root/magick/fourier.c

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DEFINITIONS

This source file includes following definitions.
  1. ComplexImages
  2. RollFourier
  3. ForwardQuadrantSwap
  4. CorrectPhaseLHS
  5. ForwardFourier
  6. ForwardFourierTransform
  7. ForwardFourierTransformChannel
  8. ForwardFourierTransformImage
  9. InverseQuadrantSwap
  10. InverseFourier
  11. InverseFourierTransform
  12. InverseFourierTransformChannel
  13. InverseFourierTransformImage

/*
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%                                                                             %
%               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 1999-2015 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                                            %
%                                                                             %
%    http://www.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 <complex.h>
#endif
#include <fftw3.h>
#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;

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%     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 == MagickSignature);
  if (images->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickSignature);
  if (images->next == (Image *) NULL)
    {
      (void) ThrowMagickException(exception,GetMagickModule(),ImageError,
        "ImageSequenceRequired","`%s'",images->filename);
      return((Image *) NULL);
    }
  image=CloneImage(images,images->columns,images->rows,MagickTrue,exception);
  if (image == (Image *) NULL)
    return((Image *) NULL);
  image->storage_class=DirectClass;
  image->depth=32UL;
  complex_images=NewImageList();
  AppendImageToList(&complex_images,image);
  image=CloneImage(images,images->columns,images->rows,MagickTrue,exception);
  if (image == (Image *) NULL)
    {
      complex_images=DestroyImageList(complex_images);
      return(complex_images);
    }
  AppendImageToList(&complex_images,image);
  complex_images->storage_class=DirectClass;
  complex_images->depth=32UL;
  /*
    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,4) shared(progress,status) \
      magick_threads(images,complex_images,images->rows,1)
#endif
  for (y=0; y < (ssize_t) images->rows; y++)
  {
    register const PixelPacket
      *restrict Ai,
      *restrict Ar,
      *restrict Bi,
      *restrict Br;

    register PixelPacket
      *restrict Ci,
      *restrict Cr;

    register ssize_t
      x;

    if (status == MagickFalse)
      continue;
    Ar=GetCacheViewVirtualPixels(Ar_view,0,y,images->columns,1,exception);
    Ai=GetCacheViewVirtualPixels(Ai_view,0,y,images->columns,1,exception);
    Br=GetCacheViewVirtualPixels(Br_view,0,y,images->columns,1,exception);
    Bi=GetCacheViewVirtualPixels(Bi_view,0,y,images->columns,1,exception);
    Cr=QueueCacheViewAuthenticPixels(Cr_view,0,y,images->columns,1,exception);
    Ci=QueueCacheViewAuthenticPixels(Ci_view,0,y,images->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) images->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*(Ar->red*Br->red+Ai->red*Bi->red);
          Ci->red=gamma*(Ai->red*Br->red-Ar->red*Bi->red);
          gamma=PerceptibleReciprocal(Br->green*Br->green+Bi->green*Bi->green+
            snr);
          Cr->green=gamma*(Ar->green*Br->green+Ai->green*Bi->green);
          Ci->green=gamma*(Ai->green*Br->green-Ar->green*Bi->green);
          gamma=PerceptibleReciprocal(Br->blue*Br->blue+Bi->blue*Bi->blue+snr);
          Cr->blue=gamma*(Ar->blue*Br->blue+Ai->blue*Bi->blue);
          Ci->blue=gamma*(Ai->blue*Br->blue-Ar->blue*Bi->blue);
          if (images->matte != MagickFalse)
            {
              gamma=PerceptibleReciprocal(Br->opacity*Br->opacity+Bi->opacity*
                Bi->opacity+snr);
              Cr->opacity=gamma*(Ar->opacity*Br->opacity+Ai->opacity*
                Bi->opacity);
              Ci->opacity=gamma*(Ai->opacity*Br->opacity-Ar->opacity*
                Bi->opacity);
            }
          break;
        }
        case MagnitudePhaseComplexOperator:
        {
          Cr->red=sqrt(Ar->red*Ar->red+Ai->red*Ai->red);
          Ci->red=atan2(Ai->red,Ar->red)/(2.0*MagickPI)+0.5;
          Cr->green=sqrt(Ar->green*Ar->green+Ai->green*Ai->green);
          Ci->green=atan2(Ai->green,Ar->green)/(2.0*MagickPI)+0.5;
          Cr->blue=sqrt(Ar->blue*Ar->blue+Ai->blue*Ai->blue);
          Ci->blue=atan2(Ai->blue,Ar->blue)/(2.0*MagickPI)+0.5;
          if (images->matte != MagickFalse)
            {
              Cr->opacity=sqrt(Ar->opacity*Ar->opacity+Ai->opacity*Ai->opacity);
              Ci->opacity=atan2(Ai->opacity,Ar->opacity)/(2.0*MagickPI)+0.5;
            }
          break;
        }
        case MultiplyComplexOperator:
        {
          Cr->red=QuantumScale*(Ar->red*Br->red-Ai->red*Bi->red);
          Ci->red=QuantumScale*(Ai->red*Br->red+Ar->red*Bi->red);
          Cr->green=QuantumScale*(Ar->green*Br->green-Ai->green*Bi->green);
          Ci->green=QuantumScale*(Ai->green*Br->green+Ar->green*Bi->green);
          Cr->blue=QuantumScale*(Ar->blue*Br->blue-Ai->blue*Bi->blue);
          Ci->blue=QuantumScale*(Ai->blue*Br->blue+Ar->blue*Bi->blue);
          if (images->matte != MagickFalse)
            {
              Cr->opacity=QuantumScale*(Ar->opacity*Br->opacity-Ai->opacity*
                Bi->opacity);
              Ci->opacity=QuantumScale*(Ai->opacity*Br->opacity+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 (images->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 critical (MagickCore_ComplexImages)
#endif
        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);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
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%                                                                             %
%     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(height,width*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) CopyMagickMemory(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) floor((double) 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-1L); 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-1L); 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[-x+width/2L-1L]=forward_pixels[x+width/2L+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->height,
    fourier_info->width*sizeof(*magnitude_pixels));
  phase_info=AcquireVirtualMemory((size_t) fourier_info->height,
    fourier_info->width*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) ResetMagickMemory(magnitude_pixels,0,fourier_info->height*
    fourier_info->width*sizeof(*magnitude_pixels));
  phase_pixels=(double *) GetVirtualMemoryBlob(phase_info);
  (void) ResetMagickMemory(phase_pixels,0,fourier_info->height*
    fourier_info->width*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->height,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->height,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->height,
    fourier_info->width*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);
  ResetMagickMemory(source_pixels,0,fourier_info->height*fourier_info->width*
    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->height,
    fourier_info->center*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(fftw_r2c_plan);
  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 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)
          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;

  size_t
    extent;

  fourier_info.width=image->columns;
  fourier_info.height=image->rows;
  if ((image->columns != image->rows) || ((image->columns % 2) != 0) ||
      ((image->rows % 2) != 0))
    {
      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) floor((double) fourier_info.width/2L)+1L;
  fourier_info.channel=channel;
  fourier_info.modulus=modulus;
  magnitude_info=AcquireVirtualMemory((size_t) fourier_info.height,
    fourier_info.center*sizeof(*magnitude_pixels));
  phase_info=AcquireVirtualMemory((size_t) fourier_info.height,
    fourier_info.center*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
      extent,
      height,
      width;

    width=image->columns;
    height=image->rows;
    if ((image->columns != image->rows) || ((image->columns % 2) != 0) ||
        ((image->rows % 2) != 0))
      {
        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) floor((double) 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->height,
    fourier_info->width*sizeof(*magnitude_pixels));
  phase_info=AcquireVirtualMemory((size_t) fourier_info->height,
    fourier_info->width*sizeof(*phase_pixels));
  inverse_info=AcquireVirtualMemory((size_t) fourier_info->height,
    fourier_info->center*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) CopyMagickMemory(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) CopyMagickMemory(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->height,
    fourier_info->width*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 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)
          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(fftw_c2r_plan);
    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;

  size_t
    extent;

  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))
    {
      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) floor((double) fourier_info.width/2L)+1L;
  fourier_info.channel=channel;
  fourier_info.modulus=modulus;
  inverse_info=AcquireVirtualMemory((size_t) fourier_info.height,
    fourier_info.center*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 == MagickSignature);
  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);
}

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