/* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % FFFFF OOO U U RRRR IIIII EEEEE RRRR % % F O O U U R R I E R R % % FFF O O U U RRRR I EEE RRRR % % F O O U U R R I E R R % % F OOO UUU R R IIIII EEEEE R R % % % % % % MagickCore Discrete Fourier Transform Methods % % % % Software Design % % Sean Burke % % Fred Weinhaus % % Cristy % % July 2009 % % % % % % Copyright 1999-2019 ImageMagick Studio LLC, a non-profit organization % % dedicated to making software imaging solutions freely available. % % % % You may not use this file except in compliance with the License. You may % % obtain a copy of the License at % % % % https://imagemagick.org/script/license.php % % % % Unless required by applicable law or agreed to in writing, software % % distributed under the License is distributed on an "AS IS" BASIS, % % WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. % % See the License for the specific language governing permissions and % % limitations under the License. % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % */ /* Include declarations. */ #include "magick/studio.h" #include "magick/artifact.h" #include "magick/attribute.h" #include "magick/blob.h" #include "magick/cache.h" #include "magick/image.h" #include "magick/image-private.h" #include "magick/list.h" #include "magick/fourier.h" #include "magick/log.h" #include "magick/memory_.h" #include "magick/monitor.h" #include "magick/monitor-private.h" #include "magick/pixel-accessor.h" #include "magick/pixel-private.h" #include "magick/property.h" #include "magick/quantum-private.h" #include "magick/resource_.h" #include "magick/string-private.h" #include "magick/thread-private.h" #if defined(MAGICKCORE_FFTW_DELEGATE) #if defined(MAGICKCORE_HAVE_COMPLEX_H) #include #endif #include #if !defined(MAGICKCORE_HAVE_CABS) #define cabs(z) (sqrt(z[0]*z[0]+z[1]*z[1])) #endif #if !defined(MAGICKCORE_HAVE_CARG) #define carg(z) (atan2(cimag(z),creal(z))) #endif #if !defined(MAGICKCORE_HAVE_CIMAG) #define cimag(z) (z[1]) #endif #if !defined(MAGICKCORE_HAVE_CREAL) #define creal(z) (z[0]) #endif #endif /* Typedef declarations. */ typedef struct _FourierInfo { ChannelType channel; MagickBooleanType modulus; size_t width, height; ssize_t center; } FourierInfo; /* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % C o m p l e x I m a g e s % % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % ComplexImages() performs complex mathematics on an image sequence. % % The format of the ComplexImages method is: % % MagickBooleanType ComplexImages(Image *images,const ComplexOperator op, % ExceptionInfo *exception) % % A description of each parameter follows: % % o image: the image. % % o op: A complex operator. % % o exception: return any errors or warnings in this structure. % */ MagickExport Image *ComplexImages(const Image *images,const ComplexOperator op, ExceptionInfo *exception) { #define ComplexImageTag "Complex/Image" CacheView *Ai_view, *Ar_view, *Bi_view, *Br_view, *Ci_view, *Cr_view; const char *artifact; const Image *Ai_image, *Ar_image, *Bi_image, *Br_image; double snr; Image *Ci_image, *complex_images, *Cr_image, *image; MagickBooleanType status; MagickOffsetType progress; ssize_t y; assert(images != (Image *) NULL); assert(images->signature == MagickCoreSignature); if (images->debug != MagickFalse) (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename); assert(exception != (ExceptionInfo *) NULL); assert(exception->signature == MagickCoreSignature); if (images->next == (Image *) NULL) { (void) ThrowMagickException(exception,GetMagickModule(),ImageError, "ImageSequenceRequired","`%s'",images->filename); return((Image *) NULL); } image=CloneImage(images,0,0,MagickTrue,exception); if (image == (Image *) NULL) return((Image *) NULL); if (SetImageStorageClass(image,DirectClass) == MagickFalse) { image=DestroyImageList(image); return(image); } image->depth=32UL; complex_images=NewImageList(); AppendImageToList(&complex_images,image); image=CloneImage(images,0,0,MagickTrue,exception); if (image == (Image *) NULL) { complex_images=DestroyImageList(complex_images); return(complex_images); } AppendImageToList(&complex_images,image); /* Apply complex mathematics to image pixels. */ artifact=GetImageArtifact(image,"complex:snr"); snr=0.0; if (artifact != (const char *) NULL) snr=StringToDouble(artifact,(char **) NULL); Ar_image=images; Ai_image=images->next; Br_image=images; Bi_image=images->next; if ((images->next->next != (Image *) NULL) && (images->next->next->next != (Image *) NULL)) { Br_image=images->next->next; Bi_image=images->next->next->next; } Cr_image=complex_images; Ci_image=complex_images->next; Ar_view=AcquireVirtualCacheView(Ar_image,exception); Ai_view=AcquireVirtualCacheView(Ai_image,exception); Br_view=AcquireVirtualCacheView(Br_image,exception); Bi_view=AcquireVirtualCacheView(Bi_image,exception); Cr_view=AcquireAuthenticCacheView(Cr_image,exception); Ci_view=AcquireAuthenticCacheView(Ci_image,exception); status=MagickTrue; progress=0; #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp parallel for schedule(static) shared(progress,status) \ magick_number_threads(Cr_image,complex_images,Cr_image->rows,1L) #endif for (y=0; y < (ssize_t) Cr_image->rows; y++) { register const PixelPacket *magick_restrict Ai, *magick_restrict Ar, *magick_restrict Bi, *magick_restrict Br; register PixelPacket *magick_restrict Ci, *magick_restrict Cr; register ssize_t x; if (status == MagickFalse) continue; Ar=GetCacheViewVirtualPixels(Ar_view,0,y,Cr_image->columns,1,exception); Ai=GetCacheViewVirtualPixels(Ai_view,0,y,Cr_image->columns,1,exception); Br=GetCacheViewVirtualPixels(Br_view,0,y,Cr_image->columns,1,exception); Bi=GetCacheViewVirtualPixels(Bi_view,0,y,Cr_image->columns,1,exception); Cr=QueueCacheViewAuthenticPixels(Cr_view,0,y,Cr_image->columns,1,exception); Ci=QueueCacheViewAuthenticPixels(Ci_view,0,y,Ci_image->columns,1,exception); if ((Ar == (const PixelPacket *) NULL) || (Ai == (const PixelPacket *) NULL) || (Br == (const PixelPacket *) NULL) || (Bi == (const PixelPacket *) NULL) || (Cr == (PixelPacket *) NULL) || (Ci == (PixelPacket *) NULL)) { status=MagickFalse; continue; } for (x=0; x < (ssize_t) Cr_image->columns; x++) { switch (op) { case AddComplexOperator: { Cr->red=Ar->red+Br->red; Ci->red=Ai->red+Bi->red; Cr->green=Ar->green+Br->green; Ci->green=Ai->green+Bi->green; Cr->blue=Ar->blue+Br->blue; Ci->blue=Ai->blue+Bi->blue; if (images->matte != MagickFalse) { Cr->opacity=Ar->opacity+Br->opacity; Ci->opacity=Ai->opacity+Bi->opacity; } break; } case ConjugateComplexOperator: default: { Cr->red=Ar->red; Ci->red=(-Bi->red); Cr->green=Ar->green; Ci->green=(-Bi->green); Cr->blue=Ar->blue; Ci->blue=(-Bi->blue); if (images->matte != MagickFalse) { Cr->opacity=Ar->opacity; Ci->opacity=(-Bi->opacity); } break; } case DivideComplexOperator: { double gamma; gamma=PerceptibleReciprocal(Br->red*Br->red+Bi->red*Bi->red+snr); Cr->red=gamma*((double) Ar->red*Br->red+(double) Ai->red*Bi->red); Ci->red=gamma*((double) Ai->red*Br->red-(double) Ar->red*Bi->red); gamma=PerceptibleReciprocal((double) Br->green*Br->green+(double) Bi->green*Bi->green+snr); Cr->green=gamma*((double) Ar->green*Br->green+(double) Ai->green*Bi->green); Ci->green=gamma*((double) Ai->green*Br->green-(double) Ar->green*Bi->green); gamma=PerceptibleReciprocal((double) Br->blue*Br->blue+(double) Bi->blue*Bi->blue+snr); Cr->blue=gamma*((double) Ar->blue*Br->blue+(double) Ai->blue*Bi->blue); Ci->blue=gamma*((double) Ai->blue*Br->blue-(double) Ar->blue*Bi->blue); if (images->matte != MagickFalse) { gamma=PerceptibleReciprocal((double) Br->opacity*Br->opacity+ (double) Bi->opacity*Bi->opacity+snr); Cr->opacity=gamma*((double) Ar->opacity*Br->opacity+(double) Ai->opacity*Bi->opacity); Ci->opacity=gamma*((double) Ai->opacity*Br->opacity-(double) Ar->opacity*Bi->opacity); } break; } case MagnitudePhaseComplexOperator: { Cr->red=sqrt((double) Ar->red*Ar->red+(double) Ai->red*Ai->red); Ci->red=atan2((double) Ai->red,(double) Ar->red)/(2.0*MagickPI)+0.5; Cr->green=sqrt((double) Ar->green*Ar->green+(double) Ai->green*Ai->green); Ci->green=atan2((double) Ai->green,(double) Ar->green)/ (2.0*MagickPI)+0.5; Cr->blue=sqrt((double) Ar->blue*Ar->blue+(double) Ai->blue*Ai->blue); Ci->blue=atan2(Ai->blue,Ar->blue)/(2.0*MagickPI)+0.5; if (images->matte != MagickFalse) { Cr->opacity=sqrt((double) Ar->opacity*Ar->opacity+(double) Ai->opacity*Ai->opacity); Ci->opacity=atan2((double) Ai->opacity,(double) Ar->opacity)/ (2.0*MagickPI)+0.5; } break; } case MultiplyComplexOperator: { Cr->red=QuantumScale*((double) Ar->red*Br->red-(double) Ai->red*Bi->red); Ci->red=QuantumScale*((double) Ai->red*Br->red+(double) Ar->red*Bi->red); Cr->green=QuantumScale*((double) Ar->green*Br->green-(double) Ai->green*Bi->green); Ci->green=QuantumScale*((double) Ai->green*Br->green+(double) Ar->green*Bi->green); Cr->blue=QuantumScale*((double) Ar->blue*Br->blue-(double) Ai->blue*Bi->blue); Ci->blue=QuantumScale*((double) Ai->blue*Br->blue+(double) Ar->blue*Bi->blue); if (images->matte != MagickFalse) { Cr->opacity=QuantumScale*((double) Ar->opacity*Br->opacity- (double) Ai->opacity*Bi->opacity); Ci->opacity=QuantumScale*((double) Ai->opacity*Br->opacity+ (double) Ar->opacity*Bi->opacity); } break; } case RealImaginaryComplexOperator: { Cr->red=Ar->red*cos(2.0*MagickPI*(Ai->red-0.5)); Ci->red=Ar->red*sin(2.0*MagickPI*(Ai->red-0.5)); Cr->green=Ar->green*cos(2.0*MagickPI*(Ai->green-0.5)); Ci->green=Ar->green*sin(2.0*MagickPI*(Ai->green-0.5)); Cr->blue=Ar->blue*cos(2.0*MagickPI*(Ai->blue-0.5)); Ci->blue=Ar->blue*sin(2.0*MagickPI*(Ai->blue-0.5)); if (images->matte != MagickFalse) { Cr->opacity=Ar->opacity*cos(2.0*MagickPI*(Ai->opacity-0.5)); Ci->opacity=Ar->opacity*sin(2.0*MagickPI*(Ai->opacity-0.5)); } break; } case SubtractComplexOperator: { Cr->red=Ar->red-Br->red; Ci->red=Ai->red-Bi->red; Cr->green=Ar->green-Br->green; Ci->green=Ai->green-Bi->green; Cr->blue=Ar->blue-Br->blue; Ci->blue=Ai->blue-Bi->blue; if (Cr_image->matte != MagickFalse) { Cr->opacity=Ar->opacity-Br->opacity; Ci->opacity=Ai->opacity-Bi->opacity; } break; } } Ar++; Ai++; Br++; Bi++; Cr++; Ci++; } if (SyncCacheViewAuthenticPixels(Ci_view,exception) == MagickFalse) status=MagickFalse; if (SyncCacheViewAuthenticPixels(Cr_view,exception) == MagickFalse) status=MagickFalse; if (images->progress_monitor != (MagickProgressMonitor) NULL) { MagickBooleanType proceed; #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp atomic #endif progress++; proceed=SetImageProgress(images,ComplexImageTag,progress,images->rows); if (proceed == MagickFalse) status=MagickFalse; } } Cr_view=DestroyCacheView(Cr_view); Ci_view=DestroyCacheView(Ci_view); Br_view=DestroyCacheView(Br_view); Bi_view=DestroyCacheView(Bi_view); Ar_view=DestroyCacheView(Ar_view); Ai_view=DestroyCacheView(Ai_view); if (status == MagickFalse) complex_images=DestroyImageList(complex_images); return(complex_images); } /* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % F o r w a r d F o u r i e r T r a n s f o r m I m a g e % % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % ForwardFourierTransformImage() implements the discrete Fourier transform % (DFT) of the image either as a magnitude / phase or real / imaginary image % pair. % % The format of the ForwadFourierTransformImage method is: % % Image *ForwardFourierTransformImage(const Image *image, % const MagickBooleanType modulus,ExceptionInfo *exception) % % A description of each parameter follows: % % o image: the image. % % o modulus: if true, return as transform as a magnitude / phase pair % otherwise a real / imaginary image pair. % % o exception: return any errors or warnings in this structure. % */ #if defined(MAGICKCORE_FFTW_DELEGATE) static MagickBooleanType RollFourier(const size_t width,const size_t height, const ssize_t x_offset,const ssize_t y_offset,double *roll_pixels) { double *source_pixels; MemoryInfo *source_info; register ssize_t i, x; ssize_t u, v, y; /* Move zero frequency (DC, average color) from (0,0) to (width/2,height/2). */ source_info=AcquireVirtualMemory(width,height*sizeof(*source_pixels)); if (source_info == (MemoryInfo *) NULL) return(MagickFalse); source_pixels=(double *) GetVirtualMemoryBlob(source_info); i=0L; for (y=0L; y < (ssize_t) height; y++) { if (y_offset < 0L) v=((y+y_offset) < 0L) ? y+y_offset+(ssize_t) height : y+y_offset; else v=((y+y_offset) > ((ssize_t) height-1L)) ? y+y_offset-(ssize_t) height : y+y_offset; for (x=0L; x < (ssize_t) width; x++) { if (x_offset < 0L) u=((x+x_offset) < 0L) ? x+x_offset+(ssize_t) width : x+x_offset; else u=((x+x_offset) > ((ssize_t) width-1L)) ? x+x_offset-(ssize_t) width : x+x_offset; source_pixels[v*width+u]=roll_pixels[i++]; } } (void) memcpy(roll_pixels,source_pixels,height*width* sizeof(*source_pixels)); source_info=RelinquishVirtualMemory(source_info); return(MagickTrue); } static MagickBooleanType ForwardQuadrantSwap(const size_t width, const size_t height,double *source_pixels,double *forward_pixels) { MagickBooleanType status; register ssize_t x; ssize_t center, y; /* Swap quadrants. */ center=(ssize_t) (width/2L)+1L; status=RollFourier((size_t) center,height,0L,(ssize_t) height/2L, source_pixels); if (status == MagickFalse) return(MagickFalse); for (y=0L; y < (ssize_t) height; y++) for (x=0L; x < (ssize_t) (width/2L); x++) forward_pixels[y*width+x+width/2L]=source_pixels[y*center+x]; for (y=1; y < (ssize_t) height; y++) for (x=0L; x < (ssize_t) (width/2L); x++) forward_pixels[(height-y)*width+width/2L-x-1L]= source_pixels[y*center+x+1L]; for (x=0L; x < (ssize_t) (width/2L); x++) forward_pixels[width/2L-x-1L]=source_pixels[x+1L]; return(MagickTrue); } static void CorrectPhaseLHS(const size_t width,const size_t height, double *fourier_pixels) { register ssize_t x; ssize_t y; for (y=0L; y < (ssize_t) height; y++) for (x=0L; x < (ssize_t) (width/2L); x++) fourier_pixels[y*width+x]*=(-1.0); } static MagickBooleanType ForwardFourier(const FourierInfo *fourier_info, Image *image,double *magnitude,double *phase,ExceptionInfo *exception) { CacheView *magnitude_view, *phase_view; double *magnitude_pixels, *phase_pixels; Image *magnitude_image, *phase_image; MagickBooleanType status; MemoryInfo *magnitude_info, *phase_info; register IndexPacket *indexes; register PixelPacket *q; register ssize_t x; ssize_t i, y; magnitude_image=GetFirstImageInList(image); phase_image=GetNextImageInList(image); if (phase_image == (Image *) NULL) { (void) ThrowMagickException(exception,GetMagickModule(),ImageError, "ImageSequenceRequired","`%s'",image->filename); return(MagickFalse); } /* Create "Fourier Transform" image from constituent arrays. */ magnitude_info=AcquireVirtualMemory((size_t) fourier_info->width, fourier_info->height*sizeof(*magnitude_pixels)); phase_info=AcquireVirtualMemory((size_t) fourier_info->width, fourier_info->height*sizeof(*phase_pixels)); if ((magnitude_info == (MemoryInfo *) NULL) || (phase_info == (MemoryInfo *) NULL)) { if (phase_info != (MemoryInfo *) NULL) phase_info=RelinquishVirtualMemory(phase_info); if (magnitude_info != (MemoryInfo *) NULL) magnitude_info=RelinquishVirtualMemory(magnitude_info); (void) ThrowMagickException(exception,GetMagickModule(), ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename); return(MagickFalse); } magnitude_pixels=(double *) GetVirtualMemoryBlob(magnitude_info); (void) memset(magnitude_pixels,0,fourier_info->width* fourier_info->height*sizeof(*magnitude_pixels)); phase_pixels=(double *) GetVirtualMemoryBlob(phase_info); (void) memset(phase_pixels,0,fourier_info->width* fourier_info->height*sizeof(*phase_pixels)); status=ForwardQuadrantSwap(fourier_info->width,fourier_info->height, magnitude,magnitude_pixels); if (status != MagickFalse) status=ForwardQuadrantSwap(fourier_info->width,fourier_info->height,phase, phase_pixels); CorrectPhaseLHS(fourier_info->width,fourier_info->height,phase_pixels); if (fourier_info->modulus != MagickFalse) { i=0L; for (y=0L; y < (ssize_t) fourier_info->height; y++) for (x=0L; x < (ssize_t) fourier_info->width; x++) { phase_pixels[i]/=(2.0*MagickPI); phase_pixels[i]+=0.5; i++; } } magnitude_view=AcquireAuthenticCacheView(magnitude_image,exception); i=0L; for (y=0L; y < (ssize_t) fourier_info->height; y++) { q=GetCacheViewAuthenticPixels(magnitude_view,0L,y,fourier_info->width,1UL, exception); if (q == (PixelPacket *) NULL) break; indexes=GetCacheViewAuthenticIndexQueue(magnitude_view); for (x=0L; x < (ssize_t) fourier_info->width; x++) { switch (fourier_info->channel) { case RedChannel: default: { SetPixelRed(q,ClampToQuantum(QuantumRange*magnitude_pixels[i])); break; } case GreenChannel: { SetPixelGreen(q,ClampToQuantum(QuantumRange*magnitude_pixels[i])); break; } case BlueChannel: { SetPixelBlue(q,ClampToQuantum(QuantumRange*magnitude_pixels[i])); break; } case OpacityChannel: { SetPixelOpacity(q,ClampToQuantum(QuantumRange*magnitude_pixels[i])); break; } case IndexChannel: { SetPixelIndex(indexes+x,ClampToQuantum(QuantumRange* magnitude_pixels[i])); break; } case GrayChannels: { SetPixelGray(q,ClampToQuantum(QuantumRange*magnitude_pixels[i])); break; } } i++; q++; } status=SyncCacheViewAuthenticPixels(magnitude_view,exception); if (status == MagickFalse) break; } magnitude_view=DestroyCacheView(magnitude_view); i=0L; phase_view=AcquireAuthenticCacheView(phase_image,exception); for (y=0L; y < (ssize_t) fourier_info->height; y++) { q=GetCacheViewAuthenticPixels(phase_view,0L,y,fourier_info->width,1UL, exception); if (q == (PixelPacket *) NULL) break; indexes=GetCacheViewAuthenticIndexQueue(phase_view); for (x=0L; x < (ssize_t) fourier_info->width; x++) { switch (fourier_info->channel) { case RedChannel: default: { SetPixelRed(q,ClampToQuantum(QuantumRange*phase_pixels[i])); break; } case GreenChannel: { SetPixelGreen(q,ClampToQuantum(QuantumRange*phase_pixels[i])); break; } case BlueChannel: { SetPixelBlue(q,ClampToQuantum(QuantumRange*phase_pixels[i])); break; } case OpacityChannel: { SetPixelOpacity(q,ClampToQuantum(QuantumRange*phase_pixels[i])); break; } case IndexChannel: { SetPixelIndex(indexes+x,ClampToQuantum(QuantumRange*phase_pixels[i])); break; } case GrayChannels: { SetPixelGray(q,ClampToQuantum(QuantumRange*phase_pixels[i])); break; } } i++; q++; } status=SyncCacheViewAuthenticPixels(phase_view,exception); if (status == MagickFalse) break; } phase_view=DestroyCacheView(phase_view); phase_info=RelinquishVirtualMemory(phase_info); magnitude_info=RelinquishVirtualMemory(magnitude_info); return(status); } static MagickBooleanType ForwardFourierTransform(FourierInfo *fourier_info, const Image *image,double *magnitude_pixels,double *phase_pixels, ExceptionInfo *exception) { CacheView *image_view; const char *value; double *source_pixels; fftw_complex *forward_pixels; fftw_plan fftw_r2c_plan; MemoryInfo *forward_info, *source_info; register const IndexPacket *indexes; register const PixelPacket *p; register ssize_t i, x; ssize_t y; /* Generate the forward Fourier transform. */ source_info=AcquireVirtualMemory((size_t) fourier_info->width, fourier_info->height*sizeof(*source_pixels)); if (source_info == (MemoryInfo *) NULL) { (void) ThrowMagickException(exception,GetMagickModule(), ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename); return(MagickFalse); } source_pixels=(double *) GetVirtualMemoryBlob(source_info); memset(source_pixels,0,fourier_info->width*fourier_info->height* sizeof(*source_pixels)); i=0L; image_view=AcquireVirtualCacheView(image,exception); for (y=0L; y < (ssize_t) fourier_info->height; y++) { p=GetCacheViewVirtualPixels(image_view,0L,y,fourier_info->width,1UL, exception); if (p == (const PixelPacket *) NULL) break; indexes=GetCacheViewVirtualIndexQueue(image_view); for (x=0L; x < (ssize_t) fourier_info->width; x++) { switch (fourier_info->channel) { case RedChannel: default: { source_pixels[i]=QuantumScale*GetPixelRed(p); break; } case GreenChannel: { source_pixels[i]=QuantumScale*GetPixelGreen(p); break; } case BlueChannel: { source_pixels[i]=QuantumScale*GetPixelBlue(p); break; } case OpacityChannel: { source_pixels[i]=QuantumScale*GetPixelOpacity(p); break; } case IndexChannel: { source_pixels[i]=QuantumScale*GetPixelIndex(indexes+x); break; } case GrayChannels: { source_pixels[i]=QuantumScale*GetPixelGray(p); break; } } i++; p++; } } image_view=DestroyCacheView(image_view); forward_info=AcquireVirtualMemory((size_t) fourier_info->width, (fourier_info->height/2+1)*sizeof(*forward_pixels)); if (forward_info == (MemoryInfo *) NULL) { (void) ThrowMagickException(exception,GetMagickModule(), ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename); source_info=(MemoryInfo *) RelinquishVirtualMemory(source_info); return(MagickFalse); } forward_pixels=(fftw_complex *) GetVirtualMemoryBlob(forward_info); #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp critical (MagickCore_ForwardFourierTransform) #endif fftw_r2c_plan=fftw_plan_dft_r2c_2d(fourier_info->width,fourier_info->height, source_pixels,forward_pixels,FFTW_ESTIMATE); fftw_execute_dft_r2c(fftw_r2c_plan,source_pixels,forward_pixels); fftw_destroy_plan(fftw_r2c_plan); source_info=(MemoryInfo *) RelinquishVirtualMemory(source_info); value=GetImageArtifact(image,"fourier:normalize"); if ((value == (const char *) NULL) || (LocaleCompare(value,"forward") == 0)) { double gamma; /* Normalize Fourier transform. */ i=0L; gamma=PerceptibleReciprocal((double) fourier_info->width* fourier_info->height); for (y=0L; y < (ssize_t) fourier_info->height; y++) for (x=0L; x < (ssize_t) fourier_info->center; x++) { #if defined(MAGICKCORE_HAVE_COMPLEX_H) forward_pixels[i]*=gamma; #else forward_pixels[i][0]*=gamma; forward_pixels[i][1]*=gamma; #endif i++; } } /* Generate magnitude and phase (or real and imaginary). */ i=0L; if (fourier_info->modulus != MagickFalse) for (y=0L; y < (ssize_t) fourier_info->height; y++) for (x=0L; x < (ssize_t) fourier_info->center; x++) { magnitude_pixels[i]=cabs(forward_pixels[i]); phase_pixels[i]=carg(forward_pixels[i]); i++; } else for (y=0L; y < (ssize_t) fourier_info->height; y++) for (x=0L; x < (ssize_t) fourier_info->center; x++) { magnitude_pixels[i]=creal(forward_pixels[i]); phase_pixels[i]=cimag(forward_pixels[i]); i++; } forward_info=(MemoryInfo *) RelinquishVirtualMemory(forward_info); return(MagickTrue); } static MagickBooleanType ForwardFourierTransformChannel(const Image *image, const ChannelType channel,const MagickBooleanType modulus, Image *fourier_image,ExceptionInfo *exception) { double *magnitude_pixels, *phase_pixels; FourierInfo fourier_info; MagickBooleanType status; MemoryInfo *magnitude_info, *phase_info; fourier_info.width=image->columns; fourier_info.height=image->rows; if ((image->columns != image->rows) || ((image->columns % 2) != 0) || ((image->rows % 2) != 0)) { size_t extent=image->columns < image->rows ? image->rows : image->columns; fourier_info.width=(extent & 0x01) == 1 ? extent+1UL : extent; } fourier_info.height=fourier_info.width; fourier_info.center=(ssize_t) (fourier_info.width/2L)+1L; fourier_info.channel=channel; fourier_info.modulus=modulus; magnitude_info=AcquireVirtualMemory((size_t) fourier_info.width, (fourier_info.height/2+1)*sizeof(*magnitude_pixels)); phase_info=AcquireVirtualMemory((size_t) fourier_info.width, (fourier_info.height/2+1)*sizeof(*phase_pixels)); if ((magnitude_info == (MemoryInfo *) NULL) || (phase_info == (MemoryInfo *) NULL)) { if (phase_info != (MemoryInfo *) NULL) phase_info=RelinquishVirtualMemory(phase_info); if (magnitude_info == (MemoryInfo *) NULL) magnitude_info=RelinquishVirtualMemory(magnitude_info); (void) ThrowMagickException(exception,GetMagickModule(), ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename); return(MagickFalse); } magnitude_pixels=(double *) GetVirtualMemoryBlob(magnitude_info); phase_pixels=(double *) GetVirtualMemoryBlob(phase_info); status=ForwardFourierTransform(&fourier_info,image,magnitude_pixels, phase_pixels,exception); if (status != MagickFalse) status=ForwardFourier(&fourier_info,fourier_image,magnitude_pixels, phase_pixels,exception); phase_info=RelinquishVirtualMemory(phase_info); magnitude_info=RelinquishVirtualMemory(magnitude_info); return(status); } #endif MagickExport Image *ForwardFourierTransformImage(const Image *image, const MagickBooleanType modulus,ExceptionInfo *exception) { Image *fourier_image; fourier_image=NewImageList(); #if !defined(MAGICKCORE_FFTW_DELEGATE) (void) modulus; (void) ThrowMagickException(exception,GetMagickModule(), MissingDelegateWarning,"DelegateLibrarySupportNotBuiltIn","`%s' (FFTW)", image->filename); #else { Image *magnitude_image; size_t height, width; width=image->columns; height=image->rows; if ((image->columns != image->rows) || ((image->columns % 2) != 0) || ((image->rows % 2) != 0)) { size_t extent=image->columns < image->rows ? image->rows : image->columns; width=(extent & 0x01) == 1 ? extent+1UL : extent; } height=width; magnitude_image=CloneImage(image,width,height,MagickTrue,exception); if (magnitude_image != (Image *) NULL) { Image *phase_image; magnitude_image->storage_class=DirectClass; magnitude_image->depth=32UL; phase_image=CloneImage(image,width,height,MagickTrue,exception); if (phase_image == (Image *) NULL) magnitude_image=DestroyImage(magnitude_image); else { MagickBooleanType is_gray, status; phase_image->storage_class=DirectClass; phase_image->depth=32UL; AppendImageToList(&fourier_image,magnitude_image); AppendImageToList(&fourier_image,phase_image); status=MagickTrue; is_gray=IsGrayImage(image,exception); #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp parallel sections #endif { #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; if (is_gray != MagickFalse) thread_status=ForwardFourierTransformChannel(image, GrayChannels,modulus,fourier_image,exception); else thread_status=ForwardFourierTransformChannel(image,RedChannel, modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; thread_status=MagickTrue; if (is_gray == MagickFalse) thread_status=ForwardFourierTransformChannel(image, GreenChannel,modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; thread_status=MagickTrue; if (is_gray == MagickFalse) thread_status=ForwardFourierTransformChannel(image, BlueChannel,modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; thread_status=MagickTrue; if (image->matte != MagickFalse) thread_status=ForwardFourierTransformChannel(image, OpacityChannel,modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; thread_status=MagickTrue; if (image->colorspace == CMYKColorspace) thread_status=ForwardFourierTransformChannel(image, IndexChannel,modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } } if (status == MagickFalse) fourier_image=DestroyImageList(fourier_image); fftw_cleanup(); } } } #endif return(fourier_image); } /* %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % % % % % % I n v e r s e F o u r i e r T r a n s f o r m I m a g e % % % % % % % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % InverseFourierTransformImage() implements the inverse discrete Fourier % transform (DFT) of the image either as a magnitude / phase or real / % imaginary image pair. % % The format of the InverseFourierTransformImage method is: % % Image *InverseFourierTransformImage(const Image *magnitude_image, % const Image *phase_image,const MagickBooleanType modulus, % ExceptionInfo *exception) % % A description of each parameter follows: % % o magnitude_image: the magnitude or real image. % % o phase_image: the phase or imaginary image. % % o modulus: if true, return transform as a magnitude / phase pair % otherwise a real / imaginary image pair. % % o exception: return any errors or warnings in this structure. % */ #if defined(MAGICKCORE_FFTW_DELEGATE) static MagickBooleanType InverseQuadrantSwap(const size_t width, const size_t height,const double *source,double *destination) { register ssize_t x; ssize_t center, y; /* Swap quadrants. */ center=(ssize_t) (width/2L)+1L; for (y=1L; y < (ssize_t) height; y++) for (x=0L; x < (ssize_t) (width/2L+1L); x++) destination[(height-y)*center-x+width/2L]=source[y*width+x]; for (y=0L; y < (ssize_t) height; y++) destination[y*center]=source[y*width+width/2L]; for (x=0L; x < center; x++) destination[x]=source[center-x-1L]; return(RollFourier(center,height,0L,(ssize_t) height/-2L,destination)); } static MagickBooleanType InverseFourier(FourierInfo *fourier_info, const Image *magnitude_image,const Image *phase_image, fftw_complex *fourier_pixels,ExceptionInfo *exception) { CacheView *magnitude_view, *phase_view; double *inverse_pixels, *magnitude_pixels, *phase_pixels; MagickBooleanType status; MemoryInfo *inverse_info, *magnitude_info, *phase_info; register const IndexPacket *indexes; register const PixelPacket *p; register ssize_t i, x; ssize_t y; /* Inverse Fourier - read image and break down into a double array. */ magnitude_info=AcquireVirtualMemory((size_t) fourier_info->width, fourier_info->height*sizeof(*magnitude_pixels)); phase_info=AcquireVirtualMemory((size_t) fourier_info->width, fourier_info->height*sizeof(*phase_pixels)); inverse_info=AcquireVirtualMemory((size_t) fourier_info->width, (fourier_info->height/2+1)*sizeof(*inverse_pixels)); if ((magnitude_info == (MemoryInfo *) NULL) || (phase_info == (MemoryInfo *) NULL) || (inverse_info == (MemoryInfo *) NULL)) { if (magnitude_info != (MemoryInfo *) NULL) magnitude_info=RelinquishVirtualMemory(magnitude_info); if (phase_info != (MemoryInfo *) NULL) phase_info=RelinquishVirtualMemory(phase_info); if (inverse_info != (MemoryInfo *) NULL) inverse_info=RelinquishVirtualMemory(inverse_info); (void) ThrowMagickException(exception,GetMagickModule(), ResourceLimitError,"MemoryAllocationFailed","`%s'", magnitude_image->filename); return(MagickFalse); } magnitude_pixels=(double *) GetVirtualMemoryBlob(magnitude_info); phase_pixels=(double *) GetVirtualMemoryBlob(phase_info); inverse_pixels=(double *) GetVirtualMemoryBlob(inverse_info); i=0L; magnitude_view=AcquireVirtualCacheView(magnitude_image,exception); for (y=0L; y < (ssize_t) fourier_info->height; y++) { p=GetCacheViewVirtualPixels(magnitude_view,0L,y,fourier_info->width,1UL, exception); if (p == (const PixelPacket *) NULL) break; indexes=GetCacheViewAuthenticIndexQueue(magnitude_view); for (x=0L; x < (ssize_t) fourier_info->width; x++) { switch (fourier_info->channel) { case RedChannel: default: { magnitude_pixels[i]=QuantumScale*GetPixelRed(p); break; } case GreenChannel: { magnitude_pixels[i]=QuantumScale*GetPixelGreen(p); break; } case BlueChannel: { magnitude_pixels[i]=QuantumScale*GetPixelBlue(p); break; } case OpacityChannel: { magnitude_pixels[i]=QuantumScale*GetPixelOpacity(p); break; } case IndexChannel: { magnitude_pixels[i]=QuantumScale*GetPixelIndex(indexes+x); break; } case GrayChannels: { magnitude_pixels[i]=QuantumScale*GetPixelGray(p); break; } } i++; p++; } } magnitude_view=DestroyCacheView(magnitude_view); status=InverseQuadrantSwap(fourier_info->width,fourier_info->height, magnitude_pixels,inverse_pixels); (void) memcpy(magnitude_pixels,inverse_pixels,fourier_info->height* fourier_info->center*sizeof(*magnitude_pixels)); i=0L; phase_view=AcquireVirtualCacheView(phase_image,exception); for (y=0L; y < (ssize_t) fourier_info->height; y++) { p=GetCacheViewVirtualPixels(phase_view,0,y,fourier_info->width,1, exception); if (p == (const PixelPacket *) NULL) break; indexes=GetCacheViewAuthenticIndexQueue(phase_view); for (x=0L; x < (ssize_t) fourier_info->width; x++) { switch (fourier_info->channel) { case RedChannel: default: { phase_pixels[i]=QuantumScale*GetPixelRed(p); break; } case GreenChannel: { phase_pixels[i]=QuantumScale*GetPixelGreen(p); break; } case BlueChannel: { phase_pixels[i]=QuantumScale*GetPixelBlue(p); break; } case OpacityChannel: { phase_pixels[i]=QuantumScale*GetPixelOpacity(p); break; } case IndexChannel: { phase_pixels[i]=QuantumScale*GetPixelIndex(indexes+x); break; } case GrayChannels: { phase_pixels[i]=QuantumScale*GetPixelGray(p); break; } } i++; p++; } } if (fourier_info->modulus != MagickFalse) { i=0L; for (y=0L; y < (ssize_t) fourier_info->height; y++) for (x=0L; x < (ssize_t) fourier_info->width; x++) { phase_pixels[i]-=0.5; phase_pixels[i]*=(2.0*MagickPI); i++; } } phase_view=DestroyCacheView(phase_view); CorrectPhaseLHS(fourier_info->width,fourier_info->height,phase_pixels); if (status != MagickFalse) status=InverseQuadrantSwap(fourier_info->width,fourier_info->height, phase_pixels,inverse_pixels); (void) memcpy(phase_pixels,inverse_pixels,fourier_info->height* fourier_info->center*sizeof(*phase_pixels)); inverse_info=RelinquishVirtualMemory(inverse_info); /* Merge two sets. */ i=0L; if (fourier_info->modulus != MagickFalse) for (y=0L; y < (ssize_t) fourier_info->height; y++) for (x=0L; x < (ssize_t) fourier_info->center; x++) { #if defined(MAGICKCORE_HAVE_COMPLEX_H) fourier_pixels[i]=magnitude_pixels[i]*cos(phase_pixels[i])+I* magnitude_pixels[i]*sin(phase_pixels[i]); #else fourier_pixels[i][0]=magnitude_pixels[i]*cos(phase_pixels[i]); fourier_pixels[i][1]=magnitude_pixels[i]*sin(phase_pixels[i]); #endif i++; } else for (y=0L; y < (ssize_t) fourier_info->height; y++) for (x=0L; x < (ssize_t) fourier_info->center; x++) { #if defined(MAGICKCORE_HAVE_COMPLEX_H) fourier_pixels[i]=magnitude_pixels[i]+I*phase_pixels[i]; #else fourier_pixels[i][0]=magnitude_pixels[i]; fourier_pixels[i][1]=phase_pixels[i]; #endif i++; } magnitude_info=RelinquishVirtualMemory(magnitude_info); phase_info=RelinquishVirtualMemory(phase_info); return(status); } static MagickBooleanType InverseFourierTransform(FourierInfo *fourier_info, fftw_complex *fourier_pixels,Image *image,ExceptionInfo *exception) { CacheView *image_view; double *source_pixels; const char *value; fftw_plan fftw_c2r_plan; MemoryInfo *source_info; register IndexPacket *indexes; register PixelPacket *q; register ssize_t i, x; ssize_t y; source_info=AcquireVirtualMemory((size_t) fourier_info->width, fourier_info->height*sizeof(*source_pixels)); if (source_info == (MemoryInfo *) NULL) { (void) ThrowMagickException(exception,GetMagickModule(), ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename); return(MagickFalse); } source_pixels=(double *) GetVirtualMemoryBlob(source_info); value=GetImageArtifact(image,"fourier:normalize"); if (LocaleCompare(value,"inverse") == 0) { double gamma; /* Normalize inverse transform. */ i=0L; gamma=PerceptibleReciprocal((double) fourier_info->width* fourier_info->height); for (y=0L; y < (ssize_t) fourier_info->height; y++) for (x=0L; x < (ssize_t) fourier_info->center; x++) { #if defined(MAGICKCORE_HAVE_COMPLEX_H) fourier_pixels[i]*=gamma; #else fourier_pixels[i][0]*=gamma; fourier_pixels[i][1]*=gamma; #endif i++; } } #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp critical (MagickCore_InverseFourierTransform) #endif fftw_c2r_plan=fftw_plan_dft_c2r_2d(fourier_info->width,fourier_info->height, fourier_pixels,source_pixels,FFTW_ESTIMATE); fftw_execute_dft_c2r(fftw_c2r_plan,fourier_pixels,source_pixels); fftw_destroy_plan(fftw_c2r_plan); i=0L; image_view=AcquireAuthenticCacheView(image,exception); for (y=0L; y < (ssize_t) fourier_info->height; y++) { if (y >= (ssize_t) image->rows) break; q=GetCacheViewAuthenticPixels(image_view,0L,y,fourier_info->width > image->columns ? image->columns : fourier_info->width,1UL,exception); if (q == (PixelPacket *) NULL) break; indexes=GetCacheViewAuthenticIndexQueue(image_view); for (x=0L; x < (ssize_t) fourier_info->width; x++) { if (x < (ssize_t) image->columns) switch (fourier_info->channel) { case RedChannel: default: { SetPixelRed(q,ClampToQuantum(QuantumRange*source_pixels[i])); break; } case GreenChannel: { SetPixelGreen(q,ClampToQuantum(QuantumRange*source_pixels[i])); break; } case BlueChannel: { SetPixelBlue(q,ClampToQuantum(QuantumRange*source_pixels[i])); break; } case OpacityChannel: { SetPixelOpacity(q,ClampToQuantum(QuantumRange*source_pixels[i])); break; } case IndexChannel: { SetPixelIndex(indexes+x,ClampToQuantum(QuantumRange* source_pixels[i])); break; } case GrayChannels: { SetPixelGray(q,ClampToQuantum(QuantumRange*source_pixels[i])); break; } } i++; q++; } if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse) break; } image_view=DestroyCacheView(image_view); source_info=RelinquishVirtualMemory(source_info); return(MagickTrue); } static MagickBooleanType InverseFourierTransformChannel( const Image *magnitude_image,const Image *phase_image, const ChannelType channel,const MagickBooleanType modulus, Image *fourier_image,ExceptionInfo *exception) { fftw_complex *inverse_pixels; FourierInfo fourier_info; MagickBooleanType status; MemoryInfo *inverse_info; fourier_info.width=magnitude_image->columns; fourier_info.height=magnitude_image->rows; if ((magnitude_image->columns != magnitude_image->rows) || ((magnitude_image->columns % 2) != 0) || ((magnitude_image->rows % 2) != 0)) { size_t extent=magnitude_image->columns < magnitude_image->rows ? magnitude_image->rows : magnitude_image->columns; fourier_info.width=(extent & 0x01) == 1 ? extent+1UL : extent; } fourier_info.height=fourier_info.width; fourier_info.center=(ssize_t) (fourier_info.width/2L)+1L; fourier_info.channel=channel; fourier_info.modulus=modulus; inverse_info=AcquireVirtualMemory((size_t) fourier_info.width, (fourier_info.height/2+1)*sizeof(*inverse_pixels)); if (inverse_info == (MemoryInfo *) NULL) { (void) ThrowMagickException(exception,GetMagickModule(), ResourceLimitError,"MemoryAllocationFailed","`%s'", magnitude_image->filename); return(MagickFalse); } inverse_pixels=(fftw_complex *) GetVirtualMemoryBlob(inverse_info); status=InverseFourier(&fourier_info,magnitude_image,phase_image, inverse_pixels,exception); if (status != MagickFalse) status=InverseFourierTransform(&fourier_info,inverse_pixels,fourier_image, exception); inverse_info=RelinquishVirtualMemory(inverse_info); return(status); } #endif MagickExport Image *InverseFourierTransformImage(const Image *magnitude_image, const Image *phase_image,const MagickBooleanType modulus, ExceptionInfo *exception) { Image *fourier_image; assert(magnitude_image != (Image *) NULL); assert(magnitude_image->signature == MagickCoreSignature); if (magnitude_image->debug != MagickFalse) (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s", magnitude_image->filename); if (phase_image == (Image *) NULL) { (void) ThrowMagickException(exception,GetMagickModule(),ImageError, "ImageSequenceRequired","`%s'",magnitude_image->filename); return((Image *) NULL); } #if !defined(MAGICKCORE_FFTW_DELEGATE) fourier_image=(Image *) NULL; (void) modulus; (void) ThrowMagickException(exception,GetMagickModule(), MissingDelegateWarning,"DelegateLibrarySupportNotBuiltIn","`%s' (FFTW)", magnitude_image->filename); #else { fourier_image=CloneImage(magnitude_image,magnitude_image->columns, magnitude_image->rows,MagickTrue,exception); if (fourier_image != (Image *) NULL) { MagickBooleanType is_gray, status; status=MagickTrue; is_gray=IsGrayImage(magnitude_image,exception); if (is_gray != MagickFalse) is_gray=IsGrayImage(phase_image,exception); #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp parallel sections #endif { #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; if (is_gray != MagickFalse) thread_status=InverseFourierTransformChannel(magnitude_image, phase_image,GrayChannels,modulus,fourier_image,exception); else thread_status=InverseFourierTransformChannel(magnitude_image, phase_image,RedChannel,modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; thread_status=MagickTrue; if (is_gray == MagickFalse) thread_status=InverseFourierTransformChannel(magnitude_image, phase_image,GreenChannel,modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; thread_status=MagickTrue; if (is_gray == MagickFalse) thread_status=InverseFourierTransformChannel(magnitude_image, phase_image,BlueChannel,modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; thread_status=MagickTrue; if (magnitude_image->matte != MagickFalse) thread_status=InverseFourierTransformChannel(magnitude_image, phase_image,OpacityChannel,modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } #if defined(MAGICKCORE_OPENMP_SUPPORT) #pragma omp section #endif { MagickBooleanType thread_status; thread_status=MagickTrue; if (magnitude_image->colorspace == CMYKColorspace) thread_status=InverseFourierTransformChannel(magnitude_image, phase_image,IndexChannel,modulus,fourier_image,exception); if (thread_status == MagickFalse) status=thread_status; } } if (status == MagickFalse) fourier_image=DestroyImage(fourier_image); } fftw_cleanup(); } #endif return(fourier_image); }