magick/compare.c

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%               CCCC   OOO   M   M  PPPP    AAA   RRRR    EEEEE               %
%              C      O   O  MM MM  P   P  A   A  R   R   E                   %
%              C      O   O  M M M  PPPP   AAAAA  RRRR    EEE                 %
%              C      O   O  M   M  P      A   A  R R     E                   %
%               CCCC   OOO   M   M  P      A   A  R  R    EEEEE               %
%                                                                             %
%                                                                             %
%                      MagickCore Image Comparison Methods                    %
%                                                                             %
%                              Software Design                                %
%                                John Cristy                                  %
%                               December 2003                                 %
%                                                                             %
%                                                                             %
%  Copyright 1999-2010 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/cache-view.h"
#include "magick/client.h"
#include "magick/color.h"
#include "magick/color-private.h"
#include "magick/colorspace.h"
#include "magick/colorspace-private.h"
#include "magick/compare.h"
#include "magick/composite-private.h"
#include "magick/constitute.h"
#include "magick/exception-private.h"
#include "magick/geometry.h"
#include "magick/image-private.h"
#include "magick/list.h"
#include "magick/log.h"
#include "magick/memory_.h"
#include "magick/monitor.h"
#include "magick/monitor-private.h"
#include "magick/option.h"
#include "magick/pixel-private.h"
#include "magick/resource_.h"
#include "magick/string_.h"
#include "magick/statistic.h"
#include "magick/transform.h"
#include "magick/utility.h"
#include "magick/version.h"

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   C o m p a r e I m a g e C h a n n e l s                                   %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  CompareImageChannels() compares one or more image channels of an image
%  to a reconstructed image and returns the difference image.
%
%  The format of the CompareImageChannels method is:
%
%      Image *CompareImageChannels(const Image *image,
%        const Image *reconstruct_image,const ChannelType channel,
%        const MetricType metric,double *distortion,ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o reconstruct_image: the reconstruct image.
%
%    o channel: the channel.
%
%    o metric: the metric.
%
%    o distortion: the computed distortion between the images.
%
%    o exception: return any errors or warnings in this structure.
%
*/

MagickExport Image *CompareImages(Image *image,const Image *reconstruct_image,
  const MetricType metric,double *distortion,ExceptionInfo *exception)
{
  Image
    *highlight_image;

  highlight_image=CompareImageChannels(image,reconstruct_image,AllChannels,
    metric,distortion,exception);
  return(highlight_image);
}

MagickExport Image *CompareImageChannels(Image *image,
  const Image *reconstruct_image,const ChannelType channel,
  const MetricType metric,double *distortion,ExceptionInfo *exception)
{
  CacheView
    *highlight_view,
    *image_view,
    *reconstruct_view;

  const char
    *artifact;

  Image
    *difference_image,
    *highlight_image;

  ssize_t
    y;

  MagickBooleanType
    status;

  MagickPixelPacket
    highlight,
    lowlight,
    zero;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  assert(reconstruct_image != (const Image *) NULL);
  assert(reconstruct_image->signature == MagickSignature);
  assert(distortion != (double *) NULL);
  *distortion=0.0;
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  if ((reconstruct_image->columns != image->columns) ||
      (reconstruct_image->rows != image->rows))
    ThrowImageException(ImageError,"ImageSizeDiffers");
  status=GetImageChannelDistortion(image,reconstruct_image,channel,metric,
    distortion,exception);
  if (status == MagickFalse)
    return((Image *) NULL);
  difference_image=CloneImage(image,0,0,MagickTrue,exception);
  if (difference_image == (Image *) NULL)
    return((Image *) NULL);
  (void) SetImageAlphaChannel(difference_image,OpaqueAlphaChannel);
  highlight_image=CloneImage(image,image->columns,image->rows,MagickTrue,
    exception);
  if (highlight_image == (Image *) NULL)
    {
      difference_image=DestroyImage(difference_image);
      return((Image *) NULL);
    }
  if (SetImageStorageClass(highlight_image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&highlight_image->exception);
      difference_image=DestroyImage(difference_image);
      highlight_image=DestroyImage(highlight_image);
      return((Image *) NULL);
    }
  (void) SetImageAlphaChannel(highlight_image,OpaqueAlphaChannel);
  (void) QueryMagickColor("#f1001ecc",&highlight,exception);
  artifact=GetImageArtifact(image,"highlight-color");
  if (artifact != (const char *) NULL)
    (void) QueryMagickColor(artifact,&highlight,exception);
  (void) QueryMagickColor("#ffffffcc",&lowlight,exception);
  artifact=GetImageArtifact(image,"lowlight-color");
  if (artifact != (const char *) NULL)
    (void) QueryMagickColor(artifact,&lowlight,exception);
  if (highlight_image->colorspace == CMYKColorspace)
    {
      ConvertRGBToCMYK(&highlight);
      ConvertRGBToCMYK(&lowlight);
    }
  /*
    Generate difference image.
  */
  status=MagickTrue;
  GetMagickPixelPacket(image,&zero);
  image_view=AcquireCacheView(image);
  reconstruct_view=AcquireCacheView(reconstruct_image);
  highlight_view=AcquireCacheView(highlight_image);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4) shared(status)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    MagickBooleanType
      sync;

    MagickPixelPacket
      pixel,
      reconstruct_pixel;

    register const IndexPacket
      *restrict indexes,
      *restrict reconstruct_indexes;

    register const PixelPacket
      *restrict p,
      *restrict q;

    register IndexPacket
      *restrict highlight_indexes;

    register ssize_t
      x;

    register PixelPacket
      *restrict r;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
      1,exception);
    r=QueueCacheViewAuthenticPixels(highlight_view,0,y,highlight_image->columns,
      1,exception);
    if ((p == (const PixelPacket *) NULL) ||
        (q == (const PixelPacket *) NULL) || (r == (PixelPacket *) NULL))
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    reconstruct_indexes=GetCacheViewVirtualIndexQueue(reconstruct_view);
    highlight_indexes=GetCacheViewAuthenticIndexQueue(highlight_view);
    pixel=zero;
    reconstruct_pixel=zero;
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      MagickStatusType
        difference;

      SetMagickPixelPacket(image,p,indexes+x,&pixel);
      SetMagickPixelPacket(reconstruct_image,q,reconstruct_indexes+x,
        &reconstruct_pixel);
      difference=MagickFalse;
      if (channel == AllChannels)
        {
          if (IsMagickColorSimilar(&pixel,&reconstruct_pixel) == MagickFalse)
            difference=MagickTrue;
        }
      else
        {
          if (((channel & RedChannel) != 0) && (p->red != q->red))
            difference=MagickTrue;
          if (((channel & GreenChannel) != 0) && (p->green != q->green))
            difference=MagickTrue;
          if (((channel & BlueChannel) != 0) && (p->blue != q->blue))
            difference=MagickTrue;
          if (((channel & OpacityChannel) != 0) &&
              (image->matte != MagickFalse) && (p->opacity != q->opacity))
            difference=MagickTrue;
          if ((((channel & IndexChannel) != 0) &&
               (image->colorspace == CMYKColorspace) &&
               (reconstruct_image->colorspace == CMYKColorspace)) &&
              (indexes[x] != reconstruct_indexes[x]))
            difference=MagickTrue;
        }
      if (difference != MagickFalse)
        SetPixelPacket(highlight_image,&highlight,r,highlight_indexes+x);
      else
        SetPixelPacket(highlight_image,&lowlight,r,highlight_indexes+x);
      p++;
      q++;
      r++;
    }
    sync=SyncCacheViewAuthenticPixels(highlight_view,exception);
    if (sync == MagickFalse)
      status=MagickFalse;
  }
  highlight_view=DestroyCacheView(highlight_view);
  reconstruct_view=DestroyCacheView(reconstruct_view);
  image_view=DestroyCacheView(image_view);
  (void) CompositeImage(difference_image,image->compose,highlight_image,0,0);
  highlight_image=DestroyImage(highlight_image);
  if (status == MagickFalse)
    difference_image=DestroyImage(difference_image);
  return(difference_image);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   G e t I m a g e C h a n n e l D i s t o r t i o n                         %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelDistortion() compares one or more image channels of an image
%  to a reconstructed image and returns the specified distortion metric.
%
%  The format of the CompareImageChannels method is:
%
%      MagickBooleanType GetImageChannelDistortion(const Image *image,
%        const Image *reconstruct_image,const ChannelType channel,
%        const MetricType metric,double *distortion,ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o reconstruct_image: the reconstruct image.
%
%    o channel: the channel.
%
%    o metric: the metric.
%
%    o distortion: the computed distortion between the images.
%
%    o exception: return any errors or warnings in this structure.
%
*/

MagickExport MagickBooleanType GetImageDistortion(Image *image,
  const Image *reconstruct_image,const MetricType metric,double *distortion,
  ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  status=GetImageChannelDistortion(image,reconstruct_image,AllChannels,
    metric,distortion,exception);
  return(status);
}

static MagickBooleanType GetAbsoluteDistortion(const Image *image,
  const Image *reconstruct_image,const ChannelType channel,double *distortion,
  ExceptionInfo *exception)
{
  CacheView
    *image_view,
    *reconstruct_view;

  ssize_t
    y;

  MagickBooleanType
    status;

  MagickPixelPacket
    zero;

  /*
    Compute the absolute difference in pixels between two images.
  */
  status=MagickTrue;
  GetMagickPixelPacket(image,&zero);
  image_view=AcquireCacheView(image);
  reconstruct_view=AcquireCacheView(reconstruct_image);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4) shared(status)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    double
      channel_distortion[AllChannels+1];

    MagickPixelPacket
      pixel,
      reconstruct_pixel;

    register const IndexPacket
      *restrict indexes,
      *restrict reconstruct_indexes;

    register const PixelPacket
      *restrict p,
      *restrict q;

    register ssize_t
      i,
      x;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
      1,exception);
    if ((p == (const PixelPacket *) NULL) || (q == (const PixelPacket *) NULL))
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    reconstruct_indexes=GetCacheViewVirtualIndexQueue(reconstruct_view);
    pixel=zero;
    reconstruct_pixel=pixel;
    (void) ResetMagickMemory(channel_distortion,0,sizeof(channel_distortion));
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      SetMagickPixelPacket(image,p,indexes+x,&pixel);
      SetMagickPixelPacket(reconstruct_image,q,reconstruct_indexes+x,
        &reconstruct_pixel);
      if (IsMagickColorSimilar(&pixel,&reconstruct_pixel) == MagickFalse)
        {
          if ((channel & RedChannel) != 0)
            channel_distortion[RedChannel]++;
          if ((channel & GreenChannel) != 0)
            channel_distortion[GreenChannel]++;
          if ((channel & BlueChannel) != 0)
            channel_distortion[BlueChannel]++;
          if (((channel & OpacityChannel) != 0) &&
              (image->matte != MagickFalse))
            channel_distortion[OpacityChannel]++;
          if (((channel & IndexChannel) != 0) &&
              (image->colorspace == CMYKColorspace))
            channel_distortion[BlackChannel]++;
          channel_distortion[AllChannels]++;
        }
      p++;
      q++;
    }
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_GetAbsoluteError)
#endif
    for (i=0; i <= (ssize_t) AllChannels; i++)
      distortion[i]+=channel_distortion[i];
  }
  reconstruct_view=DestroyCacheView(reconstruct_view);
  image_view=DestroyCacheView(image_view);
  return(status);
}

static size_t GetNumberChannels(const Image *image,
  const ChannelType channel)
{
  size_t
    channels;

  channels=0;
  if ((channel & RedChannel) != 0)
    channels++;
  if ((channel & GreenChannel) != 0)
    channels++;
  if ((channel & BlueChannel) != 0)
    channels++;
  if (((channel & OpacityChannel) != 0) &&
       (image->matte != MagickFalse))
    channels++;
  if (((channel & IndexChannel) != 0) &&
      (image->colorspace == CMYKColorspace))
    channels++;
  return(channels);
}

static MagickBooleanType GetMeanAbsoluteDistortion(const Image *image,
  const Image *reconstruct_image,const ChannelType channel,
  double *distortion,ExceptionInfo *exception)
{
  CacheView
    *image_view,
    *reconstruct_view;

  ssize_t
    y;

  MagickBooleanType
    status;

  register ssize_t
    i;

  status=MagickTrue;
  image_view=AcquireCacheView(image);
  reconstruct_view=AcquireCacheView(reconstruct_image);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4) shared(status)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    double
      channel_distortion[AllChannels+1];

    register const IndexPacket
      *restrict indexes,
      *restrict reconstruct_indexes;

    register const PixelPacket
      *restrict p,
      *restrict q;

    register ssize_t
      i,
      x;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    q=GetCacheViewVirtualPixels(reconstruct_view,0,y,
      reconstruct_image->columns,1,exception);
    if ((p == (const PixelPacket *) NULL) || (q == (const PixelPacket *) NULL))
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    reconstruct_indexes=GetCacheViewVirtualIndexQueue(reconstruct_view);
    (void) ResetMagickMemory(channel_distortion,0,sizeof(channel_distortion));
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      MagickRealType
        distance;

      if ((channel & RedChannel) != 0)
        {
          distance=QuantumScale*fabs(p->red-(double) q->red);
          channel_distortion[RedChannel]+=distance;
          channel_distortion[AllChannels]+=distance;
        }
      if ((channel & GreenChannel) != 0)
        {
          distance=QuantumScale*fabs(p->green-(double) q->green);
          channel_distortion[GreenChannel]+=distance;
          channel_distortion[AllChannels]+=distance;
        }
      if ((channel & BlueChannel) != 0)
        {
          distance=QuantumScale*fabs(p->blue-(double) q->blue);
          channel_distortion[BlueChannel]+=distance;
          channel_distortion[AllChannels]+=distance;
        }
      if (((channel & OpacityChannel) != 0) &&
          (image->matte != MagickFalse))
        {
          distance=QuantumScale*fabs(p->opacity-(double) q->opacity);
          channel_distortion[OpacityChannel]+=distance;
          channel_distortion[AllChannels]+=distance;
        }
      if (((channel & IndexChannel) != 0) &&
          (image->colorspace == CMYKColorspace))
        {
          distance=QuantumScale*fabs(indexes[x]-(double)
            reconstruct_indexes[x]);
          channel_distortion[BlackChannel]+=distance;
          channel_distortion[AllChannels]+=distance;
        }
      p++;
      q++;
    }
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_GetMeanAbsoluteError)
#endif
    for (i=0; i <= (ssize_t) AllChannels; i++)
      distortion[i]+=channel_distortion[i];
  }
  reconstruct_view=DestroyCacheView(reconstruct_view);
  image_view=DestroyCacheView(image_view);
  for (i=0; i <= (ssize_t) AllChannels; i++)
    distortion[i]/=((double) image->columns*image->rows);
  distortion[AllChannels]/=(double) GetNumberChannels(image,channel);
  return(status);
}

static MagickBooleanType GetMeanErrorPerPixel(Image *image,
  const Image *reconstruct_image,const ChannelType channel,double *distortion,
  ExceptionInfo *exception)
{
  CacheView
    *image_view,
    *reconstruct_view;

  ssize_t
    y;

  MagickBooleanType
    status;

  MagickRealType
    alpha,
    area,
    beta,
    maximum_error,
    mean_error;

  status=MagickTrue;
  alpha=1.0;
  beta=1.0;
  area=0.0;
  maximum_error=0.0;
  mean_error=0.0;
  image_view=AcquireCacheView(image);
  reconstruct_view=AcquireCacheView(reconstruct_image);
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const IndexPacket
      *restrict indexes,
      *restrict reconstruct_indexes;

    register const PixelPacket
      *restrict p,
      *restrict q;

    register ssize_t
      x;

    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
      1,exception);
    if ((p == (const PixelPacket *) NULL) || (q == (const PixelPacket *) NULL))
      {
        status=MagickFalse;
        break;
      }
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    reconstruct_indexes=GetCacheViewVirtualIndexQueue(reconstruct_view);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      MagickRealType
        distance;

      if ((channel & OpacityChannel) != 0)
        {
          if (image->matte != MagickFalse)
            alpha=(MagickRealType) (QuantumScale*(GetAlphaPixelComponent(p)));
          if (reconstruct_image->matte != MagickFalse)
            beta=(MagickRealType) (QuantumScale*GetAlphaPixelComponent(q));
        }
      if ((channel & RedChannel) != 0)
        {
          distance=fabs(alpha*p->red-beta*q->red);
          distortion[RedChannel]+=distance;
          distortion[AllChannels]+=distance;
          mean_error+=distance*distance;
          if (distance > maximum_error)
            maximum_error=distance;
          area++;
        }
      if ((channel & GreenChannel) != 0)
        {
          distance=fabs(alpha*p->green-beta*q->green);
          distortion[GreenChannel]+=distance;
          distortion[AllChannels]+=distance;
          mean_error+=distance*distance;
          if (distance > maximum_error)
            maximum_error=distance;
          area++;
        }
      if ((channel & BlueChannel) != 0)
        {
          distance=fabs(alpha*p->blue-beta*q->blue);
          distortion[BlueChannel]+=distance;
          distortion[AllChannels]+=distance;
          mean_error+=distance*distance;
          if (distance > maximum_error)
            maximum_error=distance;
          area++;
        }
      if (((channel & OpacityChannel) != 0) &&
          (image->matte != MagickFalse))
        {
          distance=fabs((double) p->opacity-q->opacity);
          distortion[OpacityChannel]+=distance;
          distortion[AllChannels]+=distance;
          mean_error+=distance*distance;
          if (distance > maximum_error)
            maximum_error=distance;
          area++;
        }
      if (((channel & IndexChannel) != 0) &&
          (image->colorspace == CMYKColorspace) &&
          (reconstruct_image->colorspace == CMYKColorspace))
        {
          distance=fabs(alpha*indexes[x]-beta*reconstruct_indexes[x]);
          distortion[BlackChannel]+=distance;
          distortion[AllChannels]+=distance;
          mean_error+=distance*distance;
          if (distance > maximum_error)
            maximum_error=distance;
          area++;
        }
      p++;
      q++;
    }
  }
  reconstruct_view=DestroyCacheView(reconstruct_view);
  image_view=DestroyCacheView(image_view);
  image->error.mean_error_per_pixel=distortion[AllChannels]/area;
  image->error.normalized_mean_error=QuantumScale*QuantumScale*mean_error/area;
  image->error.normalized_maximum_error=QuantumScale*maximum_error;
  return(status);
}

static MagickBooleanType GetMeanSquaredDistortion(const Image *image,
  const Image *reconstruct_image,const ChannelType channel,
  double *distortion,ExceptionInfo *exception)
{
  CacheView
    *image_view,
    *reconstruct_view;

  ssize_t
    y;

  MagickBooleanType
    status;

  register ssize_t
    i;

  status=MagickTrue;
  image_view=AcquireCacheView(image);
  reconstruct_view=AcquireCacheView(reconstruct_image);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4) shared(status)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    double
      channel_distortion[AllChannels+1];

    register const IndexPacket
      *restrict indexes,
      *restrict reconstruct_indexes;

    register const PixelPacket
      *restrict p,
      *restrict q;

    register ssize_t
      i,
      x;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    q=GetCacheViewVirtualPixels(reconstruct_view,0,y,
      reconstruct_image->columns,1,exception);
    if ((p == (const PixelPacket *) NULL) || (q == (const PixelPacket *) NULL))
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    reconstruct_indexes=GetCacheViewVirtualIndexQueue(reconstruct_view);
    (void) ResetMagickMemory(channel_distortion,0,sizeof(channel_distortion));
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      MagickRealType
        distance;

      if ((channel & RedChannel) != 0)
        {
          distance=QuantumScale*(p->red-(MagickRealType) q->red);
          channel_distortion[RedChannel]+=distance*distance;
          channel_distortion[AllChannels]+=distance*distance;
        }
      if ((channel & GreenChannel) != 0)
        {
          distance=QuantumScale*(p->green-(MagickRealType) q->green);
          channel_distortion[GreenChannel]+=distance*distance;
          channel_distortion[AllChannels]+=distance*distance;
        }
      if ((channel & BlueChannel) != 0)
        {
          distance=QuantumScale*(p->blue-(MagickRealType) q->blue);
          channel_distortion[BlueChannel]+=distance*distance;
          channel_distortion[AllChannels]+=distance*distance;
        }
      if (((channel & OpacityChannel) != 0) &&
          (image->matte != MagickFalse))
        {
          distance=QuantumScale*(p->opacity-(MagickRealType) q->opacity);
          channel_distortion[OpacityChannel]+=distance*distance;
          channel_distortion[AllChannels]+=distance*distance;
        }
      if (((channel & IndexChannel) != 0) &&
          (image->colorspace == CMYKColorspace) &&
          (reconstruct_image->colorspace == CMYKColorspace))
        {
          distance=QuantumScale*(indexes[x]-(MagickRealType)
            reconstruct_indexes[x]);
          channel_distortion[BlackChannel]+=distance*distance;
          channel_distortion[AllChannels]+=distance*distance;
        }
      p++;
      q++;
    }
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_GetMeanSquaredError)
#endif
    for (i=0; i <= (ssize_t) AllChannels; i++)
      distortion[i]+=channel_distortion[i];
  }
  reconstruct_view=DestroyCacheView(reconstruct_view);
  image_view=DestroyCacheView(image_view);
  for (i=0; i <= (ssize_t) AllChannels; i++)
    distortion[i]/=((double) image->columns*image->rows);
  distortion[AllChannels]/=(double) GetNumberChannels(image,channel);
  return(status);
}

static MagickBooleanType GetNormalizedCrossCorrelationDistortion(
  const Image *image,const Image *reconstruct_image,const ChannelType channel,
  double *distortion,ExceptionInfo *exception)
{
#define SimilarityImageTag  "Similarity/Image"

  CacheView
    *image_view,
    *reconstruct_view;

  ChannelStatistics
    *image_statistics,
    *reconstruct_statistics;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  MagickRealType
    area;

  register ssize_t
    i;

  ssize_t
    y;

  /*
    Normalize to account for variation due to lighting and exposure condition.
  */
  image_statistics=GetImageChannelStatistics(image,exception);
  reconstruct_statistics=GetImageChannelStatistics(reconstruct_image,exception);
  status=MagickTrue;
  progress=0;
  for (i=0; i <= (ssize_t) AllChannels; i++)
    distortion[i]=0.0;
  area=1.0/((MagickRealType) image->columns*image->rows);
  image_view=AcquireCacheView(image);
  reconstruct_view=AcquireCacheView(reconstruct_image);
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const IndexPacket
      *restrict indexes,
      *restrict reconstruct_indexes;

    register const PixelPacket
      *restrict p,
      *restrict q;

    register ssize_t
      x;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
      1,exception);
    if ((p == (const PixelPacket *) NULL) || (q == (const PixelPacket *) NULL))
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    reconstruct_indexes=GetCacheViewVirtualIndexQueue(reconstruct_view);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      if ((channel & RedChannel) != 0)
        distortion[RedChannel]+=area*QuantumScale*(p->red-
          image_statistics[RedChannel].mean)*(q->red-
          reconstruct_statistics[RedChannel].mean);
      if ((channel & GreenChannel) != 0)
        distortion[GreenChannel]+=area*QuantumScale*(p->green-
          image_statistics[GreenChannel].mean)*(q->green-
          reconstruct_statistics[GreenChannel].mean);
      if ((channel & BlueChannel) != 0)
        distortion[BlueChannel]+=area*QuantumScale*(p->blue-
          image_statistics[BlueChannel].mean)*(q->blue-
          reconstruct_statistics[BlueChannel].mean);
      if (((channel & OpacityChannel) != 0) &&
          (image->matte != MagickFalse))
        distortion[OpacityChannel]+=area*QuantumScale*(p->opacity-
          image_statistics[OpacityChannel].mean)*(q->opacity-
          reconstruct_statistics[OpacityChannel].mean);
      if (((channel & IndexChannel) != 0) &&
          (image->colorspace == CMYKColorspace) &&
          (reconstruct_image->colorspace == CMYKColorspace))
        distortion[BlackChannel]+=area*QuantumScale*(indexes[x]-
          image_statistics[OpacityChannel].mean)*(reconstruct_indexes[x]-
          reconstruct_statistics[OpacityChannel].mean);
      p++;
      q++;
    }
    if (image->progress_monitor != (MagickProgressMonitor) NULL)
      {
        MagickBooleanType
          proceed;

        proceed=SetImageProgress(image,SimilarityImageTag,progress++,
          image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  reconstruct_view=DestroyCacheView(reconstruct_view);
  image_view=DestroyCacheView(image_view);
  /*
    Divide by the standard deviation.
  */
  for (i=0; i < (ssize_t) AllChannels; i++)
  {
    MagickRealType
      gamma;

    gamma=image_statistics[i].standard_deviation*
      reconstruct_statistics[i].standard_deviation;
    gamma=1.0/(fabs((double) gamma) <= MagickEpsilon ? 1.0 : gamma);
    distortion[i]=QuantumRange*gamma*distortion[i];
  }
  distortion[AllChannels]=0.0;
  if ((channel & RedChannel) != 0)
    distortion[AllChannels]+=distortion[RedChannel]*distortion[RedChannel];
  if ((channel & GreenChannel) != 0)
    distortion[AllChannels]+=distortion[GreenChannel]*distortion[GreenChannel];
  if ((channel & BlueChannel) != 0)
    distortion[AllChannels]+=distortion[BlueChannel]*distortion[BlueChannel];
  if (((channel & OpacityChannel) != 0) && (image->matte != MagickFalse))
    distortion[AllChannels]+=distortion[OpacityChannel]*
      distortion[OpacityChannel];
  if (((channel & IndexChannel) != 0) &&
      (image->colorspace == CMYKColorspace))
    distortion[AllChannels]+=distortion[BlackChannel]*distortion[BlackChannel];
  distortion[AllChannels]=sqrt(distortion[AllChannels]/GetNumberChannels(image,
    channel));
  /*
    Free resources.
  */
  reconstruct_statistics=(ChannelStatistics *) RelinquishMagickMemory(
    reconstruct_statistics);
  image_statistics=(ChannelStatistics *) RelinquishMagickMemory(
    image_statistics);
  return(status);
}

static MagickBooleanType GetPeakAbsoluteDistortion(const Image *image,
  const Image *reconstruct_image,const ChannelType channel,
  double *distortion,ExceptionInfo *exception)
{
  CacheView
    *image_view,
    *reconstruct_view;

  ssize_t
    y;

  MagickBooleanType
    status;

  status=MagickTrue;
  image_view=AcquireCacheView(image);
  reconstruct_view=AcquireCacheView(reconstruct_image);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4) shared(status)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    double
      channel_distortion[AllChannels+1];

    register const IndexPacket
      *restrict indexes,
      *restrict reconstruct_indexes;

    register const PixelPacket
      *restrict p,
      *restrict q;

    register ssize_t
      i,
      x;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    q=GetCacheViewVirtualPixels(reconstruct_view,0,y,
      reconstruct_image->columns,1,exception);
    if ((p == (const PixelPacket *) NULL) || (q == (const PixelPacket *) NULL))
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    reconstruct_indexes=GetCacheViewVirtualIndexQueue(reconstruct_view);
    (void) ResetMagickMemory(channel_distortion,0,sizeof(channel_distortion));
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      MagickRealType
        distance;

      if ((channel & RedChannel) != 0)
        {
          distance=QuantumScale*fabs(p->red-(double) q->red);
          if (distance > channel_distortion[RedChannel])
            channel_distortion[RedChannel]=distance;
          if (distance > channel_distortion[AllChannels])
            channel_distortion[AllChannels]=distance;
        }
      if ((channel & GreenChannel) != 0)
        {
          distance=QuantumScale*fabs(p->green-(double) q->green);
          if (distance > channel_distortion[GreenChannel])
            channel_distortion[GreenChannel]=distance;
          if (distance > channel_distortion[AllChannels])
            channel_distortion[AllChannels]=distance;
        }
      if ((channel & BlueChannel) != 0)
        {
          distance=QuantumScale*fabs(p->blue-(double) q->blue);
          if (distance > channel_distortion[BlueChannel])
            channel_distortion[BlueChannel]=distance;
          if (distance > channel_distortion[AllChannels])
            channel_distortion[AllChannels]=distance;
        }
      if (((channel & OpacityChannel) != 0) &&
          (image->matte != MagickFalse))
        {
          distance=QuantumScale*fabs(p->opacity-(double) q->opacity);
          if (distance > channel_distortion[OpacityChannel])
            channel_distortion[OpacityChannel]=distance;
          if (distance > channel_distortion[AllChannels])
            channel_distortion[AllChannels]=distance;
        }
      if (((channel & IndexChannel) != 0) &&
          (image->colorspace == CMYKColorspace) &&
          (reconstruct_image->colorspace == CMYKColorspace))
        {
          distance=QuantumScale*fabs(indexes[x]-(double)
            reconstruct_indexes[x]);
          if (distance > channel_distortion[BlackChannel])
            channel_distortion[BlackChannel]=distance;
          if (distance > channel_distortion[AllChannels])
            channel_distortion[AllChannels]=distance;
        }
      p++;
      q++;
    }
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_GetPeakAbsoluteError)
#endif
    for (i=0; i <= (ssize_t) AllChannels; i++)
      if (channel_distortion[i] > distortion[i])
        distortion[i]=channel_distortion[i];
  }
  reconstruct_view=DestroyCacheView(reconstruct_view);
  image_view=DestroyCacheView(image_view);
  return(status);
}

static MagickBooleanType GetPeakSignalToNoiseRatio(const Image *image,
  const Image *reconstruct_image,const ChannelType channel,
  double *distortion,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  status=GetMeanSquaredDistortion(image,reconstruct_image,channel,distortion,
    exception);
  if ((channel & RedChannel) != 0)
    distortion[RedChannel]=20.0*log10((double) 1.0/sqrt(
      distortion[RedChannel]));
  if ((channel & GreenChannel) != 0)
    distortion[GreenChannel]=20.0*log10((double) 1.0/sqrt(
      distortion[GreenChannel]));
  if ((channel & BlueChannel) != 0)
    distortion[BlueChannel]=20.0*log10((double) 1.0/sqrt(
      distortion[BlueChannel]));
  if (((channel & OpacityChannel) != 0) &&
      (image->matte != MagickFalse))
    distortion[OpacityChannel]=20.0*log10((double) 1.0/sqrt(
      distortion[OpacityChannel]));
  if (((channel & IndexChannel) != 0) &&
      (image->colorspace == CMYKColorspace))
    distortion[BlackChannel]=20.0*log10((double) 1.0/sqrt(
      distortion[BlackChannel]));
  distortion[AllChannels]=20.0*log10((double) 1.0/sqrt(
    distortion[AllChannels]));
  return(status);
}

static MagickBooleanType GetRootMeanSquaredDistortion(const Image *image,
  const Image *reconstruct_image,const ChannelType channel,
  double *distortion,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  status=GetMeanSquaredDistortion(image,reconstruct_image,channel,distortion,
    exception);
  if ((channel & RedChannel) != 0)
    distortion[RedChannel]=sqrt(distortion[RedChannel]);
  if ((channel & GreenChannel) != 0)
    distortion[GreenChannel]=sqrt(distortion[GreenChannel]);
  if ((channel & BlueChannel) != 0)
    distortion[BlueChannel]=sqrt(distortion[BlueChannel]);
  if (((channel & OpacityChannel) != 0) &&
      (image->matte != MagickFalse))
    distortion[OpacityChannel]=sqrt(distortion[OpacityChannel]);
  if (((channel & IndexChannel) != 0) &&
      (image->colorspace == CMYKColorspace))
    distortion[BlackChannel]=sqrt(distortion[BlackChannel]);
  distortion[AllChannels]=sqrt(distortion[AllChannels]);
  return(status);
}

MagickExport MagickBooleanType GetImageChannelDistortion(Image *image,
  const Image *reconstruct_image,const ChannelType channel,
  const MetricType metric,double *distortion,ExceptionInfo *exception)
{
  double
    *channel_distortion;

  MagickBooleanType
    status;

  size_t
    length;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  assert(reconstruct_image != (const Image *) NULL);
  assert(reconstruct_image->signature == MagickSignature);
  assert(distortion != (double *) NULL);
  *distortion=0.0;
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  if ((reconstruct_image->columns != image->columns) ||
      (reconstruct_image->rows != image->rows))
    ThrowBinaryException(ImageError,"ImageSizeDiffers",image->filename);
  /*
    Get image distortion.
  */
  length=AllChannels+1UL;
  channel_distortion=(double *) AcquireQuantumMemory(length,
    sizeof(*channel_distortion));
  if (channel_distortion == (double *) NULL)
    ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
  (void) ResetMagickMemory(channel_distortion,0,length*
    sizeof(*channel_distortion));
  switch (metric)
  {
    case AbsoluteErrorMetric:
    {
      status=GetAbsoluteDistortion(image,reconstruct_image,channel,
        channel_distortion,exception);
      break;
    }
    case MeanAbsoluteErrorMetric:
    {
      status=GetMeanAbsoluteDistortion(image,reconstruct_image,channel,
        channel_distortion,exception);
      break;
    }
    case MeanErrorPerPixelMetric:
    {
      status=GetMeanErrorPerPixel(image,reconstruct_image,channel,
        channel_distortion,exception);
      break;
    }
    case MeanSquaredErrorMetric:
    {
      status=GetMeanSquaredDistortion(image,reconstruct_image,channel,
        channel_distortion,exception);
      break;
    }
    case NormalizedCrossCorrelationErrorMetric:
    default:
    {
      status=GetNormalizedCrossCorrelationDistortion(image,reconstruct_image,
        channel,channel_distortion,exception);
      break;
    }
    case PeakAbsoluteErrorMetric:
    {
      status=GetPeakAbsoluteDistortion(image,reconstruct_image,channel,
        channel_distortion,exception);
      break;
    }
    case PeakSignalToNoiseRatioMetric:
    {
      status=GetPeakSignalToNoiseRatio(image,reconstruct_image,channel,
        channel_distortion,exception);
      break;
    }
    case RootMeanSquaredErrorMetric:
    {
      status=GetRootMeanSquaredDistortion(image,reconstruct_image,channel,
        channel_distortion,exception);
      break;
    }
  }
  *distortion=channel_distortion[AllChannels];
  channel_distortion=(double *) RelinquishMagickMemory(channel_distortion);
  return(status);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   G e t I m a g e C h a n n e l D i s t o r t i o n s                       %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelDistrortion() compares the image channels of an image to a
%  reconstructed image and returns the specified distortion metric for each
%  channel.
%
%  The format of the CompareImageChannels method is:
%
%      double *GetImageChannelDistortions(const Image *image,
%        const Image *reconstruct_image,const MetricType metric,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o reconstruct_image: the reconstruct image.
%
%    o metric: the metric.
%
%    o exception: return any errors or warnings in this structure.
%
*/
MagickExport double *GetImageChannelDistortions(Image *image,
  const Image *reconstruct_image,const MetricType metric,
  ExceptionInfo *exception)
{
  double
    *channel_distortion;

  MagickBooleanType
    status;

  size_t
    length;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  assert(reconstruct_image != (const Image *) NULL);
  assert(reconstruct_image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  if ((reconstruct_image->columns != image->columns) ||
      (reconstruct_image->rows != image->rows))
    {
      (void) ThrowMagickException(&image->exception,GetMagickModule(),
        ImageError,"ImageSizeDiffers","`%s'",image->filename);
      return((double *) NULL);
    }
  /*
    Get image distortion.
  */
  length=AllChannels+1UL;
  channel_distortion=(double *) AcquireQuantumMemory(length,
    sizeof(*channel_distortion));
  if (channel_distortion == (double *) NULL)
    ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
  (void) ResetMagickMemory(channel_distortion,0,length*
    sizeof(*channel_distortion));
  switch (metric)
  {
    case AbsoluteErrorMetric:
    {
      status=GetAbsoluteDistortion(image,reconstruct_image,AllChannels,
        channel_distortion,exception);
      break;
    }
    case MeanAbsoluteErrorMetric:
    {
      status=GetMeanAbsoluteDistortion(image,reconstruct_image,AllChannels,
        channel_distortion,exception);
      break;
    }
    case MeanErrorPerPixelMetric:
    {
      status=GetMeanErrorPerPixel(image,reconstruct_image,AllChannels,
        channel_distortion,exception);
      break;
    }
    case MeanSquaredErrorMetric:
    {
      status=GetMeanSquaredDistortion(image,reconstruct_image,AllChannels,
        channel_distortion,exception);
      break;
    }
    case NormalizedCrossCorrelationErrorMetric:
    default:
    {
      status=GetNormalizedCrossCorrelationDistortion(image,reconstruct_image,
        AllChannels,channel_distortion,exception);
      break;
    }
    case PeakAbsoluteErrorMetric:
    {
      status=GetPeakAbsoluteDistortion(image,reconstruct_image,AllChannels,
        channel_distortion,exception);
      break;
    }
    case PeakSignalToNoiseRatioMetric:
    {
      status=GetPeakSignalToNoiseRatio(image,reconstruct_image,AllChannels,
        channel_distortion,exception);
      break;
    }
    case RootMeanSquaredErrorMetric:
    {
      status=GetRootMeanSquaredDistortion(image,reconstruct_image,AllChannels,
        channel_distortion,exception);
      break;
    }
  }
  return(channel_distortion);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%  I s I m a g e s E q u a l                                                  %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  IsImagesEqual() measures the difference between colors at each pixel
%  location of two images.  A value other than 0 means the colors match
%  exactly.  Otherwise an error measure is computed by summing over all
%  pixels in an image the distance squared in RGB space between each image
%  pixel and its corresponding pixel in the reconstruct image.  The error
%  measure is assigned to these image members:
%
%    o mean_error_per_pixel:  The mean error for any single pixel in
%      the image.
%
%    o normalized_mean_error:  The normalized mean quantization error for
%      any single pixel in the image.  This distance measure is normalized to
%      a range between 0 and 1.  It is independent of the range of red, green,
%      and blue values in the image.
%
%    o normalized_maximum_error:  The normalized maximum quantization
%      error for any single pixel in the image.  This distance measure is
%      normalized to a range between 0 and 1.  It is independent of the range
%      of red, green, and blue values in your image.
%
%  A small normalized mean square error, accessed as
%  image->normalized_mean_error, suggests the images are very similar in
%  spatial layout and color.
%
%  The format of the IsImagesEqual method is:
%
%      MagickBooleanType IsImagesEqual(Image *image,
%        const Image *reconstruct_image)
%
%  A description of each parameter follows.
%
%    o image: the image.
%
%    o reconstruct_image: the reconstruct image.
%
*/
MagickExport MagickBooleanType IsImagesEqual(Image *image,
  const Image *reconstruct_image)
{
  CacheView
    *image_view,
    *reconstruct_view;

  ExceptionInfo
    *exception;

  ssize_t
    y;

  MagickBooleanType
    status;

  MagickRealType
    area,
    maximum_error,
    mean_error,
    mean_error_per_pixel;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  assert(reconstruct_image != (const Image *) NULL);
  assert(reconstruct_image->signature == MagickSignature);
  if ((reconstruct_image->columns != image->columns) ||
      (reconstruct_image->rows != image->rows))
    ThrowBinaryException(ImageError,"ImageSizeDiffers",image->filename);
  area=0.0;
  maximum_error=0.0;
  mean_error_per_pixel=0.0;
  mean_error=0.0;
  exception=(&image->exception);
  image_view=AcquireCacheView(image);
  reconstruct_view=AcquireCacheView(reconstruct_image);
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const IndexPacket
      *restrict indexes,
      *restrict reconstruct_indexes;

    register const PixelPacket
      *restrict p,
      *restrict q;

    register ssize_t
      x;

    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
      1,exception);
    if ((p == (const PixelPacket *) NULL) || (q == (const PixelPacket *) NULL))
      break;
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    reconstruct_indexes=GetCacheViewVirtualIndexQueue(reconstruct_view);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      MagickRealType
        distance;

      distance=fabs(p->red-(double) q->red);
      mean_error_per_pixel+=distance;
      mean_error+=distance*distance;
      if (distance > maximum_error)
        maximum_error=distance;
      area++;
      distance=fabs(p->green-(double) q->green);
      mean_error_per_pixel+=distance;
      mean_error+=distance*distance;
      if (distance > maximum_error)
        maximum_error=distance;
      area++;
      distance=fabs(p->blue-(double) q->blue);
      mean_error_per_pixel+=distance;
      mean_error+=distance*distance;
      if (distance > maximum_error)
        maximum_error=distance;
      area++;
      if (image->matte != MagickFalse)
        {
          distance=fabs(p->opacity-(double) q->opacity);
          mean_error_per_pixel+=distance;
          mean_error+=distance*distance;
          if (distance > maximum_error)
            maximum_error=distance;
          area++;
        }
      if ((image->colorspace == CMYKColorspace) &&
          (reconstruct_image->colorspace == CMYKColorspace))
        {
          distance=fabs(indexes[x]-(double) reconstruct_indexes[x]);
          mean_error_per_pixel+=distance;
          mean_error+=distance*distance;
          if (distance > maximum_error)
            maximum_error=distance;
          area++;
        }
      p++;
      q++;
    }
  }
  reconstruct_view=DestroyCacheView(reconstruct_view);
  image_view=DestroyCacheView(image_view);
  image->error.mean_error_per_pixel=(double) (mean_error_per_pixel/area);
  image->error.normalized_mean_error=(double) (QuantumScale*QuantumScale*
    mean_error/area);
  image->error.normalized_maximum_error=(double) (QuantumScale*maximum_error);
  status=image->error.mean_error_per_pixel == 0.0 ? MagickTrue : MagickFalse;
  return(status);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   S i m i l a r i t y I m a g e                                             %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  SimilarityImage() compares the reference image of the image and returns the
%  best match offset.  In addition, it returns a similarity image such that an
%  exact match location is completely white and if none of the pixels match,
%  black, otherwise some gray level in-between.
%
%  The format of the SimilarityImageImage method is:
%
%      Image *SimilarityImage(const Image *image,const Image *reference,
%        RectangleInfo *offset,double *similarity,ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o reference: find an area of the image that closely resembles this image.
%
%    o the best match offset of the reference image within the image.
%
%    o similarity: the computed similarity between the images.
%
%    o exception: return any errors or warnings in this structure.
%
*/

static double GetNCCDistortion(const Image *image,
  const Image *reconstruct_image,
  const ChannelStatistics *reconstruct_statistics,ExceptionInfo *exception)
{
#define SimilarityImageTag  "Similarity/Image"

  CacheView
    *image_view,
    *reconstruct_view;

  ChannelStatistics
    *image_statistics;

  double
    distortion;

  MagickBooleanType
    status;

  MagickRealType
    area,
    gamma;

  ssize_t
    y;

  unsigned long
    number_channels;
  
  /*
    Normalize to account for variation due to lighting and exposure condition.
  */
  image_statistics=GetImageChannelStatistics(image,exception);
  status=MagickTrue;
  distortion=0.0;
  area=1.0/((MagickRealType) image->columns*image->rows);
  image_view=AcquireCacheView(image);
  reconstruct_view=AcquireCacheView(reconstruct_image);
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const IndexPacket
      *restrict indexes,
      *restrict reconstruct_indexes;

    register const PixelPacket
      *restrict p,
      *restrict q;

    register ssize_t
      x;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    q=GetCacheViewVirtualPixels(reconstruct_view,0,y,reconstruct_image->columns,
      1,exception);
    if ((p == (const PixelPacket *) NULL) || (q == (const PixelPacket *) NULL))
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    reconstruct_indexes=GetCacheViewVirtualIndexQueue(reconstruct_view);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      distortion+=area*QuantumScale*(p->red-
        image_statistics[RedChannel].mean)*(q->red-
        reconstruct_statistics[RedChannel].mean);
      distortion+=area*QuantumScale*(p->green-
        image_statistics[GreenChannel].mean)*(q->green-
        reconstruct_statistics[GreenChannel].mean);
      distortion+=area*QuantumScale*(p->blue-
        image_statistics[BlueChannel].mean)*(q->blue-
        reconstruct_statistics[BlueChannel].mean);
      if (image->matte != MagickFalse)
        distortion+=area*QuantumScale*(p->opacity-
          image_statistics[OpacityChannel].mean)*(q->opacity-
          reconstruct_statistics[OpacityChannel].mean);
      if ((image->colorspace == CMYKColorspace) &&
          (reconstruct_image->colorspace == CMYKColorspace))
        distortion+=area*QuantumScale*(indexes[x]-
          image_statistics[OpacityChannel].mean)*(reconstruct_indexes[x]-
          reconstruct_statistics[OpacityChannel].mean);
      p++;
      q++;
    }
  }
  reconstruct_view=DestroyCacheView(reconstruct_view);
  image_view=DestroyCacheView(image_view);
  /*
    Divide by the standard deviation.
  */
  gamma=image_statistics[AllChannels].standard_deviation*
    reconstruct_statistics[AllChannels].standard_deviation;
  gamma=1.0/(fabs((double) gamma) <= MagickEpsilon ? 1.0 : gamma);
  distortion=QuantumRange*gamma*distortion;
  number_channels=3;
  if (image->matte != MagickFalse)
    number_channels++;
  if (image->colorspace == CMYKColorspace)
    number_channels++;
  distortion=sqrt(distortion/number_channels);
  /*
    Free resources.
  */
  image_statistics=(ChannelStatistics *) RelinquishMagickMemory(
    image_statistics);
  return(1.0-distortion);
}

static double GetSimilarityMetric(const Image *image,const Image *reference,
  const ChannelStatistics *reference_statistics,const ssize_t x_offset,
  const ssize_t y_offset,ExceptionInfo *exception)
{
  double
    distortion;

  Image
    *similarity_image;

  RectangleInfo
    geometry;

  SetGeometry(reference,&geometry);
  geometry.x=x_offset;
  geometry.y=y_offset;
  similarity_image=CropImage(image,&geometry,exception);
  if (similarity_image == (Image *) NULL)
    return(0.0);
  distortion=GetNCCDistortion(reference,similarity_image,reference_statistics,
    exception);
  similarity_image=DestroyImage(similarity_image);
  return(distortion);
}

MagickExport Image *SimilarityImage(Image *image,const Image *reference,
  RectangleInfo *offset,double *similarity_metric,ExceptionInfo *exception)
{
#define SimilarityImageTag  "Similarity/Image"

  CacheView
    *similarity_view;

  ChannelStatistics
    *reference_statistics;

  Image
    *similarity_image;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  ssize_t
    y;

  assert(image != (const Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickSignature);
  assert(offset != (RectangleInfo *) NULL);
  SetGeometry(reference,offset);
  *similarity_metric=1.0;
  if ((reference->columns > image->columns) || (reference->rows > image->rows))
    ThrowImageException(ImageError,"ImageSizeDiffers");
  similarity_image=CloneImage(image,image->columns-reference->columns+1,
    image->rows-reference->rows+1,MagickTrue,exception);
  if (similarity_image == (Image *) NULL)
    return((Image *) NULL);
  if (SetImageStorageClass(similarity_image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&similarity_image->exception);
      similarity_image=DestroyImage(similarity_image);
      return((Image *) NULL);
    }
  /*
    Measure similarity of reference image against image.
  */
  status=MagickTrue;
  progress=0;
  reference_statistics=GetImageChannelStatistics(reference,exception);
  similarity_view=AcquireCacheView(similarity_image);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(dynamic,4) shared(progress,status)
#endif
  for (y=0; y < (ssize_t) (image->rows-reference->rows+1); y++)
  {
    double
      similarity;

    register ssize_t
      x;

    register PixelPacket
      *restrict q;

    if (status == MagickFalse)
      continue;
    q=GetCacheViewAuthenticPixels(similarity_view,0,y,similarity_image->columns,
      1,exception);
    if (q == (const PixelPacket *) NULL)
      {
        status=MagickFalse;
        continue;
      }
    for (x=0; x < (ssize_t) (image->columns-reference->columns+1); x++)
    {
      similarity=GetSimilarityMetric(image,reference,reference_statistics,x,y,
        exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_SimilarityImage)
#endif
      if (similarity < *similarity_metric)
        {
          *similarity_metric=similarity;
          offset->x=x;
          offset->y=y;
        }
      q->red=ClampToQuantum(QuantumRange-QuantumRange*similarity);
      q->green=q->red;
      q->blue=q->red;
      q++;
    }
    if (SyncCacheViewAuthenticPixels(similarity_view,exception) == MagickFalse)
      status=MagickFalse;
    if (image->progress_monitor != (MagickProgressMonitor) NULL)
      {
        MagickBooleanType
          proceed;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp critical (MagickCore_SimilarityImage)
#endif
        proceed=SetImageProgress(image,SimilarityImageTag,progress++,
          image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  similarity_view=DestroyCacheView(similarity_view);
  reference_statistics=(ChannelStatistics *) RelinquishMagickMemory(
    reference_statistics);
  return(similarity_image);
}