2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
6 % FFFFF OOO U U RRRR IIIII EEEEE RRRR %
7 % F O O U U R R I E R R %
8 % FFF O O U U RRRR I EEE RRRR %
9 % F O O U U R R I E R R %
10 % F OOO UUU R R IIIII EEEEE R R %
13 % MagickCore Discrete Fourier Transform Methods %
22 % Copyright 1999-2013 ImageMagick Studio LLC, a non-profit organization %
23 % dedicated to making software imaging solutions freely available. %
25 % You may not use this file except in compliance with the License. You may %
26 % obtain a copy of the License at %
28 % http://www.imagemagick.org/script/license.php %
30 % Unless required by applicable law or agreed to in writing, software %
31 % distributed under the License is distributed on an "AS IS" BASIS, %
32 % WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. %
33 % See the License for the specific language governing permissions and %
34 % limitations under the License. %
36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
45 #include "MagickCore/studio.h"
46 #include "MagickCore/artifact.h"
47 #include "MagickCore/attribute.h"
48 #include "MagickCore/blob.h"
49 #include "MagickCore/cache.h"
50 #include "MagickCore/image.h"
51 #include "MagickCore/image-private.h"
52 #include "MagickCore/list.h"
53 #include "MagickCore/fourier.h"
54 #include "MagickCore/log.h"
55 #include "MagickCore/memory_.h"
56 #include "MagickCore/monitor.h"
57 #include "MagickCore/monitor-private.h"
58 #include "MagickCore/pixel-accessor.h"
59 #include "MagickCore/pixel-private.h"
60 #include "MagickCore/property.h"
61 #include "MagickCore/quantum-private.h"
62 #include "MagickCore/resource_.h"
63 #include "MagickCore/thread-private.h"
64 #if defined(MAGICKCORE_FFTW_DELEGATE)
65 #if defined(MAGICKCORE_HAVE_COMPLEX_H)
69 #if !defined(MAGICKCORE_HAVE_CABS)
70 #define cabs(z) (sqrt(z[0]*z[0]+z[1]*z[1]))
72 #if !defined(MAGICKCORE_HAVE_CARG)
73 #define carg(z) (atan2(cimag(z),creal(z)))
75 #if !defined(MAGICKCORE_HAVE_CIMAG)
76 #define cimag(z) (z[1])
78 #if !defined(MAGICKCORE_HAVE_CREAL)
79 #define creal(z) (z[0])
86 typedef struct _FourierInfo
103 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
107 % C o m p l e x I m a g e s %
111 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
113 % ComplexImages() performs complex mathematics on an image sequence.
115 % The format of the ComplexImages method is:
117 % MagickBooleanType ComplexImages(Image *images,
118 % const ComplexOperator operator,ExceptionInfo *exception)
120 % A description of each parameter follows:
122 % o image: the image.
124 % o operator: A complex operator.
126 % o exception: return any errors or warnings in this structure.
129 MagickExport Image *ComplexImages(const Image *images,
130 const ComplexOperator operator,ExceptionInfo *exception)
132 #define ComplexImageTag "Complex/Image"
163 assert(images != (Image *) NULL);
164 assert(images->signature == MagickSignature);
165 if (images->debug != MagickFalse)
166 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
167 assert(exception != (ExceptionInfo *) NULL);
168 assert(exception->signature == MagickSignature);
169 if (images->next == (Image *) NULL)
171 (void) ThrowMagickException(exception,GetMagickModule(),ImageError,
172 "ImageSequenceRequired","`%s'",images->filename);
173 return((Image *) NULL);
175 image=CloneImage(images,images->columns,images->rows,MagickTrue,exception);
176 if (image == (Image *) NULL)
177 return((Image *) NULL);
178 if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
180 image=DestroyImageList(image);
183 complex_images=NewImageList();
184 AppendImageToList(&complex_images,image);
185 image=CloneImage(images,images->columns,images->rows,MagickTrue,exception);
186 if (image == (Image *) NULL)
188 complex_images=DestroyImageList(complex_images);
189 return(complex_images);
191 if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
193 complex_images=DestroyImageList(complex_images);
194 return(complex_images);
196 AppendImageToList(&complex_images,image);
198 Apply complex mathematics to image pixels.
201 Ai_image=images->next;
203 Bi_image=images->next;
204 if ((images->next->next != (Image *) NULL) &&
205 (images->next->next->next != (Image *) NULL))
207 Br_image=images->next->next;
208 Bi_image=images->next->next->next;
210 Cr_image=complex_images;
211 Ci_image=complex_images->next;
212 Ar_view=AcquireVirtualCacheView(Ar_image,exception);
213 Ai_view=AcquireVirtualCacheView(Ai_image,exception);
214 Br_view=AcquireVirtualCacheView(Br_image,exception);
215 Bi_view=AcquireVirtualCacheView(Bi_image,exception);
216 Cr_view=AcquireAuthenticCacheView(Cr_image,exception);
217 Ci_view=AcquireAuthenticCacheView(Ci_image,exception);
220 #if defined(MAGICKCORE_OPENMP_SUPPORT)
221 #pragma omp parallel for schedule(static,4) shared(progress,status) \
222 magick_threads(images,complex_images,images->rows,1L)
224 for (y=0; y < (ssize_t) images->rows; y++)
226 register const Quantum
239 if (status == MagickFalse)
241 Ar=GetCacheViewVirtualPixels(Ar_view,0,y,images->columns,1,exception);
242 Ai=GetCacheViewVirtualPixels(Ai_view,0,y,images->columns,1,exception);
243 Br=GetCacheViewVirtualPixels(Br_view,0,y,images->columns,1,exception);
244 Bi=GetCacheViewVirtualPixels(Bi_view,0,y,images->columns,1,exception);
245 Cr=QueueCacheViewAuthenticPixels(Cr_view,0,y,images->columns,1,exception);
246 Ci=QueueCacheViewAuthenticPixels(Ci_view,0,y,images->columns,1,exception);
247 if ((Ar == (const Quantum *) NULL) || (Ai == (const Quantum *) NULL) ||
248 (Br == (const Quantum *) NULL) || (Bi == (const Quantum *) NULL) ||
249 (Cr == (Quantum *) NULL) || (Ci == (Quantum *) NULL))
254 for (x=0; x < (ssize_t) images->columns; x++)
259 for (i=0; i < (ssize_t) GetPixelChannels(images); i++)
263 case AddComplexOperator:
269 case ConjugateComplexOperator:
276 case DivideComplexOperator:
281 gamma=PerceptibleReciprocal(Br[i]*Br[i]+Bi[i]*Bi[i]);
282 Cr[i]=gamma*(Ar[i]*Br[i]+Ai[i]*Bi[i]);
283 Ci[i]=gamma*(Ai[i]*Br[i]-Ai[i]*Bi[i]);
286 case MagnitudePhaseComplexOperator:
288 Cr[i]=sqrt(Ar[i]*Ar[i]+Ai[i]*Ai[i]);
289 Ci[i]=atan2(Ai[i],Ar[i]);
292 case MultiplyComplexOperator:
294 Cr[i]=QuantumScale*(Ar[i]*Br[i]-Ai[i]*Bi[i]);
295 Ci[i]=QuantumScale*(Ai[i]*Br[i]+Ar[i]*Bi[i]);
298 case RealImaginaryComplexOperator:
300 Cr[i]=Ar[i]*exp(Ai[i]);
301 Ci[i]=Ar[i]*(cos(Ai[i])+sin(Ai[i]));
304 case SubtractComplexOperator:
311 Ar+=GetPixelChannels(Ar_image);
312 Ai+=GetPixelChannels(Ai_image);
313 Br+=GetPixelChannels(Br_image);
314 Bi+=GetPixelChannels(Bi_image);
315 Cr+=GetPixelChannels(Cr_image);
316 Ci+=GetPixelChannels(Ci_image);
319 if (SyncCacheViewAuthenticPixels(Ci_view,exception) == MagickFalse)
321 if (SyncCacheViewAuthenticPixels(Cr_view,exception) == MagickFalse)
323 if (images->progress_monitor != (MagickProgressMonitor) NULL)
328 #if defined(MAGICKCORE_OPENMP_SUPPORT)
329 #pragma omp critical (MagickCore_ComplexImages)
331 proceed=SetImageProgress(images,ComplexImageTag,progress++,
333 if (proceed == MagickFalse)
337 Cr_view=DestroyCacheView(Cr_view);
338 Ci_view=DestroyCacheView(Ci_view);
339 Br_view=DestroyCacheView(Br_view);
340 Bi_view=DestroyCacheView(Bi_view);
341 Ar_view=DestroyCacheView(Ar_view);
342 Ai_view=DestroyCacheView(Ai_view);
343 if (status == MagickFalse)
344 complex_images=DestroyImageList(complex_images);
345 return(complex_images);
349 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
353 % 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 %
357 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
359 % ForwardFourierTransformImage() implements the discrete Fourier transform
360 % (DFT) of the image either as a magnitude / phase or real / imaginary image
363 % The format of the ForwadFourierTransformImage method is:
365 % Image *ForwardFourierTransformImage(const Image *image,
366 % const MagickBooleanType modulus,ExceptionInfo *exception)
368 % A description of each parameter follows:
370 % o image: the image.
372 % o modulus: if true, return as transform as a magnitude / phase pair
373 % otherwise a real / imaginary image pair.
375 % o exception: return any errors or warnings in this structure.
379 #if defined(MAGICKCORE_FFTW_DELEGATE)
381 static MagickBooleanType RollFourier(const size_t width,const size_t height,
382 const ssize_t x_offset,const ssize_t y_offset,double *roll_pixels)
400 Move zero frequency (DC, average color) from (0,0) to (width/2,height/2).
402 source_info=AcquireVirtualMemory(height,width*sizeof(*source_pixels));
403 if (source_info == (MemoryInfo *) NULL)
405 source_pixels=(double *) GetVirtualMemoryBlob(source_info);
407 for (y=0L; y < (ssize_t) height; y++)
410 v=((y+y_offset) < 0L) ? y+y_offset+(ssize_t) height : y+y_offset;
412 v=((y+y_offset) > ((ssize_t) height-1L)) ? y+y_offset-(ssize_t) height :
414 for (x=0L; x < (ssize_t) width; x++)
417 u=((x+x_offset) < 0L) ? x+x_offset+(ssize_t) width : x+x_offset;
419 u=((x+x_offset) > ((ssize_t) width-1L)) ? x+x_offset-(ssize_t) width :
421 source_pixels[v*width+u]=roll_pixels[i++];
424 (void) CopyMagickMemory(roll_pixels,source_pixels,height*width*
425 sizeof(*source_pixels));
426 source_info=RelinquishVirtualMemory(source_info);
430 static MagickBooleanType ForwardQuadrantSwap(const size_t width,
431 const size_t height,double *source_pixels,double *forward_pixels)
446 center=(ssize_t) floor((double) width/2L)+1L;
447 status=RollFourier((size_t) center,height,0L,(ssize_t) height/2L,
449 if (status == MagickFalse)
451 for (y=0L; y < (ssize_t) height; y++)
452 for (x=0L; x < (ssize_t) (width/2L-1L); x++)
453 forward_pixels[y*width+x+width/2L]=source_pixels[y*center+x];
454 for (y=1; y < (ssize_t) height; y++)
455 for (x=0L; x < (ssize_t) (width/2L-1L); x++)
456 forward_pixels[(height-y)*width+width/2L-x-1L]=
457 source_pixels[y*center+x+1L];
458 for (x=0L; x < (ssize_t) (width/2L); x++)
459 forward_pixels[-x+width/2L-1L]=forward_pixels[x+width/2L+1L];
463 static void CorrectPhaseLHS(const size_t width,const size_t height,
464 double *fourier_pixels)
472 for (y=0L; y < (ssize_t) height; y++)
473 for (x=0L; x < (ssize_t) (width/2L); x++)
474 fourier_pixels[y*width+x]*=(-1.0);
477 static MagickBooleanType ForwardFourier(const FourierInfo *fourier_info,
478 Image *image,double *magnitude,double *phase,ExceptionInfo *exception)
509 magnitude_image=GetFirstImageInList(image);
510 phase_image=GetNextImageInList(image);
511 if (phase_image == (Image *) NULL)
513 (void) ThrowMagickException(exception,GetMagickModule(),ImageError,
514 "TwoOrMoreImagesRequired","`%s'",image->filename);
518 Create "Fourier Transform" image from constituent arrays.
520 magnitude_info=AcquireVirtualMemory((size_t) fourier_info->height,
521 fourier_info->width*sizeof(*magnitude_pixels));
522 phase_info=AcquireVirtualMemory((size_t) fourier_info->height,
523 fourier_info->width*sizeof(*phase_pixels));
524 if ((magnitude_info == (MemoryInfo *) NULL) ||
525 (phase_info == (MemoryInfo *) NULL))
527 if (phase_info != (MemoryInfo *) NULL)
528 phase_info=RelinquishVirtualMemory(phase_info);
529 if (magnitude_info != (MemoryInfo *) NULL)
530 magnitude_info=RelinquishVirtualMemory(magnitude_info);
531 (void) ThrowMagickException(exception,GetMagickModule(),
532 ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
535 magnitude_pixels=(double *) GetVirtualMemoryBlob(magnitude_info);
536 (void) ResetMagickMemory(magnitude_pixels,0,fourier_info->height*
537 fourier_info->width*sizeof(*magnitude_pixels));
538 phase_pixels=(double *) GetVirtualMemoryBlob(phase_info);
539 (void) ResetMagickMemory(phase_pixels,0,fourier_info->height*
540 fourier_info->width*sizeof(*phase_pixels));
541 status=ForwardQuadrantSwap(fourier_info->width,fourier_info->height,
542 magnitude,magnitude_pixels);
543 if (status != MagickFalse)
544 status=ForwardQuadrantSwap(fourier_info->width,fourier_info->height,phase,
546 CorrectPhaseLHS(fourier_info->width,fourier_info->height,phase_pixels);
547 if (fourier_info->modulus != MagickFalse)
550 for (y=0L; y < (ssize_t) fourier_info->height; y++)
551 for (x=0L; x < (ssize_t) fourier_info->width; x++)
553 phase_pixels[i]/=(2.0*MagickPI);
554 phase_pixels[i]+=0.5;
558 magnitude_view=AcquireAuthenticCacheView(magnitude_image,exception);
560 for (y=0L; y < (ssize_t) fourier_info->height; y++)
562 q=GetCacheViewAuthenticPixels(magnitude_view,0L,y,fourier_info->height,1UL,
564 if (q == (Quantum *) NULL)
566 for (x=0L; x < (ssize_t) fourier_info->width; x++)
568 switch (fourier_info->channel)
570 case RedPixelChannel:
573 SetPixelRed(magnitude_image,ClampToQuantum(QuantumRange*
574 magnitude_pixels[i]),q);
577 case GreenPixelChannel:
579 SetPixelGreen(magnitude_image,ClampToQuantum(QuantumRange*
580 magnitude_pixels[i]),q);
583 case BluePixelChannel:
585 SetPixelBlue(magnitude_image,ClampToQuantum(QuantumRange*
586 magnitude_pixels[i]),q);
589 case BlackPixelChannel:
591 SetPixelBlack(magnitude_image,ClampToQuantum(QuantumRange*
592 magnitude_pixels[i]),q);
595 case AlphaPixelChannel:
597 SetPixelAlpha(magnitude_image,ClampToQuantum(QuantumRange*
598 magnitude_pixels[i]),q);
603 q+=GetPixelChannels(magnitude_image);
605 status=SyncCacheViewAuthenticPixels(magnitude_view,exception);
606 if (status == MagickFalse)
609 magnitude_view=DestroyCacheView(magnitude_view);
611 phase_view=AcquireAuthenticCacheView(phase_image,exception);
612 for (y=0L; y < (ssize_t) fourier_info->height; y++)
614 q=GetCacheViewAuthenticPixels(phase_view,0L,y,fourier_info->height,1UL,
616 if (q == (Quantum *) NULL)
618 for (x=0L; x < (ssize_t) fourier_info->width; x++)
620 switch (fourier_info->channel)
622 case RedPixelChannel:
625 SetPixelRed(phase_image,ClampToQuantum(QuantumRange*
629 case GreenPixelChannel:
631 SetPixelGreen(phase_image,ClampToQuantum(QuantumRange*
635 case BluePixelChannel:
637 SetPixelBlue(phase_image,ClampToQuantum(QuantumRange*
641 case BlackPixelChannel:
643 SetPixelBlack(phase_image,ClampToQuantum(QuantumRange*
647 case AlphaPixelChannel:
649 SetPixelAlpha(phase_image,ClampToQuantum(QuantumRange*
655 q+=GetPixelChannels(phase_image);
657 status=SyncCacheViewAuthenticPixels(phase_view,exception);
658 if (status == MagickFalse)
661 phase_view=DestroyCacheView(phase_view);
662 phase_info=RelinquishVirtualMemory(phase_info);
663 magnitude_info=RelinquishVirtualMemory(magnitude_info);
667 static MagickBooleanType ForwardFourierTransform(FourierInfo *fourier_info,
668 const Image *image,double *magnitude_pixels,double *phase_pixels,
669 ExceptionInfo *exception)
690 register const Quantum
701 Generate the forward Fourier transform.
703 source_info=AcquireVirtualMemory((size_t) fourier_info->height,
704 fourier_info->width*sizeof(*source_pixels));
705 if (source_info == (MemoryInfo *) NULL)
707 (void) ThrowMagickException(exception,GetMagickModule(),
708 ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
711 source_pixels=(double *) GetVirtualMemoryBlob(source_info);
712 ResetMagickMemory(source_pixels,0,fourier_info->height*fourier_info->width*
713 sizeof(*source_pixels));
715 image_view=AcquireVirtualCacheView(image,exception);
716 for (y=0L; y < (ssize_t) fourier_info->height; y++)
718 p=GetCacheViewVirtualPixels(image_view,0L,y,fourier_info->width,1UL,
720 if (p == (const Quantum *) NULL)
722 for (x=0L; x < (ssize_t) fourier_info->width; x++)
724 switch (fourier_info->channel)
726 case RedPixelChannel:
729 source_pixels[i]=QuantumScale*GetPixelRed(image,p);
732 case GreenPixelChannel:
734 source_pixels[i]=QuantumScale*GetPixelGreen(image,p);
737 case BluePixelChannel:
739 source_pixels[i]=QuantumScale*GetPixelBlue(image,p);
742 case BlackPixelChannel:
744 source_pixels[i]=QuantumScale*GetPixelBlack(image,p);
747 case AlphaPixelChannel:
749 source_pixels[i]=QuantumScale*GetPixelAlpha(image,p);
754 p+=GetPixelChannels(image);
757 image_view=DestroyCacheView(image_view);
758 forward_info=AcquireVirtualMemory((size_t) fourier_info->height,
759 fourier_info->center*sizeof(*forward_pixels));
760 if (forward_info == (MemoryInfo *) NULL)
762 (void) ThrowMagickException(exception,GetMagickModule(),
763 ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
764 source_info=(MemoryInfo *) RelinquishVirtualMemory(source_info);
767 forward_pixels=(fftw_complex *) GetVirtualMemoryBlob(forward_info);
768 #if defined(MAGICKCORE_OPENMP_SUPPORT)
769 #pragma omp critical (MagickCore_ForwardFourierTransform)
771 fftw_r2c_plan=fftw_plan_dft_r2c_2d(fourier_info->width,fourier_info->height,
772 source_pixels,forward_pixels,FFTW_ESTIMATE);
773 fftw_execute(fftw_r2c_plan);
774 fftw_destroy_plan(fftw_r2c_plan);
775 source_info=(MemoryInfo *) RelinquishVirtualMemory(source_info);
776 value=GetImageArtifact(image,"fourier:normalize");
777 if ((value == (const char *) NULL) || (LocaleCompare(value,"forward") == 0))
783 Normalize Fourier transform.
786 gamma=PerceptibleReciprocal((double) fourier_info->width*
787 fourier_info->height);
788 for (y=0L; y < (ssize_t) fourier_info->height; y++)
789 for (x=0L; x < (ssize_t) fourier_info->center; x++)
791 #if defined(MAGICKCORE_HAVE_COMPLEX_H)
792 forward_pixels[i]*=gamma;
794 forward_pixels[i][0]*=gamma;
795 forward_pixels[i][1]*=gamma;
801 Generate magnitude and phase (or real and imaginary).
804 if (fourier_info->modulus != MagickFalse)
805 for (y=0L; y < (ssize_t) fourier_info->height; y++)
806 for (x=0L; x < (ssize_t) fourier_info->center; x++)
808 magnitude_pixels[i]=cabs(forward_pixels[i]);
809 phase_pixels[i]=carg(forward_pixels[i]);
813 for (y=0L; y < (ssize_t) fourier_info->height; y++)
814 for (x=0L; x < (ssize_t) fourier_info->center; x++)
816 magnitude_pixels[i]=creal(forward_pixels[i]);
817 phase_pixels[i]=cimag(forward_pixels[i]);
820 forward_info=(MemoryInfo *) RelinquishVirtualMemory(forward_info);
824 static MagickBooleanType ForwardFourierTransformChannel(const Image *image,
825 const PixelChannel channel,const MagickBooleanType modulus,
826 Image *fourier_image,ExceptionInfo *exception)
845 fourier_info.width=image->columns;
846 if ((image->columns != image->rows) || ((image->columns % 2) != 0) ||
847 ((image->rows % 2) != 0))
849 extent=image->columns < image->rows ? image->rows : image->columns;
850 fourier_info.width=(extent & 0x01) == 1 ? extent+1UL : extent;
852 fourier_info.height=fourier_info.width;
853 fourier_info.center=(ssize_t) floor((double) fourier_info.width/2L)+1L;
854 fourier_info.channel=channel;
855 fourier_info.modulus=modulus;
856 magnitude_info=AcquireVirtualMemory((size_t) fourier_info.height,
857 fourier_info.center*sizeof(*magnitude_pixels));
858 phase_info=AcquireVirtualMemory((size_t) fourier_info.height,
859 fourier_info.center*sizeof(*phase_pixels));
860 if ((magnitude_info == (MemoryInfo *) NULL) ||
861 (phase_info == (MemoryInfo *) NULL))
863 if (phase_info != (MemoryInfo *) NULL)
864 phase_info=RelinquishVirtualMemory(phase_info);
865 if (magnitude_info == (MemoryInfo *) NULL)
866 magnitude_info=RelinquishVirtualMemory(magnitude_info);
867 (void) ThrowMagickException(exception,GetMagickModule(),
868 ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
871 magnitude_pixels=(double *) GetVirtualMemoryBlob(magnitude_info);
872 phase_pixels=(double *) GetVirtualMemoryBlob(phase_info);
873 status=ForwardFourierTransform(&fourier_info,image,magnitude_pixels,
874 phase_pixels,exception);
875 if (status != MagickFalse)
876 status=ForwardFourier(&fourier_info,fourier_image,magnitude_pixels,
877 phase_pixels,exception);
878 phase_info=RelinquishVirtualMemory(phase_info);
879 magnitude_info=RelinquishVirtualMemory(magnitude_info);
884 MagickExport Image *ForwardFourierTransformImage(const Image *image,
885 const MagickBooleanType modulus,ExceptionInfo *exception)
890 fourier_image=NewImageList();
891 #if !defined(MAGICKCORE_FFTW_DELEGATE)
893 (void) ThrowMagickException(exception,GetMagickModule(),
894 MissingDelegateWarning,"DelegateLibrarySupportNotBuiltIn","'%s' (FFTW)",
905 width=image->columns;
906 if ((image->columns != image->rows) || ((image->columns % 2) != 0) ||
907 ((image->rows % 2) != 0))
909 extent=image->columns < image->rows ? image->rows : image->columns;
910 width=(extent & 0x01) == 1 ? extent+1UL : extent;
912 magnitude_image=CloneImage(image,width,width,MagickTrue,exception);
913 if (magnitude_image != (Image *) NULL)
918 magnitude_image->storage_class=DirectClass;
919 magnitude_image->depth=32UL;
920 phase_image=CloneImage(image,width,width,MagickTrue,exception);
921 if (phase_image == (Image *) NULL)
922 magnitude_image=DestroyImage(magnitude_image);
929 phase_image->storage_class=DirectClass;
930 phase_image->depth=32UL;
931 AppendImageToList(&fourier_image,magnitude_image);
932 AppendImageToList(&fourier_image,phase_image);
934 is_gray=IsImageGray(image,exception);
935 #if defined(MAGICKCORE_OPENMP_SUPPORT)
936 #pragma omp parallel sections
939 #if defined(MAGICKCORE_OPENMP_SUPPORT)
946 if (is_gray != MagickFalse)
947 thread_status=ForwardFourierTransformChannel(image,
948 GrayPixelChannel,modulus,fourier_image,exception);
950 thread_status=ForwardFourierTransformChannel(image,
951 RedPixelChannel,modulus,fourier_image,exception);
952 if (thread_status == MagickFalse)
953 status=thread_status;
955 #if defined(MAGICKCORE_OPENMP_SUPPORT)
962 thread_status=MagickTrue;
963 if (is_gray == MagickFalse)
964 thread_status=ForwardFourierTransformChannel(image,
965 GreenPixelChannel,modulus,fourier_image,exception);
966 if (thread_status == MagickFalse)
967 status=thread_status;
969 #if defined(MAGICKCORE_OPENMP_SUPPORT)
976 thread_status=MagickTrue;
977 if (is_gray == MagickFalse)
978 thread_status=ForwardFourierTransformChannel(image,
979 BluePixelChannel,modulus,fourier_image,exception);
980 if (thread_status == MagickFalse)
981 status=thread_status;
983 #if defined(MAGICKCORE_OPENMP_SUPPORT)
990 thread_status=MagickTrue;
991 if (image->colorspace == CMYKColorspace)
992 thread_status=ForwardFourierTransformChannel(image,
993 BlackPixelChannel,modulus,fourier_image,exception);
994 if (thread_status == MagickFalse)
995 status=thread_status;
997 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1004 thread_status=MagickTrue;
1005 if (image->alpha_trait == BlendPixelTrait)
1006 thread_status=ForwardFourierTransformChannel(image,
1007 AlphaPixelChannel,modulus,fourier_image,exception);
1008 if (thread_status == MagickFalse)
1009 status=thread_status;
1012 if (status == MagickFalse)
1013 fourier_image=DestroyImageList(fourier_image);
1019 return(fourier_image);
1023 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1027 % 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 %
1031 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1033 % InverseFourierTransformImage() implements the inverse discrete Fourier
1034 % transform (DFT) of the image either as a magnitude / phase or real /
1035 % imaginary image pair.
1037 % The format of the InverseFourierTransformImage method is:
1039 % Image *InverseFourierTransformImage(const Image *magnitude_image,
1040 % const Image *phase_image,const MagickBooleanType modulus,
1041 % ExceptionInfo *exception)
1043 % A description of each parameter follows:
1045 % o magnitude_image: the magnitude or real image.
1047 % o phase_image: the phase or imaginary image.
1049 % o modulus: if true, return transform as a magnitude / phase pair
1050 % otherwise a real / imaginary image pair.
1052 % o exception: return any errors or warnings in this structure.
1056 #if defined(MAGICKCORE_FFTW_DELEGATE)
1057 static MagickBooleanType InverseQuadrantSwap(const size_t width,
1058 const size_t height,const double *source,double *destination)
1070 center=(ssize_t) floor((double) width/2L)+1L;
1071 for (y=1L; y < (ssize_t) height; y++)
1072 for (x=0L; x < (ssize_t) (width/2L+1L); x++)
1073 destination[(height-y)*center-x+width/2L]=source[y*width+x];
1074 for (y=0L; y < (ssize_t) height; y++)
1075 destination[y*center]=source[y*width+width/2L];
1076 for (x=0L; x < center; x++)
1077 destination[x]=source[center-x-1L];
1078 return(RollFourier(center,height,0L,(ssize_t) height/-2L,destination));
1081 static MagickBooleanType InverseFourier(FourierInfo *fourier_info,
1082 const Image *magnitude_image,const Image *phase_image,
1083 fftw_complex *fourier_pixels,ExceptionInfo *exception)
1102 register const Quantum
1113 Inverse fourier - read image and break down into a double array.
1115 magnitude_info=AcquireVirtualMemory((size_t)fourier_info->height,
1116 fourier_info->width*sizeof(*magnitude_pixels));
1117 phase_info=AcquireVirtualMemory((size_t) fourier_info->height,
1118 fourier_info->width*sizeof(*phase_pixels));
1119 inverse_info=AcquireVirtualMemory((size_t) fourier_info->height,
1120 fourier_info->center*sizeof(*inverse_pixels));
1121 if ((magnitude_info == (MemoryInfo *) NULL) ||
1122 (phase_info == (MemoryInfo *) NULL) ||
1123 (inverse_info == (MemoryInfo *) NULL))
1125 if (magnitude_info != (MemoryInfo *) NULL)
1126 magnitude_info=RelinquishVirtualMemory(magnitude_info);
1127 if (phase_info != (MemoryInfo *) NULL)
1128 phase_info=RelinquishVirtualMemory(phase_info);
1129 if (inverse_info != (MemoryInfo *) NULL)
1130 inverse_info=RelinquishVirtualMemory(inverse_info);
1131 (void) ThrowMagickException(exception,GetMagickModule(),
1132 ResourceLimitError,"MemoryAllocationFailed","`%s'",
1133 magnitude_image->filename);
1134 return(MagickFalse);
1136 magnitude_pixels=(double *) GetVirtualMemoryBlob(magnitude_info);
1137 phase_pixels=(double *) GetVirtualMemoryBlob(phase_info);
1138 inverse_pixels=(double *) GetVirtualMemoryBlob(inverse_info);
1140 magnitude_view=AcquireVirtualCacheView(magnitude_image,exception);
1141 for (y=0L; y < (ssize_t) fourier_info->height; y++)
1143 p=GetCacheViewVirtualPixels(magnitude_view,0L,y,fourier_info->width,1UL,
1145 if (p == (const Quantum *) NULL)
1147 for (x=0L; x < (ssize_t) fourier_info->width; x++)
1149 switch (fourier_info->channel)
1151 case RedPixelChannel:
1154 magnitude_pixels[i]=QuantumScale*GetPixelRed(magnitude_image,p);
1157 case GreenPixelChannel:
1159 magnitude_pixels[i]=QuantumScale*GetPixelGreen(magnitude_image,p);
1162 case BluePixelChannel:
1164 magnitude_pixels[i]=QuantumScale*GetPixelBlue(magnitude_image,p);
1167 case BlackPixelChannel:
1169 magnitude_pixels[i]=QuantumScale*GetPixelBlack(magnitude_image,p);
1172 case AlphaPixelChannel:
1174 magnitude_pixels[i]=QuantumScale*GetPixelAlpha(magnitude_image,p);
1179 p+=GetPixelChannels(magnitude_image);
1182 magnitude_view=DestroyCacheView(magnitude_view);
1183 status=InverseQuadrantSwap(fourier_info->width,fourier_info->height,
1184 magnitude_pixels,inverse_pixels);
1185 (void) CopyMagickMemory(magnitude_pixels,inverse_pixels,fourier_info->height*
1186 fourier_info->center*sizeof(*magnitude_pixels));
1188 phase_view=AcquireVirtualCacheView(phase_image,exception);
1189 for (y=0L; y < (ssize_t) fourier_info->height; y++)
1191 p=GetCacheViewVirtualPixels(phase_view,0,y,fourier_info->width,1,
1193 if (p == (const Quantum *) NULL)
1195 for (x=0L; x < (ssize_t) fourier_info->width; x++)
1197 switch (fourier_info->channel)
1199 case RedPixelChannel:
1202 phase_pixels[i]=QuantumScale*GetPixelRed(phase_image,p);
1205 case GreenPixelChannel:
1207 phase_pixels[i]=QuantumScale*GetPixelGreen(phase_image,p);
1210 case BluePixelChannel:
1212 phase_pixels[i]=QuantumScale*GetPixelBlue(phase_image,p);
1215 case BlackPixelChannel:
1217 phase_pixels[i]=QuantumScale*GetPixelBlack(phase_image,p);
1220 case AlphaPixelChannel:
1222 phase_pixels[i]=QuantumScale*GetPixelAlpha(phase_image,p);
1227 p+=GetPixelChannels(phase_image);
1230 if (fourier_info->modulus != MagickFalse)
1233 for (y=0L; y < (ssize_t) fourier_info->height; y++)
1234 for (x=0L; x < (ssize_t) fourier_info->width; x++)
1236 phase_pixels[i]-=0.5;
1237 phase_pixels[i]*=(2.0*MagickPI);
1241 phase_view=DestroyCacheView(phase_view);
1242 CorrectPhaseLHS(fourier_info->width,fourier_info->height,phase_pixels);
1243 if (status != MagickFalse)
1244 status=InverseQuadrantSwap(fourier_info->width,fourier_info->height,
1245 phase_pixels,inverse_pixels);
1246 (void) CopyMagickMemory(phase_pixels,inverse_pixels,fourier_info->height*
1247 fourier_info->center*sizeof(*phase_pixels));
1248 inverse_info=RelinquishVirtualMemory(inverse_info);
1253 if (fourier_info->modulus != MagickFalse)
1254 for (y=0L; y < (ssize_t) fourier_info->height; y++)
1255 for (x=0L; x < (ssize_t) fourier_info->center; x++)
1257 #if defined(MAGICKCORE_HAVE_COMPLEX_H)
1258 fourier_pixels[i]=magnitude_pixels[i]*cos(phase_pixels[i])+I*
1259 magnitude_pixels[i]*sin(phase_pixels[i]);
1261 fourier_pixels[i][0]=magnitude_pixels[i]*cos(phase_pixels[i]);
1262 fourier_pixels[i][1]=magnitude_pixels[i]*sin(phase_pixels[i]);
1267 for (y=0L; y < (ssize_t) fourier_info->height; y++)
1268 for (x=0L; x < (ssize_t) fourier_info->center; x++)
1270 #if defined(MAGICKCORE_HAVE_COMPLEX_H)
1271 fourier_pixels[i]=magnitude_pixels[i]+I*phase_pixels[i];
1273 fourier_pixels[i][0]=magnitude_pixels[i];
1274 fourier_pixels[i][1]=phase_pixels[i];
1278 magnitude_info=RelinquishVirtualMemory(magnitude_info);
1279 phase_info=RelinquishVirtualMemory(phase_info);
1283 static MagickBooleanType InverseFourierTransform(FourierInfo *fourier_info,
1284 fftw_complex *fourier_pixels,Image *image,ExceptionInfo *exception)
1311 source_info=AcquireVirtualMemory((size_t) fourier_info->height,
1312 fourier_info->width*sizeof(*source_pixels));
1313 if (source_info == (MemoryInfo *) NULL)
1315 (void) ThrowMagickException(exception,GetMagickModule(),
1316 ResourceLimitError,"MemoryAllocationFailed","`%s'",image->filename);
1317 return(MagickFalse);
1319 source_pixels=(double *) GetVirtualMemoryBlob(source_info);
1320 value=GetImageArtifact(image,"fourier:normalize");
1321 if (LocaleCompare(value,"inverse") == 0)
1327 Normalize inverse transform.
1330 gamma=PerceptibleReciprocal((double) fourier_info->width*
1331 fourier_info->height);
1332 for (y=0L; y < (ssize_t) fourier_info->height; y++)
1333 for (x=0L; x < (ssize_t) fourier_info->center; x++)
1335 #if defined(MAGICKCORE_HAVE_COMPLEX_H)
1336 fourier_pixels[i]*=gamma;
1338 fourier_pixels[i][0]*=gamma;
1339 fourier_pixels[i][1]*=gamma;
1344 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1345 #pragma omp critical (MagickCore_InverseFourierTransform)
1348 fftw_c2r_plan=fftw_plan_dft_c2r_2d(fourier_info->width,fourier_info->height,
1349 fourier_pixels,source_pixels,FFTW_ESTIMATE);
1350 fftw_execute(fftw_c2r_plan);
1351 fftw_destroy_plan(fftw_c2r_plan);
1354 image_view=AcquireAuthenticCacheView(image,exception);
1355 for (y=0L; y < (ssize_t) fourier_info->height; y++)
1357 if (y >= (ssize_t) image->rows)
1359 q=GetCacheViewAuthenticPixels(image_view,0L,y,fourier_info->width >
1360 image->columns ? image->columns : fourier_info->width,1UL,exception);
1361 if (q == (Quantum *) NULL)
1363 for (x=0L; x < (ssize_t) fourier_info->width; x++)
1365 if (x < (ssize_t) image->columns)
1366 switch (fourier_info->channel)
1368 case RedPixelChannel:
1371 SetPixelRed(image,ClampToQuantum(QuantumRange*source_pixels[i]),q);
1374 case GreenPixelChannel:
1376 SetPixelGreen(image,ClampToQuantum(QuantumRange*source_pixels[i]),
1380 case BluePixelChannel:
1382 SetPixelBlue(image,ClampToQuantum(QuantumRange*source_pixels[i]),
1386 case BlackPixelChannel:
1388 SetPixelBlack(image,ClampToQuantum(QuantumRange*source_pixels[i]),
1392 case AlphaPixelChannel:
1394 SetPixelAlpha(image,ClampToQuantum(QuantumRange*source_pixels[i]),
1400 q+=GetPixelChannels(image);
1402 if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1405 image_view=DestroyCacheView(image_view);
1406 source_info=RelinquishVirtualMemory(source_info);
1410 static MagickBooleanType InverseFourierTransformChannel(
1411 const Image *magnitude_image,const Image *phase_image,
1412 const PixelChannel channel,const MagickBooleanType modulus,
1413 Image *fourier_image,ExceptionInfo *exception)
1430 fourier_info.width=magnitude_image->columns;
1431 if ((magnitude_image->columns != magnitude_image->rows) ||
1432 ((magnitude_image->columns % 2) != 0) ||
1433 ((magnitude_image->rows % 2) != 0))
1435 extent=magnitude_image->columns < magnitude_image->rows ?
1436 magnitude_image->rows : magnitude_image->columns;
1437 fourier_info.width=(extent & 0x01) == 1 ? extent+1UL : extent;
1439 fourier_info.height=fourier_info.width;
1440 fourier_info.center=(ssize_t) floor((double) fourier_info.width/2L)+1L;
1441 fourier_info.channel=channel;
1442 fourier_info.modulus=modulus;
1443 inverse_info=AcquireVirtualMemory((size_t) fourier_info.height,
1444 fourier_info.center*sizeof(*inverse_pixels));
1445 if (inverse_info == (MemoryInfo *) NULL)
1447 (void) ThrowMagickException(exception,GetMagickModule(),
1448 ResourceLimitError,"MemoryAllocationFailed","`%s'",
1449 magnitude_image->filename);
1450 return(MagickFalse);
1452 inverse_pixels=(fftw_complex *) GetVirtualMemoryBlob(inverse_info);
1453 status=InverseFourier(&fourier_info,magnitude_image,phase_image,
1454 inverse_pixels,exception);
1455 if (status != MagickFalse)
1456 status=InverseFourierTransform(&fourier_info,inverse_pixels,fourier_image,
1458 inverse_info=RelinquishVirtualMemory(inverse_info);
1463 MagickExport Image *InverseFourierTransformImage(const Image *magnitude_image,
1464 const Image *phase_image,const MagickBooleanType modulus,
1465 ExceptionInfo *exception)
1470 assert(magnitude_image != (Image *) NULL);
1471 assert(magnitude_image->signature == MagickSignature);
1472 if (magnitude_image->debug != MagickFalse)
1473 (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",
1474 magnitude_image->filename);
1475 if (phase_image == (Image *) NULL)
1477 (void) ThrowMagickException(exception,GetMagickModule(),ImageError,
1478 "TwoOrMoreImagesRequired","`%s'",magnitude_image->filename);
1479 return((Image *) NULL);
1481 #if !defined(MAGICKCORE_FFTW_DELEGATE)
1482 fourier_image=(Image *) NULL;
1484 (void) ThrowMagickException(exception,GetMagickModule(),
1485 MissingDelegateWarning,"DelegateLibrarySupportNotBuiltIn","'%s' (FFTW)",
1486 magnitude_image->filename);
1489 fourier_image=CloneImage(magnitude_image,magnitude_image->columns,
1490 magnitude_image->rows,MagickTrue,exception);
1491 if (fourier_image != (Image *) NULL)
1498 is_gray=IsImageGray(magnitude_image,exception);
1499 if (is_gray != MagickFalse)
1500 is_gray=IsImageGray(phase_image,exception);
1501 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1502 #pragma omp parallel sections
1505 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1512 if (is_gray != MagickFalse)
1513 thread_status=InverseFourierTransformChannel(magnitude_image,
1514 phase_image,GrayPixelChannel,modulus,fourier_image,exception);
1516 thread_status=InverseFourierTransformChannel(magnitude_image,
1517 phase_image,RedPixelChannel,modulus,fourier_image,exception);
1518 if (thread_status == MagickFalse)
1519 status=thread_status;
1521 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1528 thread_status=MagickTrue;
1529 if (is_gray == MagickFalse)
1530 thread_status=InverseFourierTransformChannel(magnitude_image,
1531 phase_image,GreenPixelChannel,modulus,fourier_image,exception);
1532 if (thread_status == MagickFalse)
1533 status=thread_status;
1535 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1542 thread_status=MagickTrue;
1543 if (is_gray == MagickFalse)
1544 thread_status=InverseFourierTransformChannel(magnitude_image,
1545 phase_image,BluePixelChannel,modulus,fourier_image,exception);
1546 if (thread_status == MagickFalse)
1547 status=thread_status;
1549 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1556 thread_status=MagickTrue;
1557 if (magnitude_image->colorspace == CMYKColorspace)
1558 thread_status=InverseFourierTransformChannel(magnitude_image,
1559 phase_image,BlackPixelChannel,modulus,fourier_image,exception);
1560 if (thread_status == MagickFalse)
1561 status=thread_status;
1563 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1570 thread_status=MagickTrue;
1571 if (magnitude_image->alpha_trait == BlendPixelTrait)
1572 thread_status=InverseFourierTransformChannel(magnitude_image,
1573 phase_image,AlphaPixelChannel,modulus,fourier_image,exception);
1574 if (thread_status == MagickFalse)
1575 status=thread_status;
1578 if (status == MagickFalse)
1579 fourier_image=DestroyImage(fourier_image);
1584 return(fourier_image);