granicus.if.org Git - imagemagick/blob - MagickCore/statistic.c

   1 /*
   2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   3 %                                                                             %
   4 %                                                                             %
   5 %                                                                             %
   6 %        SSSSS  TTTTT   AAA   TTTTT  IIIII  SSSSS  TTTTT  IIIII   CCCC        %
   7 %        SS       T    A   A    T      I    SS       T      I    C            %
   8 %         SSS     T    AAAAA    T      I     SSS     T      I    C            %
   9 %           SS    T    A   A    T      I       SS    T      I    C            %
  10 %        SSSSS    T    A   A    T    IIIII  SSSSS    T    IIIII   CCCC        %
  11 %                                                                             %
  12 %                                                                             %
  13 %                     MagickCore Image Statistical Methods                    %
  14 %                                                                             %
  15 %                              Software Design                                %
  16 %                                   Cristy                                    %
  17 %                                 July 1992                                   %
  18 %                                                                             %
  19 %                                                                             %
  20 %  Copyright 1999-2014 ImageMagick Studio LLC, a non-profit organization      %
  21 %  dedicated to making software imaging solutions freely available.           %
  22 %                                                                             %
  23 %  You may not use this file except in compliance with the License.  You may  %
  24 %  obtain a copy of the License at                                            %
  25 %                                                                             %
  26 %    http://www.imagemagick.org/script/license.php                            %
  27 %                                                                             %
  28 %  Unless required by applicable law or agreed to in writing, software        %
  29 %  distributed under the License is distributed on an "AS IS" BASIS,          %
  30 %  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   %
  31 %  See the License for the specific language governing permissions and        %
  32 %  limitations under the License.                                             %
  33 %                                                                             %
  34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  35 %
  36 %
  37 %
  38 */
  39 \f
  40 /*
  41   Include declarations.
  42 */
  43 #include "MagickCore/studio.h"
  44 #include "MagickCore/property.h"
  45 #include "MagickCore/animate.h"
  46 #include "MagickCore/blob.h"
  47 #include "MagickCore/blob-private.h"
  48 #include "MagickCore/cache.h"
  49 #include "MagickCore/cache-private.h"
  50 #include "MagickCore/cache-view.h"
  51 #include "MagickCore/client.h"
  52 #include "MagickCore/color.h"
  53 #include "MagickCore/color-private.h"
  54 #include "MagickCore/colorspace.h"
  55 #include "MagickCore/colorspace-private.h"
  56 #include "MagickCore/composite.h"
  57 #include "MagickCore/composite-private.h"
  58 #include "MagickCore/compress.h"
  59 #include "MagickCore/constitute.h"
  60 #include "MagickCore/display.h"
  61 #include "MagickCore/draw.h"
  62 #include "MagickCore/enhance.h"
  63 #include "MagickCore/exception.h"
  64 #include "MagickCore/exception-private.h"
  65 #include "MagickCore/gem.h"
  66 #include "MagickCore/gem-private.h"
  67 #include "MagickCore/geometry.h"
  68 #include "MagickCore/list.h"
  69 #include "MagickCore/image-private.h"
  70 #include "MagickCore/magic.h"
  71 #include "MagickCore/magick.h"
  72 #include "MagickCore/memory_.h"
  73 #include "MagickCore/module.h"
  74 #include "MagickCore/monitor.h"
  75 #include "MagickCore/monitor-private.h"
  76 #include "MagickCore/option.h"
  77 #include "MagickCore/paint.h"
  78 #include "MagickCore/pixel-accessor.h"
  79 #include "MagickCore/profile.h"
  80 #include "MagickCore/quantize.h"
  81 #include "MagickCore/quantum-private.h"
  82 #include "MagickCore/random_.h"
  83 #include "MagickCore/random-private.h"
  84 #include "MagickCore/resource_.h"
  85 #include "MagickCore/segment.h"
  86 #include "MagickCore/semaphore.h"
  87 #include "MagickCore/signature-private.h"
  88 #include "MagickCore/statistic.h"
  89 #include "MagickCore/string_.h"
  90 #include "MagickCore/thread-private.h"
  91 #include "MagickCore/timer.h"
  92 #include "MagickCore/utility.h"
  93 #include "MagickCore/version.h"
  94 \f
  95 /*
  96 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  97 %                                                                             %
  98 %                                                                             %
  99 %                                                                             %
 100 %     E v a l u a t e I m a g e                                               %
 101 %                                                                             %
 102 %                                                                             %
 103 %                                                                             %
 104 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 105 %
 106 %  EvaluateImage() applies a value to the image with an arithmetic, relational,
 107 %  or logical operator to an image. Use these operations to lighten or darken
 108 %  an image, to increase or decrease contrast in an image, or to produce the
 109 %  "negative" of an image.
 110 %
 111 %  The format of the EvaluateImage method is:
 112 %
 113 %      MagickBooleanType EvaluateImage(Image *image,
 114 %        const MagickEvaluateOperator op,const double value,
 115 %        ExceptionInfo *exception)
 116 %      MagickBooleanType EvaluateImages(Image *images,
 117 %        const MagickEvaluateOperator op,const double value,
 118 %        ExceptionInfo *exception)
 119 %
 120 %  A description of each parameter follows:
 121 %
 122 %    o image: the image.
 123 %
 124 %    o op: A channel op.
 125 %
 126 %    o value: A value value.
 127 %
 128 %    o exception: return any errors or warnings in this structure.
 129 %
 130 */
 131
 132 typedef struct _PixelChannels
 133 {
 134   double
 135     channel[CompositePixelChannel];
 136 } PixelChannels;
 137
 138 static PixelChannels **DestroyPixelThreadSet(PixelChannels **pixels)
 139 {
 140   register ssize_t
 141     i;
 142
 143   assert(pixels != (PixelChannels **) NULL);
 144   for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
 145     if (pixels[i] != (PixelChannels *) NULL)
 146       pixels[i]=(PixelChannels *) RelinquishMagickMemory(pixels[i]);
 147   pixels=(PixelChannels **) RelinquishMagickMemory(pixels);
 148   return(pixels);
 149 }
 150
 151 static PixelChannels **AcquirePixelThreadSet(const Image *image,
 152   const size_t number_images)
 153 {
 154   register ssize_t
 155     i;
 156
 157   PixelChannels
 158     **pixels;
 159
 160   size_t
 161     length,
 162     number_threads;
 163
 164   number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
 165   pixels=(PixelChannels **) AcquireQuantumMemory(number_threads,
 166     sizeof(*pixels));
 167   if (pixels == (PixelChannels **) NULL)
 168     return((PixelChannels **) NULL);
 169   (void) ResetMagickMemory(pixels,0,number_threads*sizeof(*pixels));
 170   for (i=0; i < (ssize_t) number_threads; i++)
 171   {
 172     register ssize_t
 173       j;
 174
 175     length=image->columns;
 176     if (length < number_images)
 177       length=number_images;
 178     pixels[i]=(PixelChannels *) AcquireQuantumMemory(length,sizeof(**pixels));
 179     if (pixels[i] == (PixelChannels *) NULL)
 180       return(DestroyPixelThreadSet(pixels));
 181     for (j=0; j < (ssize_t) length; j++)
 182     {
 183       register ssize_t
 184         k;
 185
 186       for (k=0; k < MaxPixelChannels; k++)
 187         pixels[i][j].channel[k]=0.0;
 188     }
 189   }
 190   return(pixels);
 191 }
 192
 193 static inline double EvaluateMax(const double x,const double y)
 194 {
 195   if (x > y)
 196     return(x);
 197   return(y);
 198 }
 199
 200 #if defined(__cplusplus) || defined(c_plusplus)
 201 extern "C" {
 202 #endif
 203
 204 static int IntensityCompare(const void *x,const void *y)
 205 {
 206   const PixelChannels
 207     *color_1,
 208     *color_2;
 209
 210   double
 211     distance;
 212
 213   register ssize_t
 214     i;
 215
 216   color_1=(const PixelChannels *) x;
 217   color_2=(const PixelChannels *) y;
 218   distance=0.0;
 219   for (i=0; i < MaxPixelChannels; i++)
 220     distance+=color_1->channel[i]-(double) color_2->channel[i];
 221   return(distance < 0 ? -1 : distance > 0 ? 1 : 0);
 222 }
 223
 224 #if defined(__cplusplus) || defined(c_plusplus)
 225 }
 226 #endif
 227
 228 static inline double MagickMin(const double x,const double y)
 229 {
 230   if (x < y)
 231     return(x);
 232   return(y);
 233 }
 234
 235 static double ApplyEvaluateOperator(RandomInfo *random_info,const Quantum pixel,
 236   const MagickEvaluateOperator op,const double value)
 237 {
 238   double
 239     result;
 240
 241   result=0.0;
 242   switch (op)
 243   {
 244     case UndefinedEvaluateOperator:
 245       break;
 246     case AbsEvaluateOperator:
 247     {
 248       result=(double) fabs((double) (pixel+value));
 249       break;
 250     }
 251     case AddEvaluateOperator:
 252     {
 253       result=(double) (pixel+value);
 254       break;
 255     }
 256     case AddModulusEvaluateOperator:
 257     {
 258       /*
 259         This returns a 'floored modulus' of the addition which is a positive
 260         result.  It differs from % or fmod() that returns a 'truncated modulus'
 261         result, where floor() is replaced by trunc() and could return a
 262         negative result (which is clipped).
 263       */
 264       result=pixel+value;
 265       result-=(QuantumRange+1.0)*floor((double) result/(QuantumRange+1.0));
 266       break;
 267     }
 268     case AndEvaluateOperator:
 269     {
 270       result=(double) ((size_t) pixel & (size_t) (value+0.5));
 271       break;
 272     }
 273     case CosineEvaluateOperator:
 274     {
 275       result=(double) (QuantumRange*(0.5*cos((double) (2.0*MagickPI*
 276         QuantumScale*pixel*value))+0.5));
 277       break;
 278     }
 279     case DivideEvaluateOperator:
 280     {
 281       result=pixel/(value == 0.0 ? 1.0 : value);
 282       break;
 283     }
 284     case ExponentialEvaluateOperator:
 285     {
 286       result=(double) (QuantumRange*exp((double) (value*QuantumScale*pixel)));
 287       break;
 288     }
 289     case GaussianNoiseEvaluateOperator:
 290     {
 291       result=(double) GenerateDifferentialNoise(random_info,pixel,
 292         GaussianNoise,value);
 293       break;
 294     }
 295     case ImpulseNoiseEvaluateOperator:
 296     {
 297       result=(double) GenerateDifferentialNoise(random_info,pixel,ImpulseNoise,
 298         value);
 299       break;
 300     }
 301     case LaplacianNoiseEvaluateOperator:
 302     {
 303       result=(double) GenerateDifferentialNoise(random_info,pixel,
 304         LaplacianNoise,value);
 305       break;
 306     }
 307     case LeftShiftEvaluateOperator:
 308     {
 309       result=(double) ((size_t) pixel << (size_t) (value+0.5));
 310       break;
 311     }
 312     case LogEvaluateOperator:
 313     {
 314       if ((QuantumScale*pixel) >= MagickEpsilon)
 315         result=(double) (QuantumRange*log((double) (QuantumScale*value*pixel+
 316           1.0))/log((double) (value+1.0)));
 317       break;
 318     }
 319     case MaxEvaluateOperator:
 320     {
 321       result=(double) EvaluateMax((double) pixel,value);
 322       break;
 323     }
 324     case MeanEvaluateOperator:
 325     {
 326       result=(double) (pixel+value);
 327       break;
 328     }
 329     case MedianEvaluateOperator:
 330     {
 331       result=(double) (pixel+value);
 332       break;
 333     }
 334     case MinEvaluateOperator:
 335     {
 336       result=(double) MagickMin((double) pixel,value);
 337       break;
 338     }
 339     case MultiplicativeNoiseEvaluateOperator:
 340     {
 341       result=(double) GenerateDifferentialNoise(random_info,pixel,
 342         MultiplicativeGaussianNoise,value);
 343       break;
 344     }
 345     case MultiplyEvaluateOperator:
 346     {
 347       result=(double) (value*pixel);
 348       break;
 349     }
 350     case OrEvaluateOperator:
 351     {
 352       result=(double) ((size_t) pixel | (size_t) (value+0.5));
 353       break;
 354     }
 355     case PoissonNoiseEvaluateOperator:
 356     {
 357       result=(double) GenerateDifferentialNoise(random_info,pixel,PoissonNoise,
 358         value);
 359       break;
 360     }
 361     case PowEvaluateOperator:
 362     {
 363       result=(double) (QuantumRange*pow((double) (QuantumScale*pixel),(double)
 364         value));
 365       break;
 366     }
 367     case RightShiftEvaluateOperator:
 368     {
 369       result=(double) ((size_t) pixel >> (size_t) (value+0.5));
 370       break;
 371     }
 372     case SetEvaluateOperator:
 373     {
 374       result=value;
 375       break;
 376     }
 377     case SineEvaluateOperator:
 378     {
 379       result=(double) (QuantumRange*(0.5*sin((double) (2.0*MagickPI*
 380         QuantumScale*pixel*value))+0.5));
 381       break;
 382     }
 383     case SubtractEvaluateOperator:
 384     {
 385       result=(double) (pixel-value);
 386       break;
 387     }
 388     case SumEvaluateOperator:
 389     {
 390       result=(double) (pixel+value);
 391       break;
 392     }
 393     case ThresholdEvaluateOperator:
 394     {
 395       result=(double) (((double) pixel <= value) ? 0 : QuantumRange);
 396       break;
 397     }
 398     case ThresholdBlackEvaluateOperator:
 399     {
 400       result=(double) (((double) pixel <= value) ? 0 : pixel);
 401       break;
 402     }
 403     case ThresholdWhiteEvaluateOperator:
 404     {
 405       result=(double) (((double) pixel > value) ? QuantumRange : pixel);
 406       break;
 407     }
 408     case UniformNoiseEvaluateOperator:
 409     {
 410       result=(double) GenerateDifferentialNoise(random_info,pixel,UniformNoise,
 411         value);
 412       break;
 413     }
 414     case XorEvaluateOperator:
 415     {
 416       result=(double) ((size_t) pixel ^ (size_t) (value+0.5));
 417       break;
 418     }
 419   }
 420   return(result);
 421 }
 422
 423 MagickExport Image *EvaluateImages(const Image *images,
 424   const MagickEvaluateOperator op,ExceptionInfo *exception)
 425 {
 426 #define EvaluateImageTag  "Evaluate/Image"
 427
 428   CacheView
 429     *evaluate_view;
 430
 431   Image
 432     *image;
 433
 434   MagickBooleanType
 435     status;
 436
 437   MagickOffsetType
 438     progress;
 439
 440   PixelChannels
 441     **restrict evaluate_pixels;
 442
 443   RandomInfo
 444     **restrict random_info;
 445
 446   size_t
 447     number_images;
 448
 449   ssize_t
 450     y;
 451
 452 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 453   unsigned long
 454     key;
 455 #endif
 456
 457   assert(images != (Image *) NULL);
 458   assert(images->signature == MagickSignature);
 459   if (images->debug != MagickFalse)
 460     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
 461   assert(exception != (ExceptionInfo *) NULL);
 462   assert(exception->signature == MagickSignature);
 463   image=CloneImage(images,images->columns,images->rows,MagickTrue,
 464     exception);
 465   if (image == (Image *) NULL)
 466     return((Image *) NULL);
 467   if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
 468     {
 469       image=DestroyImage(image);
 470       return((Image *) NULL);
 471     }
 472   number_images=GetImageListLength(images);
 473   evaluate_pixels=AcquirePixelThreadSet(images,number_images);
 474   if (evaluate_pixels == (PixelChannels **) NULL)
 475     {
 476       image=DestroyImage(image);
 477       (void) ThrowMagickException(exception,GetMagickModule(),
 478         ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
 479       return((Image *) NULL);
 480     }
 481   /*
 482     Evaluate image pixels.
 483   */
 484   status=MagickTrue;
 485   progress=0;
 486   random_info=AcquireRandomInfoThreadSet();
 487 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 488   key=GetRandomSecretKey(random_info[0]);
 489 #endif
 490   evaluate_view=AcquireAuthenticCacheView(image,exception);
 491   if (op == MedianEvaluateOperator)
 492     {
 493 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 494       #pragma omp parallel for schedule(static,4) shared(progress,status) \
 495         magick_threads(image,images,image->rows,key == ~0UL)
 496 #endif
 497       for (y=0; y < (ssize_t) image->rows; y++)
 498       {
 499         CacheView
 500           *image_view;
 501
 502         const Image
 503           *next;
 504
 505         const int
 506           id = GetOpenMPThreadId();
 507
 508         register PixelChannels
 509           *evaluate_pixel;
 510
 511         register Quantum
 512           *restrict q;
 513
 514         register ssize_t
 515           x;
 516
 517         if (status == MagickFalse)
 518           continue;
 519         q=QueueCacheViewAuthenticPixels(evaluate_view,0,y,image->columns,1,
 520           exception);
 521         if (q == (Quantum *) NULL)
 522           {
 523             status=MagickFalse;
 524             continue;
 525           }
 526         evaluate_pixel=evaluate_pixels[id];
 527         for (x=0; x < (ssize_t) image->columns; x++)
 528         {
 529           register ssize_t
 530             j,
 531             k;
 532
 533           for (j=0; j < (ssize_t) number_images; j++)
 534             for (k=0; k < MaxPixelChannels; k++)
 535               evaluate_pixel[j].channel[k]=0.0;
 536           next=images;
 537           for (j=0; j < (ssize_t) number_images; j++)
 538           {
 539             register const Quantum
 540               *p;
 541
 542             register ssize_t
 543               i;
 544
 545             image_view=AcquireVirtualCacheView(next,exception);
 546             p=GetCacheViewVirtualPixels(image_view,x,y,1,1,exception);
 547             if (p == (const Quantum *) NULL)
 548               {
 549                 image_view=DestroyCacheView(image_view);
 550                 break;
 551               }
 552             for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
 553             {
 554               PixelChannel channel=GetPixelChannelChannel(image,i);
 555               PixelTrait evaluate_traits=GetPixelChannelTraits(image,channel);
 556               PixelTrait traits=GetPixelChannelTraits(next,channel);
 557               if ((traits == UndefinedPixelTrait) ||
 558                   (evaluate_traits == UndefinedPixelTrait))
 559                 continue;
 560               if ((evaluate_traits & UpdatePixelTrait) == 0)
 561                 continue;
 562               evaluate_pixel[j].channel[i]=ApplyEvaluateOperator(
 563                 random_info[id],GetPixelChannel(image,channel,p),op,
 564                 evaluate_pixel[j].channel[i]);
 565             }
 566             image_view=DestroyCacheView(image_view);
 567             next=GetNextImageInList(next);
 568           }
 569           qsort((void *) evaluate_pixel,number_images,sizeof(*evaluate_pixel),
 570             IntensityCompare);
 571           for (k=0; k < (ssize_t) GetPixelChannels(image); k++)
 572             q[k]=ClampToQuantum(evaluate_pixel[j/2].channel[k]);
 573           q+=GetPixelChannels(image);
 574         }
 575         if (SyncCacheViewAuthenticPixels(evaluate_view,exception) == MagickFalse)
 576           status=MagickFalse;
 577         if (images->progress_monitor != (MagickProgressMonitor) NULL)
 578           {
 579             MagickBooleanType
 580               proceed;
 581
 582 #if   defined(MAGICKCORE_OPENMP_SUPPORT)
 583             #pragma omp critical (MagickCore_EvaluateImages)
 584 #endif
 585             proceed=SetImageProgress(images,EvaluateImageTag,progress++,
 586               image->rows);
 587             if (proceed == MagickFalse)
 588               status=MagickFalse;
 589           }
 590       }
 591     }
 592   else
 593     {
 594 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 595       #pragma omp parallel for schedule(static,4) shared(progress,status) \
 596         magick_threads(image,images,image->rows,key == ~0UL)
 597 #endif
 598       for (y=0; y < (ssize_t) image->rows; y++)
 599       {
 600         CacheView
 601           *image_view;
 602
 603         const Image
 604           *next;
 605
 606         const int
 607           id = GetOpenMPThreadId();
 608
 609         register ssize_t
 610           i,
 611           x;
 612
 613         register PixelChannels
 614           *evaluate_pixel;
 615
 616         register Quantum
 617           *restrict q;
 618
 619         ssize_t
 620           j;
 621
 622         if (status == MagickFalse)
 623           continue;
 624         q=QueueCacheViewAuthenticPixels(evaluate_view,0,y,image->columns,1,
 625           exception);
 626         if (q == (Quantum *) NULL)
 627           {
 628             status=MagickFalse;
 629             continue;
 630           }
 631         evaluate_pixel=evaluate_pixels[id];
 632         for (j=0; j < (ssize_t) image->columns; j++)
 633           for (i=0; i < MaxPixelChannels; i++)
 634             evaluate_pixel[j].channel[i]=0.0;
 635         next=images;
 636         for (j=0; j < (ssize_t) number_images; j++)
 637         {
 638           register const Quantum
 639             *p;
 640
 641           image_view=AcquireVirtualCacheView(next,exception);
 642           p=GetCacheViewVirtualPixels(image_view,0,y,next->columns,1,exception);
 643           if (p == (const Quantum *) NULL)
 644             {
 645               image_view=DestroyCacheView(image_view);
 646               break;
 647             }
 648           for (x=0; x < (ssize_t) next->columns; x++)
 649           {
 650             register ssize_t
 651               i;
 652
 653             if (GetPixelReadMask(next,p) == 0)
 654               {
 655                 p+=GetPixelChannels(next);
 656                 continue;
 657               }
 658             for (i=0; i < (ssize_t) GetPixelChannels(next); i++)
 659             {
 660               PixelChannel channel=GetPixelChannelChannel(image,i);
 661               PixelTrait  traits=GetPixelChannelTraits(next,channel);
 662               PixelTrait  evaluate_traits=GetPixelChannelTraits(image,channel);
 663               if ((traits == UndefinedPixelTrait) ||
 664                   (evaluate_traits == UndefinedPixelTrait))
 665                 continue;
 666               if ((traits & UpdatePixelTrait) == 0)
 667                 continue;
 668               evaluate_pixel[x].channel[i]=ApplyEvaluateOperator(
 669                 random_info[id],GetPixelChannel(image,channel,p),j == 0 ?
 670                 AddEvaluateOperator : op,evaluate_pixel[x].channel[i]);
 671             }
 672             p+=GetPixelChannels(next);
 673           }
 674           image_view=DestroyCacheView(image_view);
 675           next=GetNextImageInList(next);
 676         }
 677         for (x=0; x < (ssize_t) image->columns; x++)
 678         {
 679           register ssize_t
 680              i;
 681
 682           switch (op)
 683           {
 684             case MeanEvaluateOperator:
 685             {
 686               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
 687                 evaluate_pixel[x].channel[i]/=(double) number_images;
 688               break;
 689             }
 690             case MultiplyEvaluateOperator:
 691             {
 692               for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
 693               {
 694                 register ssize_t
 695                   j;
 696
 697                 for (j=0; j < (ssize_t) (number_images-1); j++)
 698                   evaluate_pixel[x].channel[i]*=QuantumScale;
 699               }
 700               break;
 701             }
 702             default:
 703               break;
 704           }
 705         }
 706         for (x=0; x < (ssize_t) image->columns; x++)
 707         {
 708           register ssize_t
 709             i;
 710
 711           if (GetPixelReadMask(image,q) == 0)
 712             {
 713               q+=GetPixelChannels(image);
 714               continue;
 715             }
 716           for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
 717           {
 718             PixelChannel channel=GetPixelChannelChannel(image,i);
 719             PixelTrait traits=GetPixelChannelTraits(image,channel);
 720             if (traits == UndefinedPixelTrait)
 721               continue;
 722             if ((traits & UpdatePixelTrait) == 0)
 723               continue;
 724             q[i]=ClampToQuantum(evaluate_pixel[x].channel[i]);
 725           }
 726           q+=GetPixelChannels(image);
 727         }
 728         if (SyncCacheViewAuthenticPixels(evaluate_view,exception) == MagickFalse)
 729           status=MagickFalse;
 730         if (images->progress_monitor != (MagickProgressMonitor) NULL)
 731           {
 732             MagickBooleanType
 733               proceed;
 734
 735 #if   defined(MAGICKCORE_OPENMP_SUPPORT)
 736             #pragma omp critical (MagickCore_EvaluateImages)
 737 #endif
 738             proceed=SetImageProgress(images,EvaluateImageTag,progress++,
 739               image->rows);
 740             if (proceed == MagickFalse)
 741               status=MagickFalse;
 742           }
 743       }
 744     }
 745   evaluate_view=DestroyCacheView(evaluate_view);
 746   evaluate_pixels=DestroyPixelThreadSet(evaluate_pixels);
 747   random_info=DestroyRandomInfoThreadSet(random_info);
 748   if (status == MagickFalse)
 749     image=DestroyImage(image);
 750   return(image);
 751 }
 752
 753 MagickExport MagickBooleanType EvaluateImage(Image *image,
 754   const MagickEvaluateOperator op,const double value,ExceptionInfo *exception)
 755 {
 756   CacheView
 757     *image_view;
 758
 759   MagickBooleanType
 760     status;
 761
 762   MagickOffsetType
 763     progress;
 764
 765   RandomInfo
 766     **restrict random_info;
 767
 768   ssize_t
 769     y;
 770
 771 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 772   unsigned long
 773     key;
 774 #endif
 775
 776   assert(image != (Image *) NULL);
 777   assert(image->signature == MagickSignature);
 778   if (image->debug != MagickFalse)
 779     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
 780   assert(exception != (ExceptionInfo *) NULL);
 781   assert(exception->signature == MagickSignature);
 782   if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
 783     return(MagickFalse);
 784   status=MagickTrue;
 785   progress=0;
 786   random_info=AcquireRandomInfoThreadSet();
 787 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 788   key=GetRandomSecretKey(random_info[0]);
 789 #endif
 790   image_view=AcquireAuthenticCacheView(image,exception);
 791 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 792   #pragma omp parallel for schedule(static,4) shared(progress,status) \
 793     magick_threads(image,image,image->rows,key == ~0UL)
 794 #endif
 795   for (y=0; y < (ssize_t) image->rows; y++)
 796   {
 797     const int
 798       id = GetOpenMPThreadId();
 799
 800     register Quantum
 801       *restrict q;
 802
 803     register ssize_t
 804       x;
 805
 806     if (status == MagickFalse)
 807       continue;
 808     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
 809     if (q == (Quantum *) NULL)
 810       {
 811         status=MagickFalse;
 812         continue;
 813       }
 814     for (x=0; x < (ssize_t) image->columns; x++)
 815     {
 816       register ssize_t
 817         i;
 818
 819       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
 820       {
 821         PixelChannel channel=GetPixelChannelChannel(image,i);
 822         PixelTrait traits=GetPixelChannelTraits(image,channel);
 823         if (traits == UndefinedPixelTrait)
 824           continue;
 825         if (((traits & CopyPixelTrait) != 0) ||
 826             (GetPixelReadMask(image,q) == 0))
 827           continue;
 828         q[i]=ClampToQuantum(ApplyEvaluateOperator(random_info[id],q[i],op,
 829           value));
 830       }
 831       q+=GetPixelChannels(image);
 832     }
 833     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
 834       status=MagickFalse;
 835     if (image->progress_monitor != (MagickProgressMonitor) NULL)
 836       {
 837         MagickBooleanType
 838           proceed;
 839
 840 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 841         #pragma omp critical (MagickCore_EvaluateImage)
 842 #endif
 843         proceed=SetImageProgress(image,EvaluateImageTag,progress++,image->rows);
 844         if (proceed == MagickFalse)
 845           status=MagickFalse;
 846       }
 847   }
 848   image_view=DestroyCacheView(image_view);
 849   random_info=DestroyRandomInfoThreadSet(random_info);
 850   return(status);
 851 }
 852 \f
 853 /*
 854 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 855 %                                                                             %
 856 %                                                                             %
 857 %                                                                             %
 858 %     F u n c t i o n I m a g e                                               %
 859 %                                                                             %
 860 %                                                                             %
 861 %                                                                             %
 862 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 863 %
 864 %  FunctionImage() applies a value to the image with an arithmetic, relational,
 865 %  or logical operator to an image. Use these operations to lighten or darken
 866 %  an image, to increase or decrease contrast in an image, or to produce the
 867 %  "negative" of an image.
 868 %
 869 %  The format of the FunctionImage method is:
 870 %
 871 %      MagickBooleanType FunctionImage(Image *image,
 872 %        const MagickFunction function,const ssize_t number_parameters,
 873 %        const double *parameters,ExceptionInfo *exception)
 874 %
 875 %  A description of each parameter follows:
 876 %
 877 %    o image: the image.
 878 %
 879 %    o function: A channel function.
 880 %
 881 %    o parameters: one or more parameters.
 882 %
 883 %    o exception: return any errors or warnings in this structure.
 884 %
 885 */
 886
 887 static Quantum ApplyFunction(Quantum pixel,const MagickFunction function,
 888   const size_t number_parameters,const double *parameters,
 889   ExceptionInfo *exception)
 890 {
 891   double
 892     result;
 893
 894   register ssize_t
 895     i;
 896
 897   (void) exception;
 898   result=0.0;
 899   switch (function)
 900   {
 901     case PolynomialFunction:
 902     {
 903       /*
 904         Polynomial: polynomial constants, highest to lowest order (e.g. c0*x^3+
 905         c1*x^2+c2*x+c3).
 906       */
 907       result=0.0;
 908       for (i=0; i < (ssize_t) number_parameters; i++)
 909         result=result*QuantumScale*pixel+parameters[i];
 910       result*=QuantumRange;
 911       break;
 912     }
 913     case SinusoidFunction:
 914     {
 915       double
 916         amplitude,
 917         bias,
 918         frequency,
 919         phase;
 920
 921       /*
 922         Sinusoid: frequency, phase, amplitude, bias.
 923       */
 924       frequency=(number_parameters >= 1) ? parameters[0] : 1.0;
 925       phase=(number_parameters >= 2) ? parameters[1] : 0.0;
 926       amplitude=(number_parameters >= 3) ? parameters[2] : 0.5;
 927       bias=(number_parameters >= 4) ? parameters[3] : 0.5;
 928       result=(double) (QuantumRange*(amplitude*sin((double) (2.0*
 929         MagickPI*(frequency*QuantumScale*pixel+phase/360.0)))+bias));
 930       break;
 931     }
 932     case ArcsinFunction:
 933     {
 934       double
 935         bias,
 936         center,
 937         range,
 938         width;
 939
 940       /*
 941         Arcsin (peged at range limits for invalid results): width, center,
 942         range, and bias.
 943       */
 944       width=(number_parameters >= 1) ? parameters[0] : 1.0;
 945       center=(number_parameters >= 2) ? parameters[1] : 0.5;
 946       range=(number_parameters >= 3) ? parameters[2] : 1.0;
 947       bias=(number_parameters >= 4) ? parameters[3] : 0.5;
 948       result=2.0/width*(QuantumScale*pixel-center);
 949       if ( result <= -1.0 )
 950         result=bias-range/2.0;
 951       else
 952         if (result >= 1.0)
 953           result=bias+range/2.0;
 954         else
 955           result=(double) (range/MagickPI*asin((double) result)+bias);
 956       result*=QuantumRange;
 957       break;
 958     }
 959     case ArctanFunction:
 960     {
 961       double
 962         center,
 963         bias,
 964         range,
 965         slope;
 966
 967       /*
 968         Arctan: slope, center, range, and bias.
 969       */
 970       slope=(number_parameters >= 1) ? parameters[0] : 1.0;
 971       center=(number_parameters >= 2) ? parameters[1] : 0.5;
 972       range=(number_parameters >= 3) ? parameters[2] : 1.0;
 973       bias=(number_parameters >= 4) ? parameters[3] : 0.5;
 974       result=(double) (MagickPI*slope*(QuantumScale*pixel-center));
 975       result=(double) (QuantumRange*(range/MagickPI*atan((double)
 976         result)+bias));
 977       break;
 978     }
 979     case UndefinedFunction:
 980       break;
 981   }
 982   return(ClampToQuantum(result));
 983 }
 984
 985 MagickExport MagickBooleanType FunctionImage(Image *image,
 986   const MagickFunction function,const size_t number_parameters,
 987   const double *parameters,ExceptionInfo *exception)
 988 {
 989 #define FunctionImageTag  "Function/Image "
 990
 991   CacheView
 992     *image_view;
 993
 994   MagickBooleanType
 995     status;
 996
 997   MagickOffsetType
 998     progress;
 999
1000   ssize_t
1001     y;
1002
1003   assert(image != (Image *) NULL);
1004   assert(image->signature == MagickSignature);
1005   if (image->debug != MagickFalse)
1006     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1007   assert(exception != (ExceptionInfo *) NULL);
1008   assert(exception->signature == MagickSignature);
1009   if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
1010     return(MagickFalse);
1011   status=MagickTrue;
1012   progress=0;
1013   image_view=AcquireAuthenticCacheView(image,exception);
1014 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1015   #pragma omp parallel for schedule(static,4) shared(progress,status) \
1016     magick_threads(image,image,image->rows,1)
1017 #endif
1018   for (y=0; y < (ssize_t) image->rows; y++)
1019   {
1020     register Quantum
1021       *restrict q;
1022
1023     register ssize_t
1024       x;
1025
1026     if (status == MagickFalse)
1027       continue;
1028     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
1029     if (q == (Quantum *) NULL)
1030       {
1031         status=MagickFalse;
1032         continue;
1033       }
1034     for (x=0; x < (ssize_t) image->columns; x++)
1035     {
1036       register ssize_t
1037         i;
1038
1039       if (GetPixelReadMask(image,q) == 0)
1040         {
1041           q+=GetPixelChannels(image);
1042           continue;
1043         }
1044       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1045       {
1046         PixelChannel channel=GetPixelChannelChannel(image,i);
1047         PixelTrait traits=GetPixelChannelTraits(image,channel);
1048         if (traits == UndefinedPixelTrait)
1049           continue;
1050         if ((traits & UpdatePixelTrait) == 0)
1051           continue;
1052         q[i]=ApplyFunction(q[i],function,number_parameters,parameters,
1053           exception);
1054       }
1055       q+=GetPixelChannels(image);
1056     }
1057     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1058       status=MagickFalse;
1059     if (image->progress_monitor != (MagickProgressMonitor) NULL)
1060       {
1061         MagickBooleanType
1062           proceed;
1063
1064 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1065         #pragma omp critical (MagickCore_FunctionImage)
1066 #endif
1067         proceed=SetImageProgress(image,FunctionImageTag,progress++,image->rows);
1068         if (proceed == MagickFalse)
1069           status=MagickFalse;
1070       }
1071   }
1072   image_view=DestroyCacheView(image_view);
1073   return(status);
1074 }
1075 \f
1076 /*
1077 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1078 %                                                                             %
1079 %                                                                             %
1080 %                                                                             %
1081 %   G e t I m a g e E x t r e m a                                             %
1082 %                                                                             %
1083 %                                                                             %
1084 %                                                                             %
1085 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1086 %
1087 %  GetImageExtrema() returns the extrema of one or more image channels.
1088 %
1089 %  The format of the GetImageExtrema method is:
1090 %
1091 %      MagickBooleanType GetImageExtrema(const Image *image,size_t *minima,
1092 %        size_t *maxima,ExceptionInfo *exception)
1093 %
1094 %  A description of each parameter follows:
1095 %
1096 %    o image: the image.
1097 %
1098 %    o minima: the minimum value in the channel.
1099 %
1100 %    o maxima: the maximum value in the channel.
1101 %
1102 %    o exception: return any errors or warnings in this structure.
1103 %
1104 */
1105 MagickExport MagickBooleanType GetImageExtrema(const Image *image,
1106   size_t *minima,size_t *maxima,ExceptionInfo *exception)
1107 {
1108   double
1109     max,
1110     min;
1111
1112   MagickBooleanType
1113     status;
1114
1115   assert(image != (Image *) NULL);
1116   assert(image->signature == MagickSignature);
1117   if (image->debug != MagickFalse)
1118     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1119   status=GetImageRange(image,&min,&max,exception);
1120   *minima=(size_t) ceil(min-0.5);
1121   *maxima=(size_t) floor(max+0.5);
1122   return(status);
1123 }
1124 \f
1125 /*
1126 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1127 %                                                                             %
1128 %                                                                             %
1129 %                                                                             %
1130 %   G e t I m a g e K u r t o s i s                                           %
1131 %                                                                             %
1132 %                                                                             %
1133 %                                                                             %
1134 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1135 %
1136 %  GetImageKurtosis() returns the kurtosis and skewness of one or more image
1137 %  channels.
1138 %
1139 %  The format of the GetImageKurtosis method is:
1140 %
1141 %      MagickBooleanType GetImageKurtosis(const Image *image,double *kurtosis,
1142 %        double *skewness,ExceptionInfo *exception)
1143 %
1144 %  A description of each parameter follows:
1145 %
1146 %    o image: the image.
1147 %
1148 %    o kurtosis: the kurtosis of the channel.
1149 %
1150 %    o skewness: the skewness of the channel.
1151 %
1152 %    o exception: return any errors or warnings in this structure.
1153 %
1154 */
1155 MagickExport MagickBooleanType GetImageKurtosis(const Image *image,
1156   double *kurtosis,double *skewness,ExceptionInfo *exception)
1157 {
1158   CacheView
1159     *image_view;
1160
1161   double
1162     area,
1163     mean,
1164     standard_deviation,
1165     sum_squares,
1166     sum_cubes,
1167     sum_fourth_power;
1168
1169   MagickBooleanType
1170     status;
1171
1172   ssize_t
1173     y;
1174
1175   assert(image != (Image *) NULL);
1176   assert(image->signature == MagickSignature);
1177   if (image->debug != MagickFalse)
1178     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1179   status=MagickTrue;
1180   *kurtosis=0.0;
1181   *skewness=0.0;
1182   area=0.0;
1183   mean=0.0;
1184   standard_deviation=0.0;
1185   sum_squares=0.0;
1186   sum_cubes=0.0;
1187   sum_fourth_power=0.0;
1188   image_view=AcquireVirtualCacheView(image,exception);
1189 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1190   #pragma omp parallel for schedule(static,4) shared(status) \
1191     magick_threads(image,image,image->rows,1)
1192 #endif
1193   for (y=0; y < (ssize_t) image->rows; y++)
1194   {
1195     register const Quantum
1196       *restrict p;
1197
1198     register ssize_t
1199       x;
1200
1201     if (status == MagickFalse)
1202       continue;
1203     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1204     if (p == (const Quantum *) NULL)
1205       {
1206         status=MagickFalse;
1207         continue;
1208       }
1209     for (x=0; x < (ssize_t) image->columns; x++)
1210     {
1211       register ssize_t
1212         i;
1213
1214       if (GetPixelReadMask(image,p) == 0)
1215         {
1216           p+=GetPixelChannels(image);
1217           continue;
1218         }
1219       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1220       {
1221         PixelChannel channel=GetPixelChannelChannel(image,i);
1222         PixelTrait traits=GetPixelChannelTraits(image,channel);
1223         if (traits == UndefinedPixelTrait)
1224           continue;
1225         if ((traits & UpdatePixelTrait) == 0)
1226           continue;
1227 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1228         #pragma omp critical (MagickCore_GetImageKurtosis)
1229 #endif
1230         {
1231           mean+=p[i];
1232           sum_squares+=(double) p[i]*p[i];
1233           sum_cubes+=(double) p[i]*p[i]*p[i];
1234           sum_fourth_power+=(double) p[i]*p[i]*p[i]*p[i];
1235           area++;
1236         }
1237       }
1238       p+=GetPixelChannels(image);
1239     }
1240   }
1241   image_view=DestroyCacheView(image_view);
1242   if (area != 0.0)
1243     {
1244       mean/=area;
1245       sum_squares/=area;
1246       sum_cubes/=area;
1247       sum_fourth_power/=area;
1248     }
1249   standard_deviation=sqrt(sum_squares-(mean*mean));
1250   if (standard_deviation != 0.0)
1251     {
1252       *kurtosis=sum_fourth_power-4.0*mean*sum_cubes+6.0*mean*mean*sum_squares-
1253         3.0*mean*mean*mean*mean;
1254       *kurtosis/=standard_deviation*standard_deviation*standard_deviation*
1255         standard_deviation;
1256       *kurtosis-=3.0;
1257       *skewness=sum_cubes-3.0*mean*sum_squares+2.0*mean*mean*mean;
1258       *skewness/=standard_deviation*standard_deviation*standard_deviation;
1259     }
1260   return(status);
1261 }
1262 \f
1263 /*
1264 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1265 %                                                                             %
1266 %                                                                             %
1267 %                                                                             %
1268 %   G e t I m a g e M e a n                                                   %
1269 %                                                                             %
1270 %                                                                             %
1271 %                                                                             %
1272 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1273 %
1274 %  GetImageMean() returns the mean and standard deviation of one or more image
1275 %  channels.
1276 %
1277 %  The format of the GetImageMean method is:
1278 %
1279 %      MagickBooleanType GetImageMean(const Image *image,double *mean,
1280 %        double *standard_deviation,ExceptionInfo *exception)
1281 %
1282 %  A description of each parameter follows:
1283 %
1284 %    o image: the image.
1285 %
1286 %    o mean: the average value in the channel.
1287 %
1288 %    o standard_deviation: the standard deviation of the channel.
1289 %
1290 %    o exception: return any errors or warnings in this structure.
1291 %
1292 */
1293 MagickExport MagickBooleanType GetImageMean(const Image *image,double *mean,
1294   double *standard_deviation,ExceptionInfo *exception)
1295 {
1296   double
1297     area;
1298
1299   ChannelStatistics
1300     *channel_statistics;
1301
1302   register ssize_t
1303     i;
1304
1305   assert(image != (Image *) NULL);
1306   assert(image->signature == MagickSignature);
1307   if (image->debug != MagickFalse)
1308     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1309   channel_statistics=GetImageStatistics(image,exception);
1310   if (channel_statistics == (ChannelStatistics *) NULL)
1311     return(MagickFalse);
1312   area=0.0;
1313   channel_statistics[CompositePixelChannel].mean=0.0;
1314   channel_statistics[CompositePixelChannel].standard_deviation=0.0;
1315   for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1316   {
1317     PixelChannel channel=GetPixelChannelChannel(image,i);
1318     PixelTrait traits=GetPixelChannelTraits(image,channel);
1319     if (traits == UndefinedPixelTrait)
1320       continue;
1321     if ((traits & UpdatePixelTrait) == 0)
1322       continue;
1323     channel_statistics[CompositePixelChannel].mean+=channel_statistics[i].mean;
1324     channel_statistics[CompositePixelChannel].standard_deviation+=
1325       channel_statistics[i].variance-channel_statistics[i].mean*
1326       channel_statistics[i].mean;
1327     area++;
1328   }
1329   channel_statistics[CompositePixelChannel].mean/=area;
1330   channel_statistics[CompositePixelChannel].standard_deviation=
1331     sqrt(channel_statistics[CompositePixelChannel].standard_deviation/area);
1332   *mean=channel_statistics[CompositePixelChannel].mean;
1333   *standard_deviation=
1334     channel_statistics[CompositePixelChannel].standard_deviation;
1335   channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
1336     channel_statistics);
1337   return(MagickTrue);
1338 }
1339 \f
1340 /*
1341 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1342 %                                                                             %
1343 %                                                                             %
1344 %                                                                             %
1345 %   G e t I m a g e M o m e n t s                                             %
1346 %                                                                             %
1347 %                                                                             %
1348 %                                                                             %
1349 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1350 %
1351 %  GetImageMoments() returns the moments of one or more image channels.
1352 %
1353 %  The format of the GetImageMoments method is:
1354 %
1355 %      ChannelMoments *GetImageMoments(const Image *image,
1356 %        ExceptionInfo *exception)
1357 %
1358 %  A description of each parameter follows:
1359 %
1360 %    o image: the image.
1361 %
1362 %    o exception: return any errors or warnings in this structure.
1363 %
1364 */
1365 MagickExport ChannelMoments *GetImageMoments(const Image *image,
1366   ExceptionInfo *exception)
1367 {
1368 #define MaxNumberImageMoments  8
1369
1370   CacheView
1371     *image_view;
1372
1373   ChannelMoments
1374     *channel_moments;
1375
1376   double
1377     M00[MaxPixelChannels+1],
1378     M01[MaxPixelChannels+1],
1379     M02[MaxPixelChannels+1],
1380     M03[MaxPixelChannels+1],
1381     M10[MaxPixelChannels+1],
1382     M11[MaxPixelChannels+1],
1383     M12[MaxPixelChannels+1],
1384     M20[MaxPixelChannels+1],
1385     M21[MaxPixelChannels+1],
1386     M22[MaxPixelChannels+1],
1387     M30[MaxPixelChannels+1];
1388
1389   PointInfo
1390     centroid[MaxPixelChannels+1];
1391
1392   ssize_t
1393     channel,
1394     y;
1395
1396   assert(image != (Image *) NULL);
1397   assert(image->signature == MagickSignature);
1398   if (image->debug != MagickFalse)
1399     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1400   channel_moments=(ChannelMoments *) AcquireQuantumMemory(MaxPixelChannels+1,
1401     sizeof(*channel_moments));
1402   if (channel_moments == (ChannelMoments *) NULL)
1403     return(channel_moments);
1404   (void) ResetMagickMemory(channel_moments,0,(MaxPixelChannels+1)*
1405     sizeof(*channel_moments));
1406   (void) ResetMagickMemory(centroid,0,sizeof(centroid));
1407   (void) ResetMagickMemory(M00,0,sizeof(M00));
1408   (void) ResetMagickMemory(M01,0,sizeof(M01));
1409   (void) ResetMagickMemory(M02,0,sizeof(M02));
1410   (void) ResetMagickMemory(M03,0,sizeof(M03));
1411   (void) ResetMagickMemory(M10,0,sizeof(M10));
1412   (void) ResetMagickMemory(M11,0,sizeof(M11));
1413   (void) ResetMagickMemory(M12,0,sizeof(M12));
1414   (void) ResetMagickMemory(M20,0,sizeof(M20));
1415   (void) ResetMagickMemory(M21,0,sizeof(M21));
1416   (void) ResetMagickMemory(M22,0,sizeof(M22));
1417   (void) ResetMagickMemory(M30,0,sizeof(M30));
1418   image_view=AcquireVirtualCacheView(image,exception);
1419   for (y=0; y < (ssize_t) image->rows; y++)
1420   {
1421     register const Quantum
1422       *restrict p;
1423
1424     register ssize_t
1425       x;
1426
1427     /*
1428       Compute center of mass (centroid).
1429     */
1430     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1431     if (p == (const Quantum *) NULL)
1432       break;
1433     for (x=0; x < (ssize_t) image->columns; x++)
1434     {
1435       register ssize_t
1436         i;
1437
1438       if (GetPixelReadMask(image,p) == 0)
1439         {
1440           p+=GetPixelChannels(image);
1441           continue;
1442         }
1443       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1444       {
1445         PixelChannel channel=GetPixelChannelChannel(image,i);
1446         PixelTrait traits=GetPixelChannelTraits(image,channel);
1447         if (traits == UndefinedPixelTrait)
1448           continue;
1449         if ((traits & UpdatePixelTrait) == 0)
1450           continue;
1451         M00[channel]+=QuantumScale*p[i];
1452         M10[channel]+=x*QuantumScale*p[i];
1453         M01[channel]+=y*QuantumScale*p[i];
1454       }
1455       p+=GetPixelChannels(image);
1456     }
1457   }
1458   for (channel=0; channel <= MaxPixelChannels; channel++)
1459   {
1460     /*
1461        Compute center of mass (centroid).
1462     */
1463     if (M00[channel] < MagickEpsilon)
1464       {
1465         M00[channel]+=MagickEpsilon;
1466         centroid[channel].x=image->columns/2.0;
1467         centroid[channel].y=image->rows/2.0;
1468         continue;
1469       }
1470     M00[channel]+=MagickEpsilon;
1471     centroid[channel].x=M10[channel]/M00[channel];
1472     centroid[channel].y=M01[channel]/M00[channel];
1473   }
1474   for (y=0; y < (ssize_t) image->rows; y++)
1475   {
1476     register const Quantum
1477       *restrict p;
1478
1479     register ssize_t
1480       x;
1481
1482     /*
1483       Compute the image moments.
1484     */
1485     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1486     if (p == (const Quantum *) NULL)
1487       break;
1488     for (x=0; x < (ssize_t) image->columns; x++)
1489     {
1490       register ssize_t
1491         i;
1492
1493       if (GetPixelReadMask(image,p) == 0)
1494         {
1495           p+=GetPixelChannels(image);
1496           continue;
1497         }
1498       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1499       {
1500         PixelChannel channel=GetPixelChannelChannel(image,i);
1501         PixelTrait traits=GetPixelChannelTraits(image,channel);
1502         if (traits == UndefinedPixelTrait)
1503           continue;
1504         if ((traits & UpdatePixelTrait) == 0)
1505           continue;
1506         M11[channel]+=(x-centroid[channel].x)*(y-centroid[channel].y)*
1507           QuantumScale*p[i];
1508         M20[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
1509           QuantumScale*p[i];
1510         M02[channel]+=(y-centroid[channel].y)*(y-centroid[channel].y)*
1511           QuantumScale*p[i];
1512         M21[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
1513           (y-centroid[channel].y)*QuantumScale*p[i];
1514         M12[channel]+=(x-centroid[channel].x)*(y-centroid[channel].y)*
1515           (y-centroid[channel].y)*QuantumScale*p[i];
1516         M22[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
1517           (y-centroid[channel].y)*(y-centroid[channel].y)*QuantumScale*p[i];
1518         M30[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
1519           (x-centroid[channel].x)*QuantumScale*p[i];
1520         M03[channel]+=(y-centroid[channel].y)*(y-centroid[channel].y)*
1521           (y-centroid[channel].y)*QuantumScale*p[i];
1522       }
1523       p+=GetPixelChannels(image);
1524     }
1525   }
1526   for (channel=0; channel <= MaxPixelChannels; channel++)
1527   {
1528     /*
1529       Compute elliptical angle, major and minor axes, eccentricity, & intensity.
1530     */
1531     channel_moments[channel].centroid=centroid[channel];
1532     channel_moments[channel].ellipse_axis.x=sqrt((2.0/M00[channel])*
1533       ((M20[channel]+M02[channel])+sqrt(4.0*M11[channel]*M11[channel]+
1534       (M20[channel]-M02[channel])*(M20[channel]-M02[channel]))));
1535     channel_moments[channel].ellipse_axis.y=sqrt((2.0/M00[channel])*
1536       ((M20[channel]+M02[channel])-sqrt(4.0*M11[channel]*M11[channel]+
1537       (M20[channel]-M02[channel])*(M20[channel]-M02[channel]))));
1538     channel_moments[channel].ellipse_angle=RadiansToDegrees(0.5*atan(2.0*
1539       M11[channel]/(M20[channel]-M02[channel]+MagickEpsilon)));
1540     channel_moments[channel].ellipse_eccentricity=sqrt(1.0-(
1541       channel_moments[channel].ellipse_axis.y/
1542       (channel_moments[channel].ellipse_axis.x+MagickEpsilon)));
1543     channel_moments[channel].ellipse_intensity=M00[channel]/
1544       (MagickPI*channel_moments[channel].ellipse_axis.x*
1545       channel_moments[channel].ellipse_axis.y+MagickEpsilon);
1546   }
1547   for (channel=0; channel <= MaxPixelChannels; channel++)
1548   {
1549     /*
1550       Normalize image moments.
1551     */
1552     M10[channel]=0.0;
1553     M01[channel]=0.0;
1554     M11[channel]/=pow(M00[channel],1.0+(1.0+1.0)/2.0);
1555     M20[channel]/=pow(M00[channel],1.0+(2.0+0.0)/2.0);
1556     M02[channel]/=pow(M00[channel],1.0+(0.0+2.0)/2.0);
1557     M21[channel]/=pow(M00[channel],1.0+(2.0+1.0)/2.0);
1558     M12[channel]/=pow(M00[channel],1.0+(1.0+2.0)/2.0);
1559     M22[channel]/=pow(M00[channel],1.0+(2.0+2.0)/2.0);
1560     M30[channel]/=pow(M00[channel],1.0+(3.0+0.0)/2.0);
1561     M03[channel]/=pow(M00[channel],1.0+(0.0+3.0)/2.0);
1562     M00[channel]=1.0;
1563   }
1564   image_view=DestroyCacheView(image_view);
1565   for (channel=0; channel <= MaxPixelChannels; channel++)
1566   {
1567     /*
1568       Compute Hu invariant moments.
1569     */
1570     channel_moments[channel].I[0]=M20[channel]+M02[channel];
1571     channel_moments[channel].I[1]=(M20[channel]-M02[channel])*
1572       (M20[channel]-M02[channel])+4.0*M11[channel]*M11[channel];
1573     channel_moments[channel].I[2]=(M30[channel]-3.0*M12[channel])*
1574       (M30[channel]-3.0*M12[channel])+(3.0*M21[channel]-M03[channel])*
1575       (3.0*M21[channel]-M03[channel]);
1576     channel_moments[channel].I[3]=(M30[channel]+M12[channel])*
1577       (M30[channel]+M12[channel])+(M21[channel]+M03[channel])*
1578       (M21[channel]+M03[channel]);
1579     channel_moments[channel].I[4]=(M30[channel]-3.0*M12[channel])*
1580       (M30[channel]+M12[channel])*((M30[channel]+M12[channel])*
1581       (M30[channel]+M12[channel])-3.0*(M21[channel]+M03[channel])*
1582       (M21[channel]+M03[channel]))+(3.0*M21[channel]-M03[channel])*
1583       (M21[channel]+M03[channel])*(3.0*(M30[channel]+M12[channel])*
1584       (M30[channel]+M12[channel])-(M21[channel]+M03[channel])*
1585       (M21[channel]+M03[channel]));
1586     channel_moments[channel].I[5]=(M20[channel]-M02[channel])*
1587       ((M30[channel]+M12[channel])*(M30[channel]+M12[channel])-
1588       (M21[channel]+M03[channel])*(M21[channel]+M03[channel]))+
1589       4.0*M11[channel]*(M30[channel]+M12[channel])*(M21[channel]+M03[channel]);
1590     channel_moments[channel].I[6]=(3.0*M21[channel]-M03[channel])*
1591       (M30[channel]+M12[channel])*((M30[channel]+M12[channel])*
1592       (M30[channel]+M12[channel])-3.0*(M21[channel]+M03[channel])*
1593       (M21[channel]+M03[channel]))-(M30[channel]-3*M12[channel])*
1594       (M21[channel]+M03[channel])*(3.0*(M30[channel]+M12[channel])*
1595       (M30[channel]+M12[channel])-(M21[channel]+M03[channel])*
1596       (M21[channel]+M03[channel]));
1597     channel_moments[channel].I[7]=M11[channel]*((M30[channel]+M12[channel])*
1598       (M30[channel]+M12[channel])-(M03[channel]+M21[channel])*
1599       (M03[channel]+M21[channel]))-(M20[channel]-M02[channel])*
1600       (M30[channel]+M12[channel])*(M03[channel]+M21[channel]);
1601   }
1602   if (y < (ssize_t) image->rows)
1603     channel_moments=(ChannelMoments *) RelinquishMagickMemory(channel_moments);
1604   return(channel_moments);
1605 }
1606 \f
1607 /*
1608 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1609 %                                                                             %
1610 %                                                                             %
1611 %                                                                             %
1612 %   G e t I m a g e R a n g e                                                 %
1613 %                                                                             %
1614 %                                                                             %
1615 %                                                                             %
1616 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1617 %
1618 %  GetImageRange() returns the range of one or more image channels.
1619 %
1620 %  The format of the GetImageRange method is:
1621 %
1622 %      MagickBooleanType GetImageRange(const Image *image,double *minima,
1623 %        double *maxima,ExceptionInfo *exception)
1624 %
1625 %  A description of each parameter follows:
1626 %
1627 %    o image: the image.
1628 %
1629 %    o minima: the minimum value in the channel.
1630 %
1631 %    o maxima: the maximum value in the channel.
1632 %
1633 %    o exception: return any errors or warnings in this structure.
1634 %
1635 */
1636 MagickExport MagickBooleanType GetImageRange(const Image *image,double *minima,
1637   double *maxima,ExceptionInfo *exception)
1638 {
1639   CacheView
1640     *image_view;
1641
1642   MagickBooleanType
1643     initialize,
1644     status;
1645
1646   ssize_t
1647     y;
1648
1649   assert(image != (Image *) NULL);
1650   assert(image->signature == MagickSignature);
1651   if (image->debug != MagickFalse)
1652     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1653   status=MagickTrue;
1654   initialize=MagickTrue;
1655   *maxima=0.0;
1656   *minima=0.0;
1657   image_view=AcquireVirtualCacheView(image,exception);
1658 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1659   #pragma omp parallel for schedule(static,4) shared(status,initialize) \
1660     magick_threads(image,image,image->rows,1)
1661 #endif
1662   for (y=0; y < (ssize_t) image->rows; y++)
1663   {
1664     register const Quantum
1665       *restrict p;
1666
1667     register ssize_t
1668       x;
1669
1670     if (status == MagickFalse)
1671       continue;
1672     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1673     if (p == (const Quantum *) NULL)
1674       {
1675         status=MagickFalse;
1676         continue;
1677       }
1678     for (x=0; x < (ssize_t) image->columns; x++)
1679     {
1680       register ssize_t
1681         i;
1682
1683       if (GetPixelReadMask(image,p) == 0)
1684         {
1685           p+=GetPixelChannels(image);
1686           continue;
1687         }
1688       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1689       {
1690         PixelChannel channel=GetPixelChannelChannel(image,i);
1691         PixelTrait traits=GetPixelChannelTraits(image,channel);
1692         if (traits == UndefinedPixelTrait)
1693           continue;
1694         if ((traits & UpdatePixelTrait) == 0)
1695           continue;
1696 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1697         #pragma omp critical (MagickCore_GetImageRange)
1698 #endif
1699         {
1700           if (initialize != MagickFalse)
1701             {
1702               *minima=(double) p[i];
1703               *maxima=(double) p[i];
1704               initialize=MagickFalse;
1705             }
1706           else
1707             {
1708               if ((double) p[i] < *minima)
1709                 *minima=(double) p[i];
1710               if ((double) p[i] > *maxima)
1711                 *maxima=(double) p[i];
1712            }
1713         }
1714       }
1715       p+=GetPixelChannels(image);
1716     }
1717   }
1718   image_view=DestroyCacheView(image_view);
1719   return(status);
1720 }
1721 \f
1722 /*
1723 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1724 %                                                                             %
1725 %                                                                             %
1726 %                                                                             %
1727 %   G e t I m a g e S t a t i s t i c s                                       %
1728 %                                                                             %
1729 %                                                                             %
1730 %                                                                             %
1731 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1732 %
1733 %  GetImageStatistics() returns statistics for each channel in the image.  The
1734 %  statistics include the channel depth, its minima, maxima, mean, standard
1735 %  deviation, kurtosis and skewness.  You can access the red channel mean, for
1736 %  example, like this:
1737 %
1738 %      channel_statistics=GetImageStatistics(image,exception);
1739 %      red_mean=channel_statistics[RedPixelChannel].mean;
1740 %
1741 %  Use MagickRelinquishMemory() to free the statistics buffer.
1742 %
1743 %  The format of the GetImageStatistics method is:
1744 %
1745 %      ChannelStatistics *GetImageStatistics(const Image *image,
1746 %        ExceptionInfo *exception)
1747 %
1748 %  A description of each parameter follows:
1749 %
1750 %    o image: the image.
1751 %
1752 %    o exception: return any errors or warnings in this structure.
1753 %
1754 */
1755
1756 static size_t GetImageChannels(const Image *image)
1757 {
1758   register ssize_t
1759     i;
1760
1761   size_t
1762     channels;
1763
1764   channels=0;
1765   for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1766   {
1767     PixelChannel channel=GetPixelChannelChannel(image,i);
1768     PixelTrait traits=GetPixelChannelTraits(image,channel);
1769     if (traits != UndefinedPixelTrait)
1770       channels++;
1771   }
1772   return(channels);
1773 }
1774
1775 MagickExport ChannelStatistics *GetImageStatistics(const Image *image,
1776   ExceptionInfo *exception)
1777 {
1778   ChannelStatistics
1779     *channel_statistics;
1780
1781   MagickStatusType
1782     status;
1783
1784   QuantumAny
1785     range;
1786
1787   register ssize_t
1788     i;
1789
1790   size_t
1791     channels,
1792     depth;
1793
1794   ssize_t
1795     y;
1796
1797   assert(image != (Image *) NULL);
1798   assert(image->signature == MagickSignature);
1799   if (image->debug != MagickFalse)
1800     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1801   channel_statistics=(ChannelStatistics *) AcquireQuantumMemory(
1802     MaxPixelChannels+1,sizeof(*channel_statistics));
1803   if (channel_statistics == (ChannelStatistics *) NULL)
1804     return(channel_statistics);
1805   (void) ResetMagickMemory(channel_statistics,0,(MaxPixelChannels+1)*
1806     sizeof(*channel_statistics));
1807   for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
1808   {
1809     channel_statistics[i].depth=1;
1810     channel_statistics[i].maxima=(-MagickMaximumValue);
1811     channel_statistics[i].minima=MagickMaximumValue;
1812   }
1813   for (y=0; y < (ssize_t) image->rows; y++)
1814   {
1815     register const Quantum
1816       *restrict p;
1817
1818     register ssize_t
1819       x;
1820
1821     p=GetVirtualPixels(image,0,y,image->columns,1,exception);
1822     if (p == (const Quantum *) NULL)
1823       break;
1824     for (x=0; x < (ssize_t) image->columns; x++)
1825     {
1826       register ssize_t
1827         i;
1828
1829       if (GetPixelReadMask(image,p) == 0)
1830         {
1831           p+=GetPixelChannels(image);
1832           continue;
1833         }
1834       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1835       {
1836         PixelChannel channel=GetPixelChannelChannel(image,i);
1837         PixelTrait traits=GetPixelChannelTraits(image,channel);
1838         if (traits == UndefinedPixelTrait)
1839           continue;
1840         if (channel_statistics[channel].depth != MAGICKCORE_QUANTUM_DEPTH)
1841           {
1842             depth=channel_statistics[channel].depth;
1843             range=GetQuantumRange(depth);
1844             status=p[i] != ScaleAnyToQuantum(ScaleQuantumToAny(p[i],range),
1845               range) ? MagickTrue : MagickFalse;
1846             if (status != MagickFalse)
1847               {
1848                 channel_statistics[channel].depth++;
1849                 i--;
1850                 continue;
1851               }
1852           }
1853         if ((double) p[i] < channel_statistics[channel].minima)
1854           channel_statistics[channel].minima=(double) p[i];
1855         if ((double) p[i] > channel_statistics[channel].maxima)
1856           channel_statistics[channel].maxima=(double) p[i];
1857         channel_statistics[channel].sum+=p[i];
1858         channel_statistics[channel].sum_squared+=(double) p[i]*p[i];
1859         channel_statistics[channel].sum_cubed+=(double) p[i]*p[i]*p[i];
1860         channel_statistics[channel].sum_fourth_power+=(double) p[i]*p[i]*p[i]*
1861           p[i];
1862         channel_statistics[channel].area++;
1863       }
1864       p+=GetPixelChannels(image);
1865     }
1866   }
1867   for (i=0; i < (ssize_t) MaxPixelChannels; i++)
1868   {
1869     double
1870       area;
1871
1872     area=PerceptibleReciprocal(channel_statistics[i].area);
1873     channel_statistics[i].sum*=area;
1874     channel_statistics[i].sum_squared*=area;
1875     channel_statistics[i].sum_cubed*=area;
1876     channel_statistics[i].sum_fourth_power*=area;
1877     channel_statistics[i].mean=channel_statistics[i].sum;
1878     channel_statistics[i].variance=channel_statistics[i].sum_squared;
1879     channel_statistics[i].standard_deviation=sqrt(
1880       channel_statistics[i].variance-(channel_statistics[i].mean*
1881       channel_statistics[i].mean));
1882   }
1883   for (i=0; i < (ssize_t) MaxPixelChannels; i++)
1884   {
1885     channel_statistics[CompositePixelChannel].area+=channel_statistics[i].area;
1886     channel_statistics[CompositePixelChannel].minima=MagickMin(
1887       channel_statistics[CompositePixelChannel].minima,
1888       channel_statistics[i].minima);
1889     channel_statistics[CompositePixelChannel].maxima=EvaluateMax(
1890       channel_statistics[CompositePixelChannel].maxima,
1891       channel_statistics[i].maxima);
1892     channel_statistics[CompositePixelChannel].sum+=channel_statistics[i].sum;
1893     channel_statistics[CompositePixelChannel].sum_squared+=
1894       channel_statistics[i].sum_squared;
1895     channel_statistics[CompositePixelChannel].sum_cubed+=
1896       channel_statistics[i].sum_cubed;
1897     channel_statistics[CompositePixelChannel].sum_fourth_power+=
1898       channel_statistics[i].sum_fourth_power;
1899     channel_statistics[CompositePixelChannel].mean+=channel_statistics[i].mean;
1900     channel_statistics[CompositePixelChannel].variance+=
1901       channel_statistics[i].variance-channel_statistics[i].mean*
1902       channel_statistics[i].mean;
1903     channel_statistics[CompositePixelChannel].standard_deviation+=
1904       channel_statistics[i].variance-channel_statistics[i].mean*
1905       channel_statistics[i].mean;
1906   }
1907   channels=GetImageChannels(image);
1908   channel_statistics[CompositePixelChannel].area/=channels;
1909   channel_statistics[CompositePixelChannel].sum/=channels;
1910   channel_statistics[CompositePixelChannel].sum_squared/=channels;
1911   channel_statistics[CompositePixelChannel].sum_cubed/=channels;
1912   channel_statistics[CompositePixelChannel].sum_fourth_power/=channels;
1913   channel_statistics[CompositePixelChannel].mean/=channels;
1914   channel_statistics[CompositePixelChannel].variance/=channels;
1915   channel_statistics[CompositePixelChannel].standard_deviation=
1916     sqrt(channel_statistics[CompositePixelChannel].standard_deviation/channels);
1917   channel_statistics[CompositePixelChannel].kurtosis/=channels;
1918   channel_statistics[CompositePixelChannel].skewness/=channels;
1919   for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
1920   {
1921     double
1922       standard_deviation;
1923
1924     if (channel_statistics[i].standard_deviation == 0.0)
1925       continue;
1926     standard_deviation=PerceptibleReciprocal(
1927       channel_statistics[i].standard_deviation);
1928     channel_statistics[i].skewness=(channel_statistics[i].sum_cubed-3.0*
1929       channel_statistics[i].mean*channel_statistics[i].sum_squared+2.0*
1930       channel_statistics[i].mean*channel_statistics[i].mean*
1931       channel_statistics[i].mean)*(standard_deviation*standard_deviation*
1932       standard_deviation);
1933     channel_statistics[i].kurtosis=(channel_statistics[i].sum_fourth_power-4.0*
1934       channel_statistics[i].mean*channel_statistics[i].sum_cubed+6.0*
1935       channel_statistics[i].mean*channel_statistics[i].mean*
1936       channel_statistics[i].sum_squared-3.0*channel_statistics[i].mean*
1937       channel_statistics[i].mean*1.0*channel_statistics[i].mean*
1938       channel_statistics[i].mean)*(standard_deviation*standard_deviation*
1939       standard_deviation*standard_deviation)-3.0;
1940   }
1941   if (y < (ssize_t) image->rows)
1942     channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
1943       channel_statistics);
1944   return(channel_statistics);
1945 }
1946 \f
1947 /*
1948 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1949 %                                                                             %
1950 %                                                                             %
1951 %                                                                             %
1952 %     P o l y n o m i a l I m a g e                                           %
1953 %                                                                             %
1954 %                                                                             %
1955 %                                                                             %
1956 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1957 %
1958 %  PolynomialImage() returns a new image where each pixel is the sum of the
1959 %  pixels in the image sequence after applying its corresponding terms
1960 %  (coefficient and degree pairs).
1961 %
1962 %  The format of the PolynomialImage method is:
1963 %
1964 %      Image *PolynomialImage(const Image *images,const size_t number_terms,
1965 %        const double *terms,ExceptionInfo *exception)
1966 %
1967 %  A description of each parameter follows:
1968 %
1969 %    o images: the image sequence.
1970 %
1971 %    o number_terms: the number of terms in the list.  The actual list length
1972 %      is 2 x number_terms + 1 (the constant).
1973 %
1974 %    o terms: the list of polynomial coefficients and degree pairs and a
1975 %      constant.
1976 %
1977 %    o exception: return any errors or warnings in this structure.
1978 %
1979 */
1980
1981 MagickExport Image *PolynomialImage(const Image *images,
1982   const size_t number_terms,const double *terms,ExceptionInfo *exception)
1983 {
1984 #define PolynomialImageTag  "Polynomial/Image"
1985
1986   CacheView
1987     *polynomial_view;
1988
1989   Image
1990     *image;
1991
1992   MagickBooleanType
1993     status;
1994
1995   MagickOffsetType
1996     progress;
1997
1998   PixelChannels
1999     **restrict polynomial_pixels;
2000
2001   size_t
2002     number_images;
2003
2004   ssize_t
2005     y;
2006
2007   assert(images != (Image *) NULL);
2008   assert(images->signature == MagickSignature);
2009   if (images->debug != MagickFalse)
2010     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
2011   assert(exception != (ExceptionInfo *) NULL);
2012   assert(exception->signature == MagickSignature);
2013   image=CloneImage(images,images->columns,images->rows,MagickTrue,
2014     exception);
2015   if (image == (Image *) NULL)
2016     return((Image *) NULL);
2017   if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
2018     {
2019       image=DestroyImage(image);
2020       return((Image *) NULL);
2021     }
2022   number_images=GetImageListLength(images);
2023   polynomial_pixels=AcquirePixelThreadSet(images,number_images);
2024   if (polynomial_pixels == (PixelChannels **) NULL)
2025     {
2026       image=DestroyImage(image);
2027       (void) ThrowMagickException(exception,GetMagickModule(),
2028         ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
2029       return((Image *) NULL);
2030     }
2031   /*
2032     Polynomial image pixels.
2033   */
2034   status=MagickTrue;
2035   progress=0;
2036   polynomial_view=AcquireAuthenticCacheView(image,exception);
2037 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2038   #pragma omp parallel for schedule(static,4) shared(progress,status) \
2039     magick_threads(image,image,image->rows,1)
2040 #endif
2041   for (y=0; y < (ssize_t) image->rows; y++)
2042   {
2043     CacheView
2044       *image_view;
2045
2046     const Image
2047       *next;
2048
2049     const int
2050       id = GetOpenMPThreadId();
2051
2052     register ssize_t
2053       i,
2054       x;
2055
2056     register PixelChannels
2057       *polynomial_pixel;
2058
2059     register Quantum
2060       *restrict q;
2061
2062     ssize_t
2063       j;
2064
2065     if (status == MagickFalse)
2066       continue;
2067     q=QueueCacheViewAuthenticPixels(polynomial_view,0,y,image->columns,1,
2068       exception);
2069     if (q == (Quantum *) NULL)
2070       {
2071         status=MagickFalse;
2072         continue;
2073       }
2074     polynomial_pixel=polynomial_pixels[id];
2075     for (j=0; j < (ssize_t) image->columns; j++)
2076       for (i=0; i < MaxPixelChannels; i++)
2077         polynomial_pixel[j].channel[i]=0.0;
2078     next=images;
2079     for (j=0; j < (ssize_t) number_images; j++)
2080     {
2081       register const Quantum
2082         *p;
2083
2084       if (j >= (ssize_t) number_terms)
2085         continue;
2086       image_view=AcquireVirtualCacheView(next,exception);
2087       p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
2088       if (p == (const Quantum *) NULL)
2089         {
2090           image_view=DestroyCacheView(image_view);
2091           break;
2092         }
2093       for (x=0; x < (ssize_t) image->columns; x++)
2094       {
2095         register ssize_t
2096           i;
2097
2098         if (GetPixelReadMask(next,p) == 0)
2099           {
2100             p+=GetPixelChannels(next);
2101             continue;
2102           }
2103         for (i=0; i < (ssize_t) GetPixelChannels(next); i++)
2104         {
2105           MagickRealType
2106             coefficient,
2107             degree;
2108
2109           PixelChannel channel=GetPixelChannelChannel(image,i);
2110           PixelTrait traits=GetPixelChannelTraits(next,channel);
2111           PixelTrait polynomial_traits=GetPixelChannelTraits(image,channel);
2112           if ((traits == UndefinedPixelTrait) ||
2113               (polynomial_traits == UndefinedPixelTrait))
2114             continue;
2115           if ((traits & UpdatePixelTrait) == 0)
2116             continue;
2117           coefficient=(MagickRealType) terms[2*i];
2118           degree=(MagickRealType) terms[(i << 1)+1];
2119           polynomial_pixel[x].channel[i]+=coefficient*
2120             pow(QuantumScale*GetPixelChannel(image,channel,p),degree);
2121         }
2122         p+=GetPixelChannels(next);
2123       }
2124       image_view=DestroyCacheView(image_view);
2125       next=GetNextImageInList(next);
2126     }
2127     for (x=0; x < (ssize_t) image->columns; x++)
2128     {
2129       register ssize_t
2130         i;
2131
2132       if (GetPixelReadMask(image,q) == 0)
2133         {
2134           q+=GetPixelChannels(image);
2135           continue;
2136         }
2137       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
2138       {
2139         PixelChannel channel=GetPixelChannelChannel(image,i);
2140         PixelTrait traits=GetPixelChannelTraits(image,channel);
2141         if (traits == UndefinedPixelTrait)
2142           continue;
2143         if ((traits & UpdatePixelTrait) == 0)
2144           continue;
2145         q[i]=ClampToQuantum(QuantumRange*polynomial_pixel[x].channel[i]);
2146       }
2147       q+=GetPixelChannels(image);
2148     }
2149     if (SyncCacheViewAuthenticPixels(polynomial_view,exception) == MagickFalse)
2150       status=MagickFalse;
2151     if (images->progress_monitor != (MagickProgressMonitor) NULL)
2152       {
2153         MagickBooleanType
2154           proceed;
2155
2156 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2157         #pragma omp critical (MagickCore_PolynomialImages)
2158 #endif
2159         proceed=SetImageProgress(images,PolynomialImageTag,progress++,
2160           image->rows);
2161         if (proceed == MagickFalse)
2162           status=MagickFalse;
2163       }
2164   }
2165   polynomial_view=DestroyCacheView(polynomial_view);
2166   polynomial_pixels=DestroyPixelThreadSet(polynomial_pixels);
2167   if (status == MagickFalse)
2168     image=DestroyImage(image);
2169   return(image);
2170 }
2171 \f
2172 /*
2173 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2174 %                                                                             %
2175 %                                                                             %
2176 %                                                                             %
2177 %     S t a t i s t i c I m a g e                                             %
2178 %                                                                             %
2179 %                                                                             %
2180 %                                                                             %
2181 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2182 %
2183 %  StatisticImage() makes each pixel the min / max / median / mode / etc. of
2184 %  the neighborhood of the specified width and height.
2185 %
2186 %  The format of the StatisticImage method is:
2187 %
2188 %      Image *StatisticImage(const Image *image,const StatisticType type,
2189 %        const size_t width,const size_t height,ExceptionInfo *exception)
2190 %
2191 %  A description of each parameter follows:
2192 %
2193 %    o image: the image.
2194 %
2195 %    o type: the statistic type (median, mode, etc.).
2196 %
2197 %    o width: the width of the pixel neighborhood.
2198 %
2199 %    o height: the height of the pixel neighborhood.
2200 %
2201 %    o exception: return any errors or warnings in this structure.
2202 %
2203 */
2204
2205 typedef struct _SkipNode
2206 {
2207   size_t
2208     next[9],
2209     count,
2210     signature;
2211 } SkipNode;
2212
2213 typedef struct _SkipList
2214 {
2215   ssize_t
2216     level;
2217
2218   SkipNode
2219     *nodes;
2220 } SkipList;
2221
2222 typedef struct _PixelList
2223 {
2224   size_t
2225     length,
2226     seed;
2227
2228   SkipList
2229     skip_list;
2230
2231   size_t
2232     signature;
2233 } PixelList;
2234
2235 static PixelList *DestroyPixelList(PixelList *pixel_list)
2236 {
2237   if (pixel_list == (PixelList *) NULL)
2238     return((PixelList *) NULL);
2239   if (pixel_list->skip_list.nodes != (SkipNode *) NULL)
2240     pixel_list->skip_list.nodes=(SkipNode *) RelinquishMagickMemory(
2241       pixel_list->skip_list.nodes);
2242   pixel_list=(PixelList *) RelinquishMagickMemory(pixel_list);
2243   return(pixel_list);
2244 }
2245
2246 static PixelList **DestroyPixelListThreadSet(PixelList **pixel_list)
2247 {
2248   register ssize_t
2249     i;
2250
2251   assert(pixel_list != (PixelList **) NULL);
2252   for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
2253     if (pixel_list[i] != (PixelList *) NULL)
2254       pixel_list[i]=DestroyPixelList(pixel_list[i]);
2255   pixel_list=(PixelList **) RelinquishMagickMemory(pixel_list);
2256   return(pixel_list);
2257 }
2258
2259 static PixelList *AcquirePixelList(const size_t width,const size_t height)
2260 {
2261   PixelList
2262     *pixel_list;
2263
2264   pixel_list=(PixelList *) AcquireMagickMemory(sizeof(*pixel_list));
2265   if (pixel_list == (PixelList *) NULL)
2266     return(pixel_list);
2267   (void) ResetMagickMemory((void *) pixel_list,0,sizeof(*pixel_list));
2268   pixel_list->length=width*height;
2269   pixel_list->skip_list.nodes=(SkipNode *) AcquireQuantumMemory(65537UL,
2270     sizeof(*pixel_list->skip_list.nodes));
2271   if (pixel_list->skip_list.nodes == (SkipNode *) NULL)
2272     return(DestroyPixelList(pixel_list));
2273   (void) ResetMagickMemory(pixel_list->skip_list.nodes,0,65537UL*
2274     sizeof(*pixel_list->skip_list.nodes));
2275   pixel_list->signature=MagickSignature;
2276   return(pixel_list);
2277 }
2278
2279 static PixelList **AcquirePixelListThreadSet(const size_t width,
2280   const size_t height)
2281 {
2282   PixelList
2283     **pixel_list;
2284
2285   register ssize_t
2286     i;
2287
2288   size_t
2289     number_threads;
2290
2291   number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
2292   pixel_list=(PixelList **) AcquireQuantumMemory(number_threads,
2293     sizeof(*pixel_list));
2294   if (pixel_list == (PixelList **) NULL)
2295     return((PixelList **) NULL);
2296   (void) ResetMagickMemory(pixel_list,0,number_threads*sizeof(*pixel_list));
2297   for (i=0; i < (ssize_t) number_threads; i++)
2298   {
2299     pixel_list[i]=AcquirePixelList(width,height);
2300     if (pixel_list[i] == (PixelList *) NULL)
2301       return(DestroyPixelListThreadSet(pixel_list));
2302   }
2303   return(pixel_list);
2304 }
2305
2306 static void AddNodePixelList(PixelList *pixel_list,const size_t color)
2307 {
2308   register SkipList
2309     *p;
2310
2311   register ssize_t
2312     level;
2313
2314   size_t
2315     search,
2316     update[9];
2317
2318   /*
2319     Initialize the node.
2320   */
2321   p=(&pixel_list->skip_list);
2322   p->nodes[color].signature=pixel_list->signature;
2323   p->nodes[color].count=1;
2324   /*
2325     Determine where it belongs in the list.
2326   */
2327   search=65536UL;
2328   for (level=p->level; level >= 0; level--)
2329   {
2330     while (p->nodes[search].next[level] < color)
2331       search=p->nodes[search].next[level];
2332     update[level]=search;
2333   }
2334   /*
2335     Generate a pseudo-random level for this node.
2336   */
2337   for (level=0; ; level++)
2338   {
2339     pixel_list->seed=(pixel_list->seed*42893621L)+1L;
2340     if ((pixel_list->seed & 0x300) != 0x300)
2341       break;
2342   }
2343   if (level > 8)
2344     level=8;
2345   if (level > (p->level+2))
2346     level=p->level+2;
2347   /*
2348     If we're raising the list's level, link back to the root node.
2349   */
2350   while (level > p->level)
2351   {
2352     p->level++;
2353     update[p->level]=65536UL;
2354   }
2355   /*
2356     Link the node into the skip-list.
2357   */
2358   do
2359   {
2360     p->nodes[color].next[level]=p->nodes[update[level]].next[level];
2361     p->nodes[update[level]].next[level]=color;
2362   } while (level-- > 0);
2363 }
2364
2365 static inline void GetMaximumPixelList(PixelList *pixel_list,Quantum *pixel)
2366 {
2367   register SkipList
2368     *p;
2369
2370   size_t
2371     color,
2372     maximum;
2373
2374   ssize_t
2375     count;
2376
2377   /*
2378     Find the maximum value for each of the color.
2379   */
2380   p=(&pixel_list->skip_list);
2381   color=65536L;
2382   count=0;
2383   maximum=p->nodes[color].next[0];
2384   do
2385   {
2386     color=p->nodes[color].next[0];
2387     if (color > maximum)
2388       maximum=color;
2389     count+=p->nodes[color].count;
2390   } while (count < (ssize_t) pixel_list->length);
2391   *pixel=ScaleShortToQuantum((unsigned short) maximum);
2392 }
2393
2394 static inline void GetMeanPixelList(PixelList *pixel_list,Quantum *pixel)
2395 {
2396   double
2397     sum;
2398
2399   register SkipList
2400     *p;
2401
2402   size_t
2403     color;
2404
2405   ssize_t
2406     count;
2407
2408   /*
2409     Find the mean value for each of the color.
2410   */
2411   p=(&pixel_list->skip_list);
2412   color=65536L;
2413   count=0;
2414   sum=0.0;
2415   do
2416   {
2417     color=p->nodes[color].next[0];
2418     sum+=(double) p->nodes[color].count*color;
2419     count+=p->nodes[color].count;
2420   } while (count < (ssize_t) pixel_list->length);
2421   sum/=pixel_list->length;
2422   *pixel=ScaleShortToQuantum((unsigned short) sum);
2423 }
2424
2425 static inline void GetMedianPixelList(PixelList *pixel_list,Quantum *pixel)
2426 {
2427   register SkipList
2428     *p;
2429
2430   size_t
2431     color;
2432
2433   ssize_t
2434     count;
2435
2436   /*
2437     Find the median value for each of the color.
2438   */
2439   p=(&pixel_list->skip_list);
2440   color=65536L;
2441   count=0;
2442   do
2443   {
2444     color=p->nodes[color].next[0];
2445     count+=p->nodes[color].count;
2446   } while (count <= (ssize_t) (pixel_list->length >> 1));
2447   *pixel=ScaleShortToQuantum((unsigned short) color);
2448 }
2449
2450 static inline void GetMinimumPixelList(PixelList *pixel_list,Quantum *pixel)
2451 {
2452   register SkipList
2453     *p;
2454
2455   size_t
2456     color,
2457     minimum;
2458
2459   ssize_t
2460     count;
2461
2462   /*
2463     Find the minimum value for each of the color.
2464   */
2465   p=(&pixel_list->skip_list);
2466   count=0;
2467   color=65536UL;
2468   minimum=p->nodes[color].next[0];
2469   do
2470   {
2471     color=p->nodes[color].next[0];
2472     if (color < minimum)
2473       minimum=color;
2474     count+=p->nodes[color].count;
2475   } while (count < (ssize_t) pixel_list->length);
2476   *pixel=ScaleShortToQuantum((unsigned short) minimum);
2477 }
2478
2479 static inline void GetModePixelList(PixelList *pixel_list,Quantum *pixel)
2480 {
2481   register SkipList
2482     *p;
2483
2484   size_t
2485     color,
2486     max_count,
2487     mode;
2488
2489   ssize_t
2490     count;
2491
2492   /*
2493     Make each pixel the 'predominant color' of the specified neighborhood.
2494   */
2495   p=(&pixel_list->skip_list);
2496   color=65536L;
2497   mode=color;
2498   max_count=p->nodes[mode].count;
2499   count=0;
2500   do
2501   {
2502     color=p->nodes[color].next[0];
2503     if (p->nodes[color].count > max_count)
2504       {
2505         mode=color;
2506         max_count=p->nodes[mode].count;
2507       }
2508     count+=p->nodes[color].count;
2509   } while (count < (ssize_t) pixel_list->length);
2510   *pixel=ScaleShortToQuantum((unsigned short) mode);
2511 }
2512
2513 static inline void GetNonpeakPixelList(PixelList *pixel_list,Quantum *pixel)
2514 {
2515   register SkipList
2516     *p;
2517
2518   size_t
2519     color,
2520     next,
2521     previous;
2522
2523   ssize_t
2524     count;
2525
2526   /*
2527     Finds the non peak value for each of the colors.
2528   */
2529   p=(&pixel_list->skip_list);
2530   color=65536L;
2531   next=p->nodes[color].next[0];
2532   count=0;
2533   do
2534   {
2535     previous=color;
2536     color=next;
2537     next=p->nodes[color].next[0];
2538     count+=p->nodes[color].count;
2539   } while (count <= (ssize_t) (pixel_list->length >> 1));
2540   if ((previous == 65536UL) && (next != 65536UL))
2541     color=next;
2542   else
2543     if ((previous != 65536UL) && (next == 65536UL))
2544       color=previous;
2545   *pixel=ScaleShortToQuantum((unsigned short) color);
2546 }
2547
2548 static inline void GetStandardDeviationPixelList(PixelList *pixel_list,
2549   Quantum *pixel)
2550 {
2551   double
2552     sum,
2553     sum_squared;
2554
2555   register SkipList
2556     *p;
2557
2558   size_t
2559     color;
2560
2561   ssize_t
2562     count;
2563
2564   /*
2565     Find the standard-deviation value for each of the color.
2566   */
2567   p=(&pixel_list->skip_list);
2568   color=65536L;
2569   count=0;
2570   sum=0.0;
2571   sum_squared=0.0;
2572   do
2573   {
2574     register ssize_t
2575       i;
2576
2577     color=p->nodes[color].next[0];
2578     sum+=(double) p->nodes[color].count*color;
2579     for (i=0; i < (ssize_t) p->nodes[color].count; i++)
2580       sum_squared+=((double) color)*((double) color);
2581     count+=p->nodes[color].count;
2582   } while (count < (ssize_t) pixel_list->length);
2583   sum/=pixel_list->length;
2584   sum_squared/=pixel_list->length;
2585   *pixel=ScaleShortToQuantum((unsigned short) sqrt(sum_squared-(sum*sum)));
2586 }
2587
2588 static inline void InsertPixelList(const Quantum pixel,PixelList *pixel_list)
2589 {
2590   size_t
2591     signature;
2592
2593   unsigned short
2594     index;
2595
2596   index=ScaleQuantumToShort(pixel);
2597   signature=pixel_list->skip_list.nodes[index].signature;
2598   if (signature == pixel_list->signature)
2599     {
2600       pixel_list->skip_list.nodes[index].count++;
2601       return;
2602     }
2603   AddNodePixelList(pixel_list,index);
2604 }
2605
2606 static inline double MagickAbsoluteValue(const double x)
2607 {
2608   if (x < 0)
2609     return(-x);
2610   return(x);
2611 }
2612
2613 static inline size_t MagickMax(const size_t x,const size_t y)
2614 {
2615   if (x > y)
2616     return(x);
2617   return(y);
2618 }
2619
2620 static void ResetPixelList(PixelList *pixel_list)
2621 {
2622   int
2623     level;
2624
2625   register SkipNode
2626     *root;
2627
2628   register SkipList
2629     *p;
2630
2631   /*
2632     Reset the skip-list.
2633   */
2634   p=(&pixel_list->skip_list);
2635   root=p->nodes+65536UL;
2636   p->level=0;
2637   for (level=0; level < 9; level++)
2638     root->next[level]=65536UL;
2639   pixel_list->seed=pixel_list->signature++;
2640 }
2641
2642 MagickExport Image *StatisticImage(const Image *image,const StatisticType type,
2643   const size_t width,const size_t height,ExceptionInfo *exception)
2644 {
2645 #define StatisticImageTag  "Statistic/Image"
2646
2647   CacheView
2648     *image_view,
2649     *statistic_view;
2650
2651   Image
2652     *statistic_image;
2653
2654   MagickBooleanType
2655     status;
2656
2657   MagickOffsetType
2658     progress;
2659
2660   PixelList
2661     **restrict pixel_list;
2662
2663   ssize_t
2664     center,
2665     y;
2666
2667   /*
2668     Initialize statistics image attributes.
2669   */
2670   assert(image != (Image *) NULL);
2671   assert(image->signature == MagickSignature);
2672   if (image->debug != MagickFalse)
2673     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2674   assert(exception != (ExceptionInfo *) NULL);
2675   assert(exception->signature == MagickSignature);
2676   statistic_image=CloneImage(image,image->columns,image->rows,MagickTrue,
2677     exception);
2678   if (statistic_image == (Image *) NULL)
2679     return((Image *) NULL);
2680   status=SetImageStorageClass(statistic_image,DirectClass,exception);
2681   if (status == MagickFalse)
2682     {
2683       statistic_image=DestroyImage(statistic_image);
2684       return((Image *) NULL);
2685     }
2686   pixel_list=AcquirePixelListThreadSet(MagickMax(width,1),MagickMax(height,1));
2687   if (pixel_list == (PixelList **) NULL)
2688     {
2689       statistic_image=DestroyImage(statistic_image);
2690       ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
2691     }
2692   /*
2693     Make each pixel the min / max / median / mode / etc. of the neighborhood.
2694   */
2695   center=(ssize_t) GetPixelChannels(image)*(image->columns+MagickMax(width,1))*
2696     (MagickMax(height,1)/2L)+GetPixelChannels(image)*(MagickMax(width,1)/2L);
2697   status=MagickTrue;
2698   progress=0;
2699   image_view=AcquireVirtualCacheView(image,exception);
2700   statistic_view=AcquireAuthenticCacheView(statistic_image,exception);
2701 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2702   #pragma omp parallel for schedule(static,4) shared(progress,status) \
2703     magick_threads(image,statistic_image,statistic_image->rows,1)
2704 #endif
2705   for (y=0; y < (ssize_t) statistic_image->rows; y++)
2706   {
2707     const int
2708       id = GetOpenMPThreadId();
2709
2710     register const Quantum
2711       *restrict p;
2712
2713     register Quantum
2714       *restrict q;
2715
2716     register ssize_t
2717       x;
2718
2719     if (status == MagickFalse)
2720       continue;
2721     p=GetCacheViewVirtualPixels(image_view,-((ssize_t) MagickMax(width,1)/2L),y-
2722       (ssize_t) (MagickMax(height,1)/2L),image->columns+MagickMax(width,1),
2723       MagickMax(height,1),exception);
2724     q=QueueCacheViewAuthenticPixels(statistic_view,0,y,statistic_image->columns,      1,exception);
2725     if ((p == (const Quantum *) NULL) || (q == (Quantum *) NULL))
2726       {
2727         status=MagickFalse;
2728         continue;
2729       }
2730     for (x=0; x < (ssize_t) statistic_image->columns; x++)
2731     {
2732       register ssize_t
2733         i;
2734
2735       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
2736       {
2737         Quantum
2738           pixel;
2739
2740         register const Quantum
2741           *restrict pixels;
2742
2743         register ssize_t
2744           u;
2745
2746         ssize_t
2747           v;
2748
2749         PixelChannel channel=GetPixelChannelChannel(image,i);
2750         PixelTrait traits=GetPixelChannelTraits(image,channel);
2751         PixelTrait statistic_traits=GetPixelChannelTraits(statistic_image,
2752           channel);
2753         if ((traits == UndefinedPixelTrait) ||
2754             (statistic_traits == UndefinedPixelTrait))
2755           continue;
2756         if (((statistic_traits & CopyPixelTrait) != 0) ||
2757             (GetPixelReadMask(image,p) == 0))
2758           {
2759             SetPixelChannel(statistic_image,channel,p[center+i],q);
2760             continue;
2761           }
2762         pixels=p;
2763         ResetPixelList(pixel_list[id]);
2764         for (v=0; v < (ssize_t) MagickMax(height,1); v++)
2765         {
2766           for (u=0; u < (ssize_t) MagickMax(width,1); u++)
2767           {
2768             InsertPixelList(pixels[i],pixel_list[id]);
2769             pixels+=GetPixelChannels(image);
2770           }
2771           pixels+=(image->columns-1)*GetPixelChannels(image);
2772         }
2773         switch (type)
2774         {
2775           case GradientStatistic:
2776           {
2777             double
2778               maximum,
2779               minimum;
2780
2781             GetMinimumPixelList(pixel_list[id],&pixel);
2782             minimum=(double) pixel;
2783             GetMaximumPixelList(pixel_list[id],&pixel);
2784             maximum=(double) pixel;
2785             pixel=ClampToQuantum(MagickAbsoluteValue(maximum-minimum));
2786             break;
2787           }
2788           case MaximumStatistic:
2789           {
2790             GetMaximumPixelList(pixel_list[id],&pixel);
2791             break;
2792           }
2793           case MeanStatistic:
2794           {
2795             GetMeanPixelList(pixel_list[id],&pixel);
2796             break;
2797           }
2798           case MedianStatistic:
2799           default:
2800           {
2801             GetMedianPixelList(pixel_list[id],&pixel);
2802             break;
2803           }
2804           case MinimumStatistic:
2805           {
2806             GetMinimumPixelList(pixel_list[id],&pixel);
2807             break;
2808           }
2809           case ModeStatistic:
2810           {
2811             GetModePixelList(pixel_list[id],&pixel);
2812             break;
2813           }
2814           case NonpeakStatistic:
2815           {
2816             GetNonpeakPixelList(pixel_list[id],&pixel);
2817             break;
2818           }
2819           case StandardDeviationStatistic:
2820           {
2821             GetStandardDeviationPixelList(pixel_list[id],&pixel);
2822             break;
2823           }
2824         }
2825         SetPixelChannel(statistic_image,channel,pixel,q);
2826       }
2827       p+=GetPixelChannels(image);
2828       q+=GetPixelChannels(statistic_image);
2829     }
2830     if (SyncCacheViewAuthenticPixels(statistic_view,exception) == MagickFalse)
2831       status=MagickFalse;
2832     if (image->progress_monitor != (MagickProgressMonitor) NULL)
2833       {
2834         MagickBooleanType
2835           proceed;
2836
2837 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2838         #pragma omp critical (MagickCore_StatisticImage)
2839 #endif
2840         proceed=SetImageProgress(image,StatisticImageTag,progress++,
2841           image->rows);
2842         if (proceed == MagickFalse)
2843           status=MagickFalse;
2844       }
2845   }
2846   statistic_view=DestroyCacheView(statistic_view);
2847   image_view=DestroyCacheView(image_view);
2848   pixel_list=DestroyPixelListThreadSet(pixel_list);
2849   if (status == MagickFalse)
2850     statistic_image=DestroyImage(statistic_image);
2851   return(statistic_image);
2852 }