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details vigra/rfftw.hxx VIGRA

00001 /************************************************************************/
00002 /*                                                                      */
00003 /*               Copyright 1998-2002 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 1.3.2, Jan 27 2005 )                                    */
00008 /*    You may use, modify, and distribute this software according       */
00009 /*    to the terms stated in the LICENSE file included in               */
00010 /*    the VIGRA distribution.                                           */
00011 /*                                                                      */
00012 /*    The VIGRA Website is                                              */
00013 /*        http://kogs-www.informatik.uni-hamburg.de/~koethe/vigra/      */
00014 /*    Please direct questions, bug reports, and contributions to        */
00015 /*        koethe@informatik.uni-hamburg.de                              */
00016 /*                                                                      */
00017 /*  THIS SOFTWARE IS PROVIDED AS IS AND WITHOUT ANY EXPRESS OR          */
00018 /*  IMPLIED WARRANTIES, INCLUDING, WITHOUT LIMITATION, THE IMPLIED      */
00019 /*  WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. */
00020 /*                                                                      */
00021 /************************************************************************/
00022 
00023 #ifndef VIGRA_RFFTW_HXX
00024 #define VIGRA_RFFTW_HXX
00025 
00026 #include "vigra/array_vector.hxx"
00027 #include "vigra/fftw.hxx"
00028 #include <rfftw.h>
00029 
00030 namespace vigra {
00031 
00032 namespace detail {
00033 
00034 struct FFTWSinCosConfig
00035 {
00036     ArrayVector<fftw_real> twiddles;
00037     ArrayVector<fftw_real> fftwInput;
00038     ArrayVector<fftw_complex> fftwTmpResult;
00039     fftw_real norm;
00040     rfftwnd_plan fftwPlan;
00041 };
00042 
00043 template <class SrcIterator, class SrcAccessor,
00044           class DestIterator, class DestAccessor,
00045           class Config>
00046 void 
00047 cosineTransformLineImpl(SrcIterator s, SrcIterator send, SrcAccessor src, 
00048                         DestIterator d, DestAccessor dest,
00049                         Config & config)
00050 {
00051     int size = send - s;
00052     int ns2 = size / 2;
00053     int nm1 = size - 1;
00054     int modn = size % 2;
00055 
00056     if(size <= 0)
00057         return;
00058     
00059     fftw_real const * twiddles = config.twiddles.begin();
00060     fftw_real * fftwInput = config.fftwInput.begin();
00061     fftw_complex * fftwTmpResult = config.fftwTmpResult.begin();
00062     fftw_real norm = config.norm;
00063     rfftwnd_plan fftwPlan = config.fftwPlan;
00064 
00065     switch(size)
00066     {
00067       case 1:
00068       {
00069         dest.set(src(s) / norm, d);
00070         break;
00071       }
00072       case 2:
00073       {
00074         dest.set((src(s) + src(s, 1)) / norm, d);
00075         dest.set((src(s) - src(s, 1)) / norm, d, 1);
00076         break;
00077       }
00078       case 3:
00079       {
00080         fftw_real x1p3 = src(s) + src(s, 2);
00081         fftw_real tx2 =  2.0 * src(s, 1);
00082 
00083         dest.set((x1p3 + tx2) / norm, d, 0);
00084         dest.set((src(s) - src(s, 2)) / norm, d, 1);
00085         dest.set((x1p3 - tx2) / norm, d, 2);
00086         break;
00087       }
00088       default:
00089       {
00090         fftw_real c1 = src(s) - src(s, nm1);
00091         fftwInput[0] = src(s) + src(s, nm1);
00092         for(int k=1; k<ns2; ++k)
00093         {
00094             int kc = nm1 - k;
00095             fftw_real t1 = src(s, k) + src(s, kc);
00096             fftw_real t2 = src(s, k) - src(s, kc);
00097             c1 = c1 + twiddles[kc] * t2;
00098             t2 = twiddles[k] * t2;
00099             fftwInput[k] = t1 - t2;
00100             fftwInput[kc] = t1 + t2;
00101         }
00102 
00103         if (modn != 0)
00104         {
00105             fftwInput[ns2] = 2.0*src(s, ns2);
00106         }
00107         rfftwnd_one_real_to_complex(fftwPlan, fftwInput, fftwTmpResult);
00108         dest.set(fftwTmpResult[0].re / norm, d, 0);
00109         for(int k=1; k<(size+1)/2; ++k)
00110         {
00111             dest.set(fftwTmpResult[k].re, d, 2*k-1);
00112             dest.set(fftwTmpResult[k].im, d, 2*k);
00113         }
00114         fftw_real xim2 = dest(d, 1);
00115         dest.set(c1 / norm, d, 1);
00116         for(int k=3; k<size; k+=2)
00117         {
00118             fftw_real xi = dest(d, k);
00119             dest.set(dest(d, k-2) - dest(d, k-1) / norm, d, k);
00120             dest.set(xim2 / norm, d, k-1);
00121             xim2 = xi;
00122         }
00123         if (modn != 0)
00124         {
00125             dest.set(xim2 / norm, d, size-1);
00126         }
00127       }
00128     }
00129 }
00130 
00131 } // namespace detail
00132 
00133 template <class SrcTraverser, class SrcAccessor,
00134           class DestTraverser, class DestAccessor>
00135 void cosineTransformX(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
00136                       DestTraverser dul, DestAccessor dest, fftw_real norm)
00137 {
00138     int w = slr.x - sul.x;
00139     int h = slr.y - sul.y;
00140     
00141     detail::FFTWSinCosConfig config;
00142 
00143     // horizontal transformation
00144     int ns2 = w / 2;
00145     int nm1 = w - 1;
00146     int modn = w % 2;
00147     
00148     config.twiddles.resize(w+1);
00149     config.fftwInput.resize(w+1);
00150     config.fftwTmpResult.resize(w+1);
00151     config.norm = norm;
00152     config.fftwPlan = rfftw2d_create_plan(1, nm1, FFTW_REAL_TO_COMPLEX, FFTW_ESTIMATE );
00153 
00154     fftw_real dt = M_PI / nm1;
00155     for(int k=1; k<ns2; ++k)
00156     {
00157         fftw_real f = dt * k;
00158         config.twiddles[k] = 2.0*VIGRA_CSTD::sin(f);
00159         config.twiddles[nm1-k] = 2.0*VIGRA_CSTD::cos(f);
00160     }
00161 
00162     for(; sul.y != slr.y; ++sul.y, ++dul.y)
00163     {
00164         typename SrcTraverser::row_iterator s = sul.rowIterator();
00165         typename SrcTraverser::row_iterator send = s + w;
00166         typename DestTraverser::row_iterator d = dul.rowIterator();
00167         cosineTransformLineImpl(s, send, src, d, dest, config);
00168     }
00169 
00170     rfftwnd_destroy_plan(config.fftwPlan);
00171 }
00172 
00173 template <class SrcTraverser, class SrcAccessor,
00174           class DestTraverser, class DestAccessor>
00175 void cosineTransformY(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
00176                       DestTraverser dul, DestAccessor dest, fftw_real norm)
00177 {
00178     int w = slr.x - sul.x;
00179     int h = slr.y - sul.y;
00180     
00181     detail::FFTWSinCosConfig config;
00182 
00183     // horizontal transformation
00184     int ns2 = h / 2;
00185     int nm1 = h - 1;
00186     int modn = h % 2;
00187     
00188     config.twiddles.resize(h + 1);
00189     config.fftwInput.resize(h + 1);
00190     config.fftwTmpResult.resize(h + 1);
00191     config.norm = norm;
00192     config.fftwPlan = rfftw2d_create_plan(1, nm1, FFTW_REAL_TO_COMPLEX, FFTW_ESTIMATE );
00193 
00194     fftw_real dt = M_PI / nm1;
00195     for(int k=1; k<ns2; ++k)
00196     {
00197         fftw_real f = dt * k;
00198         config.twiddles[k] = 2.0*VIGRA_CSTD::sin(f);
00199         config.twiddles[nm1-k] = 2.0*VIGRA_CSTD::cos(f);
00200     }
00201 
00202     for(; sul.x != slr.x; ++sul.x, ++dul.x)
00203     {
00204         typename SrcTraverser::column_iterator s = sul.columnIterator();
00205         typename SrcTraverser::column_iterator send = s + h;
00206         typename DestTraverser::column_iterator d = dul.columnIterator();
00207         cosineTransformLineImpl(s, send, src, d, dest, config);
00208     }
00209 
00210     rfftwnd_destroy_plan(config.fftwPlan);
00211 }
00212 
00213 template <class SrcTraverser, class SrcAccessor,
00214           class DestTraverser, class DestAccessor>
00215 inline void 
00216 realFourierTransformXEvenYEven(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
00217                       DestTraverser dul, DestAccessor dest, fftw_real norm)
00218 {
00219     BasicImage<fftw_real> tmp(slr - sul);
00220     cosineTransformX(sul, slr, src, tmp.upperLeft(), tmp.accessor(), 1.0);
00221     cosineTransformY(tmp.upperLeft(), tmp.lowerRight(), tmp.accessor(), dul, dest, norm);
00222 }
00223 
00224 template <class SrcTraverser, class SrcAccessor,
00225           class DestTraverser, class DestAccessor>
00226 inline void 
00227 realFourierTransformXEvenYEven(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
00228                       pair<DestTraverser, DestAccessor> dest, fftw_real norm)
00229 {
00230     realFourierTransformXEvenYEven(src.first, src.second, src.third, dest.first, dest.second, norm);
00231 }
00232 
00233 } // namespace vigra
00234 
00235 #endif // VIGRA_RFFTW_HXX

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

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VIGRA 1.3.2 (27 Jan 2005)