]> granicus.if.org Git - imagemagick/blobdiff - MagickCore/statistic.c
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[imagemagick] / MagickCore / statistic.c
index d17a616f116ab0bd57b932a18b212687669a908f..42ea5facbb4b210791e6c34bee856980f04092fb 100644 (file)
 %                     MagickCore Image Statistical Methods                    %
 %                                                                             %
 %                              Software Design                                %
-%                                John Cristy                                  %
+%                                   Cristy                                    %
 %                                 July 1992                                   %
 %                                                                             %
 %                                                                             %
-%  Copyright 1999-2011 ImageMagick Studio LLC, a non-profit organization      %
+%  Copyright 1999-2014 ImageMagick Studio LLC, a non-profit organization      %
 %  dedicated to making software imaging solutions freely available.           %
 %                                                                             %
 %  You may not use this file except in compliance with the License.  You may  %
@@ -81,6 +81,7 @@
 #include "MagickCore/quantum-private.h"
 #include "MagickCore/random_.h"
 #include "MagickCore/random-private.h"
+#include "MagickCore/resource_.h"
 #include "MagickCore/segment.h"
 #include "MagickCore/semaphore.h"
 #include "MagickCore/signature-private.h"
 
 typedef struct _PixelChannels
 {
-  MagickRealType
+  double
     channel[CompositePixelChannel];
 } PixelChannels;
 
@@ -140,7 +141,7 @@ static PixelChannels **DestroyPixelThreadSet(PixelChannels **pixels)
     i;
 
   assert(pixels != (PixelChannels **) NULL);
-  for (i=0; i < (ssize_t) GetOpenMPMaximumThreads(); i++)
+  for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
     if (pixels[i] != (PixelChannels *) NULL)
       pixels[i]=(PixelChannels *) RelinquishMagickMemory(pixels[i]);
   pixels=(PixelChannels **) RelinquishMagickMemory(pixels);
@@ -160,8 +161,9 @@ static PixelChannels **AcquirePixelThreadSet(const Image *image,
     length,
     number_threads;
 
-  number_threads=GetOpenMPMaximumThreads();
-  pixels=(PixelChannels **) AcquireQuantumMemory(number_threads,sizeof(*pixels));
+  number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
+  pixels=(PixelChannels **) AcquireQuantumMemory(number_threads,
+    sizeof(*pixels));
   if (pixels == (PixelChannels **) NULL)
     return((PixelChannels **) NULL);
   (void) ResetMagickMemory(pixels,0,number_threads*sizeof(*pixels));
@@ -188,7 +190,7 @@ static PixelChannels **AcquirePixelThreadSet(const Image *image,
   return(pixels);
 }
 
-static inline double MagickMax(const double x,const double y)
+static inline double EvaluateMax(const double x,const double y)
 {
   if (x > y)
     return(x);
@@ -205,7 +207,7 @@ static int IntensityCompare(const void *x,const void *y)
     *color_1,
     *color_2;
 
-  MagickRealType
+  double
     distance;
 
   register ssize_t
@@ -215,7 +217,7 @@ static int IntensityCompare(const void *x,const void *y)
   color_2=(const PixelChannels *) y;
   distance=0.0;
   for (i=0; i < MaxPixelChannels; i++)
-    distance+=color_1->channel[i]-(MagickRealType) color_2->channel[i];
+    distance+=color_1->channel[i]-(double) color_2->channel[i];
   return(distance < 0 ? -1 : distance > 0 ? 1 : 0);
 }
 
@@ -230,10 +232,10 @@ static inline double MagickMin(const double x,const double y)
   return(y);
 }
 
-static MagickRealType ApplyEvaluateOperator(RandomInfo *random_info,
-  Quantum pixel,const MagickEvaluateOperator op,const MagickRealType value)
+static double ApplyEvaluateOperator(RandomInfo *random_info,const Quantum pixel,
+  const MagickEvaluateOperator op,const double value)
 {
-  MagickRealType
+  double
     result;
 
   result=0.0;
@@ -243,21 +245,21 @@ static MagickRealType ApplyEvaluateOperator(RandomInfo *random_info,
       break;
     case AbsEvaluateOperator:
     {
-      result=(MagickRealType) fabs((double) (pixel+value));
+      result=(double) fabs((double) (pixel+value));
       break;
     }
     case AddEvaluateOperator:
     {
-      result=(MagickRealType) (pixel+value);
+      result=(double) (pixel+value);
       break;
     }
     case AddModulusEvaluateOperator:
     {
       /*
-        This returns a 'floored modulus' of the addition which is a
-        positive result.  It differs from % or fmod() that returns a
-        'truncated modulus' result, where floor() is replaced by trunc() and
-        could return a negative result (which is clipped).
+        This returns a 'floored modulus' of the addition which is a positive
+        result.  It differs from % or fmod() that 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));
@@ -265,12 +267,12 @@ static MagickRealType ApplyEvaluateOperator(RandomInfo *random_info,
     }
     case AndEvaluateOperator:
     {
-      result=(MagickRealType) ((size_t) pixel & (size_t) (value+0.5));
+      result=(double) ((size_t) pixel & (size_t) (value+0.5));
       break;
     }
     case CosineEvaluateOperator:
     {
-      result=(MagickRealType) (QuantumRange*(0.5*cos((double) (2.0*MagickPI*
+      result=(double) (QuantumRange*(0.5*cos((double) (2.0*MagickPI*
         QuantumScale*pixel*value))+0.5));
       break;
     }
@@ -281,90 +283,90 @@ static MagickRealType ApplyEvaluateOperator(RandomInfo *random_info,
     }
     case ExponentialEvaluateOperator:
     {
-      result=(MagickRealType) (QuantumRange*exp((double) (value*QuantumScale*
-        pixel)));
+      result=(double) (QuantumRange*exp((double) (value*QuantumScale*pixel)));
       break;
     }
     case GaussianNoiseEvaluateOperator:
     {
-      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
+      result=(double) GenerateDifferentialNoise(random_info,pixel,
         GaussianNoise,value);
       break;
     }
     case ImpulseNoiseEvaluateOperator:
     {
-      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
-        ImpulseNoise,value);
+      result=(double) GenerateDifferentialNoise(random_info,pixel,ImpulseNoise,
+        value);
       break;
     }
     case LaplacianNoiseEvaluateOperator:
     {
-      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
+      result=(double) GenerateDifferentialNoise(random_info,pixel,
         LaplacianNoise,value);
       break;
     }
     case LeftShiftEvaluateOperator:
     {
-      result=(MagickRealType) ((size_t) pixel << (size_t) (value+0.5));
+      result=(double) ((size_t) pixel << (size_t) (value+0.5));
       break;
     }
     case LogEvaluateOperator:
     {
-      result=(MagickRealType) (QuantumRange*log((double) (QuantumScale*value*
-        pixel+1.0))/log((double) (value+1.0)));
+      if ((QuantumScale*pixel) >= MagickEpsilon)
+        result=(double) (QuantumRange*log((double) (QuantumScale*value*pixel+
+          1.0))/log((double) (value+1.0)));
       break;
     }
     case MaxEvaluateOperator:
     {
-      result=(MagickRealType) MagickMax((double) pixel,value);
+      result=(double) EvaluateMax((double) pixel,value);
       break;
     }
     case MeanEvaluateOperator:
     {
-      result=(MagickRealType) (pixel+value);
+      result=(double) (pixel+value);
       break;
     }
     case MedianEvaluateOperator:
     {
-      result=(MagickRealType) (pixel+value);
+      result=(double) (pixel+value);
       break;
     }
     case MinEvaluateOperator:
     {
-      result=(MagickRealType) MagickMin((double) pixel,value);
+      result=(double) MagickMin((double) pixel,value);
       break;
     }
     case MultiplicativeNoiseEvaluateOperator:
     {
-      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
+      result=(double) GenerateDifferentialNoise(random_info,pixel,
         MultiplicativeGaussianNoise,value);
       break;
     }
     case MultiplyEvaluateOperator:
     {
-      result=(MagickRealType) (value*pixel);
+      result=(double) (value*pixel);
       break;
     }
     case OrEvaluateOperator:
     {
-      result=(MagickRealType) ((size_t) pixel | (size_t) (value+0.5));
+      result=(double) ((size_t) pixel | (size_t) (value+0.5));
       break;
     }
     case PoissonNoiseEvaluateOperator:
     {
-      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
-        PoissonNoise,value);
+      result=(double) GenerateDifferentialNoise(random_info,pixel,PoissonNoise,
+        value);
       break;
     }
     case PowEvaluateOperator:
     {
-      result=(MagickRealType) (QuantumRange*pow((double) (QuantumScale*pixel),
-        (double) value));
+      result=(double) (QuantumRange*pow((double) (QuantumScale*pixel),(double)
+        value));
       break;
     }
     case RightShiftEvaluateOperator:
     {
-      result=(MagickRealType) ((size_t) pixel >> (size_t) (value+0.5));
+      result=(double) ((size_t) pixel >> (size_t) (value+0.5));
       break;
     }
     case SetEvaluateOperator:
@@ -374,41 +376,44 @@ static MagickRealType ApplyEvaluateOperator(RandomInfo *random_info,
     }
     case SineEvaluateOperator:
     {
-      result=(MagickRealType) (QuantumRange*(0.5*sin((double) (2.0*MagickPI*
+      result=(double) (QuantumRange*(0.5*sin((double) (2.0*MagickPI*
         QuantumScale*pixel*value))+0.5));
       break;
     }
     case SubtractEvaluateOperator:
     {
-      result=(MagickRealType) (pixel-value);
+      result=(double) (pixel-value);
+      break;
+    }
+    case SumEvaluateOperator:
+    {
+      result=(double) (pixel+value);
       break;
     }
     case ThresholdEvaluateOperator:
     {
-      result=(MagickRealType) (((MagickRealType) pixel <= value) ? 0 :
-        QuantumRange);
+      result=(double) (((double) pixel <= value) ? 0 : QuantumRange);
       break;
     }
     case ThresholdBlackEvaluateOperator:
     {
-      result=(MagickRealType) (((MagickRealType) pixel <= value) ? 0 : pixel);
+      result=(double) (((double) pixel <= value) ? 0 : pixel);
       break;
     }
     case ThresholdWhiteEvaluateOperator:
     {
-      result=(MagickRealType) (((MagickRealType) pixel > value) ? QuantumRange :
-        pixel);
+      result=(double) (((double) pixel > value) ? QuantumRange : pixel);
       break;
     }
     case UniformNoiseEvaluateOperator:
     {
-      result=(MagickRealType) GenerateDifferentialNoise(random_info,pixel,
-        UniformNoise,value);
+      result=(double) GenerateDifferentialNoise(random_info,pixel,UniformNoise,
+        value);
       break;
     }
     case XorEvaluateOperator:
     {
-      result=(MagickRealType) ((size_t) pixel ^ (size_t) (value+0.5));
+      result=(double) ((size_t) pixel ^ (size_t) (value+0.5));
       break;
     }
   }
@@ -423,11 +428,8 @@ MagickExport Image *EvaluateImages(const Image *images,
   CacheView
     *evaluate_view;
 
-  const Image
-    *next;
-
   Image
-    *evaluate_image;
+    *image;
 
   MagickBooleanType
     status;
@@ -447,39 +449,31 @@ MagickExport Image *EvaluateImages(const Image *images,
   ssize_t
     y;
 
-  /*
-    Ensure the image are the same size.
-  */
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+  unsigned long
+    key;
+#endif
+
   assert(images != (Image *) NULL);
   assert(images->signature == MagickSignature);
   if (images->debug != MagickFalse)
     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
   assert(exception != (ExceptionInfo *) NULL);
   assert(exception->signature == MagickSignature);
-  for (next=images; next != (Image *) NULL; next=GetNextImageInList(next))
-    if ((next->columns != images->columns) || (next->rows != images->rows))
-      {
-        (void) ThrowMagickException(exception,GetMagickModule(),OptionError,
-          "ImageWidthsOrHeightsDiffer","`%s'",images->filename);
-        return((Image *) NULL);
-      }
-  /*
-    Initialize evaluate next attributes.
-  */
-  evaluate_image=CloneImage(images,images->columns,images->rows,MagickTrue,
+  image=CloneImage(images,images->columns,images->rows,MagickTrue,
     exception);
-  if (evaluate_image == (Image *) NULL)
+  if (image == (Image *) NULL)
     return((Image *) NULL);
-  if (SetImageStorageClass(evaluate_image,DirectClass,exception) == MagickFalse)
+  if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
     {
-      evaluate_image=DestroyImage(evaluate_image);
+      image=DestroyImage(image);
       return((Image *) NULL);
     }
   number_images=GetImageListLength(images);
   evaluate_pixels=AcquirePixelThreadSet(images,number_images);
   if (evaluate_pixels == (PixelChannels **) NULL)
     {
-      evaluate_image=DestroyImage(evaluate_image);
+      image=DestroyImage(image);
       (void) ThrowMagickException(exception,GetMagickModule(),
         ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
       return((Image *) NULL);
@@ -490,13 +484,17 @@ MagickExport Image *EvaluateImages(const Image *images,
   status=MagickTrue;
   progress=0;
   random_info=AcquireRandomInfoThreadSet();
-  evaluate_view=AcquireCacheView(evaluate_image);
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+  key=GetRandomSecretKey(random_info[0]);
+#endif
+  evaluate_view=AcquireAuthenticCacheView(image,exception);
   if (op == MedianEvaluateOperator)
     {
-#if   defined(MAGICKCORE_OPENMP_SUPPORT)
-      #pragma omp parallel for schedule(dynamic) shared(progress,status)
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+      #pragma omp parallel for schedule(static,4) shared(progress,status) \
+        magick_threads(image,images,image->rows,key == ~0UL)
 #endif
-      for (y=0; y < (ssize_t) evaluate_image->rows; y++)
+      for (y=0; y < (ssize_t) image->rows; y++)
       {
         CacheView
           *image_view;
@@ -518,15 +516,15 @@ MagickExport Image *EvaluateImages(const Image *images,
 
         if (status == MagickFalse)
           continue;
-        q=QueueCacheViewAuthenticPixels(evaluate_view,0,y,
-          evaluate_image->columns,1,exception);
+        q=QueueCacheViewAuthenticPixels(evaluate_view,0,y,image->columns,1,
+          exception);
         if (q == (Quantum *) NULL)
           {
             status=MagickFalse;
             continue;
           }
         evaluate_pixel=evaluate_pixels[id];
-        for (x=0; x < (ssize_t) evaluate_image->columns; x++)
+        for (x=0; x < (ssize_t) image->columns; x++)
         {
           register ssize_t
             j,
@@ -544,34 +542,25 @@ MagickExport Image *EvaluateImages(const Image *images,
             register ssize_t
               i;
 
-            image_view=AcquireCacheView(next);
+            image_view=AcquireVirtualCacheView(next,exception);
             p=GetCacheViewVirtualPixels(image_view,x,y,1,1,exception);
             if (p == (const Quantum *) NULL)
               {
                 image_view=DestroyCacheView(image_view);
                 break;
               }
-            for (i=0; i < (ssize_t) GetPixelChannels(evaluate_image); i++)
+            for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
             {
-              PixelChannel
-                channel;
-
-              PixelTrait
-                evaluate_traits,
-                traits;
-
-              evaluate_traits=GetPixelChannelMapTraits(evaluate_image,
-                (PixelChannel) i);
-              channel=GetPixelChannelMapChannel(evaluate_image,
-                (PixelChannel) i);
-              traits=GetPixelChannelMapTraits(next,channel);
+              PixelChannel channel=GetPixelChannelChannel(image,i);
+              PixelTrait evaluate_traits=GetPixelChannelTraits(image,channel);
+              PixelTrait traits=GetPixelChannelTraits(next,channel);
               if ((traits == UndefinedPixelTrait) ||
                   (evaluate_traits == UndefinedPixelTrait))
                 continue;
               if ((evaluate_traits & UpdatePixelTrait) == 0)
                 continue;
               evaluate_pixel[j].channel[i]=ApplyEvaluateOperator(
-                random_info[id],GetPixelChannel(evaluate_image,channel,p),op,
+                random_info[id],GetPixelChannel(image,channel,p),op,
                 evaluate_pixel[j].channel[i]);
             }
             image_view=DestroyCacheView(image_view);
@@ -579,9 +568,9 @@ MagickExport Image *EvaluateImages(const Image *images,
           }
           qsort((void *) evaluate_pixel,number_images,sizeof(*evaluate_pixel),
             IntensityCompare);
-          for (k=0; k < (ssize_t) GetPixelChannels(evaluate_image); k++)
+          for (k=0; k < (ssize_t) GetPixelChannels(image); k++)
             q[k]=ClampToQuantum(evaluate_pixel[j/2].channel[k]);
-          q+=GetPixelChannels(evaluate_image);
+          q+=GetPixelChannels(image);
         }
         if (SyncCacheViewAuthenticPixels(evaluate_view,exception) == MagickFalse)
           status=MagickFalse;
@@ -594,7 +583,7 @@ MagickExport Image *EvaluateImages(const Image *images,
             #pragma omp critical (MagickCore_EvaluateImages)
 #endif
             proceed=SetImageProgress(images,EvaluateImageTag,progress++,
-              evaluate_image->rows);
+              image->rows);
             if (proceed == MagickFalse)
               status=MagickFalse;
           }
@@ -603,9 +592,10 @@ MagickExport Image *EvaluateImages(const Image *images,
   else
     {
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-      #pragma omp parallel for schedule(dynamic) shared(progress,status)
+      #pragma omp parallel for schedule(static,4) shared(progress,status) \
+        magick_threads(image,images,image->rows,key == ~0UL)
 #endif
-      for (y=0; y < (ssize_t) evaluate_image->rows; y++)
+      for (y=0; y < (ssize_t) image->rows; y++)
       {
         CacheView
           *image_view;
@@ -631,15 +621,15 @@ MagickExport Image *EvaluateImages(const Image *images,
 
         if (status == MagickFalse)
           continue;
-        q=QueueCacheViewAuthenticPixels(evaluate_view,0,y,
-          evaluate_image->columns,1,exception);
+        q=QueueCacheViewAuthenticPixels(evaluate_view,0,y,image->columns,1,
+          exception);
         if (q == (Quantum *) NULL)
           {
             status=MagickFalse;
             continue;
           }
         evaluate_pixel=evaluate_pixels[id];
-        for (j=0; j < (ssize_t) evaluate_image->columns; j++)
+        for (j=0; j < (ssize_t) image->columns; j++)
           for (i=0; i < MaxPixelChannels; i++)
             evaluate_pixel[j].channel[i]=0.0;
         next=images;
@@ -648,7 +638,7 @@ MagickExport Image *EvaluateImages(const Image *images,
           register const Quantum
             *p;
 
-          image_view=AcquireCacheView(next);
+          image_view=AcquireVirtualCacheView(next,exception);
           p=GetCacheViewVirtualPixels(image_view,0,y,next->columns,1,exception);
           if (p == (const Quantum *) NULL)
             {
@@ -660,35 +650,31 @@ MagickExport Image *EvaluateImages(const Image *images,
             register ssize_t
               i;
 
-            for (i=0; i < (ssize_t) GetPixelChannels(evaluate_image); i++)
+            if (GetPixelReadMask(next,p) == 0)
+              {
+                p+=GetPixelChannels(next);
+                continue;
+              }
+            for (i=0; i < (ssize_t) GetPixelChannels(next); i++)
             {
-              PixelChannel
-                channel;
-
-              PixelTrait
-                evaluate_traits,
-                traits;
-
-              evaluate_traits=GetPixelChannelMapTraits(evaluate_image,
-                (PixelChannel) i);
-              channel=GetPixelChannelMapChannel(evaluate_image,(PixelChannel)
-                i);
-              traits=GetPixelChannelMapTraits(next,channel);
+              PixelChannel channel=GetPixelChannelChannel(image,i);
+              PixelTrait  traits=GetPixelChannelTraits(next,channel);
+              PixelTrait  evaluate_traits=GetPixelChannelTraits(image,channel);
               if ((traits == UndefinedPixelTrait) ||
                   (evaluate_traits == UndefinedPixelTrait))
                 continue;
               if ((traits & UpdatePixelTrait) == 0)
                 continue;
               evaluate_pixel[x].channel[i]=ApplyEvaluateOperator(
-                random_info[id],GetPixelChannel(evaluate_image,channel,p),
-                j == 0 ? AddEvaluateOperator : op,evaluate_pixel[x].channel[i]);
+                random_info[id],GetPixelChannel(image,channel,p),j == 0 ?
+                AddEvaluateOperator : op,evaluate_pixel[x].channel[i]);
             }
             p+=GetPixelChannels(next);
           }
           image_view=DestroyCacheView(image_view);
           next=GetNextImageInList(next);
         }
-        for (x=0; x < (ssize_t) evaluate_image->columns; x++)
+        for (x=0; x < (ssize_t) image->columns; x++)
         {
           register ssize_t
              i;
@@ -697,13 +683,13 @@ MagickExport Image *EvaluateImages(const Image *images,
           {
             case MeanEvaluateOperator:
             {
-              for (i=0; i < (ssize_t) GetPixelChannels(evaluate_image); i++)
-                evaluate_pixel[x].channel[i]/=(MagickRealType) number_images;
+              for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
+                evaluate_pixel[x].channel[i]/=(double) number_images;
               break;
             }
             case MultiplyEvaluateOperator:
             {
-              for (i=0; i < (ssize_t) GetPixelChannels(evaluate_image); i++)
+              for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
               {
                 register ssize_t
                   j;
@@ -717,24 +703,27 @@ MagickExport Image *EvaluateImages(const Image *images,
               break;
           }
         }
-        for (x=0; x < (ssize_t) evaluate_image->columns; x++)
+        for (x=0; x < (ssize_t) image->columns; x++)
         {
           register ssize_t
             i;
 
-          for (i=0; i < (ssize_t) GetPixelChannels(evaluate_image); i++)
+          if (GetPixelReadMask(image,q) == 0)
+            {
+              q+=GetPixelChannels(image);
+              continue;
+            }
+          for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
           {
-            PixelTrait
-              traits;
-
-            traits=GetPixelChannelMapTraits(evaluate_image,(PixelChannel) i);
+            PixelChannel channel=GetPixelChannelChannel(image,i);
+            PixelTrait traits=GetPixelChannelTraits(image,channel);
             if (traits == UndefinedPixelTrait)
               continue;
             if ((traits & UpdatePixelTrait) == 0)
               continue;
             q[i]=ClampToQuantum(evaluate_pixel[x].channel[i]);
           }
-          q+=GetPixelChannels(evaluate_image);
+          q+=GetPixelChannels(image);
         }
         if (SyncCacheViewAuthenticPixels(evaluate_view,exception) == MagickFalse)
           status=MagickFalse;
@@ -747,7 +736,7 @@ MagickExport Image *EvaluateImages(const Image *images,
             #pragma omp critical (MagickCore_EvaluateImages)
 #endif
             proceed=SetImageProgress(images,EvaluateImageTag,progress++,
-              evaluate_image->rows);
+              image->rows);
             if (proceed == MagickFalse)
               status=MagickFalse;
           }
@@ -757,8 +746,8 @@ MagickExport Image *EvaluateImages(const Image *images,
   evaluate_pixels=DestroyPixelThreadSet(evaluate_pixels);
   random_info=DestroyRandomInfoThreadSet(random_info);
   if (status == MagickFalse)
-    evaluate_image=DestroyImage(evaluate_image);
-  return(evaluate_image);
+    image=DestroyImage(image);
+  return(image);
 }
 
 MagickExport MagickBooleanType EvaluateImage(Image *image,
@@ -779,6 +768,11 @@ MagickExport MagickBooleanType EvaluateImage(Image *image,
   ssize_t
     y;
 
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+  unsigned long
+    key;
+#endif
+
   assert(image != (Image *) NULL);
   assert(image->signature == MagickSignature);
   if (image->debug != MagickFalse)
@@ -790,9 +784,13 @@ MagickExport MagickBooleanType EvaluateImage(Image *image,
   status=MagickTrue;
   progress=0;
   random_info=AcquireRandomInfoThreadSet();
-  image_view=AcquireCacheView(image);
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp parallel for schedule(dynamic,4) shared(progress,status)
+  key=GetRandomSecretKey(random_info[0]);
+#endif
+  image_view=AcquireAuthenticCacheView(image,exception);
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+  #pragma omp parallel for schedule(static,4) shared(progress,status) \
+    magick_threads(image,image,image->rows,key == ~0UL)
 #endif
   for (y=0; y < (ssize_t) image->rows; y++)
   {
@@ -820,12 +818,13 @@ MagickExport MagickBooleanType EvaluateImage(Image *image,
 
       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
       {
-        PixelTrait
-          traits;
-
-        traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
+        PixelChannel channel=GetPixelChannelChannel(image,i);
+        PixelTrait traits=GetPixelChannelTraits(image,channel);
         if (traits == UndefinedPixelTrait)
           continue;
+        if (((traits & CopyPixelTrait) != 0) ||
+            (GetPixelReadMask(image,q) == 0))
+          continue;
         q[i]=ClampToQuantum(ApplyEvaluateOperator(random_info[id],q[i],op,
           value));
       }
@@ -839,7 +838,7 @@ MagickExport MagickBooleanType EvaluateImage(Image *image,
           proceed;
 
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp critical (MagickCore_EvaluateImage)
+        #pragma omp critical (MagickCore_EvaluateImage)
 #endif
         proceed=SetImageProgress(image,EvaluateImageTag,progress++,image->rows);
         if (proceed == MagickFalse)
@@ -889,7 +888,7 @@ static Quantum ApplyFunction(Quantum pixel,const MagickFunction function,
   const size_t number_parameters,const double *parameters,
   ExceptionInfo *exception)
 {
-  MagickRealType
+  double
     result;
 
   register ssize_t
@@ -902,8 +901,8 @@ static Quantum ApplyFunction(Quantum pixel,const MagickFunction function,
     case PolynomialFunction:
     {
       /*
-        Polynomial: polynomial constants, highest to lowest order
-        (e.g. c0*x^3 + c1*x^2 + c2*x + c3).
+        Polynomial: polynomial constants, highest to lowest order (e.g. c0*x^3+
+        c1*x^2+c2*x+c3).
       */
       result=0.0;
       for (i=0; i < (ssize_t) number_parameters; i++)
@@ -913,7 +912,7 @@ static Quantum ApplyFunction(Quantum pixel,const MagickFunction function,
     }
     case SinusoidFunction:
     {
-      MagickRealType
+      double
         amplitude,
         bias,
         frequency,
@@ -926,21 +925,21 @@ static Quantum ApplyFunction(Quantum pixel,const MagickFunction function,
       phase=(number_parameters >= 2) ? parameters[1] : 0.0;
       amplitude=(number_parameters >= 3) ? parameters[2] : 0.5;
       bias=(number_parameters >= 4) ? parameters[3] : 0.5;
-      result=(MagickRealType) (QuantumRange*(amplitude*sin((double) (2.0*
+      result=(double) (QuantumRange*(amplitude*sin((double) (2.0*
         MagickPI*(frequency*QuantumScale*pixel+phase/360.0)))+bias));
       break;
     }
     case ArcsinFunction:
     {
-      MagickRealType
+      double
         bias,
         center,
         range,
         width;
 
       /*
-        Arcsin (peged at range limits for invalid results):
-        width, center, range, and bias.
+        Arcsin (peged at range limits for invalid results): width, center,
+        range, and bias.
       */
       width=(number_parameters >= 1) ? parameters[0] : 1.0;
       center=(number_parameters >= 2) ? parameters[1] : 0.5;
@@ -953,13 +952,13 @@ static Quantum ApplyFunction(Quantum pixel,const MagickFunction function,
         if (result >= 1.0)
           result=bias+range/2.0;
         else
-          result=(MagickRealType) (range/MagickPI*asin((double) result)+bias);
+          result=(double) (range/MagickPI*asin((double) result)+bias);
       result*=QuantumRange;
       break;
     }
     case ArctanFunction:
     {
-      MagickRealType
+      double
         center,
         bias,
         range,
@@ -972,8 +971,8 @@ static Quantum ApplyFunction(Quantum pixel,const MagickFunction function,
       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=(double) (MagickPI*slope*(QuantumScale*pixel-center));
+      result=(double) (QuantumRange*(range/MagickPI*atan((double)
         result)+bias));
       break;
     }
@@ -1011,9 +1010,10 @@ MagickExport MagickBooleanType FunctionImage(Image *image,
     return(MagickFalse);
   status=MagickTrue;
   progress=0;
-  image_view=AcquireCacheView(image);
+  image_view=AcquireAuthenticCacheView(image,exception);
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp parallel for schedule(dynamic,4) shared(progress,status)
+  #pragma omp parallel for schedule(static,4) shared(progress,status) \
+    magick_threads(image,image,image->rows,1)
 #endif
   for (y=0; y < (ssize_t) image->rows; y++)
   {
@@ -1036,12 +1036,15 @@ MagickExport MagickBooleanType FunctionImage(Image *image,
       register ssize_t
         i;
 
+      if (GetPixelReadMask(image,q) == 0)
+        {
+          q+=GetPixelChannels(image);
+          continue;
+        }
       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
       {
-        PixelTrait
-          traits;
-
-        traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
+        PixelChannel channel=GetPixelChannelChannel(image,i);
+        PixelTrait traits=GetPixelChannelTraits(image,channel);
         if (traits == UndefinedPixelTrait)
           continue;
         if ((traits & UpdatePixelTrait) == 0)
@@ -1059,7 +1062,7 @@ MagickExport MagickBooleanType FunctionImage(Image *image,
           proceed;
 
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp critical (MagickCore_FunctionImage)
+        #pragma omp critical (MagickCore_FunctionImage)
 #endif
         proceed=SetImageProgress(image,FunctionImageTag,progress++,image->rows);
         if (proceed == MagickFalse)
@@ -1124,92 +1127,14 @@ MagickExport MagickBooleanType GetImageExtrema(const Image *image,
 %                                                                             %
 %                                                                             %
 %                                                                             %
-%   G e t I m a g e M e a n                                                   %
-%                                                                             %
-%                                                                             %
-%                                                                             %
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%
-%  GetImageMean() returns the mean and standard deviation of one or more
-%  image channels.
-%
-%  The format of the GetImageMean method is:
-%
-%      MagickBooleanType GetImageMean(const Image *image,double *mean,
-%        double *standard_deviation,ExceptionInfo *exception)
-%
-%  A description of each parameter follows:
-%
-%    o image: the image.
-%
-%    o mean: the average value in the channel.
-%
-%    o standard_deviation: the standard deviation of the channel.
-%
-%    o exception: return any errors or warnings in this structure.
-%
-*/
-MagickExport MagickBooleanType GetImageMean(const Image *image,double *mean,
-  double *standard_deviation,ExceptionInfo *exception)
-{
-  ChannelStatistics
-    *channel_statistics;
-
-  register ssize_t
-    i;
-
-  size_t
-    area;
-
-  assert(image != (Image *) NULL);
-  assert(image->signature == MagickSignature);
-  if (image->debug != MagickFalse)
-    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
-  channel_statistics=GetImageStatistics(image,exception);
-  if (channel_statistics == (ChannelStatistics *) NULL)
-    return(MagickFalse);
-  area=0;
-  channel_statistics[CompositePixelChannel].mean=0.0;
-  channel_statistics[CompositePixelChannel].standard_deviation=0.0;
-  for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
-  {
-    PixelTrait
-      traits;
-
-    traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
-    if (traits == UndefinedPixelTrait)
-      continue;
-    if ((traits & UpdatePixelTrait) == 0)
-      continue;
-    channel_statistics[CompositePixelChannel].mean+=channel_statistics[i].mean;
-    channel_statistics[CompositePixelChannel].standard_deviation+=
-      channel_statistics[i].variance-channel_statistics[i].mean*
-      channel_statistics[i].mean;
-    area++;
-  }
-  channel_statistics[CompositePixelChannel].mean/=area;
-  channel_statistics[CompositePixelChannel].standard_deviation=
-    sqrt(channel_statistics[CompositePixelChannel].standard_deviation/area);
-  *mean=channel_statistics[CompositePixelChannel].mean;
-  *standard_deviation=channel_statistics[CompositePixelChannel].standard_deviation;
-  channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
-    channel_statistics);
-  return(MagickTrue);
-}
-\f
-/*
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-%                                                                             %
-%                                                                             %
-%                                                                             %
 %   G e t I m a g e K u r t o s i s                                           %
 %                                                                             %
 %                                                                             %
 %                                                                             %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
-%  GetImageKurtosis() returns the kurtosis and skewness of one or more
-%  image channels.
+%  GetImageKurtosis() returns the kurtosis and skewness of one or more image
+%  channels.
 %
 %  The format of the GetImageKurtosis method is:
 %
@@ -1260,9 +1185,10 @@ MagickExport MagickBooleanType GetImageKurtosis(const Image *image,
   sum_squares=0.0;
   sum_cubes=0.0;
   sum_fourth_power=0.0;
-  image_view=AcquireCacheView(image);
+  image_view=AcquireVirtualCacheView(image,exception);
 #if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp parallel for schedule(dynamic) shared(status) omp_throttle(1)
+  #pragma omp parallel for schedule(static,4) shared(status) \
+    magick_threads(image,image,image->rows,1)
 #endif
   for (y=0; y < (ssize_t) image->rows; y++)
   {
@@ -1285,12 +1211,15 @@ MagickExport MagickBooleanType GetImageKurtosis(const Image *image,
       register ssize_t
         i;
 
+      if (GetPixelReadMask(image,p) == 0)
+        {
+          p+=GetPixelChannels(image);
+          continue;
+        }
       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
       {
-        PixelTrait
-          traits;
-
-        traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
+        PixelChannel channel=GetPixelChannelChannel(image,i);
+        PixelTrait traits=GetPixelChannelTraits(image,channel);
         if (traits == UndefinedPixelTrait)
           continue;
         if ((traits & UpdatePixelTrait) == 0)
@@ -1336,99 +1265,76 @@ MagickExport MagickBooleanType GetImageKurtosis(const Image *image,
 %                                                                             %
 %                                                                             %
 %                                                                             %
-%   G e t I m a g e R a n g e                                                 %
+%   G e t I m a g e M e a n                                                   %
 %                                                                             %
 %                                                                             %
 %                                                                             %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
-%  GetImageRange() returns the range of one or more image channels.
+%  GetImageMean() returns the mean and standard deviation of one or more image
+%  channels.
 %
-%  The format of the GetImageRange method is:
+%  The format of the GetImageMean method is:
 %
-%      MagickBooleanType GetImageRange(const Image *image,double *minima,
-%        double *maxima,ExceptionInfo *exception)
+%      MagickBooleanType GetImageMean(const Image *image,double *mean,
+%        double *standard_deviation,ExceptionInfo *exception)
 %
 %  A description of each parameter follows:
 %
 %    o image: the image.
 %
-%    o minima: the minimum value in the channel.
+%    o mean: the average value in the channel.
 %
-%    o maxima: the maximum value in the channel.
+%    o standard_deviation: the standard deviation of the channel.
 %
 %    o exception: return any errors or warnings in this structure.
 %
 */
-MagickExport MagickBooleanType GetImageRange(const Image *image,double *minima,
-  double *maxima,ExceptionInfo *exception)
+MagickExport MagickBooleanType GetImageMean(const Image *image,double *mean,
+  double *standard_deviation,ExceptionInfo *exception)
 {
-  CacheView
-    *image_view;
+  double
+    area;
 
-  MagickBooleanType
-    status;
+  ChannelStatistics
+    *channel_statistics;
 
-  ssize_t
-    y;
+  register ssize_t
+    i;
 
   assert(image != (Image *) NULL);
   assert(image->signature == MagickSignature);
   if (image->debug != MagickFalse)
     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
-  status=MagickTrue;
-  *maxima=(-MagickHuge);
-  *minima=MagickHuge;
-  image_view=AcquireCacheView(image);
-#if defined(MAGICKCORE_OPENMP_SUPPORT)
-  #pragma omp parallel for schedule(dynamic) shared(status) omp_throttle(1)
-#endif
-  for (y=0; y < (ssize_t) image->rows; y++)
+  channel_statistics=GetImageStatistics(image,exception);
+  if (channel_statistics == (ChannelStatistics *) NULL)
+    return(MagickFalse);
+  area=0.0;
+  channel_statistics[CompositePixelChannel].mean=0.0;
+  channel_statistics[CompositePixelChannel].standard_deviation=0.0;
+  for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
   {
-    register const Quantum
-      *restrict p;
-
-    register ssize_t
-      x;
-
-    if (status == MagickFalse)
+    PixelChannel channel=GetPixelChannelChannel(image,i);
+    PixelTrait traits=GetPixelChannelTraits(image,channel);
+    if (traits == UndefinedPixelTrait)
       continue;
-    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
-    if (p == (const Quantum *) NULL)
-      {
-        status=MagickFalse;
-        continue;
-      }
-    for (x=0; x < (ssize_t) image->columns; x++)
-    {
-      register ssize_t
-        i;
-
-      for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
-      {
-        PixelTrait
-          traits;
-
-        traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
-        if (traits == UndefinedPixelTrait)
-          continue;
-        if ((traits & UpdatePixelTrait) == 0)
-          continue;
-#if defined(MAGICKCORE_OPENMP_SUPPORT)
-        #pragma omp critical (MagickCore_GetImageRange)
-#endif
-        {
-          if (p[i] < *minima)
-            *minima=(double) p[i];
-          if (p[i] > *maxima)
-            *maxima=(double) p[i];
-        }
-      }
-      p+=GetPixelChannels(image);
-    }
+    if ((traits & UpdatePixelTrait) == 0)
+      continue;
+    channel_statistics[CompositePixelChannel].mean+=channel_statistics[i].mean;
+    channel_statistics[CompositePixelChannel].standard_deviation+=
+      channel_statistics[i].variance-channel_statistics[i].mean*
+      channel_statistics[i].mean;
+    area++;
   }
-  image_view=DestroyCacheView(image_view);
-  return(status);
+  channel_statistics[CompositePixelChannel].mean/=area;
+  channel_statistics[CompositePixelChannel].standard_deviation=
+    sqrt(channel_statistics[CompositePixelChannel].standard_deviation/area);
+  *mean=channel_statistics[CompositePixelChannel].mean;
+  *standard_deviation=
+    channel_statistics[CompositePixelChannel].standard_deviation;
+  channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
+    channel_statistics);
+  return(MagickTrue);
 }
 \f
 /*
@@ -1436,25 +1342,18 @@ MagickExport MagickBooleanType GetImageRange(const Image *image,double *minima,
 %                                                                             %
 %                                                                             %
 %                                                                             %
-%   G e t I m a g e S t a t i s t i c s                                       %
+%   G e t I m a g e M o m e n t s                                             %
 %                                                                             %
 %                                                                             %
 %                                                                             %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
-%  GetImageStatistics() returns statistics for each channel in the
-%  image.  The statistics include the channel depth, its minima, maxima, mean,
-%  standard deviation, kurtosis and skewness.  You can access the red channel
-%  mean, for example, like this:
-%
-%      channel_statistics=GetImageStatistics(image,exception);
-%      red_mean=channel_statistics[RedPixelChannel].mean;
-%
-%  Use MagickRelinquishMemory() to free the statistics buffer.
+%  GetImageMoments() returns the normalized moments of one or more image
+%  channels.
 %
-%  The format of the GetImageStatistics method is:
+%  The format of the GetImageMoments method is:
 %
-%      ChannelStatistics *GetImageStatistics(const Image *image,
+%      ChannelMoments *GetImageMoments(const Image *image,
 %        ExceptionInfo *exception)
 %
 %  A description of each parameter follows:
@@ -1464,68 +1363,117 @@ MagickExport MagickBooleanType GetImageRange(const Image *image,double *minima,
 %    o exception: return any errors or warnings in this structure.
 %
 */
-
-static size_t GetImageChannels(const Image *image)
-{
-  register ssize_t
-    i;
-
-  size_t
-    channels;
-
-  channels=0;
-  for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
-  {
-    PixelTrait
-      traits;
-
-    traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
-    if ((traits & UpdatePixelTrait) != 0)
-      channels++;
-  }
-  return(channels);
-}
-
-MagickExport ChannelStatistics *GetImageStatistics(const Image *image,
+MagickExport ChannelMoments *GetImageMoments(const Image *image,
   ExceptionInfo *exception)
 {
-  ChannelStatistics
-    *channel_statistics;
-
-  double
-    area;
-
-  MagickStatusType
-    status;
+#define MaxNumberImageMoments  8
 
-  QuantumAny
-    range;
+  CacheView
+    *image_view;
 
-  register ssize_t
-    i;
+  ChannelMoments
+    *channel_moments;
 
-  size_t
-    channels,
-    depth;
+  double
+    M00[MaxPixelChannels+1],
+    M01[MaxPixelChannels+1],
+    M02[MaxPixelChannels+1],
+    M03[MaxPixelChannels+1],
+    M10[MaxPixelChannels+1],
+    M11[MaxPixelChannels+1],
+    M12[MaxPixelChannels+1],
+    M20[MaxPixelChannels+1],
+    M21[MaxPixelChannels+1],
+    M22[MaxPixelChannels+1],
+    M30[MaxPixelChannels+1];
+
+  PointInfo
+    centroid[MaxPixelChannels+1];
 
   ssize_t
+    channel,
     y;
 
   assert(image != (Image *) NULL);
   assert(image->signature == MagickSignature);
   if (image->debug != MagickFalse)
     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
-  channel_statistics=(ChannelStatistics *) AcquireQuantumMemory(
-    MaxPixelChannels+1,sizeof(*channel_statistics));
-  if (channel_statistics == (ChannelStatistics *) NULL)
-    ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
-  (void) ResetMagickMemory(channel_statistics,0,(MaxPixelChannels+1)*
-    sizeof(*channel_statistics));
-  for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
+  channel_moments=(ChannelMoments *) AcquireQuantumMemory(MaxPixelChannels+1,
+    sizeof(*channel_moments));
+  if (channel_moments == (ChannelMoments *) NULL)
+    return(channel_moments);
+  (void) ResetMagickMemory(channel_moments,0,(MaxPixelChannels+1)*
+    sizeof(*channel_moments));
+  (void) ResetMagickMemory(centroid,0,sizeof(centroid));
+  (void) ResetMagickMemory(M00,0,sizeof(M00));
+  (void) ResetMagickMemory(M01,0,sizeof(M01));
+  (void) ResetMagickMemory(M02,0,sizeof(M02));
+  (void) ResetMagickMemory(M03,0,sizeof(M03));
+  (void) ResetMagickMemory(M10,0,sizeof(M10));
+  (void) ResetMagickMemory(M11,0,sizeof(M11));
+  (void) ResetMagickMemory(M12,0,sizeof(M12));
+  (void) ResetMagickMemory(M20,0,sizeof(M20));
+  (void) ResetMagickMemory(M21,0,sizeof(M21));
+  (void) ResetMagickMemory(M22,0,sizeof(M22));
+  (void) ResetMagickMemory(M30,0,sizeof(M30));
+  image_view=AcquireVirtualCacheView(image,exception);
+  for (y=0; y < (ssize_t) image->rows; y++)
   {
-    channel_statistics[i].depth=1;
-    channel_statistics[i].maxima=(-MagickHuge);
-    channel_statistics[i].minima=MagickHuge;
+    register const Quantum
+      *restrict p;
+
+    register ssize_t
+      x;
+
+    /*
+      Compute center of mass (centroid).
+    */
+    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
+    if (p == (const Quantum *) NULL)
+      break;
+    for (x=0; x < (ssize_t) image->columns; x++)
+    {
+      register ssize_t
+        i;
+
+      if (GetPixelReadMask(image,p) == 0)
+        {
+          p+=GetPixelChannels(image);
+          continue;
+        }
+      for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
+      {
+        PixelChannel channel=GetPixelChannelChannel(image,i);
+        PixelTrait traits=GetPixelChannelTraits(image,channel);
+        if (traits == UndefinedPixelTrait)
+          continue;
+        if ((traits & UpdatePixelTrait) == 0)
+          continue;
+        M00[channel]+=QuantumScale*p[i];
+        M00[MaxPixelChannels]+=QuantumScale*p[i];
+        M10[channel]+=x*QuantumScale*p[i];
+        M10[MaxPixelChannels]+=QuantumScale*p[i];
+        M01[channel]+=y*QuantumScale*p[i];
+        M01[MaxPixelChannels]+=QuantumScale*p[i];
+      }
+      p+=GetPixelChannels(image);
+    }
+  }
+  for (channel=0; channel <= MaxPixelChannels; channel++)
+  {
+    /*
+       Compute center of mass (centroid).
+    */
+    if (M00[channel] < MagickEpsilon)
+      {
+        M00[channel]+=MagickEpsilon;
+        centroid[channel].x=image->columns/2.0;
+        centroid[channel].y=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++)
   {
@@ -1535,7 +1483,10 @@ MagickExport ChannelStatistics *GetImageStatistics(const Image *image,
     register ssize_t
       x;
 
-    p=GetVirtualPixels(image,0,y,image->columns,1,exception);
+    /*
+      Compute the image moments.
+    */
+    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
     if (p == (const Quantum *) NULL)
       break;
     for (x=0; x < (ssize_t) image->columns; x++)
@@ -1543,107 +1494,1502 @@ MagickExport ChannelStatistics *GetImageStatistics(const Image *image,
       register ssize_t
         i;
 
+      if (GetPixelReadMask(image,p) == 0)
+        {
+          p+=GetPixelChannels(image);
+          continue;
+        }
       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
       {
-        PixelTrait
-          traits;
-
-        traits=GetPixelChannelMapTraits(image,(PixelChannel) i);
+        PixelChannel channel=GetPixelChannelChannel(image,i);
+        PixelTrait traits=GetPixelChannelTraits(image,channel);
         if (traits == UndefinedPixelTrait)
           continue;
-        if (channel_statistics[i].depth != MAGICKCORE_QUANTUM_DEPTH)
-          {
-            depth=channel_statistics[i].depth;
-            range=GetQuantumRange(depth);
-            status=p[i] != ScaleAnyToQuantum(ScaleQuantumToAny(p[i],range),
-              range) ? MagickTrue : MagickFalse;
-            if (status != MagickFalse)
-              {
-                channel_statistics[i].depth++;
-                continue;
-              }
-          }
-        if ((double) p[i] < channel_statistics[i].minima)
-          channel_statistics[i].minima=(double) p[i];
-        if ((double) p[i] > channel_statistics[i].maxima)
-          channel_statistics[i].maxima=(double) p[i];
-        channel_statistics[i].sum+=p[i];
-        channel_statistics[i].sum_squared+=(double) p[i]*p[i];
-        channel_statistics[i].sum_cubed+=(double) p[i]*p[i]*p[i];
-        channel_statistics[i].sum_fourth_power+=(double) p[i]*p[i]*p[i]*p[i];
+        if ((traits & UpdatePixelTrait) == 0)
+          continue;
+        M11[channel]+=(x-centroid[channel].x)*(y-centroid[channel].y)*
+          QuantumScale*p[i];
+        M11[MaxPixelChannels]+=(x-centroid[channel].x)*(y-centroid[channel].y)*
+          QuantumScale*p[i];
+        M20[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
+          QuantumScale*p[i];
+        M20[MaxPixelChannels]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
+          QuantumScale*p[i];
+        M02[channel]+=(y-centroid[channel].y)*(y-centroid[channel].y)*
+          QuantumScale*p[i];
+        M02[MaxPixelChannels]+=(y-centroid[channel].y)*(y-centroid[channel].y)*
+          QuantumScale*p[i];
+        M21[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
+          (y-centroid[channel].y)*QuantumScale*p[i];
+        M21[MaxPixelChannels]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
+          (y-centroid[channel].y)*QuantumScale*p[i];
+        M12[channel]+=(x-centroid[channel].x)*(y-centroid[channel].y)*
+          (y-centroid[channel].y)*QuantumScale*p[i];
+        M12[MaxPixelChannels]+=(x-centroid[channel].x)*(y-centroid[channel].y)*
+          (y-centroid[channel].y)*QuantumScale*p[i];
+        M22[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
+          (y-centroid[channel].y)*(y-centroid[channel].y)*QuantumScale*p[i];
+        M22[MaxPixelChannels]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
+          (y-centroid[channel].y)*(y-centroid[channel].y)*QuantumScale*p[i];
+        M30[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
+          (x-centroid[channel].x)*QuantumScale*p[i];
+        M30[MaxPixelChannels]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
+          (x-centroid[channel].x)*QuantumScale*p[i];
+        M03[channel]+=(y-centroid[channel].y)*(y-centroid[channel].y)*
+          (y-centroid[channel].y)*QuantumScale*p[i];
+        M03[MaxPixelChannels]+=(y-centroid[channel].y)*(y-centroid[channel].y)*
+          (y-centroid[channel].y)*QuantumScale*p[i];
       }
       p+=GetPixelChannels(image);
     }
   }
-  area=(double) image->columns*image->rows;
-  for (i=0; i < (ssize_t) MaxPixelChannels; i++)
+  M00[MaxPixelChannels]/=GetPixelChannels(image);
+  M01[MaxPixelChannels]/=GetPixelChannels(image);
+  M02[MaxPixelChannels]/=GetPixelChannels(image);
+  M03[MaxPixelChannels]/=GetPixelChannels(image);
+  M10[MaxPixelChannels]/=GetPixelChannels(image);
+  M11[MaxPixelChannels]/=GetPixelChannels(image);
+  M12[MaxPixelChannels]/=GetPixelChannels(image);
+  M20[MaxPixelChannels]/=GetPixelChannels(image);
+  M21[MaxPixelChannels]/=GetPixelChannels(image);
+  M22[MaxPixelChannels]/=GetPixelChannels(image);
+  M30[MaxPixelChannels]/=GetPixelChannels(image);
+  for (channel=0; channel <= MaxPixelChannels; channel++)
   {
-    channel_statistics[i].sum/=area;
-    channel_statistics[i].sum_squared/=area;
-    channel_statistics[i].sum_cubed/=area;
-    channel_statistics[i].sum_fourth_power/=area;
-    channel_statistics[i].mean=channel_statistics[i].sum;
-    channel_statistics[i].variance=channel_statistics[i].sum_squared;
-    channel_statistics[i].standard_deviation=sqrt(
-      channel_statistics[i].variance-(channel_statistics[i].mean*
-      channel_statistics[i].mean));
+    /*
+      Compute elliptical angle, major and minor axes, eccentricity, & intensity.
+    */
+    channel_moments[channel].centroid=centroid[channel];
+    channel_moments[channel].ellipse_axis.x=sqrt((2.0/M00[channel])*
+      ((M20[channel]+M02[channel])+sqrt(4.0*M11[channel]*M11[channel]+
+      (M20[channel]-M02[channel])*(M20[channel]-M02[channel]))));
+    channel_moments[channel].ellipse_axis.y=sqrt((2.0/M00[channel])*
+      ((M20[channel]+M02[channel])-sqrt(4.0*M11[channel]*M11[channel]+
+      (M20[channel]-M02[channel])*(M20[channel]-M02[channel]))));
+    channel_moments[channel].ellipse_angle=RadiansToDegrees(0.5*atan(2.0*
+      M11[channel]/(M20[channel]-M02[channel]+MagickEpsilon)));
+    channel_moments[channel].ellipse_eccentricity=sqrt(1.0-(
+      channel_moments[channel].ellipse_axis.y/
+      (channel_moments[channel].ellipse_axis.x+MagickEpsilon)));
+    channel_moments[channel].ellipse_intensity=M00[channel]/
+      (MagickPI*channel_moments[channel].ellipse_axis.x*
+      channel_moments[channel].ellipse_axis.y+MagickEpsilon);
   }
-  for (i=0; i < (ssize_t) MaxPixelChannels; i++)
+  for (channel=0; channel <= MaxPixelChannels; channel++)
   {
-    channel_statistics[CompositePixelChannel].depth=(size_t) MagickMax((double)
-      channel_statistics[CompositePixelChannel].depth,(double)
-      channel_statistics[i].depth);
-    channel_statistics[CompositePixelChannel].minima=MagickMin(
-      channel_statistics[CompositePixelChannel].minima,
-      channel_statistics[i].minima);
-    channel_statistics[CompositePixelChannel].maxima=MagickMax(
-      channel_statistics[CompositePixelChannel].maxima,
-      channel_statistics[i].maxima);
-    channel_statistics[CompositePixelChannel].sum+=channel_statistics[i].sum;
-    channel_statistics[CompositePixelChannel].sum_squared+=
-      channel_statistics[i].sum_squared;
-    channel_statistics[CompositePixelChannel].sum_cubed+=
-      channel_statistics[i].sum_cubed;
-    channel_statistics[CompositePixelChannel].sum_fourth_power+=
-      channel_statistics[i].sum_fourth_power;
-    channel_statistics[CompositePixelChannel].mean+=channel_statistics[i].mean;
-    channel_statistics[CompositePixelChannel].variance+=
-      channel_statistics[i].variance-channel_statistics[i].mean*
-      channel_statistics[i].mean;
-    channel_statistics[CompositePixelChannel].standard_deviation+=
-      channel_statistics[i].variance-channel_statistics[i].mean*
-      channel_statistics[i].mean;
+    /*
+      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;
   }
-  channels=GetImageChannels(image);
-  channel_statistics[CompositePixelChannel].sum/=channels;
-  channel_statistics[CompositePixelChannel].sum_squared/=channels;
-  channel_statistics[CompositePixelChannel].sum_cubed/=channels;
-  channel_statistics[CompositePixelChannel].sum_fourth_power/=channels;
-  channel_statistics[CompositePixelChannel].mean/=channels;
-  channel_statistics[CompositePixelChannel].variance/=channels;
-  channel_statistics[CompositePixelChannel].standard_deviation=
-    sqrt(channel_statistics[CompositePixelChannel].standard_deviation/channels);
-  channel_statistics[CompositePixelChannel].kurtosis/=channels;
-  channel_statistics[CompositePixelChannel].skewness/=channels;
-  for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
+  image_view=DestroyCacheView(image_view);
+  for (channel=0; channel <= MaxPixelChannels; channel++)
   {
-    if (channel_statistics[i].standard_deviation == 0.0)
+    /*
+      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);
+}
+\f
+/*
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%   G e t I m a g e C h a n n e l P e r c e p t u a l H a s h                 %
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%  GetImagePerceptualHash() returns the perceptual hash of one or more
+%  image channels.
+%
+%  The format of the GetImagePerceptualHash method is:
+%
+%      ChannelPerceptualHash *GetImagePerceptualHash(const Image *image,
+%        ExceptionInfo *exception)
+%
+%  A description of each parameter follows:
+%
+%    o image: the image.
+%
+%    o exception: return any errors or warnings in this structure.
+%
+*/
+
+static inline double MagickLog10(const double x)
+{
+#define Log10Epsilon  (1.0e-11)
+
+ if (fabs(x) < Log10Epsilon)
+   return(log10(Log10Epsilon));
+ return(log10(fabs(x)));
+}
+
+MagickExport ChannelPerceptualHash *GetImagePerceptualHash(
+  const Image *image,ExceptionInfo *exception)
+{
+  ChannelMoments
+    *moments;
+
+  ChannelPerceptualHash
+    *perceptual_hash;
+
+  Image
+    *hash_image;
+
+  MagickBooleanType
+    status;
+
+  register ssize_t
+    i;
+
+  ssize_t
+    channel;
+
+  /*
+    Blur then transform to sRGB colorspace.
+  */
+  hash_image=BlurImage(image,0.0,1.0,exception);
+  if (hash_image == (Image *) NULL)
+    return((ChannelPerceptualHash *) NULL);
+  hash_image->depth=8;
+  status=TransformImageColorspace(hash_image,sRGBColorspace,exception);
+  if (status == MagickFalse)
+    return((ChannelPerceptualHash *) NULL);
+  moments=GetImageMoments(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 <= MaxPixelChannels; channel++)
+    for (i=0; i < 7; 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,exception);
+  if (status == MagickFalse)
+    {
+      perceptual_hash=(ChannelPerceptualHash *) RelinquishMagickMemory(
+        perceptual_hash);
+      return((ChannelPerceptualHash *) NULL);
+    }
+  moments=GetImageMoments(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 <= MaxPixelChannels; channel++)
+    for (i=0; i < 7; i++)
+      perceptual_hash[channel].Q[i]=(-MagickLog10(moments[channel].I[i]));
+  moments=(ChannelMoments *) RelinquishMagickMemory(moments);
+  return(perceptual_hash);
+}
+\f
+/*
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%   G e t I m a g e R a n g e                                                 %
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%  GetImageRange() returns the range of one or more image channels.
+%
+%  The format of the GetImageRange method is:
+%
+%      MagickBooleanType GetImageRange(const Image *image,double *minima,
+%        double *maxima,ExceptionInfo *exception)
+%
+%  A description of each parameter follows:
+%
+%    o image: the image.
+%
+%    o minima: the minimum value in the channel.
+%
+%    o maxima: the maximum value in the channel.
+%
+%    o exception: return any errors or warnings in this structure.
+%
+*/
+MagickExport MagickBooleanType GetImageRange(const Image *image,double *minima,
+  double *maxima,ExceptionInfo *exception)
+{
+  CacheView
+    *image_view;
+
+  MagickBooleanType
+    initialize,
+    status;
+
+  ssize_t
+    y;
+
+  assert(image != (Image *) NULL);
+  assert(image->signature == MagickSignature);
+  if (image->debug != MagickFalse)
+    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
+  status=MagickTrue;
+  initialize=MagickTrue;
+  *maxima=0.0;
+  *minima=0.0;
+  image_view=AcquireVirtualCacheView(image,exception);
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+  #pragma omp parallel for schedule(static,4) shared(status,initialize) \
+    magick_threads(image,image,image->rows,1)
+#endif
+  for (y=0; y < (ssize_t) image->rows; y++)
+  {
+    register const Quantum
+      *restrict p;
+
+    register ssize_t
+      x;
+
+    if (status == MagickFalse)
       continue;
-    channel_statistics[i].skewness=(channel_statistics[i].sum_cubed-
-      3.0*channel_statistics[i].mean*channel_statistics[i].sum_squared+
-      2.0*channel_statistics[i].mean*channel_statistics[i].mean*
-      channel_statistics[i].mean)/(channel_statistics[i].standard_deviation*
-      channel_statistics[i].standard_deviation*
-      channel_statistics[i].standard_deviation);
-    channel_statistics[i].kurtosis=(channel_statistics[i].sum_fourth_power-
-      4.0*channel_statistics[i].mean*channel_statistics[i].sum_cubed+
-      6.0*channel_statistics[i].mean*channel_statistics[i].mean*
-      channel_statistics[i].sum_squared-3.0*channel_statistics[i].mean*
-      channel_statistics[i].mean*1.0*channel_statistics[i].mean*
-      channel_statistics[i].mean)/(channel_statistics[i].standard_deviation*
-      channel_statistics[i].standard_deviation*
-      channel_statistics[i].standard_deviation*
-      channel_statistics[i].standard_deviation)-3.0;
+    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
+    if (p == (const Quantum *) NULL)
+      {
+        status=MagickFalse;
+        continue;
+      }
+    for (x=0; x < (ssize_t) image->columns; x++)
+    {
+      register ssize_t
+        i;
+
+      if (GetPixelReadMask(image,p) == 0)
+        {
+          p+=GetPixelChannels(image);
+          continue;
+        }
+      for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
+      {
+        PixelChannel channel=GetPixelChannelChannel(image,i);
+        PixelTrait traits=GetPixelChannelTraits(image,channel);
+        if (traits == UndefinedPixelTrait)
+          continue;
+        if ((traits & UpdatePixelTrait) == 0)
+          continue;
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+        #pragma omp critical (MagickCore_GetImageRange)
+#endif
+        {
+          if (initialize != MagickFalse)
+            {
+              *minima=(double) p[i];
+              *maxima=(double) p[i];
+              initialize=MagickFalse;
+            }
+          else
+            {
+              if ((double) p[i] < *minima)
+                *minima=(double) p[i];
+              if ((double) p[i] > *maxima)
+                *maxima=(double) p[i];
+           }
+        }
+      }
+      p+=GetPixelChannels(image);
+    }
   }
-  return(channel_statistics);
+  image_view=DestroyCacheView(image_view);
+  return(status);
+}
+\f
+/*
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%   G e t I m a g e S t a t i s t i c s                                       %
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%  GetImageStatistics() returns statistics for each channel in the image.  The
+%  statistics include the channel depth, its minima, maxima, mean, standard
+%  deviation, kurtosis and skewness.  You can access the red channel mean, for
+%  example, like this:
+%
+%      channel_statistics=GetImageStatistics(image,exception);
+%      red_mean=channel_statistics[RedPixelChannel].mean;
+%
+%  Use MagickRelinquishMemory() to free the statistics buffer.
+%
+%  The format of the GetImageStatistics method is:
+%
+%      ChannelStatistics *GetImageStatistics(const Image *image,
+%        ExceptionInfo *exception)
+%
+%  A description of each parameter follows:
+%
+%    o image: the image.
+%
+%    o exception: return any errors or warnings in this structure.
+%
+*/
+
+static size_t GetImageChannels(const Image *image)
+{
+  register ssize_t
+    i;
+
+  size_t
+    channels;
+
+  channels=0;
+  for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
+  {
+    PixelChannel channel=GetPixelChannelChannel(image,i);
+    PixelTrait traits=GetPixelChannelTraits(image,channel);
+    if (traits != UndefinedPixelTrait)
+      channels++;
+  }
+  return(channels);
+}
+
+MagickExport ChannelStatistics *GetImageStatistics(const Image *image,
+  ExceptionInfo *exception)
+{
+  ChannelStatistics
+    *channel_statistics;
+
+  MagickStatusType
+    status;
+
+  QuantumAny
+    range;
+
+  register ssize_t
+    i;
+
+  size_t
+    channels,
+    depth;
+
+  ssize_t
+    y;
+
+  assert(image != (Image *) NULL);
+  assert(image->signature == MagickSignature);
+  if (image->debug != MagickFalse)
+    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
+  channel_statistics=(ChannelStatistics *) AcquireQuantumMemory(
+    MaxPixelChannels+1,sizeof(*channel_statistics));
+  if (channel_statistics == (ChannelStatistics *) NULL)
+    return(channel_statistics);
+  (void) ResetMagickMemory(channel_statistics,0,(MaxPixelChannels+1)*
+    sizeof(*channel_statistics));
+  for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
+  {
+    channel_statistics[i].depth=1;
+    channel_statistics[i].maxima=(-MagickMaximumValue);
+    channel_statistics[i].minima=MagickMaximumValue;
+  }
+  for (y=0; y < (ssize_t) image->rows; y++)
+  {
+    register const Quantum
+      *restrict p;
+
+    register ssize_t
+      x;
+
+    p=GetVirtualPixels(image,0,y,image->columns,1,exception);
+    if (p == (const Quantum *) NULL)
+      break;
+    for (x=0; x < (ssize_t) image->columns; x++)
+    {
+      register ssize_t
+        i;
+
+      if (GetPixelReadMask(image,p) == 0)
+        {
+          p+=GetPixelChannels(image);
+          continue;
+        }
+      for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
+      {
+        PixelChannel channel=GetPixelChannelChannel(image,i);
+        PixelTrait traits=GetPixelChannelTraits(image,channel);
+        if (traits == UndefinedPixelTrait)
+          continue;
+        if (channel_statistics[channel].depth != MAGICKCORE_QUANTUM_DEPTH)
+          {
+            depth=channel_statistics[channel].depth;
+            range=GetQuantumRange(depth);
+            status=p[i] != ScaleAnyToQuantum(ScaleQuantumToAny(p[i],range),
+              range) ? MagickTrue : MagickFalse;
+            if (status != MagickFalse)
+              {
+                channel_statistics[channel].depth++;
+                i--;
+                continue;
+              }
+          }
+        if ((double) p[i] < channel_statistics[channel].minima)
+          channel_statistics[channel].minima=(double) p[i];
+        if ((double) p[i] > channel_statistics[channel].maxima)
+          channel_statistics[channel].maxima=(double) p[i];
+        channel_statistics[channel].sum+=p[i];
+        channel_statistics[channel].sum_squared+=(double) p[i]*p[i];
+        channel_statistics[channel].sum_cubed+=(double) p[i]*p[i]*p[i];
+        channel_statistics[channel].sum_fourth_power+=(double) p[i]*p[i]*p[i]*
+          p[i];
+        channel_statistics[channel].area++;
+      }
+      p+=GetPixelChannels(image);
+    }
+  }
+  for (i=0; i < (ssize_t) MaxPixelChannels; i++)
+  {
+    double
+      area;
+
+    area=PerceptibleReciprocal(channel_statistics[i].area);
+    channel_statistics[i].sum*=area;
+    channel_statistics[i].sum_squared*=area;
+    channel_statistics[i].sum_cubed*=area;
+    channel_statistics[i].sum_fourth_power*=area;
+    channel_statistics[i].mean=channel_statistics[i].sum;
+    channel_statistics[i].variance=channel_statistics[i].sum_squared;
+    channel_statistics[i].standard_deviation=sqrt(
+      channel_statistics[i].variance-(channel_statistics[i].mean*
+      channel_statistics[i].mean));
+  }
+  for (i=0; i < (ssize_t) MaxPixelChannels; i++)
+  {
+    channel_statistics[CompositePixelChannel].area+=channel_statistics[i].area;
+    channel_statistics[CompositePixelChannel].minima=MagickMin(
+      channel_statistics[CompositePixelChannel].minima,
+      channel_statistics[i].minima);
+    channel_statistics[CompositePixelChannel].maxima=EvaluateMax(
+      channel_statistics[CompositePixelChannel].maxima,
+      channel_statistics[i].maxima);
+    channel_statistics[CompositePixelChannel].sum+=channel_statistics[i].sum;
+    channel_statistics[CompositePixelChannel].sum_squared+=
+      channel_statistics[i].sum_squared;
+    channel_statistics[CompositePixelChannel].sum_cubed+=
+      channel_statistics[i].sum_cubed;
+    channel_statistics[CompositePixelChannel].sum_fourth_power+=
+      channel_statistics[i].sum_fourth_power;
+    channel_statistics[CompositePixelChannel].mean+=channel_statistics[i].mean;
+    channel_statistics[CompositePixelChannel].variance+=
+      channel_statistics[i].variance-channel_statistics[i].mean*
+      channel_statistics[i].mean;
+    channel_statistics[CompositePixelChannel].standard_deviation+=
+      channel_statistics[i].variance-channel_statistics[i].mean*
+      channel_statistics[i].mean;
+  }
+  channels=GetImageChannels(image);
+  channel_statistics[CompositePixelChannel].area/=channels;
+  channel_statistics[CompositePixelChannel].sum/=channels;
+  channel_statistics[CompositePixelChannel].sum_squared/=channels;
+  channel_statistics[CompositePixelChannel].sum_cubed/=channels;
+  channel_statistics[CompositePixelChannel].sum_fourth_power/=channels;
+  channel_statistics[CompositePixelChannel].mean/=channels;
+  channel_statistics[CompositePixelChannel].variance/=channels;
+  channel_statistics[CompositePixelChannel].standard_deviation=
+    sqrt(channel_statistics[CompositePixelChannel].standard_deviation/channels);
+  channel_statistics[CompositePixelChannel].kurtosis/=channels;
+  channel_statistics[CompositePixelChannel].skewness/=channels;
+  for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
+  {
+    double
+      standard_deviation;
+
+    if (channel_statistics[i].standard_deviation == 0.0)
+      continue;
+    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;
+  }
+  if (y < (ssize_t) image->rows)
+    channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
+      channel_statistics);
+  return(channel_statistics);
+}
+\f
+/*
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%     P o l y n o m i a l I m a g e                                           %
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%  PolynomialImage() returns a new image where each pixel is the sum of the
+%  pixels in the image sequence after applying its corresponding terms
+%  (coefficient and degree pairs).
+%
+%  The format of the PolynomialImage method is:
+%
+%      Image *PolynomialImage(const Image *images,const size_t number_terms,
+%        const double *terms,ExceptionInfo *exception)
+%
+%  A description of each parameter follows:
+%
+%    o images: the image sequence.
+%
+%    o number_terms: the number of terms in the list.  The actual list length
+%      is 2 x number_terms + 1 (the constant).
+%
+%    o terms: the list of polynomial coefficients and degree pairs and a
+%      constant.
+%
+%    o exception: return any errors or warnings in this structure.
+%
+*/
+
+MagickExport Image *PolynomialImage(const Image *images,
+  const size_t number_terms,const double *terms,ExceptionInfo *exception)
+{
+#define PolynomialImageTag  "Polynomial/Image"
+
+  CacheView
+    *polynomial_view;
+
+  Image
+    *image;
+
+  MagickBooleanType
+    status;
+
+  MagickOffsetType
+    progress;
+
+  PixelChannels
+    **restrict polynomial_pixels;
+
+  size_t
+    number_images;
+
+  ssize_t
+    y;
+
+  assert(images != (Image *) NULL);
+  assert(images->signature == MagickSignature);
+  if (images->debug != MagickFalse)
+    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
+  assert(exception != (ExceptionInfo *) NULL);
+  assert(exception->signature == MagickSignature);
+  image=CloneImage(images,images->columns,images->rows,MagickTrue,
+    exception);
+  if (image == (Image *) NULL)
+    return((Image *) NULL);
+  if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
+    {
+      image=DestroyImage(image);
+      return((Image *) NULL);
+    }
+  number_images=GetImageListLength(images);
+  polynomial_pixels=AcquirePixelThreadSet(images,number_images);
+  if (polynomial_pixels == (PixelChannels **) NULL)
+    {
+      image=DestroyImage(image);
+      (void) ThrowMagickException(exception,GetMagickModule(),
+        ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
+      return((Image *) NULL);
+    }
+  /*
+    Polynomial image pixels.
+  */
+  status=MagickTrue;
+  progress=0;
+  polynomial_view=AcquireAuthenticCacheView(image,exception);
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+  #pragma omp parallel for schedule(static,4) shared(progress,status) \
+    magick_threads(image,image,image->rows,1)
+#endif
+  for (y=0; y < (ssize_t) image->rows; y++)
+  {
+    CacheView
+      *image_view;
+
+    const Image
+      *next;
+
+    const int
+      id = GetOpenMPThreadId();
+
+    register ssize_t
+      i,
+      x;
+
+    register PixelChannels
+      *polynomial_pixel;
+
+    register Quantum
+      *restrict q;
+
+    ssize_t
+      j;
+
+    if (status == MagickFalse)
+      continue;
+    q=QueueCacheViewAuthenticPixels(polynomial_view,0,y,image->columns,1,
+      exception);
+    if (q == (Quantum *) NULL)
+      {
+        status=MagickFalse;
+        continue;
+      }
+    polynomial_pixel=polynomial_pixels[id];
+    for (j=0; j < (ssize_t) image->columns; j++)
+      for (i=0; i < MaxPixelChannels; i++)
+        polynomial_pixel[j].channel[i]=0.0;
+    next=images;
+    for (j=0; j < (ssize_t) number_images; j++)
+    {
+      register const Quantum
+        *p;
+
+      if (j >= (ssize_t) number_terms)
+        continue;
+      image_view=AcquireVirtualCacheView(next,exception);
+      p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
+      if (p == (const Quantum *) NULL)
+        {
+          image_view=DestroyCacheView(image_view);
+          break;
+        }
+      for (x=0; x < (ssize_t) image->columns; x++)
+      {
+        register ssize_t
+          i;
+
+        if (GetPixelReadMask(next,p) == 0)
+          {
+            p+=GetPixelChannels(next);
+            continue;
+          }
+        for (i=0; i < (ssize_t) GetPixelChannels(next); i++)
+        {
+          MagickRealType
+            coefficient,
+            degree;
+
+          PixelChannel channel=GetPixelChannelChannel(image,i);
+          PixelTrait traits=GetPixelChannelTraits(next,channel);
+          PixelTrait polynomial_traits=GetPixelChannelTraits(image,channel);
+          if ((traits == UndefinedPixelTrait) ||
+              (polynomial_traits == UndefinedPixelTrait))
+            continue;
+          if ((traits & UpdatePixelTrait) == 0)
+            continue;
+          coefficient=(MagickRealType) terms[2*i];
+          degree=(MagickRealType) terms[(i << 1)+1];
+          polynomial_pixel[x].channel[i]+=coefficient*
+            pow(QuantumScale*GetPixelChannel(image,channel,p),degree);
+        }
+        p+=GetPixelChannels(next);
+      }
+      image_view=DestroyCacheView(image_view);
+      next=GetNextImageInList(next);
+    }
+    for (x=0; x < (ssize_t) image->columns; x++)
+    {
+      register ssize_t
+        i;
+
+      if (GetPixelReadMask(image,q) == 0)
+        {
+          q+=GetPixelChannels(image);
+          continue;
+        }
+      for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
+      {
+        PixelChannel channel=GetPixelChannelChannel(image,i);
+        PixelTrait traits=GetPixelChannelTraits(image,channel);
+        if (traits == UndefinedPixelTrait)
+          continue;
+        if ((traits & UpdatePixelTrait) == 0)
+          continue;
+        q[i]=ClampToQuantum(QuantumRange*polynomial_pixel[x].channel[i]);
+      }
+      q+=GetPixelChannels(image);
+    }
+    if (SyncCacheViewAuthenticPixels(polynomial_view,exception) == MagickFalse)
+      status=MagickFalse;
+    if (images->progress_monitor != (MagickProgressMonitor) NULL)
+      {
+        MagickBooleanType
+          proceed;
+
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+        #pragma omp critical (MagickCore_PolynomialImages)
+#endif
+        proceed=SetImageProgress(images,PolynomialImageTag,progress++,
+          image->rows);
+        if (proceed == MagickFalse)
+          status=MagickFalse;
+      }
+  }
+  polynomial_view=DestroyCacheView(polynomial_view);
+  polynomial_pixels=DestroyPixelThreadSet(polynomial_pixels);
+  if (status == MagickFalse)
+    image=DestroyImage(image);
+  return(image);
+}
+\f
+/*
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%     S t a t i s t i c I m a g e                                             %
+%                                                                             %
+%                                                                             %
+%                                                                             %
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%
+%  StatisticImage() makes each pixel the min / max / median / mode / etc. of
+%  the neighborhood of the specified width and height.
+%
+%  The format of the StatisticImage method is:
+%
+%      Image *StatisticImage(const Image *image,const StatisticType type,
+%        const size_t width,const size_t height,ExceptionInfo *exception)
+%
+%  A description of each parameter follows:
+%
+%    o image: the image.
+%
+%    o type: the statistic type (median, mode, etc.).
+%
+%    o width: the width of the pixel neighborhood.
+%
+%    o height: the height of the pixel neighborhood.
+%
+%    o exception: return any errors or warnings in this structure.
+%
+*/
+
+typedef struct _SkipNode
+{
+  size_t
+    next[9],
+    count,
+    signature;
+} SkipNode;
+
+typedef struct _SkipList
+{
+  ssize_t
+    level;
+
+  SkipNode
+    *nodes;
+} SkipList;
+
+typedef struct _PixelList
+{
+  size_t
+    length,
+    seed;
+
+  SkipList
+    skip_list;
+
+  size_t
+    signature;
+} PixelList;
+
+static PixelList *DestroyPixelList(PixelList *pixel_list)
+{
+  if (pixel_list == (PixelList *) NULL)
+    return((PixelList *) NULL);
+  if (pixel_list->skip_list.nodes != (SkipNode *) NULL)
+    pixel_list->skip_list.nodes=(SkipNode *) RelinquishMagickMemory(
+      pixel_list->skip_list.nodes);
+  pixel_list=(PixelList *) RelinquishMagickMemory(pixel_list);
+  return(pixel_list);
+}
+
+static PixelList **DestroyPixelListThreadSet(PixelList **pixel_list)
+{
+  register ssize_t
+    i;
+
+  assert(pixel_list != (PixelList **) NULL);
+  for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
+    if (pixel_list[i] != (PixelList *) NULL)
+      pixel_list[i]=DestroyPixelList(pixel_list[i]);
+  pixel_list=(PixelList **) RelinquishMagickMemory(pixel_list);
+  return(pixel_list);
+}
+
+static PixelList *AcquirePixelList(const size_t width,const size_t height)
+{
+  PixelList
+    *pixel_list;
+
+  pixel_list=(PixelList *) AcquireMagickMemory(sizeof(*pixel_list));
+  if (pixel_list == (PixelList *) NULL)
+    return(pixel_list);
+  (void) ResetMagickMemory((void *) pixel_list,0,sizeof(*pixel_list));
+  pixel_list->length=width*height;
+  pixel_list->skip_list.nodes=(SkipNode *) AcquireQuantumMemory(65537UL,
+    sizeof(*pixel_list->skip_list.nodes));
+  if (pixel_list->skip_list.nodes == (SkipNode *) NULL)
+    return(DestroyPixelList(pixel_list));
+  (void) ResetMagickMemory(pixel_list->skip_list.nodes,0,65537UL*
+    sizeof(*pixel_list->skip_list.nodes));
+  pixel_list->signature=MagickSignature;
+  return(pixel_list);
+}
+
+static PixelList **AcquirePixelListThreadSet(const size_t width,
+  const size_t height)
+{
+  PixelList
+    **pixel_list;
+
+  register ssize_t
+    i;
+
+  size_t
+    number_threads;
+
+  number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
+  pixel_list=(PixelList **) AcquireQuantumMemory(number_threads,
+    sizeof(*pixel_list));
+  if (pixel_list == (PixelList **) NULL)
+    return((PixelList **) NULL);
+  (void) ResetMagickMemory(pixel_list,0,number_threads*sizeof(*pixel_list));
+  for (i=0; i < (ssize_t) number_threads; i++)
+  {
+    pixel_list[i]=AcquirePixelList(width,height);
+    if (pixel_list[i] == (PixelList *) NULL)
+      return(DestroyPixelListThreadSet(pixel_list));
+  }
+  return(pixel_list);
+}
+
+static void AddNodePixelList(PixelList *pixel_list,const size_t color)
+{
+  register SkipList
+    *p;
+
+  register ssize_t
+    level;
+
+  size_t
+    search,
+    update[9];
+
+  /*
+    Initialize the node.
+  */
+  p=(&pixel_list->skip_list);
+  p->nodes[color].signature=pixel_list->signature;
+  p->nodes[color].count=1;
+  /*
+    Determine where it belongs in the list.
+  */
+  search=65536UL;
+  for (level=p->level; level >= 0; level--)
+  {
+    while (p->nodes[search].next[level] < color)
+      search=p->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 > (p->level+2))
+    level=p->level+2;
+  /*
+    If we're raising the list's level, link back to the root node.
+  */
+  while (level > p->level)
+  {
+    p->level++;
+    update[p->level]=65536UL;
+  }
+  /*
+    Link the node into the skip-list.
+  */
+  do
+  {
+    p->nodes[color].next[level]=p->nodes[update[level]].next[level];
+    p->nodes[update[level]].next[level]=color;
+  } while (level-- > 0);
+}
+
+static inline void GetMaximumPixelList(PixelList *pixel_list,Quantum *pixel)
+{
+  register SkipList
+    *p;
+
+  size_t
+    color,
+    maximum;
+
+  ssize_t
+    count;
+
+  /*
+    Find the maximum value for each of the color.
+  */
+  p=(&pixel_list->skip_list);
+  color=65536L;
+  count=0;
+  maximum=p->nodes[color].next[0];
+  do
+  {
+    color=p->nodes[color].next[0];
+    if (color > maximum)
+      maximum=color;
+    count+=p->nodes[color].count;
+  } while (count < (ssize_t) pixel_list->length);
+  *pixel=ScaleShortToQuantum((unsigned short) maximum);
+}
+
+static inline void GetMeanPixelList(PixelList *pixel_list,Quantum *pixel)
+{
+  double
+    sum;
+
+  register SkipList
+    *p;
+
+  size_t
+    color;
+
+  ssize_t
+    count;
+
+  /*
+    Find the mean value for each of the color.
+  */
+  p=(&pixel_list->skip_list);
+  color=65536L;
+  count=0;
+  sum=0.0;
+  do
+  {
+    color=p->nodes[color].next[0];
+    sum+=(double) p->nodes[color].count*color;
+    count+=p->nodes[color].count;
+  } while (count < (ssize_t) pixel_list->length);
+  sum/=pixel_list->length;
+  *pixel=ScaleShortToQuantum((unsigned short) sum);
+}
+
+static inline void GetMedianPixelList(PixelList *pixel_list,Quantum *pixel)
+{
+  register SkipList
+    *p;
+
+  size_t
+    color;
+
+  ssize_t
+    count;
+
+  /*
+    Find the median value for each of the color.
+  */
+  p=(&pixel_list->skip_list);
+  color=65536L;
+  count=0;
+  do
+  {
+    color=p->nodes[color].next[0];
+    count+=p->nodes[color].count;
+  } while (count <= (ssize_t) (pixel_list->length >> 1));
+  *pixel=ScaleShortToQuantum((unsigned short) color);
+}
+
+static inline void GetMinimumPixelList(PixelList *pixel_list,Quantum *pixel)
+{
+  register SkipList
+    *p;
+
+  size_t
+    color,
+    minimum;
+
+  ssize_t
+    count;
+
+  /*
+    Find the minimum value for each of the color.
+  */
+  p=(&pixel_list->skip_list);
+  count=0;
+  color=65536UL;
+  minimum=p->nodes[color].next[0];
+  do
+  {
+    color=p->nodes[color].next[0];
+    if (color < minimum)
+      minimum=color;
+    count+=p->nodes[color].count;
+  } while (count < (ssize_t) pixel_list->length);
+  *pixel=ScaleShortToQuantum((unsigned short) minimum);
+}
+
+static inline void GetModePixelList(PixelList *pixel_list,Quantum *pixel)
+{
+  register SkipList
+    *p;
+
+  size_t
+    color,
+    max_count,
+    mode;
+
+  ssize_t
+    count;
+
+  /*
+    Make each pixel the 'predominant color' of the specified neighborhood.
+  */
+  p=(&pixel_list->skip_list);
+  color=65536L;
+  mode=color;
+  max_count=p->nodes[mode].count;
+  count=0;
+  do
+  {
+    color=p->nodes[color].next[0];
+    if (p->nodes[color].count > max_count)
+      {
+        mode=color;
+        max_count=p->nodes[mode].count;
+      }
+    count+=p->nodes[color].count;
+  } while (count < (ssize_t) pixel_list->length);
+  *pixel=ScaleShortToQuantum((unsigned short) mode);
+}
+
+static inline void GetNonpeakPixelList(PixelList *pixel_list,Quantum *pixel)
+{
+  register SkipList
+    *p;
+
+  size_t
+    color,
+    next,
+    previous;
+
+  ssize_t
+    count;
+
+  /*
+    Finds the non peak value for each of the colors.
+  */
+  p=(&pixel_list->skip_list);
+  color=65536L;
+  next=p->nodes[color].next[0];
+  count=0;
+  do
+  {
+    previous=color;
+    color=next;
+    next=p->nodes[color].next[0];
+    count+=p->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;
+  *pixel=ScaleShortToQuantum((unsigned short) color);
+}
+
+static inline void GetStandardDeviationPixelList(PixelList *pixel_list,
+  Quantum *pixel)
+{
+  double
+    sum,
+    sum_squared;
+
+  register SkipList
+    *p;
+
+  size_t
+    color;
+
+  ssize_t
+    count;
+
+  /*
+    Find the standard-deviation value for each of the color.
+  */
+  p=(&pixel_list->skip_list);
+  color=65536L;
+  count=0;
+  sum=0.0;
+  sum_squared=0.0;
+  do
+  {
+    register ssize_t
+      i;
+
+    color=p->nodes[color].next[0];
+    sum+=(double) p->nodes[color].count*color;
+    for (i=0; i < (ssize_t) p->nodes[color].count; i++)
+      sum_squared+=((double) color)*((double) color);
+    count+=p->nodes[color].count;
+  } while (count < (ssize_t) pixel_list->length);
+  sum/=pixel_list->length;
+  sum_squared/=pixel_list->length;
+  *pixel=ScaleShortToQuantum((unsigned short) sqrt(sum_squared-(sum*sum)));
+}
+
+static inline void InsertPixelList(const Quantum pixel,PixelList *pixel_list)
+{
+  size_t
+    signature;
+
+  unsigned short
+    index;
+
+  index=ScaleQuantumToShort(pixel);
+  signature=pixel_list->skip_list.nodes[index].signature;
+  if (signature == pixel_list->signature)
+    {
+      pixel_list->skip_list.nodes[index].count++;
+      return;
+    }
+  AddNodePixelList(pixel_list,index);
+}
+
+static inline double MagickAbsoluteValue(const double x)
+{
+  if (x < 0)
+    return(-x);
+  return(x);
+}
+
+static inline size_t MagickMax(const size_t x,const size_t y)
+{
+  if (x > y)
+    return(x);
+  return(y);
+}
+
+static void ResetPixelList(PixelList *pixel_list)
+{
+  int
+    level;
+
+  register SkipNode
+    *root;
+
+  register SkipList
+    *p;
+
+  /*
+    Reset the skip-list.
+  */
+  p=(&pixel_list->skip_list);
+  root=p->nodes+65536UL;
+  p->level=0;
+  for (level=0; level < 9; level++)
+    root->next[level]=65536UL;
+  pixel_list->seed=pixel_list->signature++;
+}
+
+MagickExport Image *StatisticImage(const Image *image,const StatisticType type,
+  const size_t width,const size_t height,ExceptionInfo *exception)
+{
+#define StatisticImageTag  "Statistic/Image"
+
+  CacheView
+    *image_view,
+    *statistic_view;
+
+  Image
+    *statistic_image;
+
+  MagickBooleanType
+    status;
+
+  MagickOffsetType
+    progress;
+
+  PixelList
+    **restrict pixel_list;
+
+  ssize_t
+    center,
+    y;
+
+  /*
+    Initialize statistics image attributes.
+  */
+  assert(image != (Image *) NULL);
+  assert(image->signature == MagickSignature);
+  if (image->debug != MagickFalse)
+    (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
+  assert(exception != (ExceptionInfo *) NULL);
+  assert(exception->signature == MagickSignature);
+  statistic_image=CloneImage(image,image->columns,image->rows,MagickTrue,
+    exception);
+  if (statistic_image == (Image *) NULL)
+    return((Image *) NULL);
+  status=SetImageStorageClass(statistic_image,DirectClass,exception);
+  if (status == MagickFalse)
+    {
+      statistic_image=DestroyImage(statistic_image);
+      return((Image *) NULL);
+    }
+  pixel_list=AcquirePixelListThreadSet(MagickMax(width,1),MagickMax(height,1));
+  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.
+  */
+  center=(ssize_t) GetPixelChannels(image)*(image->columns+MagickMax(width,1))*
+    (MagickMax(height,1)/2L)+GetPixelChannels(image)*(MagickMax(width,1)/2L);
+  status=MagickTrue;
+  progress=0;
+  image_view=AcquireVirtualCacheView(image,exception);
+  statistic_view=AcquireAuthenticCacheView(statistic_image,exception);
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+  #pragma omp parallel for schedule(static,4) shared(progress,status) \
+    magick_threads(image,statistic_image,statistic_image->rows,1)
+#endif
+  for (y=0; y < (ssize_t) statistic_image->rows; y++)
+  {
+    const int
+      id = GetOpenMPThreadId();
+
+    register const Quantum
+      *restrict p;
+
+    register Quantum
+      *restrict q;
+
+    register ssize_t
+      x;
+
+    if (status == MagickFalse)
+      continue;
+    p=GetCacheViewVirtualPixels(image_view,-((ssize_t) MagickMax(width,1)/2L),y-
+      (ssize_t) (MagickMax(height,1)/2L),image->columns+MagickMax(width,1),
+      MagickMax(height,1),exception);
+    q=QueueCacheViewAuthenticPixels(statistic_view,0,y,statistic_image->columns,      1,exception);
+    if ((p == (const Quantum *) NULL) || (q == (Quantum *) NULL))
+      {
+        status=MagickFalse;
+        continue;
+      }
+    for (x=0; x < (ssize_t) statistic_image->columns; x++)
+    {
+      register ssize_t
+        i;
+
+      for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
+      {
+        Quantum
+          pixel;
+
+        register const Quantum
+          *restrict pixels;
+
+        register ssize_t
+          u;
+
+        ssize_t
+          v;
+
+        PixelChannel channel=GetPixelChannelChannel(image,i);
+        PixelTrait traits=GetPixelChannelTraits(image,channel);
+        PixelTrait statistic_traits=GetPixelChannelTraits(statistic_image,
+          channel);
+        if ((traits == UndefinedPixelTrait) ||
+            (statistic_traits == UndefinedPixelTrait))
+          continue;
+        if (((statistic_traits & CopyPixelTrait) != 0) ||
+            (GetPixelReadMask(image,p) == 0))
+          {
+            SetPixelChannel(statistic_image,channel,p[center+i],q);
+            continue;
+          }
+        pixels=p;
+        ResetPixelList(pixel_list[id]);
+        for (v=0; v < (ssize_t) MagickMax(height,1); v++)
+        {
+          for (u=0; u < (ssize_t) MagickMax(width,1); u++)
+          {
+            InsertPixelList(pixels[i],pixel_list[id]);
+            pixels+=GetPixelChannels(image);
+          }
+          pixels+=(image->columns-1)*GetPixelChannels(image);
+        }
+        switch (type)
+        {
+          case GradientStatistic:
+          {
+            double
+              maximum,
+              minimum;
+
+            GetMinimumPixelList(pixel_list[id],&pixel);
+            minimum=(double) pixel;
+            GetMaximumPixelList(pixel_list[id],&pixel);
+            maximum=(double) pixel;
+            pixel=ClampToQuantum(MagickAbsoluteValue(maximum-minimum));
+            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 StandardDeviationStatistic:
+          {
+            GetStandardDeviationPixelList(pixel_list[id],&pixel);
+            break;
+          }
+        }
+        SetPixelChannel(statistic_image,channel,pixel,q);
+      }
+      p+=GetPixelChannels(image);
+      q+=GetPixelChannels(statistic_image);
+    }
+    if (SyncCacheViewAuthenticPixels(statistic_view,exception) == MagickFalse)
+      status=MagickFalse;
+    if (image->progress_monitor != (MagickProgressMonitor) NULL)
+      {
+        MagickBooleanType
+          proceed;
+
+#if defined(MAGICKCORE_OPENMP_SUPPORT)
+        #pragma omp critical (MagickCore_StatisticImage)
+#endif
+        proceed=SetImageProgress(image,StatisticImageTag,progress++,
+          image->rows);
+        if (proceed == MagickFalse)
+          status=MagickFalse;
+      }
+  }
+  statistic_view=DestroyCacheView(statistic_view);
+  image_view=DestroyCacheView(image_view);
+  pixel_list=DestroyPixelListThreadSet(pixel_list);
+  if (status == MagickFalse)
+    statistic_image=DestroyImage(statistic_image);
+  return(statistic_image);
 }