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 (fabs(M00[channel]) < MagickEpsilon)
1464       continue;
1465     centroid[channel].x=M10[channel]/M00[channel];
1466     centroid[channel].y=M01[channel]/M00[channel];
1467   }
1468   for (y=0; y < (ssize_t) image->rows; y++)
1469   {
1470     register const Quantum
1471       *restrict p;
1472
1473     register ssize_t
1474       x;
1475
1476     /*
1477       Compute the image moments.
1478     */
1479     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1480     if (p == (const Quantum *) NULL)
1481       break;
1482     for (x=0; x < (ssize_t) image->columns; x++)
1483     {
1484       register ssize_t
1485         i;
1486
1487       if (GetPixelReadMask(image,p) == 0)
1488         {
1489           p+=GetPixelChannels(image);
1490           continue;
1491         }
1492       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1493       {
1494         PixelChannel channel=GetPixelChannelChannel(image,i);
1495         PixelTrait traits=GetPixelChannelTraits(image,channel);
1496         if (traits == UndefinedPixelTrait)
1497           continue;
1498         if ((traits & UpdatePixelTrait) == 0)
1499           continue;
1500         M11[channel]+=(x-centroid[channel].x)*(y-centroid[channel].y)*
1501           QuantumScale*p[i];
1502         M20[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
1503           QuantumScale*p[i];
1504         M02[channel]+=(y-centroid[channel].y)*(y-centroid[channel].y)*
1505           QuantumScale*p[i];
1506         M21[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
1507           (y-centroid[channel].y)*QuantumScale*p[i];
1508         M12[channel]+=(x-centroid[channel].x)*(y-centroid[channel].y)*
1509           (y-centroid[channel].y)*QuantumScale*p[i];
1510         M22[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
1511           (y-centroid[channel].y)*(y-centroid[channel].y)*QuantumScale*p[i];
1512         M30[channel]+=(x-centroid[channel].x)*(x-centroid[channel].x)*
1513           (x-centroid[channel].x)*QuantumScale*p[i];
1514         M03[channel]+=(y-centroid[channel].y)*(y-centroid[channel].y)*
1515           (y-centroid[channel].y)*QuantumScale*p[i];
1516       }
1517       p+=GetPixelChannels(image);
1518     }
1519   }
1520   for (channel=0; channel <= MaxPixelChannels; channel++)
1521   {
1522     /*
1523       Compute elliptical angle, major and minor axes, eccentricity, & intensity.
1524     */
1525     if (fabs(M00[channel]) < MagickEpsilon)
1526       continue;
1527     channel_moments[channel].centroid=centroid[channel];
1528     channel_moments[channel].ellipse_axis.x=sqrt((2.0/M00[channel])*
1529       ((M20[channel]+M02[channel])+sqrt(4.0*M11[channel]*M11[channel]+
1530       (M20[channel]-M02[channel])*(M20[channel]-M02[channel]))));
1531     channel_moments[channel].ellipse_axis.y=sqrt((2.0/M00[channel])*
1532       ((M20[channel]+M02[channel])-sqrt(4.0*M11[channel]*M11[channel]+
1533       (M20[channel]-M02[channel])*(M20[channel]-M02[channel]))));
1534     channel_moments[channel].ellipse_angle=RadiansToDegrees(0.5*atan(2.0*
1535       M11[channel]/(M20[channel]-M02[channel])));
1536     channel_moments[channel].ellipse_eccentricity=sqrt(1.0-(
1537       channel_moments[channel].ellipse_axis.y/
1538       channel_moments[channel].ellipse_axis.x));
1539     channel_moments[channel].ellipse_intensity=M00[channel]/(MagickPI*
1540       channel_moments[channel].ellipse_axis.x*
1541       channel_moments[channel].ellipse_axis.y);
1542   }
1543   for (channel=0; channel <= MaxPixelChannels; channel++)
1544   {
1545     /*
1546       Normalize image moments.
1547     */
1548     if (fabs(M00[channel]) < MagickEpsilon)
1549       continue;
1550     M11[channel]/=pow(M00[channel],(1.0+(1.0+1.0)/2.0));
1551     M20[channel]/=pow(M00[channel],(1.0+(2.0+0.0)/2.0));
1552     M02[channel]/=pow(M00[channel],(1.0+(0.0+2.0)/2.0));
1553     M21[channel]/=pow(M00[channel],(1.0+(2.0+1.0)/2.0));
1554     M12[channel]/=pow(M00[channel],(1.0+(1.0+2.0)/2.0));
1555     M22[channel]/=pow(M00[channel],(1.0+(2.0+2.0)/2.0));
1556     M30[channel]/=pow(M00[channel],(1.0+(3.0+0.0)/2.0));
1557     M03[channel]/=pow(M00[channel],(1.0+(0.0+3.0)/2.0));
1558   }
1559   image_view=DestroyCacheView(image_view);
1560   for (channel=0; channel <= MaxPixelChannels; channel++)
1561   {
1562     /*
1563       Compute Hu invariant moments.
1564     */
1565     if (fabs(M00[channel]) < MagickEpsilon)
1566       continue;
1567    channel_moments[channel].I[0]=M20[channel]+M02[channel];
1568     channel_moments[channel].I[1]=(M20[channel]-M02[channel])*
1569       (M20[channel]-M02[channel])+4.0*M11[channel]*M11[channel];
1570     channel_moments[channel].I[2]=(M30[channel]-3.0*M12[channel])*
1571       (M30[channel]-3.0*M12[channel])+(3.0*M21[channel]-M03[channel])*
1572       (3.0*M21[channel]-M03[channel]);
1573     channel_moments[channel].I[3]=(M30[channel]+M12[channel])*
1574       (M30[channel]+M12[channel])+(M21[channel]+M03[channel])*
1575       (M21[channel]+M03[channel]);
1576     channel_moments[channel].I[4]=(M30[channel]-3.0*M12[channel])*
1577       (M30[channel]+M12[channel])*((M30[channel]+M12[channel])*
1578       (M30[channel]+M12[channel])-3.0*(M21[channel]+M03[channel])*
1579       (M21[channel]+M03[channel]))+(3.0*M21[channel]-M03[channel])*
1580       (M21[channel]+M03[channel])*(3.0*(M30[channel]+M12[channel])*
1581       (M30[channel]+M12[channel])-(M21[channel]+M03[channel])*
1582       (M21[channel]+M03[channel]));
1583     channel_moments[channel].I[5]=(M20[channel]-M02[channel])*
1584       ((M30[channel]+M12[channel])*(M30[channel]+M12[channel])-
1585       (M21[channel]+M03[channel])*(M21[channel]+M03[channel]))+
1586       4.0*M11[channel]*(M30[channel]+M12[channel])*(M21[channel]+M03[channel]);
1587     channel_moments[channel].I[6]=(3.0*M21[channel]-M03[channel])*
1588       (M30[channel]+M12[channel])*((M30[channel]+M12[channel])*
1589       (M30[channel]+M12[channel])-3.0*(M21[channel]+M03[channel])*
1590       (M21[channel]+M03[channel]))-(M30[channel]-3*M12[channel])*
1591       (M21[channel]+M03[channel])*(3.0*(M30[channel]+M12[channel])*
1592       (M30[channel]+M12[channel])-(M21[channel]+M03[channel])*
1593       (M21[channel]+M03[channel]));
1594     channel_moments[channel].I[7]=M11[channel]*((M30[channel]+M12[channel])*
1595       (M30[channel]+M12[channel])-(M03[channel]+M21[channel])*
1596       (M03[channel]+M21[channel]))-(M20[channel]-M02[channel])*
1597       (M30[channel]+M12[channel])*(M03[channel]+M21[channel]);
1598   }
1599   if (y < (ssize_t) image->rows)
1600     channel_moments=(ChannelMoments *) RelinquishMagickMemory(channel_moments);
1601   return(channel_moments);
1602 }
1603 \f
1604 /*
1605 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1606 %                                                                             %
1607 %                                                                             %
1608 %                                                                             %
1609 %   G e t I m a g e R a n g e                                                 %
1610 %                                                                             %
1611 %                                                                             %
1612 %                                                                             %
1613 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1614 %
1615 %  GetImageRange() returns the range of one or more image channels.
1616 %
1617 %  The format of the GetImageRange method is:
1618 %
1619 %      MagickBooleanType GetImageRange(const Image *image,double *minima,
1620 %        double *maxima,ExceptionInfo *exception)
1621 %
1622 %  A description of each parameter follows:
1623 %
1624 %    o image: the image.
1625 %
1626 %    o minima: the minimum value in the channel.
1627 %
1628 %    o maxima: the maximum value in the channel.
1629 %
1630 %    o exception: return any errors or warnings in this structure.
1631 %
1632 */
1633 MagickExport MagickBooleanType GetImageRange(const Image *image,double *minima,
1634   double *maxima,ExceptionInfo *exception)
1635 {
1636   CacheView
1637     *image_view;
1638
1639   MagickBooleanType
1640     initialize,
1641     status;
1642
1643   ssize_t
1644     y;
1645
1646   assert(image != (Image *) NULL);
1647   assert(image->signature == MagickSignature);
1648   if (image->debug != MagickFalse)
1649     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1650   status=MagickTrue;
1651   initialize=MagickTrue;
1652   *maxima=0.0;
1653   *minima=0.0;
1654   image_view=AcquireVirtualCacheView(image,exception);
1655 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1656   #pragma omp parallel for schedule(static,4) shared(status,initialize) \
1657     magick_threads(image,image,image->rows,1)
1658 #endif
1659   for (y=0; y < (ssize_t) image->rows; y++)
1660   {
1661     register const Quantum
1662       *restrict p;
1663
1664     register ssize_t
1665       x;
1666
1667     if (status == MagickFalse)
1668       continue;
1669     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1670     if (p == (const Quantum *) NULL)
1671       {
1672         status=MagickFalse;
1673         continue;
1674       }
1675     for (x=0; x < (ssize_t) image->columns; x++)
1676     {
1677       register ssize_t
1678         i;
1679
1680       if (GetPixelReadMask(image,p) == 0)
1681         {
1682           p+=GetPixelChannels(image);
1683           continue;
1684         }
1685       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1686       {
1687         PixelChannel channel=GetPixelChannelChannel(image,i);
1688         PixelTrait traits=GetPixelChannelTraits(image,channel);
1689         if (traits == UndefinedPixelTrait)
1690           continue;
1691         if ((traits & UpdatePixelTrait) == 0)
1692           continue;
1693 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1694         #pragma omp critical (MagickCore_GetImageRange)
1695 #endif
1696         {
1697           if (initialize != MagickFalse)
1698             {
1699               *minima=(double) p[i];
1700               *maxima=(double) p[i];
1701               initialize=MagickFalse;
1702             }
1703           else
1704             {
1705               if ((double) p[i] < *minima)
1706                 *minima=(double) p[i];
1707               if ((double) p[i] > *maxima)
1708                 *maxima=(double) p[i];
1709            }
1710         }
1711       }
1712       p+=GetPixelChannels(image);
1713     }
1714   }
1715   image_view=DestroyCacheView(image_view);
1716   return(status);
1717 }
1718 \f
1719 /*
1720 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1721 %                                                                             %
1722 %                                                                             %
1723 %                                                                             %
1724 %   G e t I m a g e S t a t i s t i c s                                       %
1725 %                                                                             %
1726 %                                                                             %
1727 %                                                                             %
1728 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1729 %
1730 %  GetImageStatistics() returns statistics for each channel in the image.  The
1731 %  statistics include the channel depth, its minima, maxima, mean, standard
1732 %  deviation, kurtosis and skewness.  You can access the red channel mean, for
1733 %  example, like this:
1734 %
1735 %      channel_statistics=GetImageStatistics(image,exception);
1736 %      red_mean=channel_statistics[RedPixelChannel].mean;
1737 %
1738 %  Use MagickRelinquishMemory() to free the statistics buffer.
1739 %
1740 %  The format of the GetImageStatistics method is:
1741 %
1742 %      ChannelStatistics *GetImageStatistics(const Image *image,
1743 %        ExceptionInfo *exception)
1744 %
1745 %  A description of each parameter follows:
1746 %
1747 %    o image: the image.
1748 %
1749 %    o exception: return any errors or warnings in this structure.
1750 %
1751 */
1752
1753 static size_t GetImageChannels(const Image *image)
1754 {
1755   register ssize_t
1756     i;
1757
1758   size_t
1759     channels;
1760
1761   channels=0;
1762   for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1763   {
1764     PixelChannel channel=GetPixelChannelChannel(image,i);
1765     PixelTrait traits=GetPixelChannelTraits(image,channel);
1766     if (traits != UndefinedPixelTrait)
1767       channels++;
1768   }
1769   return(channels);
1770 }
1771
1772 MagickExport ChannelStatistics *GetImageStatistics(const Image *image,
1773   ExceptionInfo *exception)
1774 {
1775   ChannelStatistics
1776     *channel_statistics;
1777
1778   MagickStatusType
1779     status;
1780
1781   QuantumAny
1782     range;
1783
1784   register ssize_t
1785     i;
1786
1787   size_t
1788     channels,
1789     depth;
1790
1791   ssize_t
1792     y;
1793
1794   assert(image != (Image *) NULL);
1795   assert(image->signature == MagickSignature);
1796   if (image->debug != MagickFalse)
1797     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1798   channel_statistics=(ChannelStatistics *) AcquireQuantumMemory(
1799     MaxPixelChannels+1,sizeof(*channel_statistics));
1800   if (channel_statistics == (ChannelStatistics *) NULL)
1801     return(channel_statistics);
1802   (void) ResetMagickMemory(channel_statistics,0,(MaxPixelChannels+1)*
1803     sizeof(*channel_statistics));
1804   for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
1805   {
1806     channel_statistics[i].depth=1;
1807     channel_statistics[i].maxima=(-MagickHuge);
1808     channel_statistics[i].minima=MagickHuge;
1809   }
1810   for (y=0; y < (ssize_t) image->rows; y++)
1811   {
1812     register const Quantum
1813       *restrict p;
1814
1815     register ssize_t
1816       x;
1817
1818     p=GetVirtualPixels(image,0,y,image->columns,1,exception);
1819     if (p == (const Quantum *) NULL)
1820       break;
1821     for (x=0; x < (ssize_t) image->columns; x++)
1822     {
1823       register ssize_t
1824         i;
1825
1826       if (GetPixelReadMask(image,p) == 0)
1827         {
1828           p+=GetPixelChannels(image);
1829           continue;
1830         }
1831       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1832       {
1833         PixelChannel channel=GetPixelChannelChannel(image,i);
1834         PixelTrait traits=GetPixelChannelTraits(image,channel);
1835         if (traits == UndefinedPixelTrait)
1836           continue;
1837         if (channel_statistics[channel].depth != MAGICKCORE_QUANTUM_DEPTH)
1838           {
1839             depth=channel_statistics[channel].depth;
1840             range=GetQuantumRange(depth);
1841             status=p[i] != ScaleAnyToQuantum(ScaleQuantumToAny(p[i],range),
1842               range) ? MagickTrue : MagickFalse;
1843             if (status != MagickFalse)
1844               {
1845                 channel_statistics[channel].depth++;
1846                 i--;
1847                 continue;
1848               }
1849           }
1850         if ((double) p[i] < channel_statistics[channel].minima)
1851           channel_statistics[channel].minima=(double) p[i];
1852         if ((double) p[i] > channel_statistics[channel].maxima)
1853           channel_statistics[channel].maxima=(double) p[i];
1854         channel_statistics[channel].sum+=p[i];
1855         channel_statistics[channel].sum_squared+=(double) p[i]*p[i];
1856         channel_statistics[channel].sum_cubed+=(double) p[i]*p[i]*p[i];
1857         channel_statistics[channel].sum_fourth_power+=(double) p[i]*p[i]*p[i]*
1858           p[i];
1859         channel_statistics[channel].area++;
1860       }
1861       p+=GetPixelChannels(image);
1862     }
1863   }
1864   for (i=0; i < (ssize_t) MaxPixelChannels; i++)
1865   {
1866     double
1867       area;
1868
1869     area=PerceptibleReciprocal(channel_statistics[i].area);
1870     channel_statistics[i].sum*=area;
1871     channel_statistics[i].sum_squared*=area;
1872     channel_statistics[i].sum_cubed*=area;
1873     channel_statistics[i].sum_fourth_power*=area;
1874     channel_statistics[i].mean=channel_statistics[i].sum;
1875     channel_statistics[i].variance=channel_statistics[i].sum_squared;
1876     channel_statistics[i].standard_deviation=sqrt(
1877       channel_statistics[i].variance-(channel_statistics[i].mean*
1878       channel_statistics[i].mean));
1879   }
1880   for (i=0; i < (ssize_t) MaxPixelChannels; i++)
1881   {
1882     channel_statistics[CompositePixelChannel].area+=channel_statistics[i].area;
1883     channel_statistics[CompositePixelChannel].minima=MagickMin(
1884       channel_statistics[CompositePixelChannel].minima,
1885       channel_statistics[i].minima);
1886     channel_statistics[CompositePixelChannel].maxima=EvaluateMax(
1887       channel_statistics[CompositePixelChannel].maxima,
1888       channel_statistics[i].maxima);
1889     channel_statistics[CompositePixelChannel].sum+=channel_statistics[i].sum;
1890     channel_statistics[CompositePixelChannel].sum_squared+=
1891       channel_statistics[i].sum_squared;
1892     channel_statistics[CompositePixelChannel].sum_cubed+=
1893       channel_statistics[i].sum_cubed;
1894     channel_statistics[CompositePixelChannel].sum_fourth_power+=
1895       channel_statistics[i].sum_fourth_power;
1896     channel_statistics[CompositePixelChannel].mean+=channel_statistics[i].mean;
1897     channel_statistics[CompositePixelChannel].variance+=
1898       channel_statistics[i].variance-channel_statistics[i].mean*
1899       channel_statistics[i].mean;
1900     channel_statistics[CompositePixelChannel].standard_deviation+=
1901       channel_statistics[i].variance-channel_statistics[i].mean*
1902       channel_statistics[i].mean;
1903   }
1904   channels=GetImageChannels(image);
1905   channel_statistics[CompositePixelChannel].area/=channels;
1906   channel_statistics[CompositePixelChannel].sum/=channels;
1907   channel_statistics[CompositePixelChannel].sum_squared/=channels;
1908   channel_statistics[CompositePixelChannel].sum_cubed/=channels;
1909   channel_statistics[CompositePixelChannel].sum_fourth_power/=channels;
1910   channel_statistics[CompositePixelChannel].mean/=channels;
1911   channel_statistics[CompositePixelChannel].variance/=channels;
1912   channel_statistics[CompositePixelChannel].standard_deviation=
1913     sqrt(channel_statistics[CompositePixelChannel].standard_deviation/channels);
1914   channel_statistics[CompositePixelChannel].kurtosis/=channels;
1915   channel_statistics[CompositePixelChannel].skewness/=channels;
1916   for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
1917   {
1918     double
1919       standard_deviation;
1920
1921     if (channel_statistics[i].standard_deviation == 0.0)
1922       continue;
1923     standard_deviation=PerceptibleReciprocal(
1924       channel_statistics[i].standard_deviation);
1925     channel_statistics[i].skewness=(channel_statistics[i].sum_cubed-3.0*
1926       channel_statistics[i].mean*channel_statistics[i].sum_squared+2.0*
1927       channel_statistics[i].mean*channel_statistics[i].mean*
1928       channel_statistics[i].mean)*(standard_deviation*standard_deviation*
1929       standard_deviation);
1930     channel_statistics[i].kurtosis=(channel_statistics[i].sum_fourth_power-4.0*
1931       channel_statistics[i].mean*channel_statistics[i].sum_cubed+6.0*
1932       channel_statistics[i].mean*channel_statistics[i].mean*
1933       channel_statistics[i].sum_squared-3.0*channel_statistics[i].mean*
1934       channel_statistics[i].mean*1.0*channel_statistics[i].mean*
1935       channel_statistics[i].mean)*(standard_deviation*standard_deviation*
1936       standard_deviation*standard_deviation)-3.0;
1937   }
1938   if (y < (ssize_t) image->rows)
1939     channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
1940       channel_statistics);
1941   return(channel_statistics);
1942 }
1943 \f
1944 /*
1945 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1946 %                                                                             %
1947 %                                                                             %
1948 %                                                                             %
1949 %     P o l y n o m i a l I m a g e                                           %
1950 %                                                                             %
1951 %                                                                             %
1952 %                                                                             %
1953 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1954 %
1955 %  PolynomialImage() returns a new image where each pixel is the sum of the
1956 %  pixels in the image sequence after applying its corresponding terms
1957 %  (coefficient and degree pairs).
1958 %
1959 %  The format of the PolynomialImage method is:
1960 %
1961 %      Image *PolynomialImage(const Image *images,const size_t number_terms,
1962 %        const double *terms,ExceptionInfo *exception)
1963 %
1964 %  A description of each parameter follows:
1965 %
1966 %    o images: the image sequence.
1967 %
1968 %    o number_terms: the number of terms in the list.  The actual list length
1969 %      is 2 x number_terms + 1 (the constant).
1970 %
1971 %    o terms: the list of polynomial coefficients and degree pairs and a
1972 %      constant.
1973 %
1974 %    o exception: return any errors or warnings in this structure.
1975 %
1976 */
1977
1978 MagickExport Image *PolynomialImage(const Image *images,
1979   const size_t number_terms,const double *terms,ExceptionInfo *exception)
1980 {
1981 #define PolynomialImageTag  "Polynomial/Image"
1982
1983   CacheView
1984     *polynomial_view;
1985
1986   Image
1987     *image;
1988
1989   MagickBooleanType
1990     status;
1991
1992   MagickOffsetType
1993     progress;
1994
1995   PixelChannels
1996     **restrict polynomial_pixels;
1997
1998   size_t
1999     number_images;
2000
2001   ssize_t
2002     y;
2003
2004   assert(images != (Image *) NULL);
2005   assert(images->signature == MagickSignature);
2006   if (images->debug != MagickFalse)
2007     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
2008   assert(exception != (ExceptionInfo *) NULL);
2009   assert(exception->signature == MagickSignature);
2010   image=CloneImage(images,images->columns,images->rows,MagickTrue,
2011     exception);
2012   if (image == (Image *) NULL)
2013     return((Image *) NULL);
2014   if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
2015     {
2016       image=DestroyImage(image);
2017       return((Image *) NULL);
2018     }
2019   number_images=GetImageListLength(images);
2020   polynomial_pixels=AcquirePixelThreadSet(images,number_images);
2021   if (polynomial_pixels == (PixelChannels **) NULL)
2022     {
2023       image=DestroyImage(image);
2024       (void) ThrowMagickException(exception,GetMagickModule(),
2025         ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
2026       return((Image *) NULL);
2027     }
2028   /*
2029     Polynomial image pixels.
2030   */
2031   status=MagickTrue;
2032   progress=0;
2033   polynomial_view=AcquireAuthenticCacheView(image,exception);
2034 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2035   #pragma omp parallel for schedule(static,4) shared(progress,status) \
2036     magick_threads(image,image,image->rows,1)
2037 #endif
2038   for (y=0; y < (ssize_t) image->rows; y++)
2039   {
2040     CacheView
2041       *image_view;
2042
2043     const Image
2044       *next;
2045
2046     const int
2047       id = GetOpenMPThreadId();
2048
2049     register ssize_t
2050       i,
2051       x;
2052
2053     register PixelChannels
2054       *polynomial_pixel;
2055
2056     register Quantum
2057       *restrict q;
2058
2059     ssize_t
2060       j;
2061
2062     if (status == MagickFalse)
2063       continue;
2064     q=QueueCacheViewAuthenticPixels(polynomial_view,0,y,image->columns,1,
2065       exception);
2066     if (q == (Quantum *) NULL)
2067       {
2068         status=MagickFalse;
2069         continue;
2070       }
2071     polynomial_pixel=polynomial_pixels[id];
2072     for (j=0; j < (ssize_t) image->columns; j++)
2073       for (i=0; i < MaxPixelChannels; i++)
2074         polynomial_pixel[j].channel[i]=0.0;
2075     next=images;
2076     for (j=0; j < (ssize_t) number_images; j++)
2077     {
2078       register const Quantum
2079         *p;
2080
2081       if (j >= (ssize_t) number_terms)
2082         continue;
2083       image_view=AcquireVirtualCacheView(next,exception);
2084       p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
2085       if (p == (const Quantum *) NULL)
2086         {
2087           image_view=DestroyCacheView(image_view);
2088           break;
2089         }
2090       for (x=0; x < (ssize_t) image->columns; x++)
2091       {
2092         register ssize_t
2093           i;
2094
2095         if (GetPixelReadMask(next,p) == 0)
2096           {
2097             p+=GetPixelChannels(next);
2098             continue;
2099           }
2100         for (i=0; i < (ssize_t) GetPixelChannels(next); i++)
2101         {
2102           MagickRealType
2103             coefficient,
2104             degree;
2105
2106           PixelChannel channel=GetPixelChannelChannel(image,i);
2107           PixelTrait traits=GetPixelChannelTraits(next,channel);
2108           PixelTrait polynomial_traits=GetPixelChannelTraits(image,channel);
2109           if ((traits == UndefinedPixelTrait) ||
2110               (polynomial_traits == UndefinedPixelTrait))
2111             continue;
2112           if ((traits & UpdatePixelTrait) == 0)
2113             continue;
2114           coefficient=(MagickRealType) terms[2*i];
2115           degree=(MagickRealType) terms[(i << 1)+1];
2116           polynomial_pixel[x].channel[i]+=coefficient*
2117             pow(QuantumScale*GetPixelChannel(image,channel,p),degree);
2118         }
2119         p+=GetPixelChannels(next);
2120       }
2121       image_view=DestroyCacheView(image_view);
2122       next=GetNextImageInList(next);
2123     }
2124     for (x=0; x < (ssize_t) image->columns; x++)
2125     {
2126       register ssize_t
2127         i;
2128
2129       if (GetPixelReadMask(image,q) == 0)
2130         {
2131           q+=GetPixelChannels(image);
2132           continue;
2133         }
2134       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
2135       {
2136         PixelChannel channel=GetPixelChannelChannel(image,i);
2137         PixelTrait traits=GetPixelChannelTraits(image,channel);
2138         if (traits == UndefinedPixelTrait)
2139           continue;
2140         if ((traits & UpdatePixelTrait) == 0)
2141           continue;
2142         q[i]=ClampToQuantum(QuantumRange*polynomial_pixel[x].channel[i]);
2143       }
2144       q+=GetPixelChannels(image);
2145     }
2146     if (SyncCacheViewAuthenticPixels(polynomial_view,exception) == MagickFalse)
2147       status=MagickFalse;
2148     if (images->progress_monitor != (MagickProgressMonitor) NULL)
2149       {
2150         MagickBooleanType
2151           proceed;
2152
2153 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2154         #pragma omp critical (MagickCore_PolynomialImages)
2155 #endif
2156         proceed=SetImageProgress(images,PolynomialImageTag,progress++,
2157           image->rows);
2158         if (proceed == MagickFalse)
2159           status=MagickFalse;
2160       }
2161   }
2162   polynomial_view=DestroyCacheView(polynomial_view);
2163   polynomial_pixels=DestroyPixelThreadSet(polynomial_pixels);
2164   if (status == MagickFalse)
2165     image=DestroyImage(image);
2166   return(image);
2167 }
2168 \f
2169 /*
2170 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2171 %                                                                             %
2172 %                                                                             %
2173 %                                                                             %
2174 %     S t a t i s t i c I m a g e                                             %
2175 %                                                                             %
2176 %                                                                             %
2177 %                                                                             %
2178 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2179 %
2180 %  StatisticImage() makes each pixel the min / max / median / mode / etc. of
2181 %  the neighborhood of the specified width and height.
2182 %
2183 %  The format of the StatisticImage method is:
2184 %
2185 %      Image *StatisticImage(const Image *image,const StatisticType type,
2186 %        const size_t width,const size_t height,ExceptionInfo *exception)
2187 %
2188 %  A description of each parameter follows:
2189 %
2190 %    o image: the image.
2191 %
2192 %    o type: the statistic type (median, mode, etc.).
2193 %
2194 %    o width: the width of the pixel neighborhood.
2195 %
2196 %    o height: the height of the pixel neighborhood.
2197 %
2198 %    o exception: return any errors or warnings in this structure.
2199 %
2200 */
2201
2202 typedef struct _SkipNode
2203 {
2204   size_t
2205     next[9],
2206     count,
2207     signature;
2208 } SkipNode;
2209
2210 typedef struct _SkipList
2211 {
2212   ssize_t
2213     level;
2214
2215   SkipNode
2216     *nodes;
2217 } SkipList;
2218
2219 typedef struct _PixelList
2220 {
2221   size_t
2222     length,
2223     seed;
2224
2225   SkipList
2226     skip_list;
2227
2228   size_t
2229     signature;
2230 } PixelList;
2231
2232 static PixelList *DestroyPixelList(PixelList *pixel_list)
2233 {
2234   if (pixel_list == (PixelList *) NULL)
2235     return((PixelList *) NULL);
2236   if (pixel_list->skip_list.nodes != (SkipNode *) NULL)
2237     pixel_list->skip_list.nodes=(SkipNode *) RelinquishMagickMemory(
2238       pixel_list->skip_list.nodes);
2239   pixel_list=(PixelList *) RelinquishMagickMemory(pixel_list);
2240   return(pixel_list);
2241 }
2242
2243 static PixelList **DestroyPixelListThreadSet(PixelList **pixel_list)
2244 {
2245   register ssize_t
2246     i;
2247
2248   assert(pixel_list != (PixelList **) NULL);
2249   for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
2250     if (pixel_list[i] != (PixelList *) NULL)
2251       pixel_list[i]=DestroyPixelList(pixel_list[i]);
2252   pixel_list=(PixelList **) RelinquishMagickMemory(pixel_list);
2253   return(pixel_list);
2254 }
2255
2256 static PixelList *AcquirePixelList(const size_t width,const size_t height)
2257 {
2258   PixelList
2259     *pixel_list;
2260
2261   pixel_list=(PixelList *) AcquireMagickMemory(sizeof(*pixel_list));
2262   if (pixel_list == (PixelList *) NULL)
2263     return(pixel_list);
2264   (void) ResetMagickMemory((void *) pixel_list,0,sizeof(*pixel_list));
2265   pixel_list->length=width*height;
2266   pixel_list->skip_list.nodes=(SkipNode *) AcquireQuantumMemory(65537UL,
2267     sizeof(*pixel_list->skip_list.nodes));
2268   if (pixel_list->skip_list.nodes == (SkipNode *) NULL)
2269     return(DestroyPixelList(pixel_list));
2270   (void) ResetMagickMemory(pixel_list->skip_list.nodes,0,65537UL*
2271     sizeof(*pixel_list->skip_list.nodes));
2272   pixel_list->signature=MagickSignature;
2273   return(pixel_list);
2274 }
2275
2276 static PixelList **AcquirePixelListThreadSet(const size_t width,
2277   const size_t height)
2278 {
2279   PixelList
2280     **pixel_list;
2281
2282   register ssize_t
2283     i;
2284
2285   size_t
2286     number_threads;
2287
2288   number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
2289   pixel_list=(PixelList **) AcquireQuantumMemory(number_threads,
2290     sizeof(*pixel_list));
2291   if (pixel_list == (PixelList **) NULL)
2292     return((PixelList **) NULL);
2293   (void) ResetMagickMemory(pixel_list,0,number_threads*sizeof(*pixel_list));
2294   for (i=0; i < (ssize_t) number_threads; i++)
2295   {
2296     pixel_list[i]=AcquirePixelList(width,height);
2297     if (pixel_list[i] == (PixelList *) NULL)
2298       return(DestroyPixelListThreadSet(pixel_list));
2299   }
2300   return(pixel_list);
2301 }
2302
2303 static void AddNodePixelList(PixelList *pixel_list,const size_t color)
2304 {
2305   register SkipList
2306     *p;
2307
2308   register ssize_t
2309     level;
2310
2311   size_t
2312     search,
2313     update[9];
2314
2315   /*
2316     Initialize the node.
2317   */
2318   p=(&pixel_list->skip_list);
2319   p->nodes[color].signature=pixel_list->signature;
2320   p->nodes[color].count=1;
2321   /*
2322     Determine where it belongs in the list.
2323   */
2324   search=65536UL;
2325   for (level=p->level; level >= 0; level--)
2326   {
2327     while (p->nodes[search].next[level] < color)
2328       search=p->nodes[search].next[level];
2329     update[level]=search;
2330   }
2331   /*
2332     Generate a pseudo-random level for this node.
2333   */
2334   for (level=0; ; level++)
2335   {
2336     pixel_list->seed=(pixel_list->seed*42893621L)+1L;
2337     if ((pixel_list->seed & 0x300) != 0x300)
2338       break;
2339   }
2340   if (level > 8)
2341     level=8;
2342   if (level > (p->level+2))
2343     level=p->level+2;
2344   /*
2345     If we're raising the list's level, link back to the root node.
2346   */
2347   while (level > p->level)
2348   {
2349     p->level++;
2350     update[p->level]=65536UL;
2351   }
2352   /*
2353     Link the node into the skip-list.
2354   */
2355   do
2356   {
2357     p->nodes[color].next[level]=p->nodes[update[level]].next[level];
2358     p->nodes[update[level]].next[level]=color;
2359   } while (level-- > 0);
2360 }
2361
2362 static inline void GetMaximumPixelList(PixelList *pixel_list,Quantum *pixel)
2363 {
2364   register SkipList
2365     *p;
2366
2367   size_t
2368     color,
2369     maximum;
2370
2371   ssize_t
2372     count;
2373
2374   /*
2375     Find the maximum value for each of the color.
2376   */
2377   p=(&pixel_list->skip_list);
2378   color=65536L;
2379   count=0;
2380   maximum=p->nodes[color].next[0];
2381   do
2382   {
2383     color=p->nodes[color].next[0];
2384     if (color > maximum)
2385       maximum=color;
2386     count+=p->nodes[color].count;
2387   } while (count < (ssize_t) pixel_list->length);
2388   *pixel=ScaleShortToQuantum((unsigned short) maximum);
2389 }
2390
2391 static inline void GetMeanPixelList(PixelList *pixel_list,Quantum *pixel)
2392 {
2393   double
2394     sum;
2395
2396   register SkipList
2397     *p;
2398
2399   size_t
2400     color;
2401
2402   ssize_t
2403     count;
2404
2405   /*
2406     Find the mean value for each of the color.
2407   */
2408   p=(&pixel_list->skip_list);
2409   color=65536L;
2410   count=0;
2411   sum=0.0;
2412   do
2413   {
2414     color=p->nodes[color].next[0];
2415     sum+=(double) p->nodes[color].count*color;
2416     count+=p->nodes[color].count;
2417   } while (count < (ssize_t) pixel_list->length);
2418   sum/=pixel_list->length;
2419   *pixel=ScaleShortToQuantum((unsigned short) sum);
2420 }
2421
2422 static inline void GetMedianPixelList(PixelList *pixel_list,Quantum *pixel)
2423 {
2424   register SkipList
2425     *p;
2426
2427   size_t
2428     color;
2429
2430   ssize_t
2431     count;
2432
2433   /*
2434     Find the median value for each of the color.
2435   */
2436   p=(&pixel_list->skip_list);
2437   color=65536L;
2438   count=0;
2439   do
2440   {
2441     color=p->nodes[color].next[0];
2442     count+=p->nodes[color].count;
2443   } while (count <= (ssize_t) (pixel_list->length >> 1));
2444   *pixel=ScaleShortToQuantum((unsigned short) color);
2445 }
2446
2447 static inline void GetMinimumPixelList(PixelList *pixel_list,Quantum *pixel)
2448 {
2449   register SkipList
2450     *p;
2451
2452   size_t
2453     color,
2454     minimum;
2455
2456   ssize_t
2457     count;
2458
2459   /*
2460     Find the minimum value for each of the color.
2461   */
2462   p=(&pixel_list->skip_list);
2463   count=0;
2464   color=65536UL;
2465   minimum=p->nodes[color].next[0];
2466   do
2467   {
2468     color=p->nodes[color].next[0];
2469     if (color < minimum)
2470       minimum=color;
2471     count+=p->nodes[color].count;
2472   } while (count < (ssize_t) pixel_list->length);
2473   *pixel=ScaleShortToQuantum((unsigned short) minimum);
2474 }
2475
2476 static inline void GetModePixelList(PixelList *pixel_list,Quantum *pixel)
2477 {
2478   register SkipList
2479     *p;
2480
2481   size_t
2482     color,
2483     max_count,
2484     mode;
2485
2486   ssize_t
2487     count;
2488
2489   /*
2490     Make each pixel the 'predominant color' of the specified neighborhood.
2491   */
2492   p=(&pixel_list->skip_list);
2493   color=65536L;
2494   mode=color;
2495   max_count=p->nodes[mode].count;
2496   count=0;
2497   do
2498   {
2499     color=p->nodes[color].next[0];
2500     if (p->nodes[color].count > max_count)
2501       {
2502         mode=color;
2503         max_count=p->nodes[mode].count;
2504       }
2505     count+=p->nodes[color].count;
2506   } while (count < (ssize_t) pixel_list->length);
2507   *pixel=ScaleShortToQuantum((unsigned short) mode);
2508 }
2509
2510 static inline void GetNonpeakPixelList(PixelList *pixel_list,Quantum *pixel)
2511 {
2512   register SkipList
2513     *p;
2514
2515   size_t
2516     color,
2517     next,
2518     previous;
2519
2520   ssize_t
2521     count;
2522
2523   /*
2524     Finds the non peak value for each of the colors.
2525   */
2526   p=(&pixel_list->skip_list);
2527   color=65536L;
2528   next=p->nodes[color].next[0];
2529   count=0;
2530   do
2531   {
2532     previous=color;
2533     color=next;
2534     next=p->nodes[color].next[0];
2535     count+=p->nodes[color].count;
2536   } while (count <= (ssize_t) (pixel_list->length >> 1));
2537   if ((previous == 65536UL) && (next != 65536UL))
2538     color=next;
2539   else
2540     if ((previous != 65536UL) && (next == 65536UL))
2541       color=previous;
2542   *pixel=ScaleShortToQuantum((unsigned short) color);
2543 }
2544
2545 static inline void GetStandardDeviationPixelList(PixelList *pixel_list,
2546   Quantum *pixel)
2547 {
2548   double
2549     sum,
2550     sum_squared;
2551
2552   register SkipList
2553     *p;
2554
2555   size_t
2556     color;
2557
2558   ssize_t
2559     count;
2560
2561   /*
2562     Find the standard-deviation value for each of the color.
2563   */
2564   p=(&pixel_list->skip_list);
2565   color=65536L;
2566   count=0;
2567   sum=0.0;
2568   sum_squared=0.0;
2569   do
2570   {
2571     register ssize_t
2572       i;
2573
2574     color=p->nodes[color].next[0];
2575     sum+=(double) p->nodes[color].count*color;
2576     for (i=0; i < (ssize_t) p->nodes[color].count; i++)
2577       sum_squared+=((double) color)*((double) color);
2578     count+=p->nodes[color].count;
2579   } while (count < (ssize_t) pixel_list->length);
2580   sum/=pixel_list->length;
2581   sum_squared/=pixel_list->length;
2582   *pixel=ScaleShortToQuantum((unsigned short) sqrt(sum_squared-(sum*sum)));
2583 }
2584
2585 static inline void InsertPixelList(const Quantum pixel,PixelList *pixel_list)
2586 {
2587   size_t
2588     signature;
2589
2590   unsigned short
2591     index;
2592
2593   index=ScaleQuantumToShort(pixel);
2594   signature=pixel_list->skip_list.nodes[index].signature;
2595   if (signature == pixel_list->signature)
2596     {
2597       pixel_list->skip_list.nodes[index].count++;
2598       return;
2599     }
2600   AddNodePixelList(pixel_list,index);
2601 }
2602
2603 static inline double MagickAbsoluteValue(const double x)
2604 {
2605   if (x < 0)
2606     return(-x);
2607   return(x);
2608 }
2609
2610 static inline size_t MagickMax(const size_t x,const size_t y)
2611 {
2612   if (x > y)
2613     return(x);
2614   return(y);
2615 }
2616
2617 static void ResetPixelList(PixelList *pixel_list)
2618 {
2619   int
2620     level;
2621
2622   register SkipNode
2623     *root;
2624
2625   register SkipList
2626     *p;
2627
2628   /*
2629     Reset the skip-list.
2630   */
2631   p=(&pixel_list->skip_list);
2632   root=p->nodes+65536UL;
2633   p->level=0;
2634   for (level=0; level < 9; level++)
2635     root->next[level]=65536UL;
2636   pixel_list->seed=pixel_list->signature++;
2637 }
2638
2639 MagickExport Image *StatisticImage(const Image *image,const StatisticType type,
2640   const size_t width,const size_t height,ExceptionInfo *exception)
2641 {
2642 #define StatisticImageTag  "Statistic/Image"
2643
2644   CacheView
2645     *image_view,
2646     *statistic_view;
2647
2648   Image
2649     *statistic_image;
2650
2651   MagickBooleanType
2652     status;
2653
2654   MagickOffsetType
2655     progress;
2656
2657   PixelList
2658     **restrict pixel_list;
2659
2660   ssize_t
2661     center,
2662     y;
2663
2664   /*
2665     Initialize statistics image attributes.
2666   */
2667   assert(image != (Image *) NULL);
2668   assert(image->signature == MagickSignature);
2669   if (image->debug != MagickFalse)
2670     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2671   assert(exception != (ExceptionInfo *) NULL);
2672   assert(exception->signature == MagickSignature);
2673   statistic_image=CloneImage(image,image->columns,image->rows,MagickTrue,
2674     exception);
2675   if (statistic_image == (Image *) NULL)
2676     return((Image *) NULL);
2677   status=SetImageStorageClass(statistic_image,DirectClass,exception);
2678   if (status == MagickFalse)
2679     {
2680       statistic_image=DestroyImage(statistic_image);
2681       return((Image *) NULL);
2682     }
2683   pixel_list=AcquirePixelListThreadSet(MagickMax(width,1),MagickMax(height,1));
2684   if (pixel_list == (PixelList **) NULL)
2685     {
2686       statistic_image=DestroyImage(statistic_image);
2687       ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
2688     }
2689   /*
2690     Make each pixel the min / max / median / mode / etc. of the neighborhood.
2691   */
2692   center=(ssize_t) GetPixelChannels(image)*(image->columns+MagickMax(width,1))*
2693     (MagickMax(height,1)/2L)+GetPixelChannels(image)*(MagickMax(width,1)/2L);
2694   status=MagickTrue;
2695   progress=0;
2696   image_view=AcquireVirtualCacheView(image,exception);
2697   statistic_view=AcquireAuthenticCacheView(statistic_image,exception);
2698 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2699   #pragma omp parallel for schedule(static,4) shared(progress,status) \
2700     magick_threads(image,statistic_image,statistic_image->rows,1)
2701 #endif
2702   for (y=0; y < (ssize_t) statistic_image->rows; y++)
2703   {
2704     const int
2705       id = GetOpenMPThreadId();
2706
2707     register const Quantum
2708       *restrict p;
2709
2710     register Quantum
2711       *restrict q;
2712
2713     register ssize_t
2714       x;
2715
2716     if (status == MagickFalse)
2717       continue;
2718     p=GetCacheViewVirtualPixels(image_view,-((ssize_t) MagickMax(width,1)/2L),y-
2719       (ssize_t) (MagickMax(height,1)/2L),image->columns+MagickMax(width,1),
2720       MagickMax(height,1),exception);
2721     q=QueueCacheViewAuthenticPixels(statistic_view,0,y,statistic_image->columns,      1,exception);
2722     if ((p == (const Quantum *) NULL) || (q == (Quantum *) NULL))
2723       {
2724         status=MagickFalse;
2725         continue;
2726       }
2727     for (x=0; x < (ssize_t) statistic_image->columns; x++)
2728     {
2729       register ssize_t
2730         i;
2731
2732       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
2733       {
2734         Quantum
2735           pixel;
2736
2737         register const Quantum
2738           *restrict pixels;
2739
2740         register ssize_t
2741           u;
2742
2743         ssize_t
2744           v;
2745
2746         PixelChannel channel=GetPixelChannelChannel(image,i);
2747         PixelTrait traits=GetPixelChannelTraits(image,channel);
2748         PixelTrait statistic_traits=GetPixelChannelTraits(statistic_image,
2749           channel);
2750         if ((traits == UndefinedPixelTrait) ||
2751             (statistic_traits == UndefinedPixelTrait))
2752           continue;
2753         if (((statistic_traits & CopyPixelTrait) != 0) ||
2754             (GetPixelReadMask(image,p) == 0))
2755           {
2756             SetPixelChannel(statistic_image,channel,p[center+i],q);
2757             continue;
2758           }
2759         pixels=p;
2760         ResetPixelList(pixel_list[id]);
2761         for (v=0; v < (ssize_t) MagickMax(height,1); v++)
2762         {
2763           for (u=0; u < (ssize_t) MagickMax(width,1); u++)
2764           {
2765             InsertPixelList(pixels[i],pixel_list[id]);
2766             pixels+=GetPixelChannels(image);
2767           }
2768           pixels+=(image->columns-1)*GetPixelChannels(image);
2769         }
2770         switch (type)
2771         {
2772           case GradientStatistic:
2773           {
2774             double
2775               maximum,
2776               minimum;
2777
2778             GetMinimumPixelList(pixel_list[id],&pixel);
2779             minimum=(double) pixel;
2780             GetMaximumPixelList(pixel_list[id],&pixel);
2781             maximum=(double) pixel;
2782             pixel=ClampToQuantum(MagickAbsoluteValue(maximum-minimum));
2783             break;
2784           }
2785           case MaximumStatistic:
2786           {
2787             GetMaximumPixelList(pixel_list[id],&pixel);
2788             break;
2789           }
2790           case MeanStatistic:
2791           {
2792             GetMeanPixelList(pixel_list[id],&pixel);
2793             break;
2794           }
2795           case MedianStatistic:
2796           default:
2797           {
2798             GetMedianPixelList(pixel_list[id],&pixel);
2799             break;
2800           }
2801           case MinimumStatistic:
2802           {
2803             GetMinimumPixelList(pixel_list[id],&pixel);
2804             break;
2805           }
2806           case ModeStatistic:
2807           {
2808             GetModePixelList(pixel_list[id],&pixel);
2809             break;
2810           }
2811           case NonpeakStatistic:
2812           {
2813             GetNonpeakPixelList(pixel_list[id],&pixel);
2814             break;
2815           }
2816           case StandardDeviationStatistic:
2817           {
2818             GetStandardDeviationPixelList(pixel_list[id],&pixel);
2819             break;
2820           }
2821         }
2822         SetPixelChannel(statistic_image,channel,pixel,q);
2823       }
2824       p+=GetPixelChannels(image);
2825       q+=GetPixelChannels(statistic_image);
2826     }
2827     if (SyncCacheViewAuthenticPixels(statistic_view,exception) == MagickFalse)
2828       status=MagickFalse;
2829     if (image->progress_monitor != (MagickProgressMonitor) NULL)
2830       {
2831         MagickBooleanType
2832           proceed;
2833
2834 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2835         #pragma omp critical (MagickCore_StatisticImage)
2836 #endif
2837         proceed=SetImageProgress(image,StatisticImageTag,progress++,
2838           image->rows);
2839         if (proceed == MagickFalse)
2840           status=MagickFalse;
2841       }
2842   }
2843   statistic_view=DestroyCacheView(statistic_view);
2844   image_view=DestroyCacheView(image_view);
2845   pixel_list=DestroyPixelListThreadSet(pixel_list);
2846   if (status == MagickFalse)
2847     statistic_image=DestroyImage(statistic_image);
2848   return(statistic_image);
2849 }