageRange(dworkImage), destIter(dul, dest));
01176     }
01177 }
01178 
01179 } // namespace detail
01180 
01181 /********************************************************/
01182 /*                                                      */
01183 /*                   fourierTransform                   */
01184 /*                                                      */
01185 /********************************************************/
01186 
01187 /** \brief Compute forward and inverse Fourier transforms.
01188 
01189     In the forward direction, the input image may be scalar or complex, and the output image
01190     is always complex. In the inverse direction, both input and output must be complex.
01191 
01192     <b> Declarations:</b>
01193 
01194     pass arguments explicitly:
01195     \code
01196     namespace vigra {
01197         template <class SrcImageIterator, class SrcAccessor>
01198         void fourierTransform(SrcImageIterator srcUpperLeft,
01199                               SrcImageIterator srcLowerRight, SrcAccessor src,
01200                               FFTWComplexImage::traverser destUpperLeft, FFTWComplexImage::Accessor dest);
01201 
01202         void
01203         fourierTransformInverse(FFTWComplexImage::const_traverser sul,
01204                                 FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
01205                                 FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
01206     }
01207     \endcode
01208 
01209     use argument objects in conjunction with \ref ArgumentObjectFactories :
01210     \code
01211     namespace vigra {
01212         template <class SrcImageIterator, class SrcAccessor>
01213         void fourierTransform(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
01214                               pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest);
01215 
01216         void
01217         fourierTransformInverse(triple<FFTWComplexImage::const_traverser,
01218                                        FFTWComplexImage::const_traverser, FFTWComplexImage::ConstAccessor> src,
01219                                 pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest);
01220     }
01221     \endcode
01222 
01223     <b> Usage:</b>
01224 
01225     <b>\#include</b> <<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>><br>
01226     Namespace: vigra
01227 
01228     \code
01229     // compute complex Fourier transform of a real image
01230     vigra::DImage src(w, h);
01231     vigra::FFTWComplexImage fourier(w, h);
01232 
01233     fourierTransform(srcImageRange(src), destImage(fourier));
01234 
01235     // compute inverse Fourier transform
01236     // note that both source and destination image must be of type vigra::FFTWComplexImage
01237     vigra::FFTWComplexImage inverseFourier(w, h);
01238 
01239     fourierTransform(srcImageRange(fourier), destImage(inverseFourier));
01240     \endcode
01241 */
01242 doxygen_overloaded_function(template <...> void fourierTransform)
01243 
01244 inline void
01245 fourierTransform(FFTWComplexImage::const_traverser sul,
01246                  FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
01247                  FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
01248 {
01249     detail::fourierTransformImpl(sul, slr, src, dul, dest, FFTW_FORWARD);
01250 }
01251 
01252 template <class SrcImageIterator, class SrcAccessor>
01253 void fourierTransform(SrcImageIterator srcUpperLeft,
01254                       SrcImageIterator srcLowerRight, SrcAccessor sa,
01255                       FFTWComplexImage::traverser destUpperLeft, FFTWComplexImage::Accessor da)
01256 {
01257     // copy real input images into a complex one...
01258     int w= srcLowerRight.x - srcUpperLeft.x;
01259     int h= srcLowerRight.y - srcUpperLeft.y;
01260 
01261     FFTWComplexImage workImage(w, h);
01262     copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
01263               destImage(workImage, FFTWWriteRealAccessor()));
01264 
01265     // ...and call the complex -> complex version of the algorithm
01266     FFTWComplexImage const & cworkImage = workImage;
01267     fourierTransform(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
01268                      destUpperLeft, da);
01269 }
01270 
01271 template <class SrcImageIterator, class SrcAccessor>
01272 inline
01273 void fourierTransform(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
01274                       pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest)
01275 {
01276     fourierTransform(src.first, src.second, src.third, dest.first, dest.second);
01277 }
01278 
01279 /** \brief Compute inverse Fourier transforms.
01280 
01281     See \ref fourierTransform() for details.
01282 */
01283 inline void
01284 fourierTransformInverse(FFTWComplexImage::const_traverser sul,
01285                         FFTWComplexImage::const_traverser slr, FFTWComplexImage::ConstAccessor src,
01286                         FFTWComplexImage::traverser dul, FFTWComplexImage::Accessor dest)
01287 {
01288     detail::fourierTransformImpl(sul, slr, src, dul, dest, FFTW_BACKWARD);
01289 }
01290 
01291 inline void
01292 fourierTransformInverse(triple<FFTWComplexImage::const_traverser,
01293                                FFTWComplexImage::const_traverser, FFTWComplexImage::ConstAccessor> src,
01294                         pair<FFTWComplexImage::traverser, FFTWComplexImage::Accessor> dest)
01295 {
01296     fourierTransformInverse(src.first, src.second, src.third, dest.first, dest.second);
01297 }
01298 
01299 /********************************************************/
01300 /*                                                      */
01301 /*                   applyFourierFilter                 */
01302 /*                                                      */
01303 /********************************************************/
01304 
01305 /** \brief Apply a filter (defined in the frequency domain) to an image.
01306 
01307     After transferring the image into the frequency domain, it is
01308     multiplied pixel-wise with the filter and transformed back. The
01309     result is put into the given destination image which must have the right size.
01310     The result will be normalized to compensate for the two FFTs.
01311 
01312     If the destination image is scalar, only the real part of the result image is
01313     retained. In this case, you are responsible for choosing a filter image
01314     which ensures a zero imaginary part of the result (e.g. use a real, even symmetric
01315     filter image, or a purely imaginary, odd symmetric on).
01316 
01317     The DC entry of the filter must be in the upper left, which is the
01318     position where FFTW expects it (see \ref moveDCToUpperLeft()).
01319 
01320     <b> Declarations:</b>
01321 
01322     pass arguments explicitly:
01323     \code
01324     namespace vigra {
01325         template <class SrcImageIterator, class SrcAccessor,
01326                   class FilterImageIterator, class FilterAccessor,
01327                   class DestImageIterator, class DestAccessor>
01328         void applyFourierFilter(SrcImageIterator srcUpperLeft,
01329                                 SrcImageIterator srcLowerRight, SrcAccessor sa,
01330                                 FilterImageIterator filterUpperLeft, FilterAccessor fa,
01331                                 DestImageIterator destUpperLeft, DestAccessor da);
01332     }
01333     \endcode
01334 
01335     use argument objects in conjunction with \ref ArgumentObjectFactories :
01336     \code
01337     namespace vigra {
01338         template <class SrcImageIterator, class SrcAccessor,
01339                   class FilterImageIterator, class FilterAccessor,
01340                   class DestImageIterator, class DestAccessor>
01341         void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
01342                                 pair<FilterImageIterator, FilterAccessor> filter,
01343                                 pair<DestImageIterator, DestAccessor> dest);
01344     }
01345     \endcode
01346 
01347     <b> Usage:</b>
01348 
01349     <b>\#include</b> <<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>><br>
01350     Namespace: vigra
01351 
01352     \code
01353     // create a Gaussian filter in Fourier space
01354     vigra::FImage gaussFilter(w, h), filter(w, h);
01355     for(int y=0; y<h; ++y)
01356         for(int x=0; x<w; ++x)
01357         {
01358             xx = float(x - w / 2) / w;
01359             yy = float(y - h / 2) / h;
01360 
01361             gaussFilter(x,y) = std::exp(-(xx*xx + yy*yy) / 2.0 * scale);
01362         }
01363 
01364     // applyFourierFilter() expects the filter's DC in the upper left
01365     moveDCToUpperLeft(srcImageRange(gaussFilter), destImage(filter));
01366 
01367     vigra::FFTWComplexImage result(w, h);
01368 
01369     vigra::applyFourierFilter(srcImageRange(image), srcImage(filter), result);
01370     \endcode
01371 
01372     For inspection of the result, \ref FFTWMagnitudeAccessor might be
01373     useful. If you want to apply the same filter repeatedly, it may be more
01374     efficient to use the FFTW functions directly with FFTW plans optimized
01375     for good performance.
01376 */
01377 doxygen_overloaded_function(template <...> void applyFourierFilter)
01378 
01379 template <class SrcImageIterator, class SrcAccessor,
01380           class FilterImageIterator, class FilterAccessor,
01381           class DestImageIterator, class DestAccessor>
01382 void applyFourierFilter(SrcImageIterator srcUpperLeft,
01383                         SrcImageIterator srcLowerRight, SrcAccessor sa,
01384                         FilterImageIterator filterUpperLeft, FilterAccessor fa,
01385                         DestImageIterator destUpperLeft, DestAccessor da)
01386 {
01387     // copy real input images into a complex one...
01388     int w= srcLowerRight.x - srcUpperLeft.x;
01389     int h= srcLowerRight.y - srcUpperLeft.y;
01390 
01391     FFTWComplexImage workImage(w, h);
01392     copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
01393               destImage(workImage, FFTWWriteRealAccessor()));
01394 
01395     // ...and call the impl
01396     FFTWComplexImage const & cworkImage = workImage;
01397     applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
01398                            filterUpperLeft, fa,
01399                            destUpperLeft, da);
01400 }
01401 
01402 template <class FilterImageIterator, class FilterAccessor,
01403           class DestImageIterator, class DestAccessor>
01404 inline
01405 void applyFourierFilter(
01406     FFTWComplexImage::const_traverser srcUpperLeft,
01407     FFTWComplexImage::const_traverser srcLowerRight,
01408     FFTWComplexImage::ConstAccessor sa,
01409     FilterImageIterator filterUpperLeft, FilterAccessor fa,
01410     DestImageIterator destUpperLeft, DestAccessor da)
01411 {
01412     int w = srcLowerRight.x - srcUpperLeft.x;
01413     int h = srcLowerRight.y - srcUpperLeft.y;
01414 
01415     // test for right memory layout (fftw expects a 2*width*height floats array)
01416     if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
01417         applyFourierFilterImpl(srcUpperLeft, srcLowerRight, sa,
01418                                filterUpperLeft, fa,
01419                                destUpperLeft, da);
01420     else
01421     {
01422         FFTWComplexImage workImage(w, h);
01423         copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
01424                   destImage(workImage));
01425 
01426         FFTWComplexImage const & cworkImage = workImage;
01427         applyFourierFilterImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
01428                                filterUpperLeft, fa,
01429                                destUpperLeft, da);
01430     }
01431 }
01432 
01433 template <class SrcImageIterator, class SrcAccessor,
01434           class FilterImageIterator, class FilterAccessor,
01435           class DestImageIterator, class DestAccessor>
01436 inline
01437 void applyFourierFilter(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
01438                         pair<FilterImageIterator, FilterAccessor> filter,
01439                         pair<DestImageIterator, DestAccessor> dest)
01440 {
01441     applyFourierFilter(src.first, src.second, src.third,
01442                        filter.first, filter.second,
01443                        dest.first, dest.second);
01444 }
01445 
01446 template <class FilterImageIterator, class FilterAccessor,
01447           class DestImageIterator, class DestAccessor>
01448 void applyFourierFilterImpl(
01449     FFTWComplexImage::const_traverser srcUpperLeft,
01450     FFTWComplexImage::const_traverser srcLowerRight,
01451     FFTWComplexImage::ConstAccessor sa,
01452     FilterImageIterator filterUpperLeft, FilterAccessor fa,
01453     DestImageIterator destUpperLeft, DestAccessor da)
01454 {
01455     int w = srcLowerRight.x - srcUpperLeft.x;
01456     int h = srcLowerRight.y - srcUpperLeft.y;
01457 
01458     FFTWComplexImage complexResultImg(srcLowerRight - srcUpperLeft);
01459 
01460     // FFT from srcImage to complexResultImg
01461     fftw_plan forwardPlan=
01462         fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
01463                                (fftw_complex *)complexResultImg.begin(),
01464                                FFTW_FORWARD, FFTW_ESTIMATE );
01465     fftw_execute(forwardPlan);
01466     fftw_destroy_plan(forwardPlan);
01467 
01468     // convolve in freq. domain (in complexResultImg)
01469     combineTwoImages(srcImageRange(complexResultImg), srcIter(filterUpperLeft, fa),
01470                      destImage(complexResultImg), std::multiplies<FFTWComplex>());
01471 
01472     // FFT back into spatial domain (inplace in complexResultImg)
01473     fftw_plan backwardPlan=
01474         fftw_plan_dft_2d(h, w, (fftw_complex *)complexResultImg.begin(),
01475                                (fftw_complex *)complexResultImg.begin(),
01476                                FFTW_BACKWARD, FFTW_ESTIMATE);
01477     fftw_execute(backwardPlan);
01478     fftw_destroy_plan(backwardPlan);
01479 
01480     typedef typename
01481         NumericTraits<typename DestAccessor::value_type>::isScalar
01482         isScalarResult;
01483 
01484     // normalization (after FFTs), maybe stripping imaginary part
01485     applyFourierFilterImplNormalization(complexResultImg, destUpperLeft, da,
01486                                         isScalarResult());
01487 }
01488 
01489 template <class DestImageIterator, class DestAccessor>
01490 void applyFourierFilterImplNormalization(FFTWComplexImage const &srcImage,
01491                                          DestImageIterator destUpperLeft,
01492                                          DestAccessor da,
01493                                          VigraFalseType)
01494 {
01495     double normFactor= 1.0/(srcImage.width() * srcImage.height());
01496 
01497     for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
01498     {
01499         DestImageIterator dIt= destUpperLeft;
01500         for(int x= 0; x< srcImage.width(); x++, dIt.x++)
01501         {
01502             da.setComponent(srcImage(x, y).re()*normFactor, dIt, 0);
01503             da.setComponent(srcImage(x, y).im()*normFactor, dIt, 1);
01504         }
01505     }
01506 }
01507 
01508 inline
01509 void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
01510         FFTWComplexImage::traverser destUpperLeft,
01511         FFTWComplexImage::Accessor da,
01512         VigraFalseType)
01513 {
01514     transformImage(srcImageRange(srcImage), destIter(destUpperLeft, da),
01515                    linearIntensityTransform<FFTWComplex>(1.0/(srcImage.width() * srcImage.height())));
01516 }
01517 
01518 template <class DestImageIterator, class DestAccessor>
01519 void applyFourierFilterImplNormalization(FFTWComplexImage const & srcImage,
01520                                          DestImageIterator destUpperLeft,
01521                                          DestAccessor da,
01522                                          VigraTrueType)
01523 {
01524     double normFactor= 1.0/(srcImage.width() * srcImage.height());
01525 
01526     for(int y=0; y<srcImage.height(); y++, destUpperLeft.y++)
01527     {
01528         DestImageIterator dIt= destUpperLeft;
01529         for(int x= 0; x< srcImage.width(); x++, dIt.x++)
01530             da.set(srcImage(x, y).re()*normFactor, dIt);
01531     }
01532 }
01533 
01534 /**********************************************************/
01535 /*                                                        */
01536 /*                applyFourierFilterFamily                */
01537 /*                                                        */
01538 /**********************************************************/
01539 
01540 /** \brief Apply an array of filters (defined in the frequency domain) to an image.
01541 
01542     This provides the same functionality as \ref applyFourierFilter(),
01543     but applying several filters at once allows to avoid
01544     repeated Fourier transforms of the source image.
01545 
01546     Filters and result images must be stored in \ref vigra::ImageArray data
01547     structures. In contrast to \ref applyFourierFilter(), this function adjusts
01548     the size of the result images and the the length of the array.
01549 
01550     <b> Declarations:</b>
01551 
01552     pass arguments explicitly:
01553     \code
01554     namespace vigra {
01555         template <class SrcImageIterator, class SrcAccessor, class FilterType>
01556         void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
01557                                       SrcImageIterator srcLowerRight, SrcAccessor sa,
01558                                       const ImageArray<FilterType> &filters,
01559                                       ImageArray<FFTWComplexImage> &results)
01560     }
01561     \endcode
01562 
01563     use argument objects in conjunction with \ref ArgumentObjectFactories :
01564     \code
01565     namespace vigra {
01566         template <class SrcImageIterator, class SrcAccessor, class FilterType>
01567         void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
01568                                       const ImageArray<FilterType> &filters,
01569                                       ImageArray<FFTWComplexImage> &results)
01570     }
01571     \endcode
01572 
01573     <b> Usage:</b>
01574 
01575     <b>\#include</b> <<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>><br>
01576     Namespace: vigra
01577 
01578     \code
01579     // assuming the presence of a real-valued image named "image" to
01580     // be filtered in this example
01581 
01582     vigra::ImageArray<vigra::FImage> filters(16, image.size());
01583 
01584     for (int i=0; i<filters.size(); i++)
01585          // create some meaningful filters here
01586          createMyFilterOfScale(i, destImage(filters[i]));
01587 
01588     vigra::ImageArray<vigra::FFTWComplexImage> results();
01589 
01590     vigra::applyFourierFilterFamily(srcImageRange(image), filters, results);
01591     \endcode
01592 */
01593 doxygen_overloaded_function(template <...> void applyFourierFilterFamily)
01594 
01595 template <class SrcImageIterator, class SrcAccessor,
01596           class FilterType, class DestImage>
01597 inline
01598 void applyFourierFilterFamily(triple<SrcImageIterator, SrcImageIterator, SrcAccessor> src,
01599                               const ImageArray<FilterType> &filters,
01600                               ImageArray<DestImage> &results)
01601 {
01602     applyFourierFilterFamily(src.first, src.second, src.third,
01603                              filters, results);
01604 }
01605 
01606 template <class SrcImageIterator, class SrcAccessor,
01607           class FilterType, class DestImage>
01608 void applyFourierFilterFamily(SrcImageIterator srcUpperLeft,
01609                               SrcImageIterator srcLowerRight, SrcAccessor sa,
01610                               const ImageArray<FilterType> &filters,
01611                               ImageArray<DestImage> &results)
01612 {
01613     int w= srcLowerRight.x - srcUpperLeft.x;
01614     int h= srcLowerRight.y - srcUpperLeft.y;
01615 
01616     FFTWComplexImage workImage(w, h);
01617     copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
01618               destImage(workImage, FFTWWriteRealAccessor()));
01619 
01620     FFTWComplexImage const & cworkImage = workImage;
01621     applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
01622                                  filters, results);
01623 }
01624 
01625 template <class FilterType, class DestImage>
01626 inline
01627 void applyFourierFilterFamily(
01628     FFTWComplexImage::const_traverser srcUpperLeft,
01629     FFTWComplexImage::const_traverser srcLowerRight,
01630     FFTWComplexImage::ConstAccessor sa,
01631     const ImageArray<FilterType> &filters,
01632     ImageArray<DestImage> &results)
01633 {
01634     int w= srcLowerRight.x - srcUpperLeft.x;
01635 
01636     // test for right memory layout (fftw expects a 2*width*height floats array)
01637     if (&(*(srcUpperLeft + Diff2D(w, 0))) == &(*(srcUpperLeft + Diff2D(0, 1))))
01638         applyFourierFilterFamilyImpl(srcUpperLeft, srcLowerRight, sa,
01639                                      filters, results);
01640     else
01641     {
01642         int h = srcLowerRight.y - srcUpperLeft.y;
01643         FFTWComplexImage workImage(w, h);
01644         copyImage(srcIterRange(srcUpperLeft, srcLowerRight, sa),
01645                   destImage(workImage));
01646 
01647         FFTWComplexImage const & cworkImage = workImage;
01648         applyFourierFilterFamilyImpl(cworkImage.upperLeft(), cworkImage.lowerRight(), cworkImage.accessor(),
01649                                      filters, results);
01650     }
01651 }
01652 
01653 template <class FilterType, class DestImage>
01654 void applyFourierFilterFamilyImpl(
01655     FFTWComplexImage::const_traverser srcUpperLeft,
01656     FFTWComplexImage::const_traverser srcLowerRight,
01657     FFTWComplexImage::ConstAccessor sa,
01658     const ImageArray<FilterType> &filters,
01659     ImageArray<DestImage> &results)
01660 {
01661     // FIXME: sa is not used
01662     // (maybe check if StandardAccessor, else copy?)    
01663 
01664     // make sure the filter images have the right dimensions
01665     vigra_precondition((srcLowerRight - srcUpperLeft) == filters.imageSize(),
01666                        "applyFourierFilterFamily called with src image size != filters.imageSize()!");
01667 
01668     // make sure the result image array has the right dimensions
01669     results.resize(filters.size());
01670     results.resizeImages(filters.imageSize());
01671 
01672     // FFT from srcImage to freqImage
01673     int w= srcLowerRight.x - srcUpperLeft.x;
01674     int h= srcLowerRight.y - srcUpperLeft.y;
01675 
01676     FFTWComplexImage freqImage(w, h);
01677     FFTWComplexImage result(w, h);
01678 
01679     fftw_plan forwardPlan=
01680         fftw_plan_dft_2d(h, w, (fftw_complex *)&(*srcUpperLeft),
01681                                (fftw_complex *)freqImage.begin(),
01682                                FFTW_FORWARD, FFTW_ESTIMATE );
01683     fftw_execute(forwardPlan);
01684     fftw_destroy_plan(forwardPlan);
01685 
01686     fftw_plan backwardPlan=
01687         fftw_plan_dft_2d(h, w, (fftw_complex *)result.begin(),
01688                                (fftw_complex *)result.begin(),
01689                                FFTW_BACKWARD, FFTW_ESTIMATE );
01690     typedef typename
01691         NumericTraits<typename DestImage::Accessor::value_type>::isScalar
01692         isScalarResult;
01693 
01694     // convolve with filters in freq. domain
01695     for (unsigned int i= 0;  i < filters.size(); i++)
01696     {
01697         combineTwoImages(srcImageRange(freqImage), srcImage(filters[i]),
01698                          destImage(result), std::multiplies<FFTWComplex>());
01699 
01700         // FFT back into spatial domain (inplace in destImage)
01701         fftw_execute(backwardPlan);
01702 
01703         // normalization (after FFTs), maybe stripping imaginary part
01704         applyFourierFilterImplNormalization(result,
01705                                             results[i].upperLeft(), results[i].accessor(),
01706                                             isScalarResult());
01707     }
01708     fftw_destroy_plan(backwardPlan);
01709 }
01710 
01711 /********************************************************/
01712 /*                                                      */
01713 /*                fourierTransformReal                  */
01714 /*                                                      */
01715 /********************************************************/
01716 
01717 /** \brief Real Fourier transforms for even and odd boundary conditions
01718            (aka. cosine and sine transforms).
01719 
01720 
01721     If the image is real and has even symmetry, its Fourier transform
01722     is also real and has even symmetry. The Fourier transform of a real image with odd
01723     symmetry is imaginary and has odd symmetry. In either case, only about a quarter
01724     of the pixels need to be stored because the rest can be calculated from the symmetry
01725     properties. This is especially useful, if the original image is implicitly assumed
01726     to have reflective or anti-reflective boundary conditions. Then the "negative"
01727     pixel locations are defined as
01728 
01729     \code
01730     even (reflective boundary conditions):      f[-x] = f[x]     (x = 1,...,N-1)
01731     odd (anti-reflective boundary conditions):  f[-1] = 0
01732                                                 f[-x] = -f[x-2]  (x = 2,...,N-1)
01733     \endcode
01734 
01735     end similar at the other boundary (see the FFTW documentation for details).
01736     This has the advantage that more efficient Fourier transforms that use only
01737     real numbers can be implemented. These are also known as cosine and sine transforms
01738     respectively.
01739 
01740     If you use the odd transform it is important to note that in the Fourier domain,
01741     the DC component is always zero and is therefore dropped from the data structure.
01742     This means that index 0 in an odd symmetric Fourier domain image refers to
01743     the <i>first</i> harmonic. This is especially important if an image is first
01744     cosine transformed (even symmetry), then in the Fourier domain multiplied
01745     with an odd symmetric filter (e.g. a first derivative) and finally transformed
01746     back to the spatial domain with a sine transform (odd symmetric). For this to work
01747     properly the image must be shifted left or up by one pixel (depending on whether
01748     the x- or y-axis is odd symmetric) before the inverse transform can be applied.
01749     (see example below).
01750 
01751     The real Fourier transform functions are named <tt>fourierTransformReal??</tt>
01752     where the questions marks stand for either <tt>E</tt> or <tt>O</tt> indicating
01753     whether the x- and y-axis is to be transformed using even or odd symmetry.
01754     The same functions can be used for both the forward and inverse transforms,
01755     only the normalization changes. For signal processing, the following
01756     normalization factors are most appropriate:
01757 
01758     \code
01759                           forward             inverse
01760     ------------------------------------------------------------
01761     X even, Y even           1.0         4.0 * (w-1) * (h-1)
01762     X even, Y odd           -1.0        -4.0 * (w-1) * (h+1)
01763     X odd,  Y even          -1.0        -4.0 * (w+1) * (h-1)
01764     X odd,  Y odd            1.0         4.0 * (w+1) * (h+1)
01765     \endcode
01766 
01767     where <tt>w</tt> and <tt>h</tt> denote the image width and height.
01768 
01769     <b> Declarations:</b>
01770 
01771     pass arguments explicitly:
01772     \code
01773     namespace vigra {
01774         template <class SrcTraverser, class SrcAccessor,
01775                   class DestTraverser, class DestAccessor>
01776         void
01777         fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
01778                                DestTraverser dul, DestAccessor dest, fftw_real norm);
01779 
01780         fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
01781     }
01782     \endcode
01783 
01784 
01785     use argument objects in conjunction with \ref ArgumentObjectFactories :
01786     \code
01787     namespace vigra {
01788         template <class SrcTraverser, class SrcAccessor,
01789                   class DestTraverser, class DestAccessor>
01790         void
01791         fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
01792                                pair<DestTraverser, DestAccessor> dest, fftw_real norm);
01793 
01794         fourierTransformRealEO, fourierTransformRealOE, fourierTransformRealOO likewise
01795     }
01796     \endcode
01797 
01798     <b> Usage:</b>
01799 
01800         <b>\#include</b> <<a href="fftw3_8hxx-source.html">vigra/fftw3.hxx</a>><br>
01801         Namespace: vigra
01802 
01803     \code
01804     vigra::FImage spatial(width,height), fourier(width,height);
01805     ... // fill image with data
01806 
01807     // forward cosine transform == reflective boundary conditions
01808     fourierTransformRealEE(srcImageRange(spatial), destImage(fourier), (fftw_real)1.0);
01809 
01810     // multiply with a first derivative of Gaussian in x-direction
01811     for(int y = 0; y < height; ++y)
01812     {
01813         for(int x = 1; x < width; ++x)
01814         {
01815             double dx = x * M_PI / (width - 1);
01816             double dy = y * M_PI / (height - 1);
01817             fourier(x-1, y) = fourier(x, y) * dx * std::exp(-(dx*dx + dy*dy) * scale*scale / 2.0);
01818         }
01819         fourier(width-1, y) = 0.0;
01820     }
01821 
01822     // inverse transform -- odd symmetry in x-direction, even in y,
01823     //                      due to symmetry of the filter
01824     fourierTransformRealOE(srcImageRange(fourier), destImage(spatial),
01825                            (fftw_real)-4.0 * (width+1) * (height-1));
01826     \endcode
01827 */
01828 doxygen_overloaded_function(template <...> void fourierTransformReal)
01829 
01830 template <class SrcTraverser, class SrcAccessor,
01831           class DestTraverser, class DestAccessor>
01832 inline void
01833 fourierTransformRealEE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
01834                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
01835 {
01836     fourierTransformRealEE(src.first, src.second, src.third,
01837                                    dest.first, dest.second, norm);
01838 }
01839 
01840 template <class SrcTraverser, class SrcAccessor,
01841           class DestTraverser, class DestAccessor>
01842 inline void
01843 fourierTransformRealEE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
01844                                DestTraverser dul, DestAccessor dest, fftw_real norm)
01845 {
01846     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
01847                                       norm, FFTW_REDFT00, FFTW_REDFT00);
01848 }
01849 
01850 template <class DestTraverser, class DestAccessor>
01851 inline void
01852 fourierTransformRealEE(
01853          FFTWRealImage::const_traverser sul,
01854          FFTWRealImage::const_traverser slr,
01855          FFTWRealImage::Accessor src,
01856          DestTraverser dul, DestAccessor dest, fftw_real norm)
01857 {
01858     int w = slr.x - sul.x;
01859 
01860     // test for right memory layout (fftw expects a width*height fftw_real array)
01861     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
01862         fourierTransformRealImpl(sul, slr, dul, dest,
01863                                  norm, FFTW_REDFT00, FFTW_REDFT00);
01864     else
01865         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
01866                                  norm, FFTW_REDFT00, FFTW_REDFT00);
01867 }
01868 
01869 /********************************************************************/
01870 
01871 template <class SrcTraverser, class SrcAccessor,
01872           class DestTraverser, class DestAccessor>
01873 inline void
01874 fourierTransformRealOE(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
01875                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
01876 {
01877     fourierTransformRealOE(src.first, src.second, src.third,
01878                                    dest.first, dest.second, norm);
01879 }
01880 
01881 template <class SrcTraverser, class SrcAccessor,
01882           class DestTraverser, class DestAccessor>
01883 inline void
01884 fourierTransformRealOE(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
01885                                DestTraverser dul, DestAccessor dest, fftw_real norm)
01886 {
01887     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
01888                                       norm, FFTW_RODFT00, FFTW_REDFT00);
01889 }
01890 
01891 template <class DestTraverser, class DestAccessor>
01892 inline void
01893 fourierTransformRealOE(
01894          FFTWRealImage::const_traverser sul,
01895          FFTWRealImage::const_traverser slr,
01896          FFTWRealImage::Accessor src,
01897          DestTraverser dul, DestAccessor dest, fftw_real norm)
01898 {
01899     int w = slr.x - sul.x;
01900 
01901     // test for right memory layout (fftw expects a width*height fftw_real array)
01902     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
01903         fourierTransformRealImpl(sul, slr, dul, dest,
01904                                  norm, FFTW_RODFT00, FFTW_REDFT00);
01905     else
01906         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
01907                                  norm, FFTW_RODFT00, FFTW_REDFT00);
01908 }
01909 
01910 /********************************************************************/
01911 
01912 template <class SrcTraverser, class SrcAccessor,
01913           class DestTraverser, class DestAccessor>
01914 inline void
01915 fourierTransformRealEO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
01916                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
01917 {
01918     fourierTransformRealEO(src.first, src.second, src.third,
01919                                    dest.first, dest.second, norm);
01920 }
01921 
01922 template <class SrcTraverser, class SrcAccessor,
01923           class DestTraverser, class DestAccessor>
01924 inline void
01925 fourierTransformRealEO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
01926                                DestTraverser dul, DestAccessor dest, fftw_real norm)
01927 {
01928     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
01929                                       norm, FFTW_REDFT00, FFTW_RODFT00);
01930 }
01931 
01932 template <class DestTraverser, class DestAccessor>
01933 inline void
01934 fourierTransformRealEO(
01935          FFTWRealImage::const_traverser sul,
01936          FFTWRealImage::const_traverser slr,
01937          FFTWRealImage::Accessor src,
01938          DestTraverser dul, DestAccessor dest, fftw_real norm)
01939 {
01940     int w = slr.x - sul.x;
01941 
01942     // test for right memory layout (fftw expects a width*height fftw_real array)
01943     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
01944         fourierTransformRealImpl(sul, slr, dul, dest,
01945                                  norm, FFTW_REDFT00, FFTW_RODFT00);
01946     else
01947         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
01948                                  norm, FFTW_REDFT00, FFTW_RODFT00);
01949 }
01950 
01951 /********************************************************************/
01952 
01953 template <class SrcTraverser, class SrcAccessor,
01954           class DestTraverser, class DestAccessor>
01955 inline void
01956 fourierTransformRealOO(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
01957                                pair<DestTraverser, DestAccessor> dest, fftw_real norm)
01958 {
01959     fourierTransformRealOO(src.first, src.second, src.third,
01960                                    dest.first, dest.second, norm);
01961 }
01962 
01963 template <class SrcTraverser, class SrcAccessor,
01964           class DestTraverser, class DestAccessor>
01965 inline void
01966 fourierTransformRealOO(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
01967                                DestTraverser dul, DestAccessor dest, fftw_real norm)
01968 {
01969     fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
01970                                       norm, FFTW_RODFT00, FFTW_RODFT00);
01971 }
01972 
01973 template <class DestTraverser, class DestAccessor>
01974 inline void
01975 fourierTransformRealOO(
01976          FFTWRealImage::const_traverser sul,
01977          FFTWRealImage::const_traverser slr,
01978          FFTWRealImage::Accessor src,
01979          DestTraverser dul, DestAccessor dest, fftw_real norm)
01980 {
01981     int w = slr.x - sul.x;
01982 
01983     // test for right memory layout (fftw expects a width*height fftw_real array)
01984     if (&(*(sul + Diff2D(w, 0))) == &(*(sul + Diff2D(0, 1))))
01985         fourierTransformRealImpl(sul, slr, dul, dest,
01986                                  norm, FFTW_RODFT00, FFTW_RODFT00);
01987     else
01988         fourierTransformRealWorkImageImpl(sul, slr, src, dul, dest,
01989                                  norm, FFTW_RODFT00, FFTW_RODFT00);
01990 }
01991 
01992 /*******************************************************************/
01993 
01994 template <class SrcTraverser, class SrcAccessor,
01995           class DestTraverser, class DestAccessor>
01996 void
01997 fourierTransformRealWorkImageImpl(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
01998                                   DestTraverser dul, DestAccessor dest,
01999                                   fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
02000 {
02001     FFTWRealImage workImage(slr - sul);
02002     copyImage(srcIterRange(sul, slr, src), destImage(workImage));
02003     FFTWRealImage const & cworkImage = workImage;
02004     fourierTransformRealImpl(cworkImage.upperLeft(), cworkImage.lowerRight(),
02005                              dul, dest, norm, kindx, kindy);
02006 }
02007 
02008 
02009 template <class DestTraverser, class DestAccessor>
02010 void
02011 fourierTransformRealImpl(
02012          FFTWRealImage::const_traverser sul,
02013          FFTWRealImage::const_traverser slr,
02014          DestTraverser dul, DestAccessor dest,
02015          fftw_real norm, fftw_r2r_kind kindx, fftw_r2r_kind kindy)
02016 {
02017     int w = slr.x - sul.x;
02018     int h = slr.y - sul.y;
02019     BasicImage<fftw_real> res(w, h);
02020 
02021     fftw_plan plan = fftw_plan_r2r_2d(h, w,
02022                          (fftw_real *)&(*sul), (fftw_real *)res.begin(),
02023                          kindy, kindx, FFTW_ESTIMATE);
02024     fftw_execute(plan);
02025     fftw_destroy_plan(plan);
02026 
02027     if(norm != 1.0)
02028         transformImage(srcImageRange(res), destIter(dul, dest),
02029                        std::bind1st(std::multiplies<fftw_real>(), 1.0 / norm));
02030     else
02031         copyImage(srcImageRange(res), destIter(dul, dest));
02032 }
02033 
02034 
02035 //@}
02036 
02037 } // namespace vigra
02038 
02039 #endif // VIGRA_FFTW3_HXX

© Ullrich Köthe (ullrich.koethe@iwr.uni-heidelberg.de)
Heidelberg Collaboratory for Image Processing, University of Heidelberg, Germany

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VIGRA 1.6.0 (13 Aug 2008)