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 == MagickCoreSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickCoreSignature);
  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) shared(progress,status) \
    magick_number_threads(image,image,image->rows,key == ~0UL)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    const int
      id = GetOpenMPThreadId();

    IndexPacket
      *magick_restrict indexes;

    PixelPacket
      *magick_restrict q;

    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;

        proceed=SetImageProgress(image,EvaluateImageTag,progress++,image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  image_view=DestroyCacheView(image_view);
  random_info=DestroyRandomInfoThreadSet(random_info);
  return(status);
}


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

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


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);
}


static PixelList *DestroyPixelList(PixelList *pixel_list)
{
  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 *) RelinquishAlignedMemory(
        pixel_list->lists[i].nodes);
  pixel_list=(PixelList *) RelinquishMagickMemory(pixel_list);
  return(pixel_list);
}


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

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

  SkipList
    *list;

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

  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]);
}


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 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 == MagickCoreSignature);
  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);
}


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

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


static MagickPixelPacket **DestroyPixelThreadSet(const Image *images,
  MagickPixelPacket **pixels)
{
  ssize_t
    i;

  size_t
    rows;

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


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 == MagickCoreSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickCoreSignature);
  if (SetImageStorageClass(image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&image->exception);
      return(MagickFalse);
    }
#if defined(MAGICKCORE_OPENCL_SUPPORT)
  status=AccelerateFunctionImage(image,channel,function,number_parameters,
    parameters,exception);
  if (status != MagickFalse)
    return(status);
#endif
  status=MagickTrue;
  progress=0;
  image_view=AcquireAuthenticCacheView(image,exception);
#if defined(MAGICKCORE_OPENMP_SUPPORT)
  #pragma omp parallel for schedule(static) shared(progress,status) \
    magick_number_threads(image,image,image->rows,1)
#endif
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    IndexPacket
      *magick_restrict indexes;

    ssize_t
      x;

    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;

        proceed=SetImageProgress(image,FunctionImageTag,progress++,image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  image_view=DestroyCacheView(image_view);
  return(status);
}


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


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 == MagickCoreSignature);
  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);
}


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

  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) memset(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);
}


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;

  ssize_t
    y;

  assert(images != (Image *) NULL);
  assert(images->signature == MagickCoreSignature);
  if (images->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickCoreSignature);
  image=AcquireImageCanvas(images,exception);
  if (image == (Image *) NULL)
    return((Image *) NULL);
  if (SetImageStorageClass(image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&image->exception);
      image=DestroyImage(image);
      return((Image *) NULL);
    }
  polynomial_pixels=AcquirePixelThreadSet(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) shared(progress,status) \
    magick_number_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();

    IndexPacket
      *magick_restrict polynomial_indexes;

    MagickPixelPacket
      *polynomial_pixel;

    PixelPacket
      *magick_restrict q;

    ssize_t
      i,
      x;

    size_t
      number_images;

    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;
    number_images=GetImageListLength(images);
    for (i=0; i < (ssize_t) number_images; i++)
    {
      const IndexPacket
        *indexes;

      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;

        proceed=SetImageProgress(images,PolynomialImageTag,progress++,
          image->rows);
        if (proceed == MagickFalse)
          status=MagickFalse;
      }
  }
  polynomial_view=DestroyCacheView(polynomial_view);
  polynomial_pixels=DestroyPixelThreadSet(images,polynomial_pixels);
  if (status == MagickFalse)
    image=DestroyImage(image);
  return(image);
}


static MagickPixelPacket **AcquirePixelThreadSet(const Image *images)
{
  const Image
    *next;

  MagickPixelPacket
    **pixels;

  ssize_t
    i,
    j;

  size_t
    columns,
    rows;

  rows=MagickMax(GetImageListLength(images),
    (size_t) GetMagickResourceLimit(ThreadResource));
  pixels=(MagickPixelPacket **) AcquireQuantumMemory(rows,sizeof(*pixels));
  if (pixels == (MagickPixelPacket **) NULL)
    return((MagickPixelPacket **) NULL);
  (void) memset(pixels,0,rows*sizeof(*pixels));
  columns=GetImageListLength(images);
  for (next=images; next != (Image *) NULL; next=next->next)
    columns=MagickMax(next->columns,columns);
  for (i=0; i < (ssize_t) rows; i++)
  {
    pixels[i]=(MagickPixelPacket *) AcquireQuantumMemory(columns,
      sizeof(**pixels));
    if (pixels[i] == (MagickPixelPacket *) NULL)
      return(DestroyPixelThreadSet(images,pixels));
    for (j=0; j < (ssize_t) columns; j++)
      GetMagickPixelPacket(images,&pixels[i][j]);
  }
  return(pixels);
}


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

  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:
    {
      double
        bias,
        center,
        range,
        width;

      /* Arcsin Function  (peged at range limits for invalid results)
       * Parameters:   Width, Center, Range, 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*PerceptibleReciprocal(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));
}


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

  ListNode
    *root;

  SkipList
    *list;

  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++;
}


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

  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]);
}


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 == MagickCoreSignature);
  if (images->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickCoreSignature);
  image=AcquireImageCanvas(images,exception);
  if (image == (Image *) NULL)
    return((Image *) NULL);
  if (SetImageStorageClass(image,DirectClass) == MagickFalse)
    {
      InheritException(exception,&image->exception);
      image=DestroyImage(image);
      return((Image *) NULL);
    }
  evaluate_pixels=AcquirePixelThreadSet(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;
  number_images=GetImageListLength(images);
  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) shared(progress,status) \
        magick_number_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();

        IndexPacket
          *magick_restrict evaluate_indexes;

        MagickPixelPacket
          *evaluate_pixel;

        PixelPacket
          *magick_restrict q;

        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++)
        {
          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++)
          {
            const IndexPacket
              *indexes;

            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 atomic
#endif
            progress++;
            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) shared(progress,status) \
        magick_number_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();

        IndexPacket
          *magick_restrict evaluate_indexes;

        ssize_t
          i,
          x;

        MagickPixelPacket
          *evaluate_pixel;

        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++)
        {
          const IndexPacket
            *indexes;

          const PixelPacket
            *p;

          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++)
          {
            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++)
          {
            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;

            proceed=SetImageProgress(images,EvaluateImageTag,progress++,
              image->rows);
            if (proceed == MagickFalse)
              status=MagickFalse;
          }
      }
    }
  evaluate_view=DestroyCacheView(evaluate_view);
  evaluate_pixels=DestroyPixelThreadSet(images,evaluate_pixels);
  random_info=DestroyRandomInfoThreadSet(random_info);
  if (status == MagickFalse)
    image=DestroyImage(image);
  return(image);
}


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

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


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 == MagickCoreSignature);
  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++)
  {
    const IndexPacket
      *magick_restrict indexes;

    const PixelPacket
      *magick_restrict p;

    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);
}


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

  ssize_t
    i;

  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) ((ssize_t) pixel & (ssize_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 InverseLogEvaluateOperator:
    {
      result=(QuantumRange*pow((value+1.0),QuantumScale*pixel)-1.0)*
        PerceptibleReciprocal(value);
      break;
    }
    case LaplacianNoiseEvaluateOperator:
    {
      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
        LaplacianNoise,value);
      break;
    }
    case LeftShiftEvaluateOperator:
    {
      result=(double) pixel;
      for (i=0; i < (ssize_t) value; i++)
        result*=2.0;
      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) ((ssize_t) pixel | (ssize_t) (value+0.5));
      break;
    }
    case PoissonNoiseEvaluateOperator:
    {
      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
        PoissonNoise,value);
      break;
    }
    case PowEvaluateOperator:
    {
      if (pixel < 0)
        result=(MagickRealType) -(QuantumRange*pow((double) -(QuantumScale*
          pixel),(double) value));
      else
        result=(MagickRealType) (QuantumRange*pow((double) (QuantumScale*pixel),
          (double) value));
      break;
    }
    case RightShiftEvaluateOperator:
    {
      result=(MagickRealType) pixel;
      for (i=0; i < (ssize_t) value; i++)
        result/=2.0;
      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) ((ssize_t) pixel ^ (ssize_t) (value+0.5));
      break;
    }
  }
  return(result);
}


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);
}


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

  SkipList
    *list;

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

  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]);
}


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

  ChannelPerceptualHash
    *perceptual_hash;

  Image
    *hash_image;

  MagickBooleanType
    status;

  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);
}


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

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

  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]);
}


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 == MagickCoreSignature);
  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) memset(channel_moments,0,length*sizeof(*channel_moments));
  (void) memset(centroid,0,sizeof(centroid));
  (void) memset(M00,0,sizeof(M00));
  (void) memset(M01,0,sizeof(M01));
  (void) memset(M02,0,sizeof(M02));
  (void) memset(M03,0,sizeof(M03));
  (void) memset(M10,0,sizeof(M10));
  (void) memset(M11,0,sizeof(M11));
  (void) memset(M12,0,sizeof(M12));
  (void) memset(M20,0,sizeof(M20));
  (void) memset(M21,0,sizeof(M21));
  (void) memset(M22,0,sizeof(M22));
  (void) memset(M30,0,sizeof(M30));
  GetMagickPixelPacket(image,&pixel);
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    const IndexPacket
      *magick_restrict indexes;

    const PixelPacket
      *magick_restrict p;

    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++)
  {
    const IndexPacket
      *magick_restrict indexes;

    const PixelPacket
      *magick_restrict p;

    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*
      PerceptibleReciprocal(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*
      PerceptibleReciprocal(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(1.0/2.0*atan(2.0*
      M11[channel]*PerceptibleReciprocal(M20[channel]-M02[channel])));
    if (fabs(M11[channel]) < 0.0)
      {
        if ((fabs(M20[channel]-M02[channel]) >= 0.0) &&
            ((M20[channel]-M02[channel]) < 0.0))
          channel_moments[channel].ellipse_angle+=90.0;
      }
    else
      if (M11[channel] < 0.0)
        {
          if (fabs(M20[channel]-M02[channel]) >= 0.0)
            {
              if ((M20[channel]-M02[channel]) < 0.0)
                channel_moments[channel].ellipse_angle+=90.0;
              else
                channel_moments[channel].ellipse_angle+=180.0;
            }
        }
      else
        if ((fabs(M20[channel]-M02[channel]) >= 0.0) &&
            ((M20[channel]-M02[channel]) < 0.0))
          channel_moments[channel].ellipse_angle+=90.0;
    channel_moments[channel].ellipse_eccentricity=sqrt(1.0-(
      channel_moments[channel].ellipse_axis.y*
      channel_moments[channel].ellipse_axis.y*PerceptibleReciprocal(
      channel_moments[channel].ellipse_axis.x*
      channel_moments[channel].ellipse_axis.x)));
    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);
}


MagickExport ChannelStatistics *GetImageChannelStatistics(const Image *image,
  ExceptionInfo *exception)
{
  ChannelStatistics
    *channel_statistics;

  double
    area,
    standard_deviation;

  MagickPixelPacket
    number_bins,
    *histogram;

  QuantumAny
    range;

  ssize_t
    i;

  size_t
    channels,
    depth,
    length;

  ssize_t
    y;

  assert(image != (Image *) NULL);
  assert(image->signature == MagickCoreSignature);
  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) memset(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) memset(histogram,0,(MaxMap+1U)*sizeof(*histogram));
  (void) memset(&number_bins,0,sizeof(number_bins));
  for (y=0; y < (ssize_t) image->rows; y++)
  {
    const IndexPacket
      *magick_restrict indexes;

    const PixelPacket
      *magick_restrict p;

    ssize_t
      x;

    /*
      Compute pixel statistics.
    */
    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(GetPixelAlpha(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) GetPixelAlpha(p) < channel_statistics[OpacityChannel].minima)
            channel_statistics[OpacityChannel].minima=(double) GetPixelAlpha(p);
          if ((double) GetPixelAlpha(p) > channel_statistics[OpacityChannel].maxima)
            channel_statistics[OpacityChannel].maxima=(double) GetPixelAlpha(p);
          channel_statistics[OpacityChannel].sum+=GetPixelAlpha(p);
          channel_statistics[OpacityChannel].sum_squared+=(double)
            GetPixelAlpha(p)*GetPixelAlpha(p);
          channel_statistics[OpacityChannel].sum_cubed+=(double)
            GetPixelAlpha(p)*GetPixelAlpha(p)*GetPixelAlpha(p);
          channel_statistics[OpacityChannel].sum_fourth_power+=(double)
            GetPixelAlpha(p)*GetPixelAlpha(p)*GetPixelAlpha(p)*GetPixelAlpha(p);
          histogram[ScaleQuantumToMap(GetPixelAlpha(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++;
    }
  }
  for (i=0; i < (ssize_t) CompositeChannels; i++)
  {
    double
      area,
      mean,
      standard_deviation;

    /*
      Normalize pixel statistics.
    */
    area=PerceptibleReciprocal((double) image->columns*image->rows);
    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;
    standard_deviation=sqrt(channel_statistics[i].variance-(mean*mean));
    area=PerceptibleReciprocal((double) image->columns*image->rows-1.0)*
      ((double) image->columns*image->rows);
    standard_deviation=sqrt(area*standard_deviation*standard_deviation);
    channel_statistics[i].standard_deviation=standard_deviation;
  }
  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].opacity > 0.0))
      number_bins.opacity++;
    if ((image->colorspace == CMYKColorspace) && (histogram[i].index > 0.0))
      number_bins.index++;
  }
  area=PerceptibleReciprocal((double) image->columns*image->rows);
  for (i=0; i < (ssize_t) (MaxMap+1U); i++)
  {
    /*
      Compute pixel entropy.
    */
    histogram[i].red*=area;
    channel_statistics[RedChannel].entropy+=-histogram[i].red*
      MagickLog10(histogram[i].red)*
      PerceptibleReciprocal(MagickLog10((double) number_bins.red));
    histogram[i].green*=area;
    channel_statistics[GreenChannel].entropy+=-histogram[i].green*
      MagickLog10(histogram[i].green)*
      PerceptibleReciprocal(MagickLog10((double) number_bins.green));
    histogram[i].blue*=area;
    channel_statistics[BlueChannel].entropy+=-histogram[i].blue*
      MagickLog10(histogram[i].blue)*
      PerceptibleReciprocal(MagickLog10((double) number_bins.blue));
    if (image->matte != MagickFalse)
      {
        histogram[i].opacity*=area;
        channel_statistics[OpacityChannel].entropy+=-histogram[i].opacity*
          MagickLog10(histogram[i].opacity)*
          PerceptibleReciprocal(MagickLog10((double) number_bins.opacity));
      }
    if (image->colorspace == CMYKColorspace)
      {
        histogram[i].index*=area;
        channel_statistics[IndexChannel].entropy+=-histogram[i].index*
          MagickLog10(histogram[i].index)*
          PerceptibleReciprocal(MagickLog10((double) number_bins.index));
      }
  }
  /*
    Compute overall statistics.
  */
  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;
    standard_deviation=sqrt(channel_statistics[i].variance-
      (channel_statistics[i].mean*channel_statistics[i].mean));
    area=PerceptibleReciprocal((double) image->columns*image->rows-1.0)*
      ((double) image->columns*image->rows);
    standard_deviation=sqrt(area*standard_deviation*standard_deviation);
    channel_statistics[CompositeChannels].standard_deviation=standard_deviation;
    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].kurtosis/=channels;
  channel_statistics[CompositeChannels].skewness/=channels;
  channel_statistics[CompositeChannels].entropy/=channels;
  i=CompositeChannels;
  area=PerceptibleReciprocal((double) channels*image->columns*image->rows);
  channel_statistics[i].variance=channel_statistics[i].sum_squared;
  channel_statistics[i].mean=channel_statistics[i].sum;
  standard_deviation=sqrt(channel_statistics[i].variance-
    (channel_statistics[i].mean*channel_statistics[i].mean));
  standard_deviation=sqrt(PerceptibleReciprocal((double) channels*
    image->columns*image->rows-1.0)*channels*image->columns*image->rows*
    standard_deviation*standard_deviation);
  channel_statistics[i].standard_deviation=standard_deviation;
  for (i=0; i <= (ssize_t) CompositeChannels; i++)
  {
    /*
      Compute kurtosis & skewness statistics.
    */
    standard_deviation=PerceptibleReciprocal(
      channel_statistics[i].standard_deviation);
    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)*(standard_deviation*standard_deviation*
      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)*(standard_deviation*standard_deviation*
      standard_deviation*standard_deviation)-3.0;
  }
  channel_statistics[CompositeChannels].mean=0.0;
  channel_statistics[CompositeChannels].standard_deviation=0.0;
  for (i=0; i < (ssize_t) CompositeChannels; i++)
  {
    channel_statistics[CompositeChannels].mean+=
      channel_statistics[i].mean;
    channel_statistics[CompositeChannels].standard_deviation+=
      channel_statistics[i].standard_deviation;
  }
  channel_statistics[CompositeChannels].mean/=(double) channels;
  channel_statistics[CompositeChannels].standard_deviation/=(double) channels;
  histogram=(MagickPixelPacket *) RelinquishMagickMemory(histogram);
  if (y < (ssize_t) image->rows)
    channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
      channel_statistics);
  return(channel_statistics);
}


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

  ssize_t
    i;

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


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

  SkipList
    *list;

  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]);
}


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 == MagickCoreSignature);
  if (image->debug != MagickFalse)
    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
  assert(exception != (ExceptionInfo *) NULL);
  assert(exception->signature == MagickCoreSignature);
  statistic_image=CloneImage(image,0,0,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) shared(progress,status) \
    magick_number_threads(image,statistic_image,statistic_image->rows,1)
#endif
  for (y=0; y < (ssize_t) statistic_image->rows; y++)
  {
    const int
      id = GetOpenMPThreadId();

    const IndexPacket
      *magick_restrict indexes;

    const PixelPacket
      *magick_restrict p;

    IndexPacket
      *magick_restrict statistic_indexes;

    PixelPacket
      *magick_restrict q;

    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;

      const IndexPacket
        *magick_restrict s;

      const PixelPacket
        *magick_restrict r;

      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;

        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);
}


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 == MagickCoreSignature);
  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].standard_deviation;
      channels++;
    }
  if ((channel & GreenChannel) != 0)
    {
      channel_statistics[CompositeChannels].mean+=
        channel_statistics[GreenChannel].mean;
      channel_statistics[CompositeChannels].standard_deviation+=
        channel_statistics[GreenChannel].standard_deviation;
      channels++;
    }
  if ((channel & BlueChannel) != 0)
    {
      channel_statistics[CompositeChannels].mean+=
        channel_statistics[BlueChannel].mean;
      channel_statistics[CompositeChannels].standard_deviation+=
        channel_statistics[BlueChannel].standard_deviation;
      channels++;
    }
  if (((channel & OpacityChannel) != 0) && (image->matte != MagickFalse))
    {
      channel_statistics[CompositeChannels].mean+=
        (QuantumRange-channel_statistics[OpacityChannel].mean);
      channel_statistics[CompositeChannels].standard_deviation+=
        channel_statistics[OpacityChannel].standard_deviation;
      channels++;
    }
  if (((channel & IndexChannel) != 0) && (image->colorspace == CMYKColorspace))
    {
      channel_statistics[CompositeChannels].mean+=
        channel_statistics[BlackChannel].mean;
      channel_statistics[CompositeChannels].standard_deviation+=
        channel_statistics[CompositeChannels].standard_deviation;
      channels++;
    }
  channel_statistics[CompositeChannels].mean/=channels;
  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);
}


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


static Image *AcquireImageCanvas(const Image *images,ExceptionInfo *exception)
{
  const Image
    *p,
    *q;

  size_t
    columns,
    number_channels,
    rows;

  q=images;
  columns=images->columns;
  rows=images->rows;
  number_channels=0;
  for (p=images; p != (Image *) NULL; p=p->next)
  {
    size_t
      channels;

    channels=3;
    if (p->matte != MagickFalse)
      channels+=1;
    if (p->colorspace == CMYKColorspace)
      channels+=1;
    if (channels > number_channels)
      {
        number_channels=channels;
        q=p;
      }
    if (p->columns > columns)
      columns=p->columns;
    if (p->rows > rows)
      rows=p->rows;
  }
  return(CloneImage(q,columns,rows,MagickTrue,exception));
}


void remove_pending_change_notify_requests_by_fid(files_struct *fsp,
						  NTSTATUS status)
{
	if (fsp->notify == NULL) {
		return;
	}

	while (fsp->notify->requests != NULL) {
		change_notify_reply(fsp->notify->requests->req,
				    status, 0, NULL,
				    fsp->notify->requests->reply_fn);
		change_notify_remove_request(fsp->conn->sconn,
					     fsp->notify->requests);
	}
}

s3: smbd: Ensure change notifies can't get set unless the directory handle is open for SEC_DIR_LIST.

Remove knownfail entry.

CVE-2020-14318

BUG: https://bugzilla.samba.org/show_bug.cgi?id=14434

Signed-off-by: Jeremy Allison <jra@samba.org>