root/magick/statistic.c

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DEFINITIONS

This source file includes following definitions.
  1. DestroyPixelThreadSet
  2. AcquirePixelThreadSet
  3. EvaluateMax
  4. IntensityCompare
  5. ApplyEvaluateOperator
  6. EvaluateImage
  7. EvaluateImages
  8. EvaluateImageChannel
  9. ApplyFunction
  10. FunctionImage
  11. FunctionImageChannel
  12. GetImageEntropy
  13. GetImageChannelEntropy
  14. GetImageExtrema
  15. GetImageChannelExtrema
  16. GetImageKurtosis
  17. GetImageChannelKurtosis
  18. GetImageMean
  19. GetImageChannelMean
  20. GetImageChannelMoments
  21. MagickLog10
  22. GetImageChannelPerceptualHash
  23. GetImageRange
  24. GetImageChannelRange
  25. GetImageChannelStatistics
  26. PolynomialImage
  27. PolynomialImageChannel
  28. DestroyPixelList
  29. DestroyPixelListThreadSet
  30. AcquirePixelList
  31. AcquirePixelListThreadSet
  32. AddNodePixelList
  33. GetMaximumPixelList
  34. GetMeanPixelList
  35. GetMedianPixelList
  36. GetMinimumPixelList
  37. GetModePixelList
  38. GetNonpeakPixelList
  39. GetRootMeanSquarePixelList
  40. GetStandardDeviationPixelList
  41. InsertPixelList
  42. ResetPixelList
  43. StatisticImage
  44. StatisticImageChannel

/*
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%        SSSSS  TTTTT   AAA   TTTTT  IIIII  SSSSS  TTTTT  IIIII   CCCC        %
%        SS       T    A   A    T      I    SS       T      I    C            %
%         SSS     T    AAAAA    T      I     SSS     T      I    C            %
%           SS    T    A   A    T      I       SS    T      I    C            %
%        SSSSS    T    A   A    T    IIIII  SSSSS    T    IIIII   CCCC        %
%                                                                             %
%                                                                             %
%                     MagickCore Image Statistical Methods                    %
%                                                                             %
%                              Software Design                                %
%                                   Cristy                                    %
%                                 July 1992                                   %
%                                                                             %
%                                                                             %
%  Copyright 1999-2016 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/accelerate.h"
#include "magick/animate.h"
#include "magick/animate.h"
#include "magick/blob.h"
#include "magick/blob-private.h"
#include "magick/cache.h"
#include "magick/cache-private.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/composite.h"
#include "magick/composite-private.h"
#include "magick/compress.h"
#include "magick/constitute.h"
#include "magick/deprecate.h"
#include "magick/display.h"
#include "magick/draw.h"
#include "magick/enhance.h"
#include "magick/exception.h"
#include "magick/exception-private.h"
#include "magick/gem.h"
#include "magick/geometry.h"
#include "magick/list.h"
#include "magick/image-private.h"
#include "magick/magic.h"
#include "magick/magick.h"
#include "magick/memory_.h"
#include "magick/module.h"
#include "magick/monitor.h"
#include "magick/monitor-private.h"
#include "magick/option.h"
#include "magick/paint.h"
#include "magick/pixel-private.h"
#include "magick/profile.h"
#include "magick/property.h"
#include "magick/quantize.h"
#include "magick/random_.h"
#include "magick/random-private.h"
#include "magick/resource_.h"
#include "magick/segment.h"
#include "magick/semaphore.h"
#include "magick/signature-private.h"
#include "magick/statistic.h"
#include "magick/string_.h"
#include "magick/thread-private.h"
#include "magick/timer.h"
#include "magick/utility.h"
#include "magick/version.h"

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%     E v a l u a t e I m a g e                                               %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  EvaluateImage() applies a value to the image with an arithmetic, relational,
%  or logical operator to an image. Use these operations to lighten or darken
%  an image, to increase or decrease contrast in an image, or to produce the
%  "negative" of an image.
%
%  The format of the EvaluateImageChannel method is:
%
%      MagickBooleanType EvaluateImage(Image *image,
%        const MagickEvaluateOperator op,const double value,
%        ExceptionInfo *exception)
%      MagickBooleanType EvaluateImages(Image *images,
%        const MagickEvaluateOperator op,const double value,
%        ExceptionInfo *exception)
%      MagickBooleanType EvaluateImageChannel(Image *image,
%        const ChannelType channel,const MagickEvaluateOperator op,
%        const double value,ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o channel: the channel.
%
%    o op: A channel op.
%
%    o value: A value value.
%
%    o exception: return any errors or warnings in this structure.
%
*/

static MagickPixelPacket **DestroyPixelThreadSet(MagickPixelPacket **pixels)
{
  register ssize_t
    i;

  assert(pixels != (MagickPixelPacket **) NULL);
  for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
    if (pixels[i] != (MagickPixelPacket *) NULL)
      pixels[i]=(MagickPixelPacket *) RelinquishMagickMemory(pixels[i]);
  pixels=(MagickPixelPacket **) RelinquishMagickMemory(pixels);
  return(pixels);
}

static MagickPixelPacket **AcquirePixelThreadSet(const Image *image,
  const size_t number_images)
{
  register ssize_t
    i,
    j;

  MagickPixelPacket
    **pixels;

  size_t
    length,
    number_threads;

  number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
  pixels=(MagickPixelPacket **) AcquireQuantumMemory(number_threads,
    sizeof(*pixels));
  if (pixels == (MagickPixelPacket **) NULL)
    return((MagickPixelPacket **) NULL);
  (void) ResetMagickMemory(pixels,0,number_threads*sizeof(*pixels));
  for (i=0; i < (ssize_t) number_threads; i++)
  {
    length=image->columns;
    if (length < number_images)
      length=number_images;
    pixels[i]=(MagickPixelPacket *) AcquireQuantumMemory(length,
      sizeof(**pixels));
    if (pixels[i] == (MagickPixelPacket *) NULL)
      return(DestroyPixelThreadSet(pixels));
    for (j=0; j < (ssize_t) length; j++)
      GetMagickPixelPacket(image,&pixels[i][j]);
  }
  return(pixels);
}

static inline double EvaluateMax(const double x,const double y)
{
  if (x > y)
    return(x);
  return(y);
}

#if defined(__cplusplus) || defined(c_plusplus)
extern "C" {
#endif

static int IntensityCompare(const void *x,const void *y)
{
  const MagickPixelPacket
    *color_1,
    *color_2;

  int
    intensity;

  color_1=(const MagickPixelPacket *) x;
  color_2=(const MagickPixelPacket *) y;
  intensity=(int) MagickPixelIntensity(color_2)-
    (int) MagickPixelIntensity(color_1);
  return(intensity);
}

#if defined(__cplusplus) || defined(c_plusplus)
}
#endif

static MagickRealType ApplyEvaluateOperator(RandomInfo *random_info,
  const Quantum pixel,const MagickEvaluateOperator op,
  const MagickRealType value)
{
  MagickRealType
    result;

  result=0.0;
  switch (op)
  {
    case UndefinedEvaluateOperator:
      break;
    case AbsEvaluateOperator:
    {
      result=(MagickRealType) fabs((double) (pixel+value));
      break;
    }
    case AddEvaluateOperator:
    {
      result=(MagickRealType) (pixel+value);
      break;
    }
    case AddModulusEvaluateOperator:
    {
      /*
        This returns a 'floored modulus' of the addition which is a
        positive result.  It differs from  % or fmod() which returns a
        'truncated modulus' result, where floor() is replaced by trunc()
        and could return a negative result (which is clipped).
      */
      result=pixel+value;
      result-=(QuantumRange+1.0)*floor((double) result/(QuantumRange+1.0));
      break;
    }
    case AndEvaluateOperator:
    {
      result=(MagickRealType) ((size_t) pixel & (size_t) (value+0.5));
      break;
    }
    case CosineEvaluateOperator:
    {
      result=(MagickRealType) (QuantumRange*(0.5*cos((double) (2.0*MagickPI*
        QuantumScale*pixel*value))+0.5));
      break;
    }
    case DivideEvaluateOperator:
    {
      result=pixel/(value == 0.0 ? 1.0 : value);
      break;
    }
    case ExponentialEvaluateOperator:
    {
      result=(MagickRealType) (QuantumRange*exp((double) (value*QuantumScale*
        pixel)));
      break;
    }
    case GaussianNoiseEvaluateOperator:
    {
      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
        GaussianNoise,value);
      break;
    }
    case ImpulseNoiseEvaluateOperator:
    {
      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
        ImpulseNoise,value);
      break;
    }
    case LaplacianNoiseEvaluateOperator:
    {
      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
        LaplacianNoise,value);
      break;
    }
    case LeftShiftEvaluateOperator:
    {
      result=(MagickRealType) ((size_t) pixel << (size_t) (value+0.5));
      break;
    }
    case LogEvaluateOperator:
    {
      if ((QuantumScale*pixel) >= MagickEpsilon)
        result=(MagickRealType) (QuantumRange*log((double) (QuantumScale*value*
          pixel+1.0))/log((double) (value+1.0)));
      break;
    }
    case MaxEvaluateOperator:
    {
      result=(MagickRealType) EvaluateMax((double) pixel,value);
      break;
    }
    case MeanEvaluateOperator:
    {
      result=(MagickRealType) (pixel+value);
      break;
    }
    case MedianEvaluateOperator:
    {
      result=(MagickRealType) (pixel+value);
      break;
    }
    case MinEvaluateOperator:
    {
      result=(MagickRealType) MagickMin((double) pixel,value);
      break;
    }
    case MultiplicativeNoiseEvaluateOperator:
    {
      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
        MultiplicativeGaussianNoise,value);
      break;
    }
    case MultiplyEvaluateOperator:
    {
      result=(MagickRealType) (value*pixel);
      break;
    }
    case OrEvaluateOperator:
    {
      result=(MagickRealType) ((size_t) pixel | (size_t) (value+0.5));
      break;
    }
    case PoissonNoiseEvaluateOperator:
    {
      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
        PoissonNoise,value);
      break;
    }
    case PowEvaluateOperator:
    {
      result=(MagickRealType) (QuantumRange*pow((double) (QuantumScale*pixel),
        (double) value));
      break;
    }
    case RightShiftEvaluateOperator:
    {
      result=(MagickRealType) ((size_t) pixel >> (size_t) (value+0.5));
      break;
    }
    case RootMeanSquareEvaluateOperator:
    {
      result=(MagickRealType) (pixel*pixel+value);
      break;
    }
    case SetEvaluateOperator:
    {
      result=value;
      break;
    }
    case SineEvaluateOperator:
    {
      result=(MagickRealType) (QuantumRange*(0.5*sin((double) (2.0*MagickPI*
        QuantumScale*pixel*value))+0.5));
      break;
    }
    case SubtractEvaluateOperator:
    {
      result=(MagickRealType) (pixel-value);
      break;
    }
    case SumEvaluateOperator:
    {
      result=(MagickRealType) (pixel+value);
      break;
    }
    case ThresholdEvaluateOperator:
    {
      result=(MagickRealType) (((MagickRealType) pixel <= value) ? 0 :
        QuantumRange);
      break;
    }
    case ThresholdBlackEvaluateOperator:
    {
      result=(MagickRealType) (((MagickRealType) pixel <= value) ? 0 : pixel);
      break;
    }
    case ThresholdWhiteEvaluateOperator:
    {
      result=(MagickRealType) (((MagickRealType) pixel > value) ? QuantumRange :
        pixel);
      break;
    }
    case UniformNoiseEvaluateOperator:
    {
      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
        UniformNoise,value);
      break;
    }
    case XorEvaluateOperator:
    {
      result=(MagickRealType) ((size_t) pixel ^ (size_t) (value+0.5));
      break;
    }
  }
  return(result);
}

MagickExport MagickBooleanType EvaluateImage(Image *image,
  const MagickEvaluateOperator op,const double value,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  status=EvaluateImageChannel(image,CompositeChannels,op,value,exception);
  return(status);
}

MagickExport Image *EvaluateImages(const Image *images,
  const MagickEvaluateOperator op,ExceptionInfo *exception)
{
#define EvaluateImageTag  "Evaluate/Image"

  CacheView
    *evaluate_view;

  Image
    *image;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  MagickPixelPacket
    **magick_restrict evaluate_pixels,
    zero;

  RandomInfo
    **magick_restrict random_info;

  size_t
    number_images;

  ssize_t
    y;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
  unsigned long
    key;
#endif

  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);
  image=CloneImage(images,images->columns,images->rows,MagickTrue,exception);
  if (image == (Image *) NULL)
    return((Image *) NULL);
  if (SetImageStorageClass(image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&image->exception);
      image=DestroyImage(image);
      return((Image *) NULL);
    }
  number_images=GetImageListLength(images);
  evaluate_pixels=AcquirePixelThreadSet(images,number_images);
  if (evaluate_pixels == (MagickPixelPacket **) NULL)
    {
      image=DestroyImage(image);
      (void) ThrowMagickException(exception,GetMagickModule(),
        ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
      return((Image *) NULL);
    }
  /*
    Evaluate image pixels.
  */
  status=MagickTrue;
  progress=0;
  GetMagickPixelPacket(images,&zero);
  random_info=AcquireRandomInfoThreadSet();
  evaluate_view=AcquireAuthenticCacheView(image,exception);
  if (op == MedianEvaluateOperator)
    {
#if defined(MAGICKCORE_OPENMP_SUPPORT)
      key=GetRandomSecretKey(random_info[0]);
      #pragma omp parallel for schedule(static,4) shared(progress,status) \
        magick_threads(image,images,image->rows,key == ~0UL)
#endif
      for (y=0; y < (ssize_t) image->rows; y++)
      {
        CacheView
          *image_view;

        const Image
          *next;

        const int
          id = GetOpenMPThreadId();

        register IndexPacket
          *magick_restrict evaluate_indexes;

        register MagickPixelPacket
          *evaluate_pixel;

        register PixelPacket
          *magick_restrict q;

        register ssize_t
          x;

        if (status == MagickFalse)
          continue;
        q=QueueCacheViewAuthenticPixels(evaluate_view,0,y,
          image->columns,1,exception);
        if (q == (PixelPacket *) NULL)
          {
            status=MagickFalse;
            continue;
          }
        evaluate_indexes=GetCacheViewAuthenticIndexQueue(evaluate_view);
        evaluate_pixel=evaluate_pixels[id];
        for (x=0; x < (ssize_t) image->columns; x++)
        {
          register ssize_t
            i;

          for (i=0; i < (ssize_t) number_images; i++)
            evaluate_pixel[i]=zero;
          next=images;
          for (i=0; i < (ssize_t) number_images; i++)
          {
            register const IndexPacket
              *indexes;

            register const PixelPacket
              *p;

            image_view=AcquireVirtualCacheView(next,exception);
            p=GetCacheViewVirtualPixels(image_view,x,y,1,1,exception);
            if (p == (const PixelPacket *) NULL)
              {
                image_view=DestroyCacheView(image_view);
                break;
              }
            indexes=GetCacheViewVirtualIndexQueue(image_view);
            evaluate_pixel[i].red=ApplyEvaluateOperator(random_info[id],
              GetPixelRed(p),op,evaluate_pixel[i].red);
            evaluate_pixel[i].green=ApplyEvaluateOperator(random_info[id],
              GetPixelGreen(p),op,evaluate_pixel[i].green);
            evaluate_pixel[i].blue=ApplyEvaluateOperator(random_info[id],
              GetPixelBlue(p),op,evaluate_pixel[i].blue);
            evaluate_pixel[i].opacity=ApplyEvaluateOperator(random_info[id],
              GetPixelAlpha(p),op,evaluate_pixel[i].opacity);
            if (image->colorspace == CMYKColorspace)
              evaluate_pixel[i].index=ApplyEvaluateOperator(random_info[id],
                *indexes,op,evaluate_pixel[i].index);
            image_view=DestroyCacheView(image_view);
            next=GetNextImageInList(next);
          }
          qsort((void *) evaluate_pixel,number_images,sizeof(*evaluate_pixel),
            IntensityCompare);
          SetPixelRed(q,ClampToQuantum(evaluate_pixel[i/2].red));
          SetPixelGreen(q,ClampToQuantum(evaluate_pixel[i/2].green));
          SetPixelBlue(q,ClampToQuantum(evaluate_pixel[i/2].blue));
          SetPixelAlpha(q,ClampToQuantum(evaluate_pixel[i/2].opacity));
          if (image->colorspace == CMYKColorspace)
            SetPixelIndex(evaluate_indexes+i,ClampToQuantum(
              evaluate_pixel[i/2].index));
          q++;
        }
        if (SyncCacheViewAuthenticPixels(evaluate_view,exception) == MagickFalse)
          status=MagickFalse;
        if (images->progress_monitor != (MagickProgressMonitor) NULL)
          {
            MagickBooleanType
              proceed;

#if   defined(MAGICKCORE_OPENMP_SUPPORT)
            #pragma omp critical (MagickCore_EvaluateImages)
#endif
            proceed=SetImageProgress(images,EvaluateImageTag,progress++,
              image->rows);
            if (proceed == MagickFalse)
              status=MagickFalse;
          }
      }
    }
  else
    {
#if defined(MAGICKCORE_OPENMP_SUPPORT)
      key=GetRandomSecretKey(random_info[0]);
      #pragma omp parallel for schedule(static,4) shared(progress,status) \
        magick_threads(image,images,image->rows,key == ~0UL)
#endif
      for (y=0; y < (ssize_t) image->rows; y++)
      {
        CacheView
          *image_view;

        const Image
          *next;

        const int
          id = GetOpenMPThreadId();

        register IndexPacket
          *magick_restrict evaluate_indexes;

        register ssize_t
          i,
          x;

        register MagickPixelPacket
          *evaluate_pixel;

        register PixelPacket
          *magick_restrict q;

        if (status == MagickFalse)
          continue;
        q=QueueCacheViewAuthenticPixels(evaluate_view,0,y,
          image->columns,1,exception);
        if (q == (PixelPacket *) NULL)
          {
            status=MagickFalse;
            continue;
          }
        evaluate_indexes=GetCacheViewAuthenticIndexQueue(evaluate_view);
        evaluate_pixel=evaluate_pixels[id];
        for (x=0; x < (ssize_t) image->columns; x++)
          evaluate_pixel[x]=zero;
        next=images;
        for (i=0; i < (ssize_t) number_images; i++)
        {
          register const IndexPacket
            *indexes;

          register const PixelPacket
            *p;

          image_view=AcquireVirtualCacheView(next,exception);
          p=GetCacheViewVirtualPixels(image_view,0,y,next->columns,1,exception);
          if (p == (const PixelPacket *) NULL)
            {
              image_view=DestroyCacheView(image_view);
              break;
            }
          indexes=GetCacheViewVirtualIndexQueue(image_view);
          for (x=0; x < (ssize_t) next->columns; x++)
          {
            evaluate_pixel[x].red=ApplyEvaluateOperator(random_info[id],
              GetPixelRed(p),i == 0 ? AddEvaluateOperator : op,
              evaluate_pixel[x].red);
            evaluate_pixel[x].green=ApplyEvaluateOperator(random_info[id],
              GetPixelGreen(p),i == 0 ? AddEvaluateOperator : op,
              evaluate_pixel[x].green);
            evaluate_pixel[x].blue=ApplyEvaluateOperator(random_info[id],
              GetPixelBlue(p),i == 0 ? AddEvaluateOperator : op,
              evaluate_pixel[x].blue);
            evaluate_pixel[x].opacity=ApplyEvaluateOperator(random_info[id],
              GetPixelAlpha(p),i == 0 ? AddEvaluateOperator : op,
              evaluate_pixel[x].opacity);
            if (image->colorspace == CMYKColorspace)
              evaluate_pixel[x].index=ApplyEvaluateOperator(random_info[id],
                GetPixelIndex(indexes+x),i == 0 ? AddEvaluateOperator : op,
                evaluate_pixel[x].index);
            p++;
          }
          image_view=DestroyCacheView(image_view);
          next=GetNextImageInList(next);
        }
        if (op == MeanEvaluateOperator)
          for (x=0; x < (ssize_t) image->columns; x++)
          {
            evaluate_pixel[x].red/=number_images;
            evaluate_pixel[x].green/=number_images;
            evaluate_pixel[x].blue/=number_images;
            evaluate_pixel[x].opacity/=number_images;
            evaluate_pixel[x].index/=number_images;
          }
        if (op == RootMeanSquareEvaluateOperator)
          for (x=0; x < (ssize_t) image->columns; x++)
          {
            evaluate_pixel[x].red=sqrt((double) evaluate_pixel[x].red/
              number_images);
            evaluate_pixel[x].green=sqrt((double) evaluate_pixel[x].green/
              number_images);
            evaluate_pixel[x].blue=sqrt((double) evaluate_pixel[x].blue/
              number_images);
            evaluate_pixel[x].opacity=sqrt((double) evaluate_pixel[x].opacity/
              number_images);
            evaluate_pixel[x].index=sqrt((double) evaluate_pixel[x].index/
              number_images);
          }
        if (op == MultiplyEvaluateOperator)
          for (x=0; x < (ssize_t) image->columns; x++)
          {
            register ssize_t
              j;

            for (j=0; j < (ssize_t) (number_images-1); j++)
            {
              evaluate_pixel[x].red*=(MagickRealType) QuantumScale;
              evaluate_pixel[x].green*=(MagickRealType) QuantumScale;
              evaluate_pixel[x].blue*=(MagickRealType) QuantumScale;
              evaluate_pixel[x].opacity*=(MagickRealType) QuantumScale;
              evaluate_pixel[x].index*=(MagickRealType) QuantumScale;
            }
          }
        for (x=0; x < (ssize_t) image->columns; x++)
        {
          SetPixelRed(q,ClampToQuantum(evaluate_pixel[x].red));
          SetPixelGreen(q,ClampToQuantum(evaluate_pixel[x].green));
          SetPixelBlue(q,ClampToQuantum(evaluate_pixel[x].blue));
          SetPixelAlpha(q,ClampToQuantum(evaluate_pixel[x].opacity));
          if (image->colorspace == CMYKColorspace)
            SetPixelIndex(evaluate_indexes+x,ClampToQuantum(
              evaluate_pixel[x].index));
          q++;
        }
        if (SyncCacheViewAuthenticPixels(evaluate_view,exception) == MagickFalse)
          status=MagickFalse;
        if (images->progress_monitor != (MagickProgressMonitor) NULL)
          {
            MagickBooleanType
              proceed;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
            #pragma omp critical (MagickCore_EvaluateImages)
#endif
            proceed=SetImageProgress(images,EvaluateImageTag,progress++,
              image->rows);
            if (proceed == MagickFalse)
              status=MagickFalse;
          }
      }
    }
  evaluate_view=DestroyCacheView(evaluate_view);
  evaluate_pixels=DestroyPixelThreadSet(evaluate_pixels);
  random_info=DestroyRandomInfoThreadSet(random_info);
  if (status == MagickFalse)
    image=DestroyImage(image);
  return(image);
}

MagickExport MagickBooleanType EvaluateImageChannel(Image *image,
  const ChannelType channel,const MagickEvaluateOperator op,const double value,
  ExceptionInfo *exception)
{
  CacheView
    *image_view;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  RandomInfo
    **magick_restrict random_info;

  ssize_t
    y;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
  unsigned long
    key;
#endif

  assert(image != (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);
  if (SetImageStorageClass(image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&image->exception);
      return(MagickFalse);
    }
  status=MagickTrue;
  progress=0;
  random_info=AcquireRandomInfoThreadSet();
  image_view=AcquireAuthenticCacheView(image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  key=GetRandomSecretKey(random_info[0]);
  #pragma omp parallel for schedule(static,4) shared(progress,status) \
    magick_threads(image,image,image->rows,key == ~0UL)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    const int
      id = GetOpenMPThreadId();

    register IndexPacket
      *magick_restrict indexes;

    register PixelPacket
      *magick_restrict q;

    register ssize_t
      x;

    if (status == MagickFalse)
      continue;
    q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
    if (q == (PixelPacket *) NULL)
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewAuthenticIndexQueue(image_view);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      MagickRealType
        result;

      if ((channel & RedChannel) != 0)
        {
          result=ApplyEvaluateOperator(random_info[id],GetPixelRed(q),op,value);
          if (op == MeanEvaluateOperator)
            result/=2.0;
          SetPixelRed(q,ClampToQuantum(result));
        }
      if ((channel & GreenChannel) != 0)
        {
          result=ApplyEvaluateOperator(random_info[id],GetPixelGreen(q),op,
            value);
          if (op == MeanEvaluateOperator)
            result/=2.0;
          SetPixelGreen(q,ClampToQuantum(result));
        }
      if ((channel & BlueChannel) != 0)
        {
          result=ApplyEvaluateOperator(random_info[id],GetPixelBlue(q),op,
            value);
          if (op == MeanEvaluateOperator)
            result/=2.0;
          SetPixelBlue(q,ClampToQuantum(result));
        }
      if ((channel & OpacityChannel) != 0)
        {
          if (image->matte == MagickFalse)
            {
              result=ApplyEvaluateOperator(random_info[id],GetPixelOpacity(q),
                op,value);
              if (op == MeanEvaluateOperator)
                result/=2.0;
              SetPixelOpacity(q,ClampToQuantum(result));
            }
          else
            {
              result=ApplyEvaluateOperator(random_info[id],GetPixelAlpha(q),
                op,value);
              if (op == MeanEvaluateOperator)
                result/=2.0;
              SetPixelAlpha(q,ClampToQuantum(result));
            }
        }
      if (((channel & IndexChannel) != 0) && (indexes != (IndexPacket *) NULL))
        {
          result=ApplyEvaluateOperator(random_info[id],GetPixelIndex(indexes+x),
            op,value);
          if (op == MeanEvaluateOperator)
            result/=2.0;
          SetPixelIndex(indexes+x,ClampToQuantum(result));
        }
      q++;
    }
    if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
      status=MagickFalse;
    if (image->progress_monitor != (MagickProgressMonitor) NULL)
      {
        MagickBooleanType
          proceed;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
        #pragma omp critical (MagickCore_EvaluateImageChannel)
#endif
        proceed=SetImageProgress(image,EvaluateImageTag,progress++,image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  image_view=DestroyCacheView(image_view);
  random_info=DestroyRandomInfoThreadSet(random_info);
  return(status);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%     F u n c t i o n I m a g e                                               %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  FunctionImage() applies a value to the image with an arithmetic, relational,
%  or logical operator to an image. Use these operations to lighten or darken
%  an image, to increase or decrease contrast in an image, or to produce the
%  "negative" of an image.
%
%  The format of the FunctionImageChannel method is:
%
%      MagickBooleanType FunctionImage(Image *image,
%        const MagickFunction function,const ssize_t number_parameters,
%        const double *parameters,ExceptionInfo *exception)
%      MagickBooleanType FunctionImageChannel(Image *image,
%        const ChannelType channel,const MagickFunction function,
%        const ssize_t number_parameters,const double *argument,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o channel: the channel.
%
%    o function: A channel function.
%
%    o parameters: one or more parameters.
%
%    o exception: return any errors or warnings in this structure.
%
*/

static Quantum ApplyFunction(Quantum pixel,const MagickFunction function,
  const size_t number_parameters,const double *parameters,
  ExceptionInfo *exception)
{
  MagickRealType
    result;

  register ssize_t
    i;

  (void) exception;
  result=0.0;
  switch (function)
  {
    case PolynomialFunction:
    {
      /*
       * Polynomial
       * Parameters:   polynomial constants,  highest to lowest order
       *   For example:      c0*x^3 + c1*x^2 + c2*x  + c3
       */
      result=0.0;
      for (i=0; i < (ssize_t) number_parameters; i++)
        result=result*QuantumScale*pixel + parameters[i];
      result*=QuantumRange;
      break;
    }
    case SinusoidFunction:
    {
      /* Sinusoid Function
       * Parameters:   Freq, Phase, Ampl, bias
       */
      double  freq,phase,ampl,bias;
      freq  = ( number_parameters >= 1 ) ? parameters[0] : 1.0;
      phase = ( number_parameters >= 2 ) ? parameters[1] : 0.0;
      ampl  = ( number_parameters >= 3 ) ? parameters[2] : 0.5;
      bias  = ( number_parameters >= 4 ) ? parameters[3] : 0.5;
      result=(MagickRealType) (QuantumRange*(ampl*sin((double) (2.0*MagickPI*
        (freq*QuantumScale*pixel + phase/360.0) )) + bias ) );
      break;
    }
    case ArcsinFunction:
    {
      /* Arcsin Function  (peged at range limits for invalid results)
       * Parameters:   Width, Center, Range, Bias
       */
      double  width,range,center,bias;
      width  = ( number_parameters >= 1 ) ? parameters[0] : 1.0;
      center = ( number_parameters >= 2 ) ? parameters[1] : 0.5;
      range  = ( number_parameters >= 3 ) ? parameters[2] : 1.0;
      bias   = ( number_parameters >= 4 ) ? parameters[3] : 0.5;
      result = 2.0/width*(QuantumScale*pixel - center);
      if ( result <= -1.0 )
        result = bias - range/2.0;
      else if ( result >= 1.0 )
        result = bias + range/2.0;
      else
        result=(MagickRealType) (range/MagickPI*asin((double) result)+bias);
      result *= QuantumRange;
      break;
    }
    case ArctanFunction:
    {
      /* Arctan Function
       * Parameters:   Slope, Center, Range, Bias
       */
      double  slope,range,center,bias;
      slope  = ( number_parameters >= 1 ) ? parameters[0] : 1.0;
      center = ( number_parameters >= 2 ) ? parameters[1] : 0.5;
      range  = ( number_parameters >= 3 ) ? parameters[2] : 1.0;
      bias   = ( number_parameters >= 4 ) ? parameters[3] : 0.5;
      result=(MagickRealType) (MagickPI*slope*(QuantumScale*pixel-center));
      result=(MagickRealType) (QuantumRange*(range/MagickPI*atan((double)
                  result) + bias ) );
      break;
    }
    case UndefinedFunction:
      break;
  }
  return(ClampToQuantum(result));
}

MagickExport MagickBooleanType FunctionImage(Image *image,
  const MagickFunction function,const size_t number_parameters,
  const double *parameters,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  status=FunctionImageChannel(image,CompositeChannels,function,
    number_parameters,parameters,exception);
  return(status);
}

MagickExport MagickBooleanType FunctionImageChannel(Image *image,
  const ChannelType channel,const MagickFunction function,
  const size_t number_parameters,const double *parameters,
  ExceptionInfo *exception)
{
#define FunctionImageTag  "Function/Image "

  CacheView
    *image_view;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  ssize_t
    y;

  assert(image != (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);
  if (SetImageStorageClass(image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&image->exception);
      return(MagickFalse);
    }
  status=AccelerateFunctionImage(image,channel,function,number_parameters,
    parameters,exception);
  if (status != MagickFalse)
    return(status);
  status=MagickTrue;
  progress=0;
  image_view=AcquireAuthenticCacheView(image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(static,4) shared(progress,status) \
    magick_threads(image,image,image->rows,1)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register IndexPacket
      *magick_restrict indexes;

    register ssize_t
      x;

    register PixelPacket
      *magick_restrict q;

    if (status == MagickFalse)
      continue;
    q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
    if (q == (PixelPacket *) NULL)
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewAuthenticIndexQueue(image_view);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      if ((channel & RedChannel) != 0)
        SetPixelRed(q,ApplyFunction(GetPixelRed(q),function,
          number_parameters,parameters,exception));
      if ((channel & GreenChannel) != 0)
        SetPixelGreen(q,ApplyFunction(GetPixelGreen(q),function,
          number_parameters,parameters,exception));
      if ((channel & BlueChannel) != 0)
        SetPixelBlue(q,ApplyFunction(GetPixelBlue(q),function,
          number_parameters,parameters,exception));
      if ((channel & OpacityChannel) != 0)
        {
          if (image->matte == MagickFalse)
            SetPixelOpacity(q,ApplyFunction(GetPixelOpacity(q),function,
              number_parameters,parameters,exception));
          else
            SetPixelAlpha(q,ApplyFunction((Quantum) GetPixelAlpha(q),function,
              number_parameters,parameters,exception));
        }
      if (((channel & IndexChannel) != 0) && (indexes != (IndexPacket *) NULL))
        SetPixelIndex(indexes+x,ApplyFunction(GetPixelIndex(indexes+x),function,
          number_parameters,parameters,exception));
      q++;
    }
    if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
      status=MagickFalse;
    if (image->progress_monitor != (MagickProgressMonitor) NULL)
      {
        MagickBooleanType
          proceed;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
        #pragma omp critical (MagickCore_FunctionImageChannel)
#endif
        proceed=SetImageProgress(image,FunctionImageTag,progress++,image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  image_view=DestroyCacheView(image_view);
  return(status);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   G e t I m a g e C h a n n e l E n t r o p y                               %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelEntropy() returns the entropy of one or more image channels.
%
%  The format of the GetImageChannelEntropy method is:
%
%      MagickBooleanType GetImageChannelEntropy(const Image *image,
%        const ChannelType channel,double *entropy,ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o channel: the channel.
%
%    o entropy: the average entropy of the selected channels.
%
%    o exception: return any errors or warnings in this structure.
%
*/

MagickExport MagickBooleanType GetImageEntropy(const Image *image,
  double *entropy,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  status=GetImageChannelEntropy(image,CompositeChannels,entropy,exception);
  return(status);
}

MagickExport MagickBooleanType GetImageChannelEntropy(const Image *image,
  const ChannelType channel,double *entropy,ExceptionInfo *exception)
{
  ChannelStatistics
    *channel_statistics;

  size_t
    channels;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  channel_statistics=GetImageChannelStatistics(image,exception);
  if (channel_statistics == (ChannelStatistics *) NULL)
    return(MagickFalse);
  channels=0;
  channel_statistics[CompositeChannels].entropy=0.0;
  if ((channel & RedChannel) != 0)
    {
      channel_statistics[CompositeChannels].entropy+=
        channel_statistics[RedChannel].entropy;
      channels++;
    }
  if ((channel & GreenChannel) != 0)
    {
      channel_statistics[CompositeChannels].entropy+=
        channel_statistics[GreenChannel].entropy;
      channels++;
    }
  if ((channel & BlueChannel) != 0)
    {
      channel_statistics[CompositeChannels].entropy+=
        channel_statistics[BlueChannel].entropy;
      channels++;
    }
  if (((channel & OpacityChannel) != 0) &&
      (image->matte != MagickFalse))
    {
      channel_statistics[CompositeChannels].entropy+=
        channel_statistics[OpacityChannel].entropy;
      channels++;
    }
  if (((channel & IndexChannel) != 0) &&
      (image->colorspace == CMYKColorspace))
    {
      channel_statistics[CompositeChannels].entropy+=
        channel_statistics[BlackChannel].entropy;
      channels++;
    }
  channel_statistics[CompositeChannels].entropy/=channels;
  *entropy=channel_statistics[CompositeChannels].entropy;
  channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
    channel_statistics);
  return(MagickTrue);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
+   G e t I m a g e C h a n n e l E x t r e m a                               %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelExtrema() returns the extrema of one or more image channels.
%
%  The format of the GetImageChannelExtrema method is:
%
%      MagickBooleanType GetImageChannelExtrema(const Image *image,
%        const ChannelType channel,size_t *minima,size_t *maxima,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o channel: the channel.
%
%    o minima: the minimum value in the channel.
%
%    o maxima: the maximum value in the channel.
%
%    o exception: return any errors or warnings in this structure.
%
*/

MagickExport MagickBooleanType GetImageExtrema(const Image *image,
  size_t *minima,size_t *maxima,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  status=GetImageChannelExtrema(image,CompositeChannels,minima,maxima,
    exception);
  return(status);
}

MagickExport MagickBooleanType GetImageChannelExtrema(const Image *image,
  const ChannelType channel,size_t *minima,size_t *maxima,
  ExceptionInfo *exception)
{
  double
    max,
    min;

  MagickBooleanType
    status;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  status=GetImageChannelRange(image,channel,&min,&max,exception);
  *minima=(size_t) ceil(min-0.5);
  *maxima=(size_t) floor(max+0.5);
  return(status);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   G e t I m a g e C h a n n e l K u r t o s i s                             %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelKurtosis() returns the kurtosis and skewness of one or more
%  image channels.
%
%  The format of the GetImageChannelKurtosis method is:
%
%      MagickBooleanType GetImageChannelKurtosis(const Image *image,
%        const ChannelType channel,double *kurtosis,double *skewness,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o channel: the channel.
%
%    o kurtosis: the kurtosis of the channel.
%
%    o skewness: the skewness of the channel.
%
%    o exception: return any errors or warnings in this structure.
%
*/

MagickExport MagickBooleanType GetImageKurtosis(const Image *image,
  double *kurtosis,double *skewness,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  status=GetImageChannelKurtosis(image,CompositeChannels,kurtosis,skewness,
    exception);
  return(status);
}

MagickExport MagickBooleanType GetImageChannelKurtosis(const Image *image,
  const ChannelType channel,double *kurtosis,double *skewness,
  ExceptionInfo *exception)
{
  double
    area,
    mean,
    standard_deviation,
    sum_squares,
    sum_cubes,
    sum_fourth_power;

  ssize_t
    y;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  *kurtosis=0.0;
  *skewness=0.0;
  area=0.0;
  mean=0.0;
  standard_deviation=0.0;
  sum_squares=0.0;
  sum_cubes=0.0;
  sum_fourth_power=0.0;
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const IndexPacket
      *magick_restrict indexes;

    register const PixelPacket
      *magick_restrict p;

    register ssize_t
      x;

    p=GetVirtualPixels(image,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      break;
    indexes=GetVirtualIndexQueue(image);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      if ((channel & RedChannel) != 0)
        {
          mean+=GetPixelRed(p);
          sum_squares+=(double) GetPixelRed(p)*GetPixelRed(p);
          sum_cubes+=(double) GetPixelRed(p)*GetPixelRed(p)*GetPixelRed(p);
          sum_fourth_power+=(double) GetPixelRed(p)*GetPixelRed(p)*
            GetPixelRed(p)*GetPixelRed(p);
          area++;
        }
      if ((channel & GreenChannel) != 0)
        {
          mean+=GetPixelGreen(p);
          sum_squares+=(double) GetPixelGreen(p)*GetPixelGreen(p);
          sum_cubes+=(double) GetPixelGreen(p)*GetPixelGreen(p)*
            GetPixelGreen(p);
          sum_fourth_power+=(double) GetPixelGreen(p)*GetPixelGreen(p)*
            GetPixelGreen(p)*GetPixelGreen(p);
          area++;
        }
      if ((channel & BlueChannel) != 0)
        {
          mean+=GetPixelBlue(p);
          sum_squares+=(double) GetPixelBlue(p)*GetPixelBlue(p);
          sum_cubes+=(double) GetPixelBlue(p)*GetPixelBlue(p)*GetPixelBlue(p);
          sum_fourth_power+=(double) GetPixelBlue(p)*GetPixelBlue(p)*
            GetPixelBlue(p)*GetPixelBlue(p);
          area++;
        }
      if ((channel & OpacityChannel) != 0)
        {
          mean+=GetPixelOpacity(p);
          sum_squares+=(double) GetPixelOpacity(p)*GetPixelOpacity(p);
          sum_cubes+=(double) GetPixelOpacity(p)*GetPixelOpacity(p)*
            GetPixelOpacity(p);
          sum_fourth_power+=(double) GetPixelOpacity(p)*GetPixelOpacity(p)*
            GetPixelOpacity(p)*GetPixelOpacity(p);
          area++;
        }
      if (((channel & IndexChannel) != 0) &&
          (image->colorspace == CMYKColorspace))
        {
          double
            index;

          index=GetPixelIndex(indexes+x);
          mean+=index;
          sum_squares+=index*index;
          sum_cubes+=index*index*index;
          sum_fourth_power+=index*index*index*index;
          area++;
        }
      p++;
    }
  }
  if (y < (ssize_t) image->rows)
    return(MagickFalse);
  if (area != 0.0)
    {
      mean/=area;
      sum_squares/=area;
      sum_cubes/=area;
      sum_fourth_power/=area;
    }
  standard_deviation=sqrt(sum_squares-(mean*mean));
  if (standard_deviation != 0.0)
    {
      *kurtosis=sum_fourth_power-4.0*mean*sum_cubes+6.0*mean*mean*sum_squares-
        3.0*mean*mean*mean*mean;
      *kurtosis/=standard_deviation*standard_deviation*standard_deviation*
        standard_deviation;
      *kurtosis-=3.0;
      *skewness=sum_cubes-3.0*mean*sum_squares+2.0*mean*mean*mean;
      *skewness/=standard_deviation*standard_deviation*standard_deviation;
    }
  return(y == (ssize_t) image->rows ? MagickTrue : MagickFalse);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   G e t I m a g e C h a n n e l M e a n                                     %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelMean() returns the mean and standard deviation of one or more
%  image channels.
%
%  The format of the GetImageChannelMean method is:
%
%      MagickBooleanType GetImageChannelMean(const Image *image,
%        const ChannelType channel,double *mean,double *standard_deviation,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o channel: the channel.
%
%    o mean: the average value in the channel.
%
%    o standard_deviation: the standard deviation of the channel.
%
%    o exception: return any errors or warnings in this structure.
%
*/

MagickExport MagickBooleanType GetImageMean(const Image *image,double *mean,
  double *standard_deviation,ExceptionInfo *exception)
{
  MagickBooleanType
    status;

  status=GetImageChannelMean(image,CompositeChannels,mean,standard_deviation,
    exception);
  return(status);
}

MagickExport MagickBooleanType GetImageChannelMean(const Image *image,
  const ChannelType channel,double *mean,double *standard_deviation,
  ExceptionInfo *exception)
{
  ChannelStatistics
    *channel_statistics;

  size_t
    channels;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  channel_statistics=GetImageChannelStatistics(image,exception);
  if (channel_statistics == (ChannelStatistics *) NULL)
    return(MagickFalse);
  channels=0;
  channel_statistics[CompositeChannels].mean=0.0;
  channel_statistics[CompositeChannels].standard_deviation=0.0;
  if ((channel & RedChannel) != 0)
    {
      channel_statistics[CompositeChannels].mean+=
        channel_statistics[RedChannel].mean;
      channel_statistics[CompositeChannels].standard_deviation+=
        channel_statistics[RedChannel].variance-
        channel_statistics[RedChannel].mean*
        channel_statistics[RedChannel].mean;
      channels++;
    }
  if ((channel & GreenChannel) != 0)
    {
      channel_statistics[CompositeChannels].mean+=
        channel_statistics[GreenChannel].mean;
      channel_statistics[CompositeChannels].standard_deviation+=
        channel_statistics[GreenChannel].variance-
        channel_statistics[GreenChannel].mean*
        channel_statistics[GreenChannel].mean;
      channels++;
    }
  if ((channel & BlueChannel) != 0)
    {
      channel_statistics[CompositeChannels].mean+=
        channel_statistics[BlueChannel].mean;
      channel_statistics[CompositeChannels].standard_deviation+=
        channel_statistics[BlueChannel].variance-
        channel_statistics[BlueChannel].mean*
        channel_statistics[BlueChannel].mean;
      channels++;
    }
  if (((channel & OpacityChannel) != 0) &&
      (image->matte != MagickFalse))
    {
      channel_statistics[CompositeChannels].mean+=
        channel_statistics[OpacityChannel].mean;
      channel_statistics[CompositeChannels].standard_deviation+=
        channel_statistics[OpacityChannel].variance-
        channel_statistics[OpacityChannel].mean*
        channel_statistics[OpacityChannel].mean;
      channels++;
    }
  if (((channel & IndexChannel) != 0) &&
      (image->colorspace == CMYKColorspace))
    {
      channel_statistics[CompositeChannels].mean+=
        channel_statistics[BlackChannel].mean;
      channel_statistics[CompositeChannels].standard_deviation+=
        channel_statistics[BlackChannel].variance-
        channel_statistics[BlackChannel].mean*
        channel_statistics[BlackChannel].mean;
      channels++;
    }
  channel_statistics[CompositeChannels].mean/=channels;
  channel_statistics[CompositeChannels].standard_deviation=
    sqrt(channel_statistics[CompositeChannels].standard_deviation/channels);
  *mean=channel_statistics[CompositeChannels].mean;
  *standard_deviation=channel_statistics[CompositeChannels].standard_deviation;
  channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
    channel_statistics);
  return(MagickTrue);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   G e t I m a g e C h a n n e l M o m e n t s                               %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelMoments() returns the normalized moments of one or more image
%  channels.
%
%  The format of the GetImageChannelMoments method is:
%
%      ChannelMoments *GetImageChannelMoments(const Image *image,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o exception: return any errors or warnings in this structure.
%
*/
MagickExport ChannelMoments *GetImageChannelMoments(const Image *image,
  ExceptionInfo *exception)
{
#define MaxNumberImageMoments  8

  ChannelMoments
    *channel_moments;

  double
    M00[CompositeChannels+1],
    M01[CompositeChannels+1],
    M02[CompositeChannels+1],
    M03[CompositeChannels+1],
    M10[CompositeChannels+1],
    M11[CompositeChannels+1],
    M12[CompositeChannels+1],
    M20[CompositeChannels+1],
    M21[CompositeChannels+1],
    M22[CompositeChannels+1],
    M30[CompositeChannels+1];

  MagickPixelPacket
    pixel;

  PointInfo
    centroid[CompositeChannels+1];

  ssize_t
    channel,
    channels,
    y;

  size_t
    length;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  length=CompositeChannels+1UL;
  channel_moments=(ChannelMoments *) AcquireQuantumMemory(length,
    sizeof(*channel_moments));
  if (channel_moments == (ChannelMoments *) NULL)
    return(channel_moments);
  (void) ResetMagickMemory(channel_moments,0,length*sizeof(*channel_moments));
  (void) ResetMagickMemory(centroid,0,sizeof(centroid));
  (void) ResetMagickMemory(M00,0,sizeof(M00));
  (void) ResetMagickMemory(M01,0,sizeof(M01));
  (void) ResetMagickMemory(M02,0,sizeof(M02));
  (void) ResetMagickMemory(M03,0,sizeof(M03));
  (void) ResetMagickMemory(M10,0,sizeof(M10));
  (void) ResetMagickMemory(M11,0,sizeof(M11));
  (void) ResetMagickMemory(M12,0,sizeof(M12));
  (void) ResetMagickMemory(M20,0,sizeof(M20));
  (void) ResetMagickMemory(M21,0,sizeof(M21));
  (void) ResetMagickMemory(M22,0,sizeof(M22));
  (void) ResetMagickMemory(M30,0,sizeof(M30));
  GetMagickPixelPacket(image,&pixel);
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const IndexPacket
      *magick_restrict indexes;

    register const PixelPacket
      *magick_restrict p;

    register ssize_t
      x;

    /*
      Compute center of mass (centroid).
    */
    p=GetVirtualPixels(image,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      break;
    indexes=GetVirtualIndexQueue(image);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      SetMagickPixelPacket(image,p,indexes+x,&pixel);
      M00[RedChannel]+=QuantumScale*pixel.red;
      M10[RedChannel]+=x*QuantumScale*pixel.red;
      M01[RedChannel]+=y*QuantumScale*pixel.red;
      M00[GreenChannel]+=QuantumScale*pixel.green;
      M10[GreenChannel]+=x*QuantumScale*pixel.green;
      M01[GreenChannel]+=y*QuantumScale*pixel.green;
      M00[BlueChannel]+=QuantumScale*pixel.blue;
      M10[BlueChannel]+=x*QuantumScale*pixel.blue;
      M01[BlueChannel]+=y*QuantumScale*pixel.blue;
      if (image->matte != MagickFalse)
        {
          M00[OpacityChannel]+=QuantumScale*pixel.opacity;
          M10[OpacityChannel]+=x*QuantumScale*pixel.opacity;
          M01[OpacityChannel]+=y*QuantumScale*pixel.opacity;
        }
      if (image->colorspace == CMYKColorspace)
        {
          M00[IndexChannel]+=QuantumScale*pixel.index;
          M10[IndexChannel]+=x*QuantumScale*pixel.index;
          M01[IndexChannel]+=y*QuantumScale*pixel.index;
        }
      p++;
    }
  }
  for (channel=0; channel <= CompositeChannels; channel++)
  {
    /*
      Compute center of mass (centroid).
    */
    if (M00[channel] < MagickEpsilon)
      {
        M00[channel]+=MagickEpsilon;
        centroid[channel].x=(double) image->columns/2.0;
        centroid[channel].y=(double) image->rows/2.0;
        continue;
      }
    M00[channel]+=MagickEpsilon;
    centroid[channel].x=M10[channel]/M00[channel];
    centroid[channel].y=M01[channel]/M00[channel];
  }
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const IndexPacket
      *magick_restrict indexes;

    register const PixelPacket
      *magick_restrict p;

    register ssize_t
      x;

    /*
      Compute the image moments.
    */
    p=GetVirtualPixels(image,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      break;
    indexes=GetVirtualIndexQueue(image);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      SetMagickPixelPacket(image,p,indexes+x,&pixel);
      M11[RedChannel]+=(x-centroid[RedChannel].x)*(y-
        centroid[RedChannel].y)*QuantumScale*pixel.red;
      M20[RedChannel]+=(x-centroid[RedChannel].x)*(x-
        centroid[RedChannel].x)*QuantumScale*pixel.red;
      M02[RedChannel]+=(y-centroid[RedChannel].y)*(y-
        centroid[RedChannel].y)*QuantumScale*pixel.red;
      M21[RedChannel]+=(x-centroid[RedChannel].x)*(x-
        centroid[RedChannel].x)*(y-centroid[RedChannel].y)*QuantumScale*
        pixel.red;
      M12[RedChannel]+=(x-centroid[RedChannel].x)*(y-
        centroid[RedChannel].y)*(y-centroid[RedChannel].y)*QuantumScale*
        pixel.red;
      M22[RedChannel]+=(x-centroid[RedChannel].x)*(x-
        centroid[RedChannel].x)*(y-centroid[RedChannel].y)*(y-
        centroid[RedChannel].y)*QuantumScale*pixel.red;
      M30[RedChannel]+=(x-centroid[RedChannel].x)*(x-
        centroid[RedChannel].x)*(x-centroid[RedChannel].x)*QuantumScale*
        pixel.red;
      M03[RedChannel]+=(y-centroid[RedChannel].y)*(y-
        centroid[RedChannel].y)*(y-centroid[RedChannel].y)*QuantumScale*
        pixel.red;
      M11[GreenChannel]+=(x-centroid[GreenChannel].x)*(y-
        centroid[GreenChannel].y)*QuantumScale*pixel.green;
      M20[GreenChannel]+=(x-centroid[GreenChannel].x)*(x-
        centroid[GreenChannel].x)*QuantumScale*pixel.green;
      M02[GreenChannel]+=(y-centroid[GreenChannel].y)*(y-
        centroid[GreenChannel].y)*QuantumScale*pixel.green;
      M21[GreenChannel]+=(x-centroid[GreenChannel].x)*(x-
        centroid[GreenChannel].x)*(y-centroid[GreenChannel].y)*QuantumScale*
        pixel.green;
      M12[GreenChannel]+=(x-centroid[GreenChannel].x)*(y-
        centroid[GreenChannel].y)*(y-centroid[GreenChannel].y)*QuantumScale*
        pixel.green;
      M22[GreenChannel]+=(x-centroid[GreenChannel].x)*(x-
        centroid[GreenChannel].x)*(y-centroid[GreenChannel].y)*(y-
        centroid[GreenChannel].y)*QuantumScale*pixel.green;
      M30[GreenChannel]+=(x-centroid[GreenChannel].x)*(x-
        centroid[GreenChannel].x)*(x-centroid[GreenChannel].x)*QuantumScale*
        pixel.green;
      M03[GreenChannel]+=(y-centroid[GreenChannel].y)*(y-
        centroid[GreenChannel].y)*(y-centroid[GreenChannel].y)*QuantumScale*
        pixel.green;
      M11[BlueChannel]+=(x-centroid[BlueChannel].x)*(y-
        centroid[BlueChannel].y)*QuantumScale*pixel.blue;
      M20[BlueChannel]+=(x-centroid[BlueChannel].x)*(x-
        centroid[BlueChannel].x)*QuantumScale*pixel.blue;
      M02[BlueChannel]+=(y-centroid[BlueChannel].y)*(y-
        centroid[BlueChannel].y)*QuantumScale*pixel.blue;
      M21[BlueChannel]+=(x-centroid[BlueChannel].x)*(x-
        centroid[BlueChannel].x)*(y-centroid[BlueChannel].y)*QuantumScale*
        pixel.blue;
      M12[BlueChannel]+=(x-centroid[BlueChannel].x)*(y-
        centroid[BlueChannel].y)*(y-centroid[BlueChannel].y)*QuantumScale*
        pixel.blue;
      M22[BlueChannel]+=(x-centroid[BlueChannel].x)*(x-
        centroid[BlueChannel].x)*(y-centroid[BlueChannel].y)*(y-
        centroid[BlueChannel].y)*QuantumScale*pixel.blue;
      M30[BlueChannel]+=(x-centroid[BlueChannel].x)*(x-
        centroid[BlueChannel].x)*(x-centroid[BlueChannel].x)*QuantumScale*
        pixel.blue;
      M03[BlueChannel]+=(y-centroid[BlueChannel].y)*(y-
        centroid[BlueChannel].y)*(y-centroid[BlueChannel].y)*QuantumScale*
        pixel.blue;
      if (image->matte != MagickFalse)
        {
          M11[OpacityChannel]+=(x-centroid[OpacityChannel].x)*(y-
            centroid[OpacityChannel].y)*QuantumScale*pixel.opacity;
          M20[OpacityChannel]+=(x-centroid[OpacityChannel].x)*(x-
            centroid[OpacityChannel].x)*QuantumScale*pixel.opacity;
          M02[OpacityChannel]+=(y-centroid[OpacityChannel].y)*(y-
            centroid[OpacityChannel].y)*QuantumScale*pixel.opacity;
          M21[OpacityChannel]+=(x-centroid[OpacityChannel].x)*(x-
            centroid[OpacityChannel].x)*(y-centroid[OpacityChannel].y)*
            QuantumScale*pixel.opacity;
          M12[OpacityChannel]+=(x-centroid[OpacityChannel].x)*(y-
            centroid[OpacityChannel].y)*(y-centroid[OpacityChannel].y)*
            QuantumScale*pixel.opacity;
          M22[OpacityChannel]+=(x-centroid[OpacityChannel].x)*(x-
            centroid[OpacityChannel].x)*(y-centroid[OpacityChannel].y)*(y-
            centroid[OpacityChannel].y)*QuantumScale*pixel.opacity;
          M30[OpacityChannel]+=(x-centroid[OpacityChannel].x)*(x-
            centroid[OpacityChannel].x)*(x-centroid[OpacityChannel].x)*
            QuantumScale*pixel.opacity;
          M03[OpacityChannel]+=(y-centroid[OpacityChannel].y)*(y-
            centroid[OpacityChannel].y)*(y-centroid[OpacityChannel].y)*
            QuantumScale*pixel.opacity;
        }
      if (image->colorspace == CMYKColorspace)
        {
          M11[IndexChannel]+=(x-centroid[IndexChannel].x)*(y-
            centroid[IndexChannel].y)*QuantumScale*pixel.index;
          M20[IndexChannel]+=(x-centroid[IndexChannel].x)*(x-
            centroid[IndexChannel].x)*QuantumScale*pixel.index;
          M02[IndexChannel]+=(y-centroid[IndexChannel].y)*(y-
            centroid[IndexChannel].y)*QuantumScale*pixel.index;
          M21[IndexChannel]+=(x-centroid[IndexChannel].x)*(x-
            centroid[IndexChannel].x)*(y-centroid[IndexChannel].y)*
            QuantumScale*pixel.index;
          M12[IndexChannel]+=(x-centroid[IndexChannel].x)*(y-
            centroid[IndexChannel].y)*(y-centroid[IndexChannel].y)*
            QuantumScale*pixel.index;
          M22[IndexChannel]+=(x-centroid[IndexChannel].x)*(x-
            centroid[IndexChannel].x)*(y-centroid[IndexChannel].y)*(y-
            centroid[IndexChannel].y)*QuantumScale*pixel.index;
          M30[IndexChannel]+=(x-centroid[IndexChannel].x)*(x-
            centroid[IndexChannel].x)*(x-centroid[IndexChannel].x)*
            QuantumScale*pixel.index;
          M03[IndexChannel]+=(y-centroid[IndexChannel].y)*(y-
            centroid[IndexChannel].y)*(y-centroid[IndexChannel].y)*
            QuantumScale*pixel.index;
        }
      p++;
    }
  }
  channels=3;
  M00[CompositeChannels]+=(M00[RedChannel]+M00[GreenChannel]+M00[BlueChannel]);
  M01[CompositeChannels]+=(M01[RedChannel]+M01[GreenChannel]+M01[BlueChannel]);
  M02[CompositeChannels]+=(M02[RedChannel]+M02[GreenChannel]+M02[BlueChannel]);
  M03[CompositeChannels]+=(M03[RedChannel]+M03[GreenChannel]+M03[BlueChannel]);
  M10[CompositeChannels]+=(M10[RedChannel]+M10[GreenChannel]+M10[BlueChannel]);
  M11[CompositeChannels]+=(M11[RedChannel]+M11[GreenChannel]+M11[BlueChannel]);
  M12[CompositeChannels]+=(M12[RedChannel]+M12[GreenChannel]+M12[BlueChannel]);
  M20[CompositeChannels]+=(M20[RedChannel]+M20[GreenChannel]+M20[BlueChannel]);
  M21[CompositeChannels]+=(M21[RedChannel]+M21[GreenChannel]+M21[BlueChannel]);
  M22[CompositeChannels]+=(M22[RedChannel]+M22[GreenChannel]+M22[BlueChannel]);
  M30[CompositeChannels]+=(M30[RedChannel]+M30[GreenChannel]+M30[BlueChannel]);
  if (image->matte != MagickFalse)
    {
      channels+=1;
      M00[CompositeChannels]+=M00[OpacityChannel];
      M01[CompositeChannels]+=M01[OpacityChannel];
      M02[CompositeChannels]+=M02[OpacityChannel];
      M03[CompositeChannels]+=M03[OpacityChannel];
      M10[CompositeChannels]+=M10[OpacityChannel];
      M11[CompositeChannels]+=M11[OpacityChannel];
      M12[CompositeChannels]+=M12[OpacityChannel];
      M20[CompositeChannels]+=M20[OpacityChannel];
      M21[CompositeChannels]+=M21[OpacityChannel];
      M22[CompositeChannels]+=M22[OpacityChannel];
      M30[CompositeChannels]+=M30[OpacityChannel];
    }
  if (image->colorspace == CMYKColorspace)
    {
      channels+=1;
      M00[CompositeChannels]+=M00[IndexChannel];
      M01[CompositeChannels]+=M01[IndexChannel];
      M02[CompositeChannels]+=M02[IndexChannel];
      M03[CompositeChannels]+=M03[IndexChannel];
      M10[CompositeChannels]+=M10[IndexChannel];
      M11[CompositeChannels]+=M11[IndexChannel];
      M12[CompositeChannels]+=M12[IndexChannel];
      M20[CompositeChannels]+=M20[IndexChannel];
      M21[CompositeChannels]+=M21[IndexChannel];
      M22[CompositeChannels]+=M22[IndexChannel];
      M30[CompositeChannels]+=M30[IndexChannel];
    }
  M00[CompositeChannels]/=(double) channels;
  M01[CompositeChannels]/=(double) channels;
  M02[CompositeChannels]/=(double) channels;
  M03[CompositeChannels]/=(double) channels;
  M10[CompositeChannels]/=(double) channels;
  M11[CompositeChannels]/=(double) channels;
  M12[CompositeChannels]/=(double) channels;
  M20[CompositeChannels]/=(double) channels;
  M21[CompositeChannels]/=(double) channels;
  M22[CompositeChannels]/=(double) channels;
  M30[CompositeChannels]/=(double) channels;
  for (channel=0; channel <= CompositeChannels; channel++)
  {
    /*
      Compute elliptical angle, major and minor axes, eccentricity, & intensity.
    */
    channel_moments[channel].centroid=centroid[channel];
    channel_moments[channel].ellipse_axis.x=sqrt((2.0/M00[channel])*
      ((M20[channel]+M02[channel])+sqrt(4.0*M11[channel]*M11[channel]+
      (M20[channel]-M02[channel])*(M20[channel]-M02[channel]))));
    channel_moments[channel].ellipse_axis.y=sqrt((2.0/M00[channel])*
      ((M20[channel]+M02[channel])-sqrt(4.0*M11[channel]*M11[channel]+
      (M20[channel]-M02[channel])*(M20[channel]-M02[channel]))));
    channel_moments[channel].ellipse_angle=RadiansToDegrees(0.5*atan(2.0*
      M11[channel]/(M20[channel]-M02[channel]+MagickEpsilon)));
    channel_moments[channel].ellipse_eccentricity=sqrt(1.0-(
      channel_moments[channel].ellipse_axis.y/
      (channel_moments[channel].ellipse_axis.x+MagickEpsilon)));
    channel_moments[channel].ellipse_intensity=M00[channel]/
      (MagickPI*channel_moments[channel].ellipse_axis.x*
      channel_moments[channel].ellipse_axis.y+MagickEpsilon);
  }
  for (channel=0; channel <= CompositeChannels; channel++)
  {
    /*
      Normalize image moments.
    */
    M10[channel]=0.0;
    M01[channel]=0.0;
    M11[channel]/=pow(M00[channel],1.0+(1.0+1.0)/2.0);
    M20[channel]/=pow(M00[channel],1.0+(2.0+0.0)/2.0);
    M02[channel]/=pow(M00[channel],1.0+(0.0+2.0)/2.0);
    M21[channel]/=pow(M00[channel],1.0+(2.0+1.0)/2.0);
    M12[channel]/=pow(M00[channel],1.0+(1.0+2.0)/2.0);
    M22[channel]/=pow(M00[channel],1.0+(2.0+2.0)/2.0);
    M30[channel]/=pow(M00[channel],1.0+(3.0+0.0)/2.0);
    M03[channel]/=pow(M00[channel],1.0+(0.0+3.0)/2.0);
    M00[channel]=1.0;
  }
  for (channel=0; channel <= CompositeChannels; channel++)
  {
    /*
      Compute Hu invariant moments.
    */
    channel_moments[channel].I[0]=M20[channel]+M02[channel];
    channel_moments[channel].I[1]=(M20[channel]-M02[channel])*
      (M20[channel]-M02[channel])+4.0*M11[channel]*M11[channel];
    channel_moments[channel].I[2]=(M30[channel]-3.0*M12[channel])*
      (M30[channel]-3.0*M12[channel])+(3.0*M21[channel]-M03[channel])*
      (3.0*M21[channel]-M03[channel]);
    channel_moments[channel].I[3]=(M30[channel]+M12[channel])*
      (M30[channel]+M12[channel])+(M21[channel]+M03[channel])*
      (M21[channel]+M03[channel]);
    channel_moments[channel].I[4]=(M30[channel]-3.0*M12[channel])*
      (M30[channel]+M12[channel])*((M30[channel]+M12[channel])*
      (M30[channel]+M12[channel])-3.0*(M21[channel]+M03[channel])*
      (M21[channel]+M03[channel]))+(3.0*M21[channel]-M03[channel])*
      (M21[channel]+M03[channel])*(3.0*(M30[channel]+M12[channel])*
      (M30[channel]+M12[channel])-(M21[channel]+M03[channel])*
      (M21[channel]+M03[channel]));
    channel_moments[channel].I[5]=(M20[channel]-M02[channel])*
      ((M30[channel]+M12[channel])*(M30[channel]+M12[channel])-
      (M21[channel]+M03[channel])*(M21[channel]+M03[channel]))+
      4.0*M11[channel]*(M30[channel]+M12[channel])*(M21[channel]+M03[channel]);
    channel_moments[channel].I[6]=(3.0*M21[channel]-M03[channel])*
      (M30[channel]+M12[channel])*((M30[channel]+M12[channel])*
      (M30[channel]+M12[channel])-3.0*(M21[channel]+M03[channel])*
      (M21[channel]+M03[channel]))-(M30[channel]-3*M12[channel])*
      (M21[channel]+M03[channel])*(3.0*(M30[channel]+M12[channel])*
      (M30[channel]+M12[channel])-(M21[channel]+M03[channel])*
      (M21[channel]+M03[channel]));
    channel_moments[channel].I[7]=M11[channel]*((M30[channel]+M12[channel])*
      (M30[channel]+M12[channel])-(M03[channel]+M21[channel])*
      (M03[channel]+M21[channel]))-(M20[channel]-M02[channel])*
      (M30[channel]+M12[channel])*(M03[channel]+M21[channel]);
  }
  if (y < (ssize_t) image->rows)
    channel_moments=(ChannelMoments *) RelinquishMagickMemory(channel_moments);
  return(channel_moments);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   G e t I m a g e C h a n n e l P e r c e p t u a l H a s h                 %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelPerceptualHash() returns the perceptual hash of one or more
%  image channels.
%
%  The format of the GetImageChannelPerceptualHash method is:
%
%      ChannelPerceptualHash *GetImageChannelPerceptualHash(const Image *image,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o exception: return any errors or warnings in this structure.
%
*/

static inline double MagickLog10(const double x)
{
#define Log10Epsilon  (1.0e-11)

 if (fabs(x) < Log10Epsilon)
   return(log10(Log10Epsilon));
 return(log10(fabs(x)));
}

MagickExport ChannelPerceptualHash *GetImageChannelPerceptualHash(
  const Image *image,ExceptionInfo *exception)
{
  ChannelMoments
    *moments;

  ChannelPerceptualHash
    *perceptual_hash;

  Image
    *hash_image;

  MagickBooleanType
    status;

  register ssize_t
    i;

  ssize_t
    channel;

  /*
    Blur then transform to sRGB colorspace.
  */
  hash_image=BlurImage(image,0.0,1.0,exception);
  if (hash_image == (Image *) NULL)
    return((ChannelPerceptualHash *) NULL);
  hash_image->depth=8;
  status=TransformImageColorspace(hash_image,sRGBColorspace);
  if (status == MagickFalse)
    return((ChannelPerceptualHash *) NULL);
  moments=GetImageChannelMoments(hash_image,exception);
  hash_image=DestroyImage(hash_image);
  if (moments == (ChannelMoments *) NULL)
    return((ChannelPerceptualHash *) NULL);
  perceptual_hash=(ChannelPerceptualHash *) AcquireQuantumMemory(
    CompositeChannels+1UL,sizeof(*perceptual_hash));
  if (perceptual_hash == (ChannelPerceptualHash *) NULL)
    return((ChannelPerceptualHash *) NULL);
  for (channel=0; channel <= CompositeChannels; channel++)
    for (i=0; i < MaximumNumberOfImageMoments; i++)
      perceptual_hash[channel].P[i]=(-MagickLog10(moments[channel].I[i]));
  moments=(ChannelMoments *) RelinquishMagickMemory(moments);
  /*
    Blur then transform to HCLp colorspace.
  */
  hash_image=BlurImage(image,0.0,1.0,exception);
  if (hash_image == (Image *) NULL)
    {
      perceptual_hash=(ChannelPerceptualHash *) RelinquishMagickMemory(
        perceptual_hash);
      return((ChannelPerceptualHash *) NULL);
    }
  hash_image->depth=8;
  status=TransformImageColorspace(hash_image,HCLpColorspace);
  if (status == MagickFalse)
    {
      perceptual_hash=(ChannelPerceptualHash *) RelinquishMagickMemory(
        perceptual_hash);
      return((ChannelPerceptualHash *) NULL);
    }
  moments=GetImageChannelMoments(hash_image,exception);
  hash_image=DestroyImage(hash_image);
  if (moments == (ChannelMoments *) NULL)
    {
      perceptual_hash=(ChannelPerceptualHash *) RelinquishMagickMemory(
        perceptual_hash);
      return((ChannelPerceptualHash *) NULL);
    }
  for (channel=0; channel <= CompositeChannels; channel++)
    for (i=0; i < MaximumNumberOfImageMoments; i++)
      perceptual_hash[channel].Q[i]=(-MagickLog10(moments[channel].I[i]));
  moments=(ChannelMoments *) RelinquishMagickMemory(moments);
  return(perceptual_hash);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   G e t I m a g e C h a n n e l R a n g e                                   %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelRange() returns the range of one or more image channels.
%
%  The format of the GetImageChannelRange method is:
%
%      MagickBooleanType GetImageChannelRange(const Image *image,
%        const ChannelType channel,double *minima,double *maxima,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o channel: the channel.
%
%    o minima: the minimum value in the channel.
%
%    o maxima: the maximum value in the channel.
%
%    o exception: return any errors or warnings in this structure.
%
*/

MagickExport MagickBooleanType GetImageRange(const Image *image,
  double *minima,double *maxima,ExceptionInfo *exception)
{
  return(GetImageChannelRange(image,CompositeChannels,minima,maxima,exception));
}

MagickExport MagickBooleanType GetImageChannelRange(const Image *image,
  const ChannelType channel,double *minima,double *maxima,
  ExceptionInfo *exception)
{
  MagickPixelPacket
    pixel;

  ssize_t
    y;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  *maxima=(-MagickMaximumValue);
  *minima=MagickMaximumValue;
  GetMagickPixelPacket(image,&pixel);
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const IndexPacket
      *magick_restrict indexes;

    register const PixelPacket
      *magick_restrict p;

    register ssize_t
      x;

    p=GetVirtualPixels(image,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      break;
    indexes=GetVirtualIndexQueue(image);
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      SetMagickPixelPacket(image,p,indexes+x,&pixel);
      if ((channel & RedChannel) != 0)
        {
          if (pixel.red < *minima)
            *minima=(double) pixel.red;
          if (pixel.red > *maxima)
            *maxima=(double) pixel.red;
        }
      if ((channel & GreenChannel) != 0)
        {
          if (pixel.green < *minima)
            *minima=(double) pixel.green;
          if (pixel.green > *maxima)
            *maxima=(double) pixel.green;
        }
      if ((channel & BlueChannel) != 0)
        {
          if (pixel.blue < *minima)
            *minima=(double) pixel.blue;
          if (pixel.blue > *maxima)
            *maxima=(double) pixel.blue;
        }
      if (((channel & OpacityChannel) != 0) &&
          (image->matte != MagickFalse))
        {
          if ((QuantumRange-pixel.opacity) < *minima)
            *minima=(double) (QuantumRange-pixel.opacity);
          if ((QuantumRange-pixel.opacity) > *maxima)
            *maxima=(double) (QuantumRange-pixel.opacity);
        }
      if (((channel & IndexChannel) != 0) &&
          (image->colorspace == CMYKColorspace))
        {
          if ((double) pixel.index < *minima)
            *minima=(double) pixel.index;
          if ((double) pixel.index > *maxima)
            *maxima=(double) pixel.index;
        }
      p++;
    }
  }
  return(y == (ssize_t) image->rows ? MagickTrue : MagickFalse);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   G e t I m a g e C h a n n e l S t a t i s t i c s                         %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  GetImageChannelStatistics() returns statistics for each channel in the
%  image.  The statistics include the channel depth, its minima, maxima, mean,
%  standard deviation, kurtosis and skewness.  You can access the red channel
%  mean, for example, like this:
%
%      channel_statistics=GetImageChannelStatistics(image,exception);
%      red_mean=channel_statistics[RedChannel].mean;
%
%  Use MagickRelinquishMemory() to free the statistics buffer.
%
%  The format of the GetImageChannelStatistics method is:
%
%      ChannelStatistics *GetImageChannelStatistics(const Image *image,
%        ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o exception: return any errors or warnings in this structure.
%
*/
MagickExport ChannelStatistics *GetImageChannelStatistics(const Image *image,
  ExceptionInfo *exception)
{
  ChannelStatistics
    *channel_statistics;

  double
    area;

  MagickPixelPacket
    number_bins,
    *histogram;

  QuantumAny
    range;

  register ssize_t
    i;

  size_t
    channels,
    depth,
    length;

  ssize_t
    y;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  length=CompositeChannels+1UL;
  channel_statistics=(ChannelStatistics *) AcquireQuantumMemory(length,
    sizeof(*channel_statistics));
  histogram=(MagickPixelPacket *) AcquireQuantumMemory(MaxMap+1U,
    sizeof(*histogram));
  if ((channel_statistics == (ChannelStatistics *) NULL) ||
      (histogram == (MagickPixelPacket *) NULL))
    {
      if (histogram != (MagickPixelPacket *) NULL)
        histogram=(MagickPixelPacket *) RelinquishMagickMemory(histogram);
      if (channel_statistics != (ChannelStatistics *) NULL)
        channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
          channel_statistics);
      return(channel_statistics);
    }
  (void) ResetMagickMemory(channel_statistics,0,length*
    sizeof(*channel_statistics));
  for (i=0; i <= (ssize_t) CompositeChannels; i++)
  {
    channel_statistics[i].depth=1;
    channel_statistics[i].maxima=(-MagickMaximumValue);
    channel_statistics[i].minima=MagickMaximumValue;
  }
  (void) ResetMagickMemory(histogram,0,(MaxMap+1U)*sizeof(*histogram));
  (void) ResetMagickMemory(&number_bins,0,sizeof(number_bins));
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    register const IndexPacket
      *magick_restrict indexes;

    register const PixelPacket
      *magick_restrict p;

    register ssize_t
      x;

    p=GetVirtualPixels(image,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      break;
    indexes=GetVirtualIndexQueue(image);
    for (x=0; x < (ssize_t) image->columns; )
    {
      if (channel_statistics[RedChannel].depth != MAGICKCORE_QUANTUM_DEPTH)
        {
          depth=channel_statistics[RedChannel].depth;
          range=GetQuantumRange(depth);
          if (IsPixelAtDepth(GetPixelRed(p),range) == MagickFalse)
            {
              channel_statistics[RedChannel].depth++;
              continue;
            }
        }
      if (channel_statistics[GreenChannel].depth != MAGICKCORE_QUANTUM_DEPTH)
        {
          depth=channel_statistics[GreenChannel].depth;
          range=GetQuantumRange(depth);
          if (IsPixelAtDepth(GetPixelGreen(p),range) == MagickFalse)
            {
              channel_statistics[GreenChannel].depth++;
              continue;
            }
        }
      if (channel_statistics[BlueChannel].depth != MAGICKCORE_QUANTUM_DEPTH)
        {
          depth=channel_statistics[BlueChannel].depth;
          range=GetQuantumRange(depth);
          if (IsPixelAtDepth(GetPixelBlue(p),range) == MagickFalse)
            {
              channel_statistics[BlueChannel].depth++;
              continue;
            }
        }
      if (image->matte != MagickFalse)
        {
          if (channel_statistics[OpacityChannel].depth != MAGICKCORE_QUANTUM_DEPTH)
            {
              depth=channel_statistics[OpacityChannel].depth;
              range=GetQuantumRange(depth);
              if (IsPixelAtDepth(GetPixelOpacity(p),range) == MagickFalse)
                {
                  channel_statistics[OpacityChannel].depth++;
                  continue;
                }
            }
          }
      if (image->colorspace == CMYKColorspace)
        {
          if (channel_statistics[BlackChannel].depth != MAGICKCORE_QUANTUM_DEPTH)
            {
              depth=channel_statistics[BlackChannel].depth;
              range=GetQuantumRange(depth);
              if (IsPixelAtDepth(GetPixelIndex(indexes+x),range) == MagickFalse)
                {
                  channel_statistics[BlackChannel].depth++;
                  continue;
                }
            }
        }
      if ((double) GetPixelRed(p) < channel_statistics[RedChannel].minima)
        channel_statistics[RedChannel].minima=(double) GetPixelRed(p);
      if ((double) GetPixelRed(p) > channel_statistics[RedChannel].maxima)
        channel_statistics[RedChannel].maxima=(double) GetPixelRed(p);
      channel_statistics[RedChannel].sum+=GetPixelRed(p);
      channel_statistics[RedChannel].sum_squared+=(double) GetPixelRed(p)*
        GetPixelRed(p);
      channel_statistics[RedChannel].sum_cubed+=(double)
        GetPixelRed(p)*GetPixelRed(p)*GetPixelRed(p);
      channel_statistics[RedChannel].sum_fourth_power+=(double)
        GetPixelRed(p)*GetPixelRed(p)*GetPixelRed(p)*GetPixelRed(p);
      if ((double) GetPixelGreen(p) < channel_statistics[GreenChannel].minima)
        channel_statistics[GreenChannel].minima=(double) GetPixelGreen(p);
      if ((double) GetPixelGreen(p) > channel_statistics[GreenChannel].maxima)
        channel_statistics[GreenChannel].maxima=(double) GetPixelGreen(p);
      channel_statistics[GreenChannel].sum+=GetPixelGreen(p);
      channel_statistics[GreenChannel].sum_squared+=(double) GetPixelGreen(p)*
        GetPixelGreen(p);
      channel_statistics[GreenChannel].sum_cubed+=(double) GetPixelGreen(p)*
        GetPixelGreen(p)*GetPixelGreen(p);
      channel_statistics[GreenChannel].sum_fourth_power+=(double)
        GetPixelGreen(p)*GetPixelGreen(p)*GetPixelGreen(p)*GetPixelGreen(p);
      if ((double) GetPixelBlue(p) < channel_statistics[BlueChannel].minima)
        channel_statistics[BlueChannel].minima=(double) GetPixelBlue(p);
      if ((double) GetPixelBlue(p) > channel_statistics[BlueChannel].maxima)
        channel_statistics[BlueChannel].maxima=(double) GetPixelBlue(p);
      channel_statistics[BlueChannel].sum+=GetPixelBlue(p);
      channel_statistics[BlueChannel].sum_squared+=(double) GetPixelBlue(p)*
        GetPixelBlue(p);
      channel_statistics[BlueChannel].sum_cubed+=(double) GetPixelBlue(p)*
        GetPixelBlue(p)*GetPixelBlue(p);
      channel_statistics[BlueChannel].sum_fourth_power+=(double)
        GetPixelBlue(p)*GetPixelBlue(p)*GetPixelBlue(p)*GetPixelBlue(p);
      histogram[ScaleQuantumToMap(GetPixelRed(p))].red++;
      histogram[ScaleQuantumToMap(GetPixelGreen(p))].green++;
      histogram[ScaleQuantumToMap(GetPixelBlue(p))].blue++;
      if (image->matte != MagickFalse)
        {
          if ((double) GetPixelOpacity(p) < channel_statistics[OpacityChannel].minima)
            channel_statistics[OpacityChannel].minima=(double)
              GetPixelOpacity(p);
          if ((double) GetPixelOpacity(p) > channel_statistics[OpacityChannel].maxima)
            channel_statistics[OpacityChannel].maxima=(double)
              GetPixelOpacity(p);
          channel_statistics[OpacityChannel].sum+=GetPixelOpacity(p);
          channel_statistics[OpacityChannel].sum_squared+=(double)
            GetPixelOpacity(p)*GetPixelOpacity(p);
          channel_statistics[OpacityChannel].sum_cubed+=(double)
            GetPixelOpacity(p)*GetPixelOpacity(p)*GetPixelOpacity(p);
          channel_statistics[OpacityChannel].sum_fourth_power+=(double)
            GetPixelOpacity(p)*GetPixelOpacity(p)*GetPixelOpacity(p)*
            GetPixelOpacity(p);
          histogram[ScaleQuantumToMap(GetPixelOpacity(p))].opacity++;
        }
      if (image->colorspace == CMYKColorspace)
        {
          if ((double) GetPixelIndex(indexes+x) < channel_statistics[BlackChannel].minima)
            channel_statistics[BlackChannel].minima=(double)
              GetPixelIndex(indexes+x);
          if ((double) GetPixelIndex(indexes+x) > channel_statistics[BlackChannel].maxima)
            channel_statistics[BlackChannel].maxima=(double)
              GetPixelIndex(indexes+x);
          channel_statistics[BlackChannel].sum+=GetPixelIndex(indexes+x);
          channel_statistics[BlackChannel].sum_squared+=(double)
            GetPixelIndex(indexes+x)*GetPixelIndex(indexes+x);
          channel_statistics[BlackChannel].sum_cubed+=(double)
            GetPixelIndex(indexes+x)*GetPixelIndex(indexes+x)*
            GetPixelIndex(indexes+x);
          channel_statistics[BlackChannel].sum_fourth_power+=(double)
            GetPixelIndex(indexes+x)*GetPixelIndex(indexes+x)*
            GetPixelIndex(indexes+x)*GetPixelIndex(indexes+x);
          histogram[ScaleQuantumToMap(GetPixelIndex(indexes+x))].index++;
        }
      x++;
      p++;
    }
  }
  area=(double) image->columns*image->rows;
  for (i=0; i < (ssize_t) CompositeChannels; i++)
  {
    double
      mean;

    mean=channel_statistics[i].sum/area;
    channel_statistics[i].sum=mean;
    channel_statistics[i].sum_squared/=area;
    channel_statistics[i].sum_cubed/=area;
    channel_statistics[i].sum_fourth_power/=area;
    channel_statistics[i].mean=mean;
    channel_statistics[i].variance=channel_statistics[i].sum_squared;
    channel_statistics[i].standard_deviation=sqrt(
      channel_statistics[i].variance-(mean*mean));
  }
  for (i=0; i < (ssize_t) (MaxMap+1U); i++)
  {
    if (histogram[i].red > 0.0)
      number_bins.red++;
    if (histogram[i].green > 0.0)
      number_bins.green++;
    if (histogram[i].blue > 0.0)
      number_bins.blue++;
    if ((image->matte != MagickFalse) && (histogram[i].red > 0.0))
      number_bins.opacity++;
    if ((image->colorspace == CMYKColorspace) && (histogram[i].red > 0.0))
      number_bins.index++;
  }
  for (i=0; i < (ssize_t) (MaxMap+1U); i++)
  {
    histogram[i].red/=area;
    channel_statistics[RedChannel].entropy+=-histogram[i].red*
      MagickLog10(histogram[i].red)/MagickLog10((double) number_bins.red);
    histogram[i].green/=area;
    channel_statistics[GreenChannel].entropy+=-histogram[i].green*
      MagickLog10(histogram[i].green)/MagickLog10((double) number_bins.green);
    histogram[i].blue/=area;
    channel_statistics[BlueChannel].entropy+=-histogram[i].blue*
      MagickLog10(histogram[i].blue)/MagickLog10((double) number_bins.blue);
    if (image->matte != MagickFalse)
      {
        histogram[i].opacity/=area;
        channel_statistics[OpacityChannel].entropy+=-histogram[i].opacity*
          MagickLog10(histogram[i].opacity)/MagickLog10((double)
          number_bins.opacity);
      }
    if (image->colorspace == CMYKColorspace)
      {
        histogram[i].index/=area;
        channel_statistics[IndexChannel].entropy+=-histogram[i].index*
          MagickLog10(histogram[i].index)/MagickLog10((double)
          number_bins.index);
      }
  }
  for (i=0; i < (ssize_t) CompositeChannels; i++)
  {
    channel_statistics[CompositeChannels].depth=(size_t) EvaluateMax((double)
      channel_statistics[CompositeChannels].depth,(double)
      channel_statistics[i].depth);
    channel_statistics[CompositeChannels].minima=MagickMin(
      channel_statistics[CompositeChannels].minima,
      channel_statistics[i].minima);
    channel_statistics[CompositeChannels].maxima=EvaluateMax(
      channel_statistics[CompositeChannels].maxima,
      channel_statistics[i].maxima);
    channel_statistics[CompositeChannels].sum+=channel_statistics[i].sum;
    channel_statistics[CompositeChannels].sum_squared+=
      channel_statistics[i].sum_squared;
    channel_statistics[CompositeChannels].sum_cubed+=
      channel_statistics[i].sum_cubed;
    channel_statistics[CompositeChannels].sum_fourth_power+=
      channel_statistics[i].sum_fourth_power;
    channel_statistics[CompositeChannels].mean+=channel_statistics[i].mean;
    channel_statistics[CompositeChannels].variance+=
      channel_statistics[i].variance-channel_statistics[i].mean*
      channel_statistics[i].mean;
    channel_statistics[CompositeChannels].standard_deviation+=
      channel_statistics[i].variance-channel_statistics[i].mean*
      channel_statistics[i].mean;
    channel_statistics[CompositeChannels].entropy+=
      channel_statistics[i].entropy;
  }
  channels=3;
  if (image->matte != MagickFalse)
    channels++;
  if (image->colorspace == CMYKColorspace)
    channels++;
  channel_statistics[CompositeChannels].sum/=channels;
  channel_statistics[CompositeChannels].sum_squared/=channels;
  channel_statistics[CompositeChannels].sum_cubed/=channels;
  channel_statistics[CompositeChannels].sum_fourth_power/=channels;
  channel_statistics[CompositeChannels].mean/=channels;
  channel_statistics[CompositeChannels].variance/=channels;
  channel_statistics[CompositeChannels].standard_deviation=
    sqrt(channel_statistics[CompositeChannels].standard_deviation/channels);
  channel_statistics[CompositeChannels].kurtosis/=channels;
  channel_statistics[CompositeChannels].skewness/=channels;
  channel_statistics[CompositeChannels].entropy/=channels;
  for (i=0; i <= (ssize_t) CompositeChannels; i++)
  {
    if (channel_statistics[i].standard_deviation == 0.0)
      continue;
    channel_statistics[i].skewness=(channel_statistics[i].sum_cubed-
      3.0*channel_statistics[i].mean*channel_statistics[i].sum_squared+
      2.0*channel_statistics[i].mean*channel_statistics[i].mean*
      channel_statistics[i].mean)/(channel_statistics[i].standard_deviation*
      channel_statistics[i].standard_deviation*
      channel_statistics[i].standard_deviation);
    channel_statistics[i].kurtosis=(channel_statistics[i].sum_fourth_power-
      4.0*channel_statistics[i].mean*channel_statistics[i].sum_cubed+
      6.0*channel_statistics[i].mean*channel_statistics[i].mean*
      channel_statistics[i].sum_squared-3.0*channel_statistics[i].mean*
      channel_statistics[i].mean*1.0*channel_statistics[i].mean*
      channel_statistics[i].mean)/(channel_statistics[i].standard_deviation*
      channel_statistics[i].standard_deviation*
      channel_statistics[i].standard_deviation*
      channel_statistics[i].standard_deviation)-3.0;
  }
  histogram=(MagickPixelPacket *) RelinquishMagickMemory(histogram);
  if (y < (ssize_t) image->rows)
    channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
      channel_statistics);
  return(channel_statistics);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%     P o l y n o m i a l I m a g e                                           %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  PolynomialImage() returns a new image where each pixel is the sum of the
%  pixels in the image sequence after applying its corresponding terms
%  (coefficient and degree pairs).
%
%  The format of the PolynomialImage method is:
%
%      Image *PolynomialImage(const Image *images,const size_t number_terms,
%        const double *terms,ExceptionInfo *exception)
%      Image *PolynomialImageChannel(const Image *images,
%        const size_t number_terms,const ChannelType channel,
%        const double *terms,ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o images: the image sequence.
%
%    o channel: the channel.
%
%    o number_terms: the number of terms in the list.  The actual list length
%      is 2 x number_terms + 1 (the constant).
%
%    o terms: the list of polynomial coefficients and degree pairs and a
%      constant.
%
%    o exception: return any errors or warnings in this structure.
%
*/
MagickExport Image *PolynomialImage(const Image *images,
  const size_t number_terms,const double *terms,ExceptionInfo *exception)
{
  Image
    *polynomial_image;

  polynomial_image=PolynomialImageChannel(images,DefaultChannels,number_terms,
    terms,exception);
  return(polynomial_image);
}

MagickExport Image *PolynomialImageChannel(const Image *images,
  const ChannelType channel,const size_t number_terms,const double *terms,
  ExceptionInfo *exception)
{
#define PolynomialImageTag  "Polynomial/Image"

  CacheView
    *polynomial_view;

  Image
    *image;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  MagickPixelPacket
    **magick_restrict polynomial_pixels,
    zero;

  size_t
    number_images;

  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);
  image=CloneImage(images,images->columns,images->rows,MagickTrue,exception);
  if (image == (Image *) NULL)
    return((Image *) NULL);
  if (SetImageStorageClass(image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&image->exception);
      image=DestroyImage(image);
      return((Image *) NULL);
    }
  number_images=GetImageListLength(images);
  polynomial_pixels=AcquirePixelThreadSet(images,number_images);
  if (polynomial_pixels == (MagickPixelPacket **) NULL)
    {
      image=DestroyImage(image);
      (void) ThrowMagickException(exception,GetMagickModule(),
        ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
      return((Image *) NULL);
    }
  /*
    Polynomial image pixels.
  */
  status=MagickTrue;
  progress=0;
  GetMagickPixelPacket(images,&zero);
  polynomial_view=AcquireAuthenticCacheView(image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(static,4) shared(progress,status) \
    magick_threads(image,image,image->rows,1)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    CacheView
      *image_view;

    const Image
      *next;

    const int
      id = GetOpenMPThreadId();

    register IndexPacket
      *magick_restrict polynomial_indexes;

    register MagickPixelPacket
      *polynomial_pixel;

    register PixelPacket
      *magick_restrict q;

    register ssize_t
      i,
      x;

    if (status == MagickFalse)
      continue;
    q=QueueCacheViewAuthenticPixels(polynomial_view,0,y,image->columns,1,
      exception);
    if (q == (PixelPacket *) NULL)
      {
        status=MagickFalse;
        continue;
      }
    polynomial_indexes=GetCacheViewAuthenticIndexQueue(polynomial_view);
    polynomial_pixel=polynomial_pixels[id];
    for (x=0; x < (ssize_t) image->columns; x++)
      polynomial_pixel[x]=zero;
    next=images;
    for (i=0; i < (ssize_t) number_images; i++)
    {
      register const IndexPacket
        *indexes;

      register const PixelPacket
        *p;

      if (i >= (ssize_t) number_terms)
        break;
      image_view=AcquireVirtualCacheView(next,exception);
      p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
      if (p == (const PixelPacket *) NULL)
        {
          image_view=DestroyCacheView(image_view);
          break;
        }
      indexes=GetCacheViewVirtualIndexQueue(image_view);
      for (x=0; x < (ssize_t) image->columns; x++)
      {
        double
          coefficient,
          degree;

        coefficient=terms[i << 1];
        degree=terms[(i << 1)+1];
        if ((channel & RedChannel) != 0)
          polynomial_pixel[x].red+=coefficient*pow(QuantumScale*p->red,degree);
        if ((channel & GreenChannel) != 0)
          polynomial_pixel[x].green+=coefficient*pow(QuantumScale*p->green,
            degree);
        if ((channel & BlueChannel) != 0)
          polynomial_pixel[x].blue+=coefficient*pow(QuantumScale*p->blue,
            degree);
        if ((channel & OpacityChannel) != 0)
          polynomial_pixel[x].opacity+=coefficient*pow(QuantumScale*
            (QuantumRange-p->opacity),degree);
        if (((channel & IndexChannel) != 0) &&
            (image->colorspace == CMYKColorspace))
          polynomial_pixel[x].index+=coefficient*pow(QuantumScale*indexes[x],
            degree);
        p++;
      }
      image_view=DestroyCacheView(image_view);
      next=GetNextImageInList(next);
    }
    for (x=0; x < (ssize_t) image->columns; x++)
    {
      SetPixelRed(q,ClampToQuantum(QuantumRange*polynomial_pixel[x].red));
      SetPixelGreen(q,ClampToQuantum(QuantumRange*polynomial_pixel[x].green));
      SetPixelBlue(q,ClampToQuantum(QuantumRange*polynomial_pixel[x].blue));
      if (image->matte == MagickFalse)
        SetPixelOpacity(q,ClampToQuantum(QuantumRange-QuantumRange*
          polynomial_pixel[x].opacity));
      else
        SetPixelAlpha(q,ClampToQuantum(QuantumRange-QuantumRange*
          polynomial_pixel[x].opacity));
      if (image->colorspace == CMYKColorspace)
        SetPixelIndex(polynomial_indexes+x,ClampToQuantum(QuantumRange*
          polynomial_pixel[x].index));
      q++;
    }
    if (SyncCacheViewAuthenticPixels(polynomial_view,exception) == MagickFalse)
      status=MagickFalse;
    if (images->progress_monitor != (MagickProgressMonitor) NULL)
      {
        MagickBooleanType
          proceed;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
        #pragma omp critical (MagickCore_PolynomialImages)
#endif
        proceed=SetImageProgress(images,PolynomialImageTag,progress++,
          image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  polynomial_view=DestroyCacheView(polynomial_view);
  polynomial_pixels=DestroyPixelThreadSet(polynomial_pixels);
  if (status == MagickFalse)
    image=DestroyImage(image);
  return(image);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%     S t a t i s t i c I m a g e                                             %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  StatisticImage() makes each pixel the min / max / median / mode / etc. of
%  the neighborhood of the specified width and height.
%
%  The format of the StatisticImage method is:
%
%      Image *StatisticImage(const Image *image,const StatisticType type,
%        const size_t width,const size_t height,ExceptionInfo *exception)
%      Image *StatisticImageChannel(const Image *image,
%        const ChannelType channel,const StatisticType type,
%        const size_t width,const size_t height,ExceptionInfo *exception)
%
%  A description of each parameter follows:
%
%    o image: the image.
%
%    o channel: the image channel.
%
%    o type: the statistic type (median, mode, etc.).
%
%    o width: the width of the pixel neighborhood.
%
%    o height: the height of the pixel neighborhood.
%
%    o exception: return any errors or warnings in this structure.
%
*/

#define ListChannels  5

typedef struct _ListNode
{
  size_t
    next[9],
    count,
    signature;
} ListNode;

typedef struct _SkipList
{
  ssize_t
    level;

  ListNode
    *nodes;
} SkipList;

typedef struct _PixelList
{
  size_t
    length,
    seed,
    signature;

  SkipList
    lists[ListChannels];
} PixelList;

static PixelList *DestroyPixelList(PixelList *pixel_list)
{
  register ssize_t
    i;

  if (pixel_list == (PixelList *) NULL)
    return((PixelList *) NULL);
  for (i=0; i < ListChannels; i++)
    if (pixel_list->lists[i].nodes != (ListNode *) NULL)
      pixel_list->lists[i].nodes=(ListNode *) RelinquishMagickMemory(
        pixel_list->lists[i].nodes);
  pixel_list=(PixelList *) RelinquishMagickMemory(pixel_list);
  return(pixel_list);
}

static PixelList **DestroyPixelListThreadSet(PixelList **pixel_list)
{
  register ssize_t
    i;

  assert(pixel_list != (PixelList **) NULL);
  for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
    if (pixel_list[i] != (PixelList *) NULL)
      pixel_list[i]=DestroyPixelList(pixel_list[i]);
  pixel_list=(PixelList **) RelinquishMagickMemory(pixel_list);
  return(pixel_list);
}

static PixelList *AcquirePixelList(const size_t width,const size_t height)
{
  PixelList
    *pixel_list;

  register ssize_t
    i;

  pixel_list=(PixelList *) AcquireMagickMemory(sizeof(*pixel_list));
  if (pixel_list == (PixelList *) NULL)
    return(pixel_list);
  (void) ResetMagickMemory((void *) pixel_list,0,sizeof(*pixel_list));
  pixel_list->length=width*height;
  for (i=0; i < ListChannels; i++)
  {
    pixel_list->lists[i].nodes=(ListNode *) AcquireQuantumMemory(65537UL,
      sizeof(*pixel_list->lists[i].nodes));
    if (pixel_list->lists[i].nodes == (ListNode *) NULL)
      return(DestroyPixelList(pixel_list));
    (void) ResetMagickMemory(pixel_list->lists[i].nodes,0,65537UL*
      sizeof(*pixel_list->lists[i].nodes));
  }
  pixel_list->signature=MagickSignature;
  return(pixel_list);
}

static PixelList **AcquirePixelListThreadSet(const size_t width,
  const size_t height)
{
  PixelList
    **pixel_list;

  register ssize_t
    i;

  size_t
    number_threads;

  number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
  pixel_list=(PixelList **) AcquireQuantumMemory(number_threads,
    sizeof(*pixel_list));
  if (pixel_list == (PixelList **) NULL)
    return((PixelList **) NULL);
  (void) ResetMagickMemory(pixel_list,0,number_threads*sizeof(*pixel_list));
  for (i=0; i < (ssize_t) number_threads; i++)
  {
    pixel_list[i]=AcquirePixelList(width,height);
    if (pixel_list[i] == (PixelList *) NULL)
      return(DestroyPixelListThreadSet(pixel_list));
  }
  return(pixel_list);
}

static void AddNodePixelList(PixelList *pixel_list,const ssize_t channel,
  const size_t color)
{
  register SkipList
    *list;

  register ssize_t
    level;

  size_t
    search,
    update[9];

  /*
    Initialize the node.
  */
  list=pixel_list->lists+channel;
  list->nodes[color].signature=pixel_list->signature;
  list->nodes[color].count=1;
  /*
    Determine where it belongs in the list.
  */
  search=65536UL;
  for (level=list->level; level >= 0; level--)
  {
    while (list->nodes[search].next[level] < color)
      search=list->nodes[search].next[level];
    update[level]=search;
  }
  /*
    Generate a pseudo-random level for this node.
  */
  for (level=0; ; level++)
  {
    pixel_list->seed=(pixel_list->seed*42893621L)+1L;
    if ((pixel_list->seed & 0x300) != 0x300)
      break;
  }
  if (level > 8)
    level=8;
  if (level > (list->level+2))
    level=list->level+2;
  /*
    If we're raising the list's level, link back to the root node.
  */
  while (level > list->level)
  {
    list->level++;
    update[list->level]=65536UL;
  }
  /*
    Link the node into the skip-list.
  */
  do
  {
    list->nodes[color].next[level]=list->nodes[update[level]].next[level];
    list->nodes[update[level]].next[level]=color;
  } while (level-- > 0);
}

static void GetMaximumPixelList(PixelList *pixel_list,MagickPixelPacket *pixel)
{
  register SkipList
    *list;

  register ssize_t
    channel;

  size_t
    color,
    maximum;

  ssize_t
    count;

  unsigned short
    channels[ListChannels];

  /*
    Find the maximum value for each of the color.
  */
  for (channel=0; channel < 5; channel++)
  {
    list=pixel_list->lists+channel;
    color=65536L;
    count=0;
    maximum=list->nodes[color].next[0];
    do
    {
      color=list->nodes[color].next[0];
      if (color > maximum)
        maximum=color;
      count+=list->nodes[color].count;
    } while (count < (ssize_t) pixel_list->length);
    channels[channel]=(unsigned short) maximum;
  }
  pixel->red=(MagickRealType) ScaleShortToQuantum(channels[0]);
  pixel->green=(MagickRealType) ScaleShortToQuantum(channels[1]);
  pixel->blue=(MagickRealType) ScaleShortToQuantum(channels[2]);
  pixel->opacity=(MagickRealType) ScaleShortToQuantum(channels[3]);
  pixel->index=(MagickRealType) ScaleShortToQuantum(channels[4]);
}

static void GetMeanPixelList(PixelList *pixel_list,MagickPixelPacket *pixel)
{
  MagickRealType
    sum;

  register SkipList
    *list;

  register ssize_t
    channel;

  size_t
    color;

  ssize_t
    count;

  unsigned short
    channels[ListChannels];

  /*
    Find the mean value for each of the color.
  */
  for (channel=0; channel < 5; channel++)
  {
    list=pixel_list->lists+channel;
    color=65536L;
    count=0;
    sum=0.0;
    do
    {
      color=list->nodes[color].next[0];
      sum+=(MagickRealType) list->nodes[color].count*color;
      count+=list->nodes[color].count;
    } while (count < (ssize_t) pixel_list->length);
    sum/=pixel_list->length;
    channels[channel]=(unsigned short) sum;
  }
  pixel->red=(MagickRealType) ScaleShortToQuantum(channels[0]);
  pixel->green=(MagickRealType) ScaleShortToQuantum(channels[1]);
  pixel->blue=(MagickRealType) ScaleShortToQuantum(channels[2]);
  pixel->opacity=(MagickRealType) ScaleShortToQuantum(channels[3]);
  pixel->index=(MagickRealType) ScaleShortToQuantum(channels[4]);
}

static void GetMedianPixelList(PixelList *pixel_list,MagickPixelPacket *pixel)
{
  register SkipList
    *list;

  register ssize_t
    channel;

  size_t
    color;

  ssize_t
    count;

  unsigned short
    channels[ListChannels];

  /*
    Find the median value for each of the color.
  */
  for (channel=0; channel < 5; channel++)
  {
    list=pixel_list->lists+channel;
    color=65536L;
    count=0;
    do
    {
      color=list->nodes[color].next[0];
      count+=list->nodes[color].count;
    } while (count <= (ssize_t) (pixel_list->length >> 1));
    channels[channel]=(unsigned short) color;
  }
  GetMagickPixelPacket((const Image *) NULL,pixel);
  pixel->red=(MagickRealType) ScaleShortToQuantum(channels[0]);
  pixel->green=(MagickRealType) ScaleShortToQuantum(channels[1]);
  pixel->blue=(MagickRealType) ScaleShortToQuantum(channels[2]);
  pixel->opacity=(MagickRealType) ScaleShortToQuantum(channels[3]);
  pixel->index=(MagickRealType) ScaleShortToQuantum(channels[4]);
}

static void GetMinimumPixelList(PixelList *pixel_list,MagickPixelPacket *pixel)
{
  register SkipList
    *list;

  register ssize_t
    channel;

  size_t
    color,
    minimum;

  ssize_t
    count;

  unsigned short
    channels[ListChannels];

  /*
    Find the minimum value for each of the color.
  */
  for (channel=0; channel < 5; channel++)
  {
    list=pixel_list->lists+channel;
    count=0;
    color=65536UL;
    minimum=list->nodes[color].next[0];
    do
    {
      color=list->nodes[color].next[0];
      if (color < minimum)
        minimum=color;
      count+=list->nodes[color].count;
    } while (count < (ssize_t) pixel_list->length);
    channels[channel]=(unsigned short) minimum;
  }
  pixel->red=(MagickRealType) ScaleShortToQuantum(channels[0]);
  pixel->green=(MagickRealType) ScaleShortToQuantum(channels[1]);
  pixel->blue=(MagickRealType) ScaleShortToQuantum(channels[2]);
  pixel->opacity=(MagickRealType) ScaleShortToQuantum(channels[3]);
  pixel->index=(MagickRealType) ScaleShortToQuantum(channels[4]);
}

static void GetModePixelList(PixelList *pixel_list,MagickPixelPacket *pixel)
{
  register SkipList
    *list;

  register ssize_t
    channel;

  size_t
    color,
    max_count,
    mode;

  ssize_t
    count;

  unsigned short
    channels[5];

  /*
    Make each pixel the 'predominant color' of the specified neighborhood.
  */
  for (channel=0; channel < 5; channel++)
  {
    list=pixel_list->lists+channel;
    color=65536L;
    mode=color;
    max_count=list->nodes[mode].count;
    count=0;
    do
    {
      color=list->nodes[color].next[0];
      if (list->nodes[color].count > max_count)
        {
          mode=color;
          max_count=list->nodes[mode].count;
        }
      count+=list->nodes[color].count;
    } while (count < (ssize_t) pixel_list->length);
    channels[channel]=(unsigned short) mode;
  }
  pixel->red=(MagickRealType) ScaleShortToQuantum(channels[0]);
  pixel->green=(MagickRealType) ScaleShortToQuantum(channels[1]);
  pixel->blue=(MagickRealType) ScaleShortToQuantum(channels[2]);
  pixel->opacity=(MagickRealType) ScaleShortToQuantum(channels[3]);
  pixel->index=(MagickRealType) ScaleShortToQuantum(channels[4]);
}

static void GetNonpeakPixelList(PixelList *pixel_list,MagickPixelPacket *pixel)
{
  register SkipList
    *list;

  register ssize_t
    channel;

  size_t
    color,
    next,
    previous;

  ssize_t
    count;

  unsigned short
    channels[5];

  /*
    Finds the non peak value for each of the colors.
  */
  for (channel=0; channel < 5; channel++)
  {
    list=pixel_list->lists+channel;
    color=65536L;
    next=list->nodes[color].next[0];
    count=0;
    do
    {
      previous=color;
      color=next;
      next=list->nodes[color].next[0];
      count+=list->nodes[color].count;
    } while (count <= (ssize_t) (pixel_list->length >> 1));
    if ((previous == 65536UL) && (next != 65536UL))
      color=next;
    else
      if ((previous != 65536UL) && (next == 65536UL))
        color=previous;
    channels[channel]=(unsigned short) color;
  }
  pixel->red=(MagickRealType) ScaleShortToQuantum(channels[0]);
  pixel->green=(MagickRealType) ScaleShortToQuantum(channels[1]);
  pixel->blue=(MagickRealType) ScaleShortToQuantum(channels[2]);
  pixel->opacity=(MagickRealType) ScaleShortToQuantum(channels[3]);
  pixel->index=(MagickRealType) ScaleShortToQuantum(channels[4]);
}

static void GetRootMeanSquarePixelList(PixelList *pixel_list,
  MagickPixelPacket *pixel)
{
  MagickRealType
    sum;

  register SkipList
    *list;

  register ssize_t
    channel;

  size_t
    color;

  ssize_t
    count;

  unsigned short
    channels[ListChannels];

  /*
    Find the root mean square value for each of the color.
  */
  for (channel=0; channel < 5; channel++)
  {
    list=pixel_list->lists+channel;
    color=65536L;
    count=0;
    sum=0.0;
    do
    {
      color=list->nodes[color].next[0];
      sum+=(MagickRealType) (list->nodes[color].count*color*color);
      count+=list->nodes[color].count;
    } while (count < (ssize_t) pixel_list->length);
    sum/=pixel_list->length;
    channels[channel]=(unsigned short) sqrt(sum);
  }
  pixel->red=(MagickRealType) ScaleShortToQuantum(channels[0]);
  pixel->green=(MagickRealType) ScaleShortToQuantum(channels[1]);
  pixel->blue=(MagickRealType) ScaleShortToQuantum(channels[2]);
  pixel->opacity=(MagickRealType) ScaleShortToQuantum(channels[3]);
  pixel->index=(MagickRealType) ScaleShortToQuantum(channels[4]);
}

static void GetStandardDeviationPixelList(PixelList *pixel_list,
  MagickPixelPacket *pixel)
{
  MagickRealType
    sum,
    sum_squared;

  register SkipList
    *list;

  register ssize_t
    channel;

  size_t
    color;

  ssize_t
    count;

  unsigned short
    channels[ListChannels];

  /*
    Find the standard-deviation value for each of the color.
  */
  for (channel=0; channel < 5; channel++)
  {
    list=pixel_list->lists+channel;
    color=65536L;
    count=0;
    sum=0.0;
    sum_squared=0.0;
    do
    {
      register ssize_t
        i;

      color=list->nodes[color].next[0];
      sum+=(MagickRealType) list->nodes[color].count*color;
      for (i=0; i < (ssize_t) list->nodes[color].count; i++)
        sum_squared+=((MagickRealType) color)*((MagickRealType) color);
      count+=list->nodes[color].count;
    } while (count < (ssize_t) pixel_list->length);
    sum/=pixel_list->length;
    sum_squared/=pixel_list->length;
    channels[channel]=(unsigned short) sqrt(sum_squared-(sum*sum));
  }
  pixel->red=(MagickRealType) ScaleShortToQuantum(channels[0]);
  pixel->green=(MagickRealType) ScaleShortToQuantum(channels[1]);
  pixel->blue=(MagickRealType) ScaleShortToQuantum(channels[2]);
  pixel->opacity=(MagickRealType) ScaleShortToQuantum(channels[3]);
  pixel->index=(MagickRealType) ScaleShortToQuantum(channels[4]);
}

static inline void InsertPixelList(const Image *image,const PixelPacket *pixel,
  const IndexPacket *indexes,PixelList *pixel_list)
{
  size_t
    signature;

  unsigned short
    index;

  index=ScaleQuantumToShort(GetPixelRed(pixel));
  signature=pixel_list->lists[0].nodes[index].signature;
  if (signature == pixel_list->signature)
    pixel_list->lists[0].nodes[index].count++;
  else
    AddNodePixelList(pixel_list,0,index);
  index=ScaleQuantumToShort(GetPixelGreen(pixel));
  signature=pixel_list->lists[1].nodes[index].signature;
  if (signature == pixel_list->signature)
    pixel_list->lists[1].nodes[index].count++;
  else
    AddNodePixelList(pixel_list,1,index);
  index=ScaleQuantumToShort(GetPixelBlue(pixel));
  signature=pixel_list->lists[2].nodes[index].signature;
  if (signature == pixel_list->signature)
    pixel_list->lists[2].nodes[index].count++;
  else
    AddNodePixelList(pixel_list,2,index);
  index=ScaleQuantumToShort(GetPixelOpacity(pixel));
  signature=pixel_list->lists[3].nodes[index].signature;
  if (signature == pixel_list->signature)
    pixel_list->lists[3].nodes[index].count++;
  else
    AddNodePixelList(pixel_list,3,index);
  if (image->colorspace == CMYKColorspace)
    index=ScaleQuantumToShort(GetPixelIndex(indexes));
  signature=pixel_list->lists[4].nodes[index].signature;
  if (signature == pixel_list->signature)
    pixel_list->lists[4].nodes[index].count++;
  else
    AddNodePixelList(pixel_list,4,index);
}

static void ResetPixelList(PixelList *pixel_list)
{
  int
    level;

  register ListNode
    *root;

  register SkipList
    *list;

  register ssize_t
    channel;

  /*
    Reset the skip-list.
  */
  for (channel=0; channel < 5; channel++)
  {
    list=pixel_list->lists+channel;
    root=list->nodes+65536UL;
    list->level=0;
    for (level=0; level < 9; level++)
      root->next[level]=65536UL;
  }
  pixel_list->seed=pixel_list->signature++;
}

MagickExport Image *StatisticImage(const Image *image,const StatisticType type,
  const size_t width,const size_t height,ExceptionInfo *exception)
{
  Image
    *statistic_image;

  statistic_image=StatisticImageChannel(image,DefaultChannels,type,width,
    height,exception);
  return(statistic_image);
}

MagickExport Image *StatisticImageChannel(const Image *image,
  const ChannelType channel,const StatisticType type,const size_t width,
  const size_t height,ExceptionInfo *exception)
{
#define StatisticImageTag  "Statistic/Image"

  CacheView
    *image_view,
    *statistic_view;

  Image
    *statistic_image;

  MagickBooleanType
    status;

  MagickOffsetType
    progress;

  PixelList
    **magick_restrict pixel_list;

  size_t
    neighbor_height,
    neighbor_width;

  ssize_t
    y;

  /*
    Initialize statistics image attributes.
  */
  assert(image != (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);
  statistic_image=CloneImage(image,image->columns,image->rows,MagickTrue,
    exception);
  if (statistic_image == (Image *) NULL)
    return((Image *) NULL);
  if (SetImageStorageClass(statistic_image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&statistic_image->exception);
      statistic_image=DestroyImage(statistic_image);
      return((Image *) NULL);
    }
  neighbor_width=width == 0 ? GetOptimalKernelWidth2D((double) width,0.5) :
    width;
  neighbor_height=height == 0 ? GetOptimalKernelWidth2D((double) height,0.5) :
    height;
  pixel_list=AcquirePixelListThreadSet(neighbor_width,neighbor_height);
  if (pixel_list == (PixelList **) NULL)
    {
      statistic_image=DestroyImage(statistic_image);
      ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
    }
  /*
    Make each pixel the min / max / median / mode / etc. of the neighborhood.
  */
  status=MagickTrue;
  progress=0;
  image_view=AcquireVirtualCacheView(image,exception);
  statistic_view=AcquireAuthenticCacheView(statistic_image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(static,4) shared(progress,status) \
    magick_threads(image,statistic_image,statistic_image->rows,1)
#endif
  for (y=0; y < (ssize_t) statistic_image->rows; y++)
  {
    const int
      id = GetOpenMPThreadId();

    register const IndexPacket
      *magick_restrict indexes;

    register const PixelPacket
      *magick_restrict p;

    register IndexPacket
      *magick_restrict statistic_indexes;

    register PixelPacket
      *magick_restrict q;

    register ssize_t
      x;

    if (status == MagickFalse)
      continue;
    p=GetCacheViewVirtualPixels(image_view,-((ssize_t) neighbor_width/2L),y-
      (ssize_t) (neighbor_height/2L),image->columns+neighbor_width,
      neighbor_height,exception);
    q=QueueCacheViewAuthenticPixels(statistic_view,0,y,statistic_image->columns,      1,exception);
    if ((p == (const PixelPacket *) NULL) || (q == (PixelPacket *) NULL))
      {
        status=MagickFalse;
        continue;
      }
    indexes=GetCacheViewVirtualIndexQueue(image_view);
    statistic_indexes=GetCacheViewAuthenticIndexQueue(statistic_view);
    for (x=0; x < (ssize_t) statistic_image->columns; x++)
    {
      MagickPixelPacket
        pixel;

      register const IndexPacket
        *magick_restrict s;

      register const PixelPacket
        *magick_restrict r;

      register ssize_t
        u,
        v;

      r=p;
      s=indexes+x;
      ResetPixelList(pixel_list[id]);
      for (v=0; v < (ssize_t) neighbor_height; v++)
      {
        for (u=0; u < (ssize_t) neighbor_width; u++)
          InsertPixelList(image,r+u,s+u,pixel_list[id]);
        r+=image->columns+neighbor_width;
        s+=image->columns+neighbor_width;
      }
      GetMagickPixelPacket(image,&pixel);
      SetMagickPixelPacket(image,p+neighbor_width*neighbor_height/2,indexes+x+
        neighbor_width*neighbor_height/2,&pixel);
      switch (type)
      {
        case GradientStatistic:
        {
          MagickPixelPacket
            maximum,
            minimum;

          GetMinimumPixelList(pixel_list[id],&pixel);
          minimum=pixel;
          GetMaximumPixelList(pixel_list[id],&pixel);
          maximum=pixel;
          pixel.red=MagickAbsoluteValue(maximum.red-minimum.red);
          pixel.green=MagickAbsoluteValue(maximum.green-minimum.green);
          pixel.blue=MagickAbsoluteValue(maximum.blue-minimum.blue);
          pixel.opacity=MagickAbsoluteValue(maximum.opacity-minimum.opacity);
          if (image->colorspace == CMYKColorspace)
            pixel.index=MagickAbsoluteValue(maximum.index-minimum.index);
          break;
        }
        case MaximumStatistic:
        {
          GetMaximumPixelList(pixel_list[id],&pixel);
          break;
        }
        case MeanStatistic:
        {
          GetMeanPixelList(pixel_list[id],&pixel);
          break;
        }
        case MedianStatistic:
        default:
        {
          GetMedianPixelList(pixel_list[id],&pixel);
          break;
        }
        case MinimumStatistic:
        {
          GetMinimumPixelList(pixel_list[id],&pixel);
          break;
        }
        case ModeStatistic:
        {
          GetModePixelList(pixel_list[id],&pixel);
          break;
        }
        case NonpeakStatistic:
        {
          GetNonpeakPixelList(pixel_list[id],&pixel);
          break;
        }
        case RootMeanSquareStatistic:
        {
          GetRootMeanSquarePixelList(pixel_list[id],&pixel);
          break;
        }
        case StandardDeviationStatistic:
        {
          GetStandardDeviationPixelList(pixel_list[id],&pixel);
          break;
        }
      }
      if ((channel & RedChannel) != 0)
        SetPixelRed(q,ClampToQuantum(pixel.red));
      if ((channel & GreenChannel) != 0)
        SetPixelGreen(q,ClampToQuantum(pixel.green));
      if ((channel & BlueChannel) != 0)
        SetPixelBlue(q,ClampToQuantum(pixel.blue));
      if ((channel & OpacityChannel) != 0)
        SetPixelOpacity(q,ClampToQuantum(pixel.opacity));
      if (((channel & IndexChannel) != 0) &&
          (image->colorspace == CMYKColorspace))
        SetPixelIndex(statistic_indexes+x,ClampToQuantum(pixel.index));
      p++;
      q++;
    }
    if (SyncCacheViewAuthenticPixels(statistic_view,exception) == MagickFalse)
      status=MagickFalse;
    if (image->progress_monitor != (MagickProgressMonitor) NULL)
      {
        MagickBooleanType
          proceed;

#if defined(MAGICKCORE_OPENMP_SUPPORT)
        #pragma omp critical (MagickCore_StatisticImage)
#endif
        proceed=SetImageProgress(image,StatisticImageTag,progress++,
          image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  statistic_view=DestroyCacheView(statistic_view);
  image_view=DestroyCacheView(image_view);
  pixel_list=DestroyPixelListThreadSet(pixel_list);
  if (status == MagickFalse)
    statistic_image=DestroyImage(statistic_image);
  return(statistic_image);
}

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