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vigra/rfftw.hxx VIGRA

00001 /************************************************************************/
00002 /*                                                                      */
00003 /*               Copyright 1998-2002 by Ullrich Koethe                  */
00004 /*                                                                      */
00005 /*    This file is part of the VIGRA computer vision library.           */
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00010 /*        vigra@informatik.uni-hamburg.de                               */
00011 /*                                                                      */
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00019 /*    conditions:                                                       */
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00023 /*    Software.                                                         */
00024 /*                                                                      */
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00033 /*                                                                      */
00034 /************************************************************************/
00035 
00036 #ifndef VIGRA_RFFTW_HXX
00037 #define VIGRA_RFFTW_HXX
00038 
00039 #include "array_vector.hxx"
00040 #include "fftw.hxx"
00041 #include <rfftw.h>
00042 
00043 namespace vigra {
00044 
00045 namespace detail {
00046 
00047 struct FFTWSinCosConfig
00048 {
00049     ArrayVector<fftw_real> twiddles;
00050     ArrayVector<fftw_real> fftwInput;
00051     ArrayVector<fftw_complex> fftwTmpResult;
00052     fftw_real norm;
00053     rfftwnd_plan fftwPlan;
00054 };
00055 
00056 template <class SrcIterator, class SrcAccessor,
00057           class DestIterator, class DestAccessor,
00058           class Config>
00059 void 
00060 cosineTransformLineImpl(SrcIterator s, SrcIterator send, SrcAccessor src, 
00061                         DestIterator d, DestAccessor dest,
00062                         Config & config)
00063 {
00064     int size = send - s;
00065     int ns2 = size / 2;
00066     int nm1 = size - 1;
00067     int modn = size % 2;
00068 
00069     if(size <= 0)
00070         return;
00071     
00072     fftw_real const * twiddles = config.twiddles.begin();
00073     fftw_real * fftwInput = config.fftwInput.begin();
00074     fftw_complex * fftwTmpResult = config.fftwTmpResult.begin();
00075     fftw_real norm = config.norm;
00076     rfftwnd_plan fftwPlan = config.fftwPlan;
00077 
00078     switch(size)
00079     {
00080       case 1:
00081       {
00082         dest.set(src(s) / norm, d);
00083         break;
00084       }
00085       case 2:
00086       {
00087         dest.set((src(s) + src(s, 1)) / norm, d);
00088         dest.set((src(s) - src(s, 1)) / norm, d, 1);
00089         break;
00090       }
00091       case 3:
00092       {
00093         fftw_real x1p3 = src(s) + src(s, 2);
00094         fftw_real tx2 =  2.0 * src(s, 1);
00095 
00096         dest.set((x1p3 + tx2) / norm, d, 0);
00097         dest.set((src(s) - src(s, 2)) / norm, d, 1);
00098         dest.set((x1p3 - tx2) / norm, d, 2);
00099         break;
00100       }
00101       default:
00102       {
00103         fftw_real c1 = src(s) - src(s, nm1);
00104         fftwInput[0] = src(s) + src(s, nm1);
00105         for(int k=1; k<ns2; ++k)
00106         {
00107             int kc = nm1 - k;
00108             fftw_real t1 = src(s, k) + src(s, kc);
00109             fftw_real t2 = src(s, k) - src(s, kc);
00110             c1 = c1 + twiddles[kc] * t2;
00111             t2 = twiddles[k] * t2;
00112             fftwInput[k] = t1 - t2;
00113             fftwInput[kc] = t1 + t2;
00114         }
00115 
00116         if (modn != 0)
00117         {
00118             fftwInput[ns2] = 2.0*src(s, ns2);
00119         }
00120         rfftwnd_one_real_to_complex(fftwPlan, fftwInput, fftwTmpResult);
00121         dest.set(fftwTmpResult[0].re / norm, d, 0);
00122         for(int k=1; k<(size+1)/2; ++k)
00123         {
00124             dest.set(fftwTmpResult[k].re, d, 2*k-1);
00125             dest.set(fftwTmpResult[k].im, d, 2*k);
00126         }
00127         fftw_real xim2 = dest(d, 1);
00128         dest.set(c1 / norm, d, 1);
00129         for(int k=3; k<size; k+=2)
00130         {
00131             fftw_real xi = dest(d, k);
00132             dest.set(dest(d, k-2) - dest(d, k-1) / norm, d, k);
00133             dest.set(xim2 / norm, d, k-1);
00134             xim2 = xi;
00135         }
00136         if (modn != 0)
00137         {
00138             dest.set(xim2 / norm, d, size-1);
00139         }
00140       }
00141     }
00142 }
00143 
00144 } // namespace detail
00145 
00146 template <class SrcTraverser, class SrcAccessor,
00147           class DestTraverser, class DestAccessor>
00148 void cosineTransformX(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
00149                       DestTraverser dul, DestAccessor dest, fftw_real norm)
00150 {
00151     int w = slr.x - sul.x;
00152     int h = slr.y - sul.y;
00153     
00154     detail::FFTWSinCosConfig config;
00155 
00156     // horizontal transformation
00157     int ns2 = w / 2;
00158     int nm1 = w - 1;
00159     int modn = w % 2;
00160     
00161     config.twiddles.resize(w+1);
00162     config.fftwInput.resize(w+1);
00163     config.fftwTmpResult.resize(w+1);
00164     config.norm = norm;
00165     config.fftwPlan = rfftw2d_create_plan(1, nm1, FFTW_REAL_TO_COMPLEX, FFTW_ESTIMATE );
00166 
00167     fftw_real dt = M_PI / nm1;
00168     for(int k=1; k<ns2; ++k)
00169     {
00170         fftw_real f = dt * k;
00171         config.twiddles[k] = 2.0*VIGRA_CSTD::sin(f);
00172         config.twiddles[nm1-k] = 2.0*VIGRA_CSTD::cos(f);
00173     }
00174 
00175     for(; sul.y != slr.y; ++sul.y, ++dul.y)
00176     {
00177         typename SrcTraverser::row_iterator s = sul.rowIterator();
00178         typename SrcTraverser::row_iterator send = s + w;
00179         typename DestTraverser::row_iterator d = dul.rowIterator();
00180         cosineTransformLineImpl(s, send, src, d, dest, config);
00181     }
00182 
00183     rfftwnd_destroy_plan(config.fftwPlan);
00184 }
00185 
00186 template <class SrcTraverser, class SrcAccessor,
00187           class DestTraverser, class DestAccessor>
00188 void cosineTransformY(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
00189                       DestTraverser dul, DestAccessor dest, fftw_real norm)
00190 {
00191     int w = slr.x - sul.x;
00192     int h = slr.y - sul.y;
00193     
00194     detail::FFTWSinCosConfig config;
00195 
00196     // horizontal transformation
00197     int ns2 = h / 2;
00198     int nm1 = h - 1;
00199     int modn = h % 2;
00200     
00201     config.twiddles.resize(h + 1);
00202     config.fftwInput.resize(h + 1);
00203     config.fftwTmpResult.resize(h + 1);
00204     config.norm = norm;
00205     config.fftwPlan = rfftw2d_create_plan(1, nm1, FFTW_REAL_TO_COMPLEX, FFTW_ESTIMATE );
00206 
00207     fftw_real dt = M_PI / nm1;
00208     for(int k=1; k<ns2; ++k)
00209     {
00210         fftw_real f = dt * k;
00211         config.twiddles[k] = 2.0*VIGRA_CSTD::sin(f);
00212         config.twiddles[nm1-k] = 2.0*VIGRA_CSTD::cos(f);
00213     }
00214 
00215     for(; sul.x != slr.x; ++sul.x, ++dul.x)
00216     {
00217         typename SrcTraverser::column_iterator s = sul.columnIterator();
00218         typename SrcTraverser::column_iterator send = s + h;
00219         typename DestTraverser::column_iterator d = dul.columnIterator();
00220         cosineTransformLineImpl(s, send, src, d, dest, config);
00221     }
00222 
00223     rfftwnd_destroy_plan(config.fftwPlan);
00224 }
00225 
00226 template <class SrcTraverser, class SrcAccessor,
00227           class DestTraverser, class DestAccessor>
00228 inline void 
00229 realFourierTransformXEvenYEven(SrcTraverser sul, SrcTraverser slr, SrcAccessor src,
00230                       DestTraverser dul, DestAccessor dest, fftw_real norm)
00231 {
00232     BasicImage<fftw_real> tmp(slr - sul);
00233     cosineTransformX(sul, slr, src, tmp.upperLeft(), tmp.accessor(), 1.0);
00234     cosineTransformY(tmp.upperLeft(), tmp.lowerRight(), tmp.accessor(), dul, dest, norm);
00235 }
00236 
00237 template <class SrcTraverser, class SrcAccessor,
00238           class DestTraverser, class DestAccessor>
00239 inline void 
00240 realFourierTransformXEvenYEven(triple<SrcTraverser, SrcTraverser, SrcAccessor> src,
00241                       pair<DestTraverser, DestAccessor> dest, fftw_real norm)
00242 {
00243     realFourierTransformXEvenYEven(src.first, src.second, src.third, dest.first, dest.second, norm);
00244 }
00245 
00246 } // namespace vigra
00247 
00248 #endif // VIGRA_RFFTW_HXX

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

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