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   MagickBooleanType
1377     initialize,
1378     status;
1379
1380   register ssize_t
1381     i;
1382
1383   size_t
1384     length;
1385
1386   ssize_t
1387     y;
1388
1389   assert(image != (Image *) NULL);
1390   assert(image->signature == MagickSignature);
1391   if (image->debug != MagickFalse)
1392     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1393   length=MaxPixelChannels+1;
1394   channel_moments=(ChannelMoments *) AcquireQuantumMemory(length,
1395     sizeof(*channel_moments));
1396   if (channel_moments == (ChannelMoments *) NULL)
1397     return(channel_moments);
1398   (void) ResetMagickMemory(channel_moments,0,length*sizeof(*channel_moments));
1399   for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
1400   {
1401     channel_moments[i].I1=0.0;
1402     channel_moments[i].I2=0.0;
1403     channel_moments[i].I3=0.0;
1404     channel_moments[i].I4=0.0;
1405     channel_moments[i].I5=0.0;
1406     channel_moments[i].I6=0.0;
1407     channel_moments[i].I7=0.0;
1408     channel_moments[i].I8=0.0;
1409   }
1410   status=MagickTrue;
1411   initialize=MagickTrue;
1412   image_view=AcquireVirtualCacheView(image,exception);
1413 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1414   #pragma omp parallel for schedule(static,4) shared(status,initialize) \
1415     magick_threads(image,image,image->rows,1)
1416 #endif
1417   for (y=0; y < (ssize_t) image->rows; y++)
1418   {
1419     register const Quantum
1420       *restrict p;
1421
1422     register ssize_t
1423       x;
1424
1425     if (status == MagickFalse)
1426       continue;
1427     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1428     if (p == (const Quantum *) NULL)
1429       {
1430         status=MagickFalse;
1431         continue;
1432       }
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 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1452         #pragma omp critical (MagickCore_GetImageMoments)
1453 #endif
1454         {
1455           if (initialize != MagickFalse)
1456             {
1457               initialize=MagickFalse;
1458             }
1459           else
1460             {
1461            }
1462         }
1463       }
1464       p+=GetPixelChannels(image);
1465     }
1466   }
1467   image_view=DestroyCacheView(image_view);
1468   if (status == MagickFalse)
1469     channel_moments=(ChannelMoments *) RelinquishMagickMemory(channel_moments);
1470   return(channel_moments);
1471 }
1472 \f
1473 /*
1474 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1475 %                                                                             %
1476 %                                                                             %
1477 %                                                                             %
1478 %   G e t I m a g e R a n g e                                                 %
1479 %                                                                             %
1480 %                                                                             %
1481 %                                                                             %
1482 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1483 %
1484 %  GetImageRange() returns the range of one or more image channels.
1485 %
1486 %  The format of the GetImageRange method is:
1487 %
1488 %      MagickBooleanType GetImageRange(const Image *image,double *minima,
1489 %        double *maxima,ExceptionInfo *exception)
1490 %
1491 %  A description of each parameter follows:
1492 %
1493 %    o image: the image.
1494 %
1495 %    o minima: the minimum value in the channel.
1496 %
1497 %    o maxima: the maximum value in the channel.
1498 %
1499 %    o exception: return any errors or warnings in this structure.
1500 %
1501 */
1502 MagickExport MagickBooleanType GetImageRange(const Image *image,double *minima,
1503   double *maxima,ExceptionInfo *exception)
1504 {
1505   CacheView
1506     *image_view;
1507
1508   MagickBooleanType
1509     initialize,
1510     status;
1511
1512   ssize_t
1513     y;
1514
1515   assert(image != (Image *) NULL);
1516   assert(image->signature == MagickSignature);
1517   if (image->debug != MagickFalse)
1518     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1519   status=MagickTrue;
1520   initialize=MagickTrue;
1521   *maxima=0.0;
1522   *minima=0.0;
1523   image_view=AcquireVirtualCacheView(image,exception);
1524 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1525   #pragma omp parallel for schedule(static,4) shared(status,initialize) \
1526     magick_threads(image,image,image->rows,1)
1527 #endif
1528   for (y=0; y < (ssize_t) image->rows; y++)
1529   {
1530     register const Quantum
1531       *restrict p;
1532
1533     register ssize_t
1534       x;
1535
1536     if (status == MagickFalse)
1537       continue;
1538     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1539     if (p == (const Quantum *) NULL)
1540       {
1541         status=MagickFalse;
1542         continue;
1543       }
1544     for (x=0; x < (ssize_t) image->columns; x++)
1545     {
1546       register ssize_t
1547         i;
1548
1549       if (GetPixelReadMask(image,p) == 0)
1550         {
1551           p+=GetPixelChannels(image);
1552           continue;
1553         }
1554       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1555       {
1556         PixelChannel channel=GetPixelChannelChannel(image,i);
1557         PixelTrait traits=GetPixelChannelTraits(image,channel);
1558         if (traits == UndefinedPixelTrait)
1559           continue;
1560         if ((traits & UpdatePixelTrait) == 0)
1561           continue;
1562 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1563         #pragma omp critical (MagickCore_GetImageRange)
1564 #endif
1565         {
1566           if (initialize != MagickFalse)
1567             {
1568               *minima=(double) p[i];
1569               *maxima=(double) p[i];
1570               initialize=MagickFalse;
1571             }
1572           else
1573             {
1574               if ((double) p[i] < *minima)
1575                 *minima=(double) p[i];
1576               if ((double) p[i] > *maxima)
1577                 *maxima=(double) p[i];
1578            }
1579         }
1580       }
1581       p+=GetPixelChannels(image);
1582     }
1583   }
1584   image_view=DestroyCacheView(image_view);
1585   return(status);
1586 }
1587 \f
1588 /*
1589 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1590 %                                                                             %
1591 %                                                                             %
1592 %                                                                             %
1593 %   G e t I m a g e S t a t i s t i c s                                       %
1594 %                                                                             %
1595 %                                                                             %
1596 %                                                                             %
1597 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1598 %
1599 %  GetImageStatistics() returns statistics for each channel in the image.  The
1600 %  statistics include the channel depth, its minima, maxima, mean, standard
1601 %  deviation, kurtosis and skewness.  You can access the red channel mean, for
1602 %  example, like this:
1603 %
1604 %      channel_statistics=GetImageStatistics(image,exception);
1605 %      red_mean=channel_statistics[RedPixelChannel].mean;
1606 %
1607 %  Use MagickRelinquishMemory() to free the statistics buffer.
1608 %
1609 %  The format of the GetImageStatistics method is:
1610 %
1611 %      ChannelStatistics *GetImageStatistics(const Image *image,
1612 %        ExceptionInfo *exception)
1613 %
1614 %  A description of each parameter follows:
1615 %
1616 %    o image: the image.
1617 %
1618 %    o exception: return any errors or warnings in this structure.
1619 %
1620 */
1621
1622 static size_t GetImageChannels(const Image *image)
1623 {
1624   register ssize_t
1625     i;
1626
1627   size_t
1628     channels;
1629
1630   channels=0;
1631   for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1632   {
1633     PixelChannel channel=GetPixelChannelChannel(image,i);
1634     PixelTrait traits=GetPixelChannelTraits(image,channel);
1635     if (traits != UndefinedPixelTrait)
1636       channels++;
1637   }
1638   return(channels);
1639 }
1640
1641 MagickExport ChannelStatistics *GetImageStatistics(const Image *image,
1642   ExceptionInfo *exception)
1643 {
1644   ChannelStatistics
1645     *channel_statistics;
1646
1647   MagickStatusType
1648     status;
1649
1650   QuantumAny
1651     range;
1652
1653   register ssize_t
1654     i;
1655
1656   size_t
1657     channels,
1658     depth;
1659
1660   ssize_t
1661     y;
1662
1663   assert(image != (Image *) NULL);
1664   assert(image->signature == MagickSignature);
1665   if (image->debug != MagickFalse)
1666     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1667   channel_statistics=(ChannelStatistics *) AcquireQuantumMemory(
1668     MaxPixelChannels+1,sizeof(*channel_statistics));
1669   if (channel_statistics == (ChannelStatistics *) NULL)
1670     return(channel_statistics);
1671   (void) ResetMagickMemory(channel_statistics,0,(MaxPixelChannels+1)*
1672     sizeof(*channel_statistics));
1673   for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
1674   {
1675     channel_statistics[i].depth=1;
1676     channel_statistics[i].maxima=(-MagickHuge);
1677     channel_statistics[i].minima=MagickHuge;
1678   }
1679   for (y=0; y < (ssize_t) image->rows; y++)
1680   {
1681     register const Quantum
1682       *restrict p;
1683
1684     register ssize_t
1685       x;
1686
1687     p=GetVirtualPixels(image,0,y,image->columns,1,exception);
1688     if (p == (const Quantum *) NULL)
1689       break;
1690     for (x=0; x < (ssize_t) image->columns; x++)
1691     {
1692       register ssize_t
1693         i;
1694
1695       if (GetPixelReadMask(image,p) == 0)
1696         {
1697           p+=GetPixelChannels(image);
1698           continue;
1699         }
1700       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
1701       {
1702         PixelChannel channel=GetPixelChannelChannel(image,i);
1703         PixelTrait traits=GetPixelChannelTraits(image,channel);
1704         if (traits == UndefinedPixelTrait)
1705           continue;
1706         if (channel_statistics[channel].depth != MAGICKCORE_QUANTUM_DEPTH)
1707           {
1708             depth=channel_statistics[channel].depth;
1709             range=GetQuantumRange(depth);
1710             status=p[i] != ScaleAnyToQuantum(ScaleQuantumToAny(p[i],range),
1711               range) ? MagickTrue : MagickFalse;
1712             if (status != MagickFalse)
1713               {
1714                 channel_statistics[channel].depth++;
1715                 i--;
1716                 continue;
1717               }
1718           }
1719         if ((double) p[i] < channel_statistics[channel].minima)
1720           channel_statistics[channel].minima=(double) p[i];
1721         if ((double) p[i] > channel_statistics[channel].maxima)
1722           channel_statistics[channel].maxima=(double) p[i];
1723         channel_statistics[channel].sum+=p[i];
1724         channel_statistics[channel].sum_squared+=(double) p[i]*p[i];
1725         channel_statistics[channel].sum_cubed+=(double) p[i]*p[i]*p[i];
1726         channel_statistics[channel].sum_fourth_power+=(double) p[i]*p[i]*p[i]*
1727           p[i];
1728         channel_statistics[channel].area++;
1729       }
1730       p+=GetPixelChannels(image);
1731     }
1732   }
1733   for (i=0; i < (ssize_t) MaxPixelChannels; i++)
1734   {
1735     double
1736       area;
1737
1738     area=PerceptibleReciprocal(channel_statistics[i].area);
1739     channel_statistics[i].sum*=area;
1740     channel_statistics[i].sum_squared*=area;
1741     channel_statistics[i].sum_cubed*=area;
1742     channel_statistics[i].sum_fourth_power*=area;
1743     channel_statistics[i].mean=channel_statistics[i].sum;
1744     channel_statistics[i].variance=channel_statistics[i].sum_squared;
1745     channel_statistics[i].standard_deviation=sqrt(
1746       channel_statistics[i].variance-(channel_statistics[i].mean*
1747       channel_statistics[i].mean));
1748   }
1749   for (i=0; i < (ssize_t) MaxPixelChannels; i++)
1750   {
1751     channel_statistics[CompositePixelChannel].area+=channel_statistics[i].area;
1752     channel_statistics[CompositePixelChannel].minima=MagickMin(
1753       channel_statistics[CompositePixelChannel].minima,
1754       channel_statistics[i].minima);
1755     channel_statistics[CompositePixelChannel].maxima=EvaluateMax(
1756       channel_statistics[CompositePixelChannel].maxima,
1757       channel_statistics[i].maxima);
1758     channel_statistics[CompositePixelChannel].sum+=channel_statistics[i].sum;
1759     channel_statistics[CompositePixelChannel].sum_squared+=
1760       channel_statistics[i].sum_squared;
1761     channel_statistics[CompositePixelChannel].sum_cubed+=
1762       channel_statistics[i].sum_cubed;
1763     channel_statistics[CompositePixelChannel].sum_fourth_power+=
1764       channel_statistics[i].sum_fourth_power;
1765     channel_statistics[CompositePixelChannel].mean+=channel_statistics[i].mean;
1766     channel_statistics[CompositePixelChannel].variance+=
1767       channel_statistics[i].variance-channel_statistics[i].mean*
1768       channel_statistics[i].mean;
1769     channel_statistics[CompositePixelChannel].standard_deviation+=
1770       channel_statistics[i].variance-channel_statistics[i].mean*
1771       channel_statistics[i].mean;
1772   }
1773   channels=GetImageChannels(image);
1774   channel_statistics[CompositePixelChannel].area/=channels;
1775   channel_statistics[CompositePixelChannel].sum/=channels;
1776   channel_statistics[CompositePixelChannel].sum_squared/=channels;
1777   channel_statistics[CompositePixelChannel].sum_cubed/=channels;
1778   channel_statistics[CompositePixelChannel].sum_fourth_power/=channels;
1779   channel_statistics[CompositePixelChannel].mean/=channels;
1780   channel_statistics[CompositePixelChannel].variance/=channels;
1781   channel_statistics[CompositePixelChannel].standard_deviation=
1782     sqrt(channel_statistics[CompositePixelChannel].standard_deviation/channels);
1783   channel_statistics[CompositePixelChannel].kurtosis/=channels;
1784   channel_statistics[CompositePixelChannel].skewness/=channels;
1785   for (i=0; i <= (ssize_t) MaxPixelChannels; i++)
1786   {
1787     double
1788       standard_deviation;
1789
1790     if (channel_statistics[i].standard_deviation == 0.0)
1791       continue;
1792     standard_deviation=PerceptibleReciprocal(
1793       channel_statistics[i].standard_deviation);
1794     channel_statistics[i].skewness=(channel_statistics[i].sum_cubed-3.0*
1795       channel_statistics[i].mean*channel_statistics[i].sum_squared+2.0*
1796       channel_statistics[i].mean*channel_statistics[i].mean*
1797       channel_statistics[i].mean)*(standard_deviation*standard_deviation*
1798       standard_deviation);
1799     channel_statistics[i].kurtosis=(channel_statistics[i].sum_fourth_power-4.0*
1800       channel_statistics[i].mean*channel_statistics[i].sum_cubed+6.0*
1801       channel_statistics[i].mean*channel_statistics[i].mean*
1802       channel_statistics[i].sum_squared-3.0*channel_statistics[i].mean*
1803       channel_statistics[i].mean*1.0*channel_statistics[i].mean*
1804       channel_statistics[i].mean)*(standard_deviation*standard_deviation*
1805       standard_deviation*standard_deviation)-3.0;
1806   }
1807   if (y < (ssize_t) image->rows)
1808     channel_statistics=(ChannelStatistics *) RelinquishMagickMemory(
1809       channel_statistics);
1810   return(channel_statistics);
1811 }
1812 \f
1813 /*
1814 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1815 %                                                                             %
1816 %                                                                             %
1817 %                                                                             %
1818 %     P o l y n o m i a l I m a g e                                           %
1819 %                                                                             %
1820 %                                                                             %
1821 %                                                                             %
1822 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1823 %
1824 %  PolynomialImage() returns a new image where each pixel is the sum of the
1825 %  pixels in the image sequence after applying its corresponding terms
1826 %  (coefficient and degree pairs).
1827 %
1828 %  The format of the PolynomialImage method is:
1829 %
1830 %      Image *PolynomialImage(const Image *images,const size_t number_terms,
1831 %        const double *terms,ExceptionInfo *exception)
1832 %
1833 %  A description of each parameter follows:
1834 %
1835 %    o images: the image sequence.
1836 %
1837 %    o number_terms: the number of terms in the list.  The actual list length
1838 %      is 2 x number_terms + 1 (the constant).
1839 %
1840 %    o terms: the list of polynomial coefficients and degree pairs and a
1841 %      constant.
1842 %
1843 %    o exception: return any errors or warnings in this structure.
1844 %
1845 */
1846
1847 MagickExport Image *PolynomialImage(const Image *images,
1848   const size_t number_terms,const double *terms,ExceptionInfo *exception)
1849 {
1850 #define PolynomialImageTag  "Polynomial/Image"
1851
1852   CacheView
1853     *polynomial_view;
1854
1855   Image
1856     *image;
1857
1858   MagickBooleanType
1859     status;
1860
1861   MagickOffsetType
1862     progress;
1863
1864   PixelChannels
1865     **restrict polynomial_pixels;
1866
1867   size_t
1868     number_images;
1869
1870   ssize_t
1871     y;
1872
1873   assert(images != (Image *) NULL);
1874   assert(images->signature == MagickSignature);
1875   if (images->debug != MagickFalse)
1876     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
1877   assert(exception != (ExceptionInfo *) NULL);
1878   assert(exception->signature == MagickSignature);
1879   image=CloneImage(images,images->columns,images->rows,MagickTrue,
1880     exception);
1881   if (image == (Image *) NULL)
1882     return((Image *) NULL);
1883   if (SetImageStorageClass(image,DirectClass,exception) == MagickFalse)
1884     {
1885       image=DestroyImage(image);
1886       return((Image *) NULL);
1887     }
1888   number_images=GetImageListLength(images);
1889   polynomial_pixels=AcquirePixelThreadSet(images,number_images);
1890   if (polynomial_pixels == (PixelChannels **) NULL)
1891     {
1892       image=DestroyImage(image);
1893       (void) ThrowMagickException(exception,GetMagickModule(),
1894         ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
1895       return((Image *) NULL);
1896     }
1897   /*
1898     Polynomial image pixels.
1899   */
1900   status=MagickTrue;
1901   progress=0;
1902   polynomial_view=AcquireAuthenticCacheView(image,exception);
1903 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1904   #pragma omp parallel for schedule(static,4) shared(progress,status) \
1905     magick_threads(image,image,image->rows,1)
1906 #endif
1907   for (y=0; y < (ssize_t) image->rows; y++)
1908   {
1909     CacheView
1910       *image_view;
1911
1912     const Image
1913       *next;
1914
1915     const int
1916       id = GetOpenMPThreadId();
1917
1918     register ssize_t
1919       i,
1920       x;
1921
1922     register PixelChannels
1923       *polynomial_pixel;
1924
1925     register Quantum
1926       *restrict q;
1927
1928     ssize_t
1929       j;
1930
1931     if (status == MagickFalse)
1932       continue;
1933     q=QueueCacheViewAuthenticPixels(polynomial_view,0,y,image->columns,1,
1934       exception);
1935     if (q == (Quantum *) NULL)
1936       {
1937         status=MagickFalse;
1938         continue;
1939       }
1940     polynomial_pixel=polynomial_pixels[id];
1941     for (j=0; j < (ssize_t) image->columns; j++)
1942       for (i=0; i < MaxPixelChannels; i++)
1943         polynomial_pixel[j].channel[i]=0.0;
1944     next=images;
1945     for (j=0; j < (ssize_t) number_images; j++)
1946     {
1947       register const Quantum
1948         *p;
1949
1950       if (j >= (ssize_t) number_terms)
1951         continue;
1952       image_view=AcquireVirtualCacheView(next,exception);
1953       p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
1954       if (p == (const Quantum *) NULL)
1955         {
1956           image_view=DestroyCacheView(image_view);
1957           break;
1958         }
1959       for (x=0; x < (ssize_t) image->columns; x++)
1960       {
1961         register ssize_t
1962           i;
1963
1964         if (GetPixelReadMask(next,p) == 0)
1965           {
1966             p+=GetPixelChannels(next);
1967             continue;
1968           }
1969         for (i=0; i < (ssize_t) GetPixelChannels(next); i++)
1970         {
1971           MagickRealType
1972             coefficient,
1973             degree;
1974
1975           PixelChannel channel=GetPixelChannelChannel(image,i);
1976           PixelTrait traits=GetPixelChannelTraits(next,channel);
1977           PixelTrait polynomial_traits=GetPixelChannelTraits(image,channel);
1978           if ((traits == UndefinedPixelTrait) ||
1979               (polynomial_traits == UndefinedPixelTrait))
1980             continue;
1981           if ((traits & UpdatePixelTrait) == 0)
1982             continue;
1983           coefficient=(MagickRealType) terms[2*i];
1984           degree=(MagickRealType) terms[(i << 1)+1];
1985           polynomial_pixel[x].channel[i]+=coefficient*
1986             pow(QuantumScale*GetPixelChannel(image,channel,p),degree);
1987         }
1988         p+=GetPixelChannels(next);
1989       }
1990       image_view=DestroyCacheView(image_view);
1991       next=GetNextImageInList(next);
1992     }
1993     for (x=0; x < (ssize_t) image->columns; x++)
1994     {
1995       register ssize_t
1996         i;
1997
1998       if (GetPixelReadMask(image,q) == 0)
1999         {
2000           q+=GetPixelChannels(image);
2001           continue;
2002         }
2003       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
2004       {
2005         PixelChannel channel=GetPixelChannelChannel(image,i);
2006         PixelTrait traits=GetPixelChannelTraits(image,channel);
2007         if (traits == UndefinedPixelTrait)
2008           continue;
2009         if ((traits & UpdatePixelTrait) == 0)
2010           continue;
2011         q[i]=ClampToQuantum(QuantumRange*polynomial_pixel[x].channel[i]);
2012       }
2013       q+=GetPixelChannels(image);
2014     }
2015     if (SyncCacheViewAuthenticPixels(polynomial_view,exception) == MagickFalse)
2016       status=MagickFalse;
2017     if (images->progress_monitor != (MagickProgressMonitor) NULL)
2018       {
2019         MagickBooleanType
2020           proceed;
2021
2022 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2023         #pragma omp critical (MagickCore_PolynomialImages)
2024 #endif
2025         proceed=SetImageProgress(images,PolynomialImageTag,progress++,
2026           image->rows);
2027         if (proceed == MagickFalse)
2028           status=MagickFalse;
2029       }
2030   }
2031   polynomial_view=DestroyCacheView(polynomial_view);
2032   polynomial_pixels=DestroyPixelThreadSet(polynomial_pixels);
2033   if (status == MagickFalse)
2034     image=DestroyImage(image);
2035   return(image);
2036 }
2037 \f
2038 /*
2039 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2040 %                                                                             %
2041 %                                                                             %
2042 %                                                                             %
2043 %     S t a t i s t i c I m a g e                                             %
2044 %                                                                             %
2045 %                                                                             %
2046 %                                                                             %
2047 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2048 %
2049 %  StatisticImage() makes each pixel the min / max / median / mode / etc. of
2050 %  the neighborhood of the specified width and height.
2051 %
2052 %  The format of the StatisticImage method is:
2053 %
2054 %      Image *StatisticImage(const Image *image,const StatisticType type,
2055 %        const size_t width,const size_t height,ExceptionInfo *exception)
2056 %
2057 %  A description of each parameter follows:
2058 %
2059 %    o image: the image.
2060 %
2061 %    o type: the statistic type (median, mode, etc.).
2062 %
2063 %    o width: the width of the pixel neighborhood.
2064 %
2065 %    o height: the height of the pixel neighborhood.
2066 %
2067 %    o exception: return any errors or warnings in this structure.
2068 %
2069 */
2070
2071 typedef struct _SkipNode
2072 {
2073   size_t
2074     next[9],
2075     count,
2076     signature;
2077 } SkipNode;
2078
2079 typedef struct _SkipList
2080 {
2081   ssize_t
2082     level;
2083
2084   SkipNode
2085     *nodes;
2086 } SkipList;
2087
2088 typedef struct _PixelList
2089 {
2090   size_t
2091     length,
2092     seed;
2093
2094   SkipList
2095     skip_list;
2096
2097   size_t
2098     signature;
2099 } PixelList;
2100
2101 static PixelList *DestroyPixelList(PixelList *pixel_list)
2102 {
2103   if (pixel_list == (PixelList *) NULL)
2104     return((PixelList *) NULL);
2105   if (pixel_list->skip_list.nodes != (SkipNode *) NULL)
2106     pixel_list->skip_list.nodes=(SkipNode *) RelinquishMagickMemory(
2107       pixel_list->skip_list.nodes);
2108   pixel_list=(PixelList *) RelinquishMagickMemory(pixel_list);
2109   return(pixel_list);
2110 }
2111
2112 static PixelList **DestroyPixelListThreadSet(PixelList **pixel_list)
2113 {
2114   register ssize_t
2115     i;
2116
2117   assert(pixel_list != (PixelList **) NULL);
2118   for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
2119     if (pixel_list[i] != (PixelList *) NULL)
2120       pixel_list[i]=DestroyPixelList(pixel_list[i]);
2121   pixel_list=(PixelList **) RelinquishMagickMemory(pixel_list);
2122   return(pixel_list);
2123 }
2124
2125 static PixelList *AcquirePixelList(const size_t width,const size_t height)
2126 {
2127   PixelList
2128     *pixel_list;
2129
2130   pixel_list=(PixelList *) AcquireMagickMemory(sizeof(*pixel_list));
2131   if (pixel_list == (PixelList *) NULL)
2132     return(pixel_list);
2133   (void) ResetMagickMemory((void *) pixel_list,0,sizeof(*pixel_list));
2134   pixel_list->length=width*height;
2135   pixel_list->skip_list.nodes=(SkipNode *) AcquireQuantumMemory(65537UL,
2136     sizeof(*pixel_list->skip_list.nodes));
2137   if (pixel_list->skip_list.nodes == (SkipNode *) NULL)
2138     return(DestroyPixelList(pixel_list));
2139   (void) ResetMagickMemory(pixel_list->skip_list.nodes,0,65537UL*
2140     sizeof(*pixel_list->skip_list.nodes));
2141   pixel_list->signature=MagickSignature;
2142   return(pixel_list);
2143 }
2144
2145 static PixelList **AcquirePixelListThreadSet(const size_t width,
2146   const size_t height)
2147 {
2148   PixelList
2149     **pixel_list;
2150
2151   register ssize_t
2152     i;
2153
2154   size_t
2155     number_threads;
2156
2157   number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
2158   pixel_list=(PixelList **) AcquireQuantumMemory(number_threads,
2159     sizeof(*pixel_list));
2160   if (pixel_list == (PixelList **) NULL)
2161     return((PixelList **) NULL);
2162   (void) ResetMagickMemory(pixel_list,0,number_threads*sizeof(*pixel_list));
2163   for (i=0; i < (ssize_t) number_threads; i++)
2164   {
2165     pixel_list[i]=AcquirePixelList(width,height);
2166     if (pixel_list[i] == (PixelList *) NULL)
2167       return(DestroyPixelListThreadSet(pixel_list));
2168   }
2169   return(pixel_list);
2170 }
2171
2172 static void AddNodePixelList(PixelList *pixel_list,const size_t color)
2173 {
2174   register SkipList
2175     *p;
2176
2177   register ssize_t
2178     level;
2179
2180   size_t
2181     search,
2182     update[9];
2183
2184   /*
2185     Initialize the node.
2186   */
2187   p=(&pixel_list->skip_list);
2188   p->nodes[color].signature=pixel_list->signature;
2189   p->nodes[color].count=1;
2190   /*
2191     Determine where it belongs in the list.
2192   */
2193   search=65536UL;
2194   for (level=p->level; level >= 0; level--)
2195   {
2196     while (p->nodes[search].next[level] < color)
2197       search=p->nodes[search].next[level];
2198     update[level]=search;
2199   }
2200   /*
2201     Generate a pseudo-random level for this node.
2202   */
2203   for (level=0; ; level++)
2204   {
2205     pixel_list->seed=(pixel_list->seed*42893621L)+1L;
2206     if ((pixel_list->seed & 0x300) != 0x300)
2207       break;
2208   }
2209   if (level > 8)
2210     level=8;
2211   if (level > (p->level+2))
2212     level=p->level+2;
2213   /*
2214     If we're raising the list's level, link back to the root node.
2215   */
2216   while (level > p->level)
2217   {
2218     p->level++;
2219     update[p->level]=65536UL;
2220   }
2221   /*
2222     Link the node into the skip-list.
2223   */
2224   do
2225   {
2226     p->nodes[color].next[level]=p->nodes[update[level]].next[level];
2227     p->nodes[update[level]].next[level]=color;
2228   } while (level-- > 0);
2229 }
2230
2231 static inline void GetMaximumPixelList(PixelList *pixel_list,Quantum *pixel)
2232 {
2233   register SkipList
2234     *p;
2235
2236   size_t
2237     color,
2238     maximum;
2239
2240   ssize_t
2241     count;
2242
2243   /*
2244     Find the maximum value for each of the color.
2245   */
2246   p=(&pixel_list->skip_list);
2247   color=65536L;
2248   count=0;
2249   maximum=p->nodes[color].next[0];
2250   do
2251   {
2252     color=p->nodes[color].next[0];
2253     if (color > maximum)
2254       maximum=color;
2255     count+=p->nodes[color].count;
2256   } while (count < (ssize_t) pixel_list->length);
2257   *pixel=ScaleShortToQuantum((unsigned short) maximum);
2258 }
2259
2260 static inline void GetMeanPixelList(PixelList *pixel_list,Quantum *pixel)
2261 {
2262   double
2263     sum;
2264
2265   register SkipList
2266     *p;
2267
2268   size_t
2269     color;
2270
2271   ssize_t
2272     count;
2273
2274   /*
2275     Find the mean value for each of the color.
2276   */
2277   p=(&pixel_list->skip_list);
2278   color=65536L;
2279   count=0;
2280   sum=0.0;
2281   do
2282   {
2283     color=p->nodes[color].next[0];
2284     sum+=(double) p->nodes[color].count*color;
2285     count+=p->nodes[color].count;
2286   } while (count < (ssize_t) pixel_list->length);
2287   sum/=pixel_list->length;
2288   *pixel=ScaleShortToQuantum((unsigned short) sum);
2289 }
2290
2291 static inline void GetMedianPixelList(PixelList *pixel_list,Quantum *pixel)
2292 {
2293   register SkipList
2294     *p;
2295
2296   size_t
2297     color;
2298
2299   ssize_t
2300     count;
2301
2302   /*
2303     Find the median value for each of the color.
2304   */
2305   p=(&pixel_list->skip_list);
2306   color=65536L;
2307   count=0;
2308   do
2309   {
2310     color=p->nodes[color].next[0];
2311     count+=p->nodes[color].count;
2312   } while (count <= (ssize_t) (pixel_list->length >> 1));
2313   *pixel=ScaleShortToQuantum((unsigned short) color);
2314 }
2315
2316 static inline void GetMinimumPixelList(PixelList *pixel_list,Quantum *pixel)
2317 {
2318   register SkipList
2319     *p;
2320
2321   size_t
2322     color,
2323     minimum;
2324
2325   ssize_t
2326     count;
2327
2328   /*
2329     Find the minimum value for each of the color.
2330   */
2331   p=(&pixel_list->skip_list);
2332   count=0;
2333   color=65536UL;
2334   minimum=p->nodes[color].next[0];
2335   do
2336   {
2337     color=p->nodes[color].next[0];
2338     if (color < minimum)
2339       minimum=color;
2340     count+=p->nodes[color].count;
2341   } while (count < (ssize_t) pixel_list->length);
2342   *pixel=ScaleShortToQuantum((unsigned short) minimum);
2343 }
2344
2345 static inline void GetModePixelList(PixelList *pixel_list,Quantum *pixel)
2346 {
2347   register SkipList
2348     *p;
2349
2350   size_t
2351     color,
2352     max_count,
2353     mode;
2354
2355   ssize_t
2356     count;
2357
2358   /*
2359     Make each pixel the 'predominant color' of the specified neighborhood.
2360   */
2361   p=(&pixel_list->skip_list);
2362   color=65536L;
2363   mode=color;
2364   max_count=p->nodes[mode].count;
2365   count=0;
2366   do
2367   {
2368     color=p->nodes[color].next[0];
2369     if (p->nodes[color].count > max_count)
2370       {
2371         mode=color;
2372         max_count=p->nodes[mode].count;
2373       }
2374     count+=p->nodes[color].count;
2375   } while (count < (ssize_t) pixel_list->length);
2376   *pixel=ScaleShortToQuantum((unsigned short) mode);
2377 }
2378
2379 static inline void GetNonpeakPixelList(PixelList *pixel_list,Quantum *pixel)
2380 {
2381   register SkipList
2382     *p;
2383
2384   size_t
2385     color,
2386     next,
2387     previous;
2388
2389   ssize_t
2390     count;
2391
2392   /*
2393     Finds the non peak value for each of the colors.
2394   */
2395   p=(&pixel_list->skip_list);
2396   color=65536L;
2397   next=p->nodes[color].next[0];
2398   count=0;
2399   do
2400   {
2401     previous=color;
2402     color=next;
2403     next=p->nodes[color].next[0];
2404     count+=p->nodes[color].count;
2405   } while (count <= (ssize_t) (pixel_list->length >> 1));
2406   if ((previous == 65536UL) && (next != 65536UL))
2407     color=next;
2408   else
2409     if ((previous != 65536UL) && (next == 65536UL))
2410       color=previous;
2411   *pixel=ScaleShortToQuantum((unsigned short) color);
2412 }
2413
2414 static inline void GetStandardDeviationPixelList(PixelList *pixel_list,
2415   Quantum *pixel)
2416 {
2417   double
2418     sum,
2419     sum_squared;
2420
2421   register SkipList
2422     *p;
2423
2424   size_t
2425     color;
2426
2427   ssize_t
2428     count;
2429
2430   /*
2431     Find the standard-deviation value for each of the color.
2432   */
2433   p=(&pixel_list->skip_list);
2434   color=65536L;
2435   count=0;
2436   sum=0.0;
2437   sum_squared=0.0;
2438   do
2439   {
2440     register ssize_t
2441       i;
2442
2443     color=p->nodes[color].next[0];
2444     sum+=(double) p->nodes[color].count*color;
2445     for (i=0; i < (ssize_t) p->nodes[color].count; i++)
2446       sum_squared+=((double) color)*((double) color);
2447     count+=p->nodes[color].count;
2448   } while (count < (ssize_t) pixel_list->length);
2449   sum/=pixel_list->length;
2450   sum_squared/=pixel_list->length;
2451   *pixel=ScaleShortToQuantum((unsigned short) sqrt(sum_squared-(sum*sum)));
2452 }
2453
2454 static inline void InsertPixelList(const Quantum pixel,PixelList *pixel_list)
2455 {
2456   size_t
2457     signature;
2458
2459   unsigned short
2460     index;
2461
2462   index=ScaleQuantumToShort(pixel);
2463   signature=pixel_list->skip_list.nodes[index].signature;
2464   if (signature == pixel_list->signature)
2465     {
2466       pixel_list->skip_list.nodes[index].count++;
2467       return;
2468     }
2469   AddNodePixelList(pixel_list,index);
2470 }
2471
2472 static inline double MagickAbsoluteValue(const double x)
2473 {
2474   if (x < 0)
2475     return(-x);
2476   return(x);
2477 }
2478
2479 static inline size_t MagickMax(const size_t x,const size_t y)
2480 {
2481   if (x > y)
2482     return(x);
2483   return(y);
2484 }
2485
2486 static void ResetPixelList(PixelList *pixel_list)
2487 {
2488   int
2489     level;
2490
2491   register SkipNode
2492     *root;
2493
2494   register SkipList
2495     *p;
2496
2497   /*
2498     Reset the skip-list.
2499   */
2500   p=(&pixel_list->skip_list);
2501   root=p->nodes+65536UL;
2502   p->level=0;
2503   for (level=0; level < 9; level++)
2504     root->next[level]=65536UL;
2505   pixel_list->seed=pixel_list->signature++;
2506 }
2507
2508 MagickExport Image *StatisticImage(const Image *image,const StatisticType type,
2509   const size_t width,const size_t height,ExceptionInfo *exception)
2510 {
2511 #define StatisticImageTag  "Statistic/Image"
2512
2513   CacheView
2514     *image_view,
2515     *statistic_view;
2516
2517   Image
2518     *statistic_image;
2519
2520   MagickBooleanType
2521     status;
2522
2523   MagickOffsetType
2524     progress;
2525
2526   PixelList
2527     **restrict pixel_list;
2528
2529   ssize_t
2530     center,
2531     y;
2532
2533   /*
2534     Initialize statistics image attributes.
2535   */
2536   assert(image != (Image *) NULL);
2537   assert(image->signature == MagickSignature);
2538   if (image->debug != MagickFalse)
2539     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2540   assert(exception != (ExceptionInfo *) NULL);
2541   assert(exception->signature == MagickSignature);
2542   statistic_image=CloneImage(image,image->columns,image->rows,MagickTrue,
2543     exception);
2544   if (statistic_image == (Image *) NULL)
2545     return((Image *) NULL);
2546   status=SetImageStorageClass(statistic_image,DirectClass,exception);
2547   if (status == MagickFalse)
2548     {
2549       statistic_image=DestroyImage(statistic_image);
2550       return((Image *) NULL);
2551     }
2552   pixel_list=AcquirePixelListThreadSet(MagickMax(width,1),MagickMax(height,1));
2553   if (pixel_list == (PixelList **) NULL)
2554     {
2555       statistic_image=DestroyImage(statistic_image);
2556       ThrowImageException(ResourceLimitError,"MemoryAllocationFailed");
2557     }
2558   /*
2559     Make each pixel the min / max / median / mode / etc. of the neighborhood.
2560   */
2561   center=(ssize_t) GetPixelChannels(image)*(image->columns+MagickMax(width,1))*
2562     (MagickMax(height,1)/2L)+GetPixelChannels(image)*(MagickMax(width,1)/2L);
2563   status=MagickTrue;
2564   progress=0;
2565   image_view=AcquireVirtualCacheView(image,exception);
2566   statistic_view=AcquireAuthenticCacheView(statistic_image,exception);
2567 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2568   #pragma omp parallel for schedule(static,4) shared(progress,status) \
2569     magick_threads(image,statistic_image,statistic_image->rows,1)
2570 #endif
2571   for (y=0; y < (ssize_t) statistic_image->rows; y++)
2572   {
2573     const int
2574       id = GetOpenMPThreadId();
2575
2576     register const Quantum
2577       *restrict p;
2578
2579     register Quantum
2580       *restrict q;
2581
2582     register ssize_t
2583       x;
2584
2585     if (status == MagickFalse)
2586       continue;
2587     p=GetCacheViewVirtualPixels(image_view,-((ssize_t) MagickMax(width,1)/2L),y-
2588       (ssize_t) (MagickMax(height,1)/2L),image->columns+MagickMax(width,1),
2589       MagickMax(height,1),exception);
2590     q=QueueCacheViewAuthenticPixels(statistic_view,0,y,statistic_image->columns,      1,exception);
2591     if ((p == (const Quantum *) NULL) || (q == (Quantum *) NULL))
2592       {
2593         status=MagickFalse;
2594         continue;
2595       }
2596     for (x=0; x < (ssize_t) statistic_image->columns; x++)
2597     {
2598       register ssize_t
2599         i;
2600
2601       for (i=0; i < (ssize_t) GetPixelChannels(image); i++)
2602       {
2603         Quantum
2604           pixel;
2605
2606         register const Quantum
2607           *restrict pixels;
2608
2609         register ssize_t
2610           u;
2611
2612         ssize_t
2613           v;
2614
2615         PixelChannel channel=GetPixelChannelChannel(image,i);
2616         PixelTrait traits=GetPixelChannelTraits(image,channel);
2617         PixelTrait statistic_traits=GetPixelChannelTraits(statistic_image,
2618           channel);
2619         if ((traits == UndefinedPixelTrait) ||
2620             (statistic_traits == UndefinedPixelTrait))
2621           continue;
2622         if (((statistic_traits & CopyPixelTrait) != 0) ||
2623             (GetPixelReadMask(image,p) == 0))
2624           {
2625             SetPixelChannel(statistic_image,channel,p[center+i],q);
2626             continue;
2627           }
2628         pixels=p;
2629         ResetPixelList(pixel_list[id]);
2630         for (v=0; v < (ssize_t) MagickMax(height,1); v++)
2631         {
2632           for (u=0; u < (ssize_t) MagickMax(width,1); u++)
2633           {
2634             InsertPixelList(pixels[i],pixel_list[id]);
2635             pixels+=GetPixelChannels(image);
2636           }
2637           pixels+=(image->columns-1)*GetPixelChannels(image);
2638         }
2639         switch (type)
2640         {
2641           case GradientStatistic:
2642           {
2643             double
2644               maximum,
2645               minimum;
2646
2647             GetMinimumPixelList(pixel_list[id],&pixel);
2648             minimum=(double) pixel;
2649             GetMaximumPixelList(pixel_list[id],&pixel);
2650             maximum=(double) pixel;
2651             pixel=ClampToQuantum(MagickAbsoluteValue(maximum-minimum));
2652             break;
2653           }
2654           case MaximumStatistic:
2655           {
2656             GetMaximumPixelList(pixel_list[id],&pixel);
2657             break;
2658           }
2659           case MeanStatistic:
2660           {
2661             GetMeanPixelList(pixel_list[id],&pixel);
2662             break;
2663           }
2664           case MedianStatistic:
2665           default:
2666           {
2667             GetMedianPixelList(pixel_list[id],&pixel);
2668             break;
2669           }
2670           case MinimumStatistic:
2671           {
2672             GetMinimumPixelList(pixel_list[id],&pixel);
2673             break;
2674           }
2675           case ModeStatistic:
2676           {
2677             GetModePixelList(pixel_list[id],&pixel);
2678             break;
2679           }
2680           case NonpeakStatistic:
2681           {
2682             GetNonpeakPixelList(pixel_list[id],&pixel);
2683             break;
2684           }
2685           case StandardDeviationStatistic:
2686           {
2687             GetStandardDeviationPixelList(pixel_list[id],&pixel);
2688             break;
2689           }
2690         }
2691         SetPixelChannel(statistic_image,channel,pixel,q);
2692       }
2693       p+=GetPixelChannels(image);
2694       q+=GetPixelChannels(statistic_image);
2695     }
2696     if (SyncCacheViewAuthenticPixels(statistic_view,exception) == MagickFalse)
2697       status=MagickFalse;
2698     if (image->progress_monitor != (MagickProgressMonitor) NULL)
2699       {
2700         MagickBooleanType
2701           proceed;
2702
2703 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2704         #pragma omp critical (MagickCore_StatisticImage)
2705 #endif
2706         proceed=SetImageProgress(image,StatisticImageTag,progress++,
2707           image->rows);
2708         if (proceed == MagickFalse)
2709           status=MagickFalse;
2710       }
2711   }
2712   statistic_view=DestroyCacheView(statistic_view);
2713   image_view=DestroyCacheView(image_view);
2714   pixel_list=DestroyPixelListThreadSet(pixel_list);
2715   if (status == MagickFalse)
2716     statistic_image=DestroyImage(statistic_image);
2717   return(statistic_image);
2718 }