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details vigra/fftw3.hxx VIGRA

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

© Ullrich Köthe (koethe@informatik.uni-hamburg.de)
Cognitive Systems Group, University of Hamburg, Germany

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VIGRA 1.4.0 (21 Dec 2005)