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

   1 /*
   2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   3 %                                                                             %
   4 %                                                                             %
   5 %                                                                             %
   6 %           QQQ   U   U   AAA   N   N  TTTTT  IIIII   ZZZZZ  EEEEE            %
   7 %          Q   Q  U   U  A   A  NN  N    T      I        ZZ  E                %
   8 %          Q   Q  U   U  AAAAA  N N N    T      I      ZZZ   EEEEE            %
   9 %          Q  QQ  U   U  A   A  N  NN    T      I     ZZ     E                %
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  11 %                                                                             %
  12 %                                                                             %
  13 %    MagickCore Methods to Reduce the Number of Unique Colors in an Image     %
  14 %                                                                             %
  15 %                           Software Design                                   %
  16 %                             John Cristy                                     %
  17 %                              July 1992                                      %
  18 %                                                                             %
  19 %                                                                             %
  20 %  Copyright 1999-2013 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 %  Realism in computer graphics typically requires using 24 bits/pixel to
  37 %  generate an image.  Yet many graphic display devices do not contain the
  38 %  amount of memory necessary to match the spatial and color resolution of
  39 %  the human eye.  The Quantize methods takes a 24 bit image and reduces
  40 %  the number of colors so it can be displayed on raster device with less
  41 %  bits per pixel.  In most instances, the quantized image closely
  42 %  resembles the original reference image.
  43 %
  44 %  A reduction of colors in an image is also desirable for image
  45 %  transmission and real-time animation.
  46 %
  47 %  QuantizeImage() takes a standard RGB or monochrome images and quantizes
  48 %  them down to some fixed number of colors.
  49 %
  50 %  For purposes of color allocation, an image is a set of n pixels, where
  51 %  each pixel is a point in RGB space.  RGB space is a 3-dimensional
  52 %  vector space, and each pixel, Pi,  is defined by an ordered triple of
  53 %  red, green, and blue coordinates, (Ri, Gi, Bi).
  54 %
  55 %  Each primary color component (red, green, or blue) represents an
  56 %  intensity which varies linearly from 0 to a maximum value, Cmax, which
  57 %  corresponds to full saturation of that color.  Color allocation is
  58 %  defined over a domain consisting of the cube in RGB space with opposite
  59 %  vertices at (0,0,0) and (Cmax, Cmax, Cmax).  QUANTIZE requires Cmax =
  60 %  255.
  61 %
  62 %  The algorithm maps this domain onto a tree in which each node
  63 %  represents a cube within that domain.  In the following discussion
  64 %  these cubes are defined by the coordinate of two opposite vertices:
  65 %  The vertex nearest the origin in RGB space and the vertex farthest from
  66 %  the origin.
  67 %
  68 %  The tree's root node represents the entire domain, (0,0,0) through
  69 %  (Cmax,Cmax,Cmax).  Each lower level in the tree is generated by
  70 %  subdividing one node's cube into eight smaller cubes of equal size.
  71 %  This corresponds to bisecting the parent cube with planes passing
  72 %  through the midpoints of each edge.
  73 %
  74 %  The basic algorithm operates in three phases: Classification,
  75 %  Reduction, and Assignment.  Classification builds a color description
  76 %  tree for the image.  Reduction collapses the tree until the number it
  77 %  represents, at most, the number of colors desired in the output image.
  78 %  Assignment defines the output image's color map and sets each pixel's
  79 %  color by restorage_class in the reduced tree.  Our goal is to minimize
  80 %  the numerical discrepancies between the original colors and quantized
  81 %  colors (quantization error).
  82 %
  83 %  Classification begins by initializing a color description tree of
  84 %  sufficient depth to represent each possible input color in a leaf.
  85 %  However, it is impractical to generate a fully-formed color description
  86 %  tree in the storage_class phase for realistic values of Cmax.  If
  87 %  colors components in the input image are quantized to k-bit precision,
  88 %  so that Cmax= 2k-1, the tree would need k levels below the root node to
  89 %  allow representing each possible input color in a leaf.  This becomes
  90 %  prohibitive because the tree's total number of nodes is 1 +
  91 %  sum(i=1, k, 8k).
  92 %
  93 %  A complete tree would require 19,173,961 nodes for k = 8, Cmax = 255.
  94 %  Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
  95 %  Initializes data structures for nodes only as they are needed;  (2)
  96 %  Chooses a maximum depth for the tree as a function of the desired
  97 %  number of colors in the output image (currently log2(colormap size)).
  98 %
  99 %  For each pixel in the input image, storage_class scans downward from
 100 %  the root of the color description tree.  At each level of the tree it
 101 %  identifies the single node which represents a cube in RGB space
 102 %  containing the pixel's color.  It updates the following data for each
 103 %  such node:
 104 %
 105 %    n1: Number of pixels whose color is contained in the RGB cube which
 106 %    this node represents;
 107 %
 108 %    n2: Number of pixels whose color is not represented in a node at
 109 %    lower depth in the tree;  initially,  n2 = 0 for all nodes except
 110 %    leaves of the tree.
 111 %
 112 %    Sr, Sg, Sb: Sums of the red, green, and blue component values for all
 113 %    pixels not classified at a lower depth. The combination of these sums
 114 %    and n2  will ultimately characterize the mean color of a set of
 115 %    pixels represented by this node.
 116 %
 117 %    E: the distance squared in RGB space between each pixel contained
 118 %    within a node and the nodes' center.  This represents the
 119 %    quantization error for a node.
 120 %
 121 %  Reduction repeatedly prunes the tree until the number of nodes with n2
 122 %  > 0 is less than or equal to the maximum number of colors allowed in
 123 %  the output image.  On any given iteration over the tree, it selects
 124 %  those nodes whose E count is minimal for pruning and merges their color
 125 %  statistics upward. It uses a pruning threshold, Ep, to govern node
 126 %  selection as follows:
 127 %
 128 %    Ep = 0
 129 %    while number of nodes with (n2 > 0) > required maximum number of colors
 130 %      prune all nodes such that E <= Ep
 131 %      Set Ep to minimum E in remaining nodes
 132 %
 133 %  This has the effect of minimizing any quantization error when merging
 134 %  two nodes together.
 135 %
 136 %  When a node to be pruned has offspring, the pruning procedure invokes
 137 %  itself recursively in order to prune the tree from the leaves upward.
 138 %  n2,  Sr, Sg,  and  Sb in a node being pruned are always added to the
 139 %  corresponding data in that node's parent.  This retains the pruned
 140 %  node's color characteristics for later averaging.
 141 %
 142 %  For each node, n2 pixels exist for which that node represents the
 143 %  smallest volume in RGB space containing those pixel's colors.  When n2
 144 %  > 0 the node will uniquely define a color in the output image. At the
 145 %  beginning of reduction,  n2 = 0  for all nodes except a the leaves of
 146 %  the tree which represent colors present in the input image.
 147 %
 148 %  The other pixel count, n1, indicates the total number of colors within
 149 %  the cubic volume which the node represents.  This includes n1 - n2
 150 %  pixels whose colors should be defined by nodes at a lower level in the
 151 %  tree.
 152 %
 153 %  Assignment generates the output image from the pruned tree.  The output
 154 %  image consists of two parts: (1)  A color map, which is an array of
 155 %  color descriptions (RGB triples) for each color present in the output
 156 %  image;  (2)  A pixel array, which represents each pixel as an index
 157 %  into the color map array.
 158 %
 159 %  First, the assignment phase makes one pass over the pruned color
 160 %  description tree to establish the image's color map.  For each node
 161 %  with n2  > 0, it divides Sr, Sg, and Sb by n2 .  This produces the mean
 162 %  color of all pixels that classify no lower than this node.  Each of
 163 %  these colors becomes an entry in the color map.
 164 %
 165 %  Finally,  the assignment phase reclassifies each pixel in the pruned
 166 %  tree to identify the deepest node containing the pixel's color.  The
 167 %  pixel's value in the pixel array becomes the index of this node's mean
 168 %  color in the color map.
 169 %
 170 %  This method is based on a similar algorithm written by Paul Raveling.
 171 %
 172 */
 173 \f
 174 /*
 175   Include declarations.
 176 */
 177 #include "MagickCore/studio.h"
 178 #include "MagickCore/attribute.h"
 179 #include "MagickCore/cache-view.h"
 180 #include "MagickCore/color.h"
 181 #include "MagickCore/color-private.h"
 182 #include "MagickCore/colormap.h"
 183 #include "MagickCore/colorspace.h"
 184 #include "MagickCore/colorspace-private.h"
 185 #include "MagickCore/enhance.h"
 186 #include "MagickCore/exception.h"
 187 #include "MagickCore/exception-private.h"
 188 #include "MagickCore/histogram.h"
 189 #include "MagickCore/image.h"
 190 #include "MagickCore/image-private.h"
 191 #include "MagickCore/list.h"
 192 #include "MagickCore/memory_.h"
 193 #include "MagickCore/monitor.h"
 194 #include "MagickCore/monitor-private.h"
 195 #include "MagickCore/option.h"
 196 #include "MagickCore/pixel-accessor.h"
 197 #include "MagickCore/pixel-private.h"
 198 #include "MagickCore/quantize.h"
 199 #include "MagickCore/quantum.h"
 200 #include "MagickCore/quantum-private.h"
 201 #include "MagickCore/resource_.h"
 202 #include "MagickCore/string_.h"
 203 #include "MagickCore/thread-private.h"
 204 \f
 205 /*
 206   Define declarations.
 207 */
 208 #if !defined(__APPLE__) && !defined(TARGET_OS_IPHONE)
 209 #define CacheShift  2
 210 #else
 211 #define CacheShift  3
 212 #endif
 213 #define ErrorQueueLength  16
 214 #define MaxNodes  266817
 215 #define MaxTreeDepth  8
 216 #define NodesInAList  1920
 217 \f
 218 /*
 219   Typdef declarations.
 220 */
 221 typedef struct _RealPixelInfo
 222 {
 223   double
 224     red,
 225     green,
 226     blue,
 227     alpha;
 228 } RealPixelInfo;
 229
 230 typedef struct _NodeInfo
 231 {
 232   struct _NodeInfo
 233     *parent,
 234     *child[16];
 235
 236   MagickSizeType
 237     number_unique;
 238
 239   RealPixelInfo
 240     total_color;
 241
 242   double
 243     quantize_error;
 244
 245   size_t
 246     color_number,
 247     id,
 248     level;
 249 } NodeInfo;
 250
 251 typedef struct _Nodes
 252 {
 253   NodeInfo
 254     *nodes;
 255
 256   struct _Nodes
 257     *next;
 258 } Nodes;
 259
 260 typedef struct _CubeInfo
 261 {
 262   NodeInfo
 263     *root;
 264
 265   size_t
 266     colors,
 267     maximum_colors;
 268
 269   ssize_t
 270     transparent_index;
 271
 272   MagickSizeType
 273     transparent_pixels;
 274
 275   RealPixelInfo
 276     target;
 277
 278   double
 279     distance,
 280     pruning_threshold,
 281     next_threshold;
 282
 283   size_t
 284     nodes,
 285     free_nodes,
 286     color_number;
 287
 288   NodeInfo
 289     *next_node;
 290
 291   Nodes
 292     *node_queue;
 293
 294   MemoryInfo
 295     *memory_info;
 296
 297   ssize_t
 298     *cache;
 299
 300   RealPixelInfo
 301     error[ErrorQueueLength];
 302
 303   double
 304     weights[ErrorQueueLength];
 305
 306   QuantizeInfo
 307     *quantize_info;
 308
 309   MagickBooleanType
 310     associate_alpha;
 311
 312   ssize_t
 313     x,
 314     y;
 315
 316   size_t
 317     depth;
 318
 319   MagickOffsetType
 320     offset;
 321
 322   MagickSizeType
 323     span;
 324 } CubeInfo;
 325 \f
 326 /*
 327   Method prototypes.
 328 */
 329 static CubeInfo
 330   *GetCubeInfo(const QuantizeInfo *,const size_t,const size_t);
 331
 332 static NodeInfo
 333   *GetNodeInfo(CubeInfo *,const size_t,const size_t,NodeInfo *);
 334
 335 static MagickBooleanType
 336   AssignImageColors(Image *,CubeInfo *,ExceptionInfo *),
 337   ClassifyImageColors(CubeInfo *,const Image *,ExceptionInfo *),
 338   DitherImage(Image *,CubeInfo *,ExceptionInfo *),
 339   SetGrayscaleImage(Image *,ExceptionInfo *);
 340
 341 static size_t
 342   DefineImageColormap(Image *,CubeInfo *,NodeInfo *);
 343
 344 static void
 345   ClosestColor(const Image *,CubeInfo *,const NodeInfo *),
 346   DestroyCubeInfo(CubeInfo *),
 347   PruneLevel(const Image *,CubeInfo *,const NodeInfo *),
 348   PruneToCubeDepth(const Image *,CubeInfo *,const NodeInfo *),
 349   ReduceImageColors(const Image *,CubeInfo *);
 350 \f
 351 /*
 352 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 353 %                                                                             %
 354 %                                                                             %
 355 %                                                                             %
 356 %   A c q u i r e Q u a n t i z e I n f o                                     %
 357 %                                                                             %
 358 %                                                                             %
 359 %                                                                             %
 360 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 361 %
 362 %  AcquireQuantizeInfo() allocates the QuantizeInfo structure.
 363 %
 364 %  The format of the AcquireQuantizeInfo method is:
 365 %
 366 %      QuantizeInfo *AcquireQuantizeInfo(const ImageInfo *image_info)
 367 %
 368 %  A description of each parameter follows:
 369 %
 370 %    o image_info: the image info.
 371 %
 372 */
 373 MagickExport QuantizeInfo *AcquireQuantizeInfo(const ImageInfo *image_info)
 374 {
 375   QuantizeInfo
 376     *quantize_info;
 377
 378   quantize_info=(QuantizeInfo *) AcquireMagickMemory(sizeof(*quantize_info));
 379   if (quantize_info == (QuantizeInfo *) NULL)
 380     ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
 381   GetQuantizeInfo(quantize_info);
 382   if (image_info != (ImageInfo *) NULL)
 383     {
 384       const char
 385         *option;
 386
 387       quantize_info->dither_method=image_info->dither == MagickFalse ?
 388         NoDitherMethod : RiemersmaDitherMethod;
 389       option=GetImageOption(image_info,"dither");
 390       if (option != (const char *) NULL)
 391         quantize_info->dither_method=(DitherMethod) ParseCommandOption(
 392           MagickDitherOptions,MagickFalse,option);
 393       quantize_info->measure_error=image_info->verbose;
 394     }
 395   return(quantize_info);
 396 }
 397 \f
 398 /*
 399 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 400 %                                                                             %
 401 %                                                                             %
 402 %                                                                             %
 403 +   A s s i g n I m a g e C o l o r s                                         %
 404 %                                                                             %
 405 %                                                                             %
 406 %                                                                             %
 407 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 408 %
 409 %  AssignImageColors() generates the output image from the pruned tree.  The
 410 %  output image consists of two parts: (1)  A color map, which is an array
 411 %  of color descriptions (RGB triples) for each color present in the
 412 %  output image;  (2)  A pixel array, which represents each pixel as an
 413 %  index into the color map array.
 414 %
 415 %  First, the assignment phase makes one pass over the pruned color
 416 %  description tree to establish the image's color map.  For each node
 417 %  with n2  > 0, it divides Sr, Sg, and Sb by n2 .  This produces the mean
 418 %  color of all pixels that classify no lower than this node.  Each of
 419 %  these colors becomes an entry in the color map.
 420 %
 421 %  Finally,  the assignment phase reclassifies each pixel in the pruned
 422 %  tree to identify the deepest node containing the pixel's color.  The
 423 %  pixel's value in the pixel array becomes the index of this node's mean
 424 %  color in the color map.
 425 %
 426 %  The format of the AssignImageColors() method is:
 427 %
 428 %      MagickBooleanType AssignImageColors(Image *image,CubeInfo *cube_info)
 429 %
 430 %  A description of each parameter follows.
 431 %
 432 %    o image: the image.
 433 %
 434 %    o cube_info: A pointer to the Cube structure.
 435 %
 436 */
 437
 438 static inline void AssociateAlphaPixel(const Image *image,
 439   const CubeInfo *cube_info,const Quantum *pixel,RealPixelInfo *alpha_pixel)
 440 {
 441   double
 442     alpha;
 443
 444   if ((cube_info->associate_alpha == MagickFalse) ||
 445       (GetPixelAlpha(image,pixel)== OpaqueAlpha))
 446     {
 447       alpha_pixel->red=(double) GetPixelRed(image,pixel);
 448       alpha_pixel->green=(double) GetPixelGreen(image,pixel);
 449       alpha_pixel->blue=(double) GetPixelBlue(image,pixel);
 450       alpha_pixel->alpha=(double) GetPixelAlpha(image,pixel);
 451       return;
 452     }
 453   alpha=(double) (QuantumScale*GetPixelAlpha(image,pixel));
 454   alpha_pixel->red=alpha*GetPixelRed(image,pixel);
 455   alpha_pixel->green=alpha*GetPixelGreen(image,pixel);
 456   alpha_pixel->blue=alpha*GetPixelBlue(image,pixel);
 457   alpha_pixel->alpha=(double) GetPixelAlpha(image,pixel);
 458 }
 459
 460 static inline void AssociateAlphaPixelInfo(const CubeInfo *cube_info,
 461   const PixelInfo *pixel,RealPixelInfo *alpha_pixel)
 462 {
 463   double
 464     alpha;
 465
 466   if ((cube_info->associate_alpha == MagickFalse) ||
 467       (pixel->alpha == OpaqueAlpha))
 468     {
 469       alpha_pixel->red=(double) pixel->red;
 470       alpha_pixel->green=(double) pixel->green;
 471       alpha_pixel->blue=(double) pixel->blue;
 472       alpha_pixel->alpha=(double) pixel->alpha;
 473       return;
 474     }
 475   alpha=(double) (QuantumScale*pixel->alpha);
 476   alpha_pixel->red=alpha*pixel->red;
 477   alpha_pixel->green=alpha*pixel->green;
 478   alpha_pixel->blue=alpha*pixel->blue;
 479   alpha_pixel->alpha=(double) pixel->alpha;
 480 }
 481
 482 static inline Quantum ClampPixel(const MagickRealType value)
 483 {
 484   if (value < 0.0f)
 485     return(0);
 486   if (value >= (MagickRealType) QuantumRange)
 487     return((Quantum) QuantumRange);
 488 #if !defined(MAGICKCORE_HDRI_SUPPORT)
 489   return((Quantum) (value+0.5f));
 490 #else
 491   return(value);
 492 #endif
 493 }
 494
 495 static inline size_t ColorToNodeId(const CubeInfo *cube_info,
 496   const RealPixelInfo *pixel,size_t index)
 497 {
 498   size_t
 499     id;
 500
 501   id=(size_t) (((ScaleQuantumToChar(ClampPixel(pixel->red)) >> index) & 0x01) |
 502     ((ScaleQuantumToChar(ClampPixel(pixel->green)) >> index) & 0x01) << 1 |
 503     ((ScaleQuantumToChar(ClampPixel(pixel->blue)) >> index) & 0x01) << 2);
 504   if (cube_info->associate_alpha != MagickFalse)
 505     id|=((ScaleQuantumToChar(ClampPixel(pixel->alpha)) >> index) & 0x1) << 3;
 506   return(id);
 507 }
 508
 509 static MagickBooleanType AssignImageColors(Image *image,CubeInfo *cube_info,
 510   ExceptionInfo *exception)
 511 {
 512 #define AssignImageTag  "Assign/Image"
 513
 514   ssize_t
 515     y;
 516
 517   /*
 518     Allocate image colormap.
 519   */
 520   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
 521       (cube_info->quantize_info->colorspace != CMYKColorspace))
 522     (void) TransformImageColorspace((Image *) image,
 523       cube_info->quantize_info->colorspace,exception);
 524   else
 525     if (IssRGBCompatibleColorspace(image->colorspace) == MagickFalse)
 526       (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
 527   if (AcquireImageColormap(image,cube_info->colors,exception) == MagickFalse)
 528     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 529       image->filename);
 530   image->colors=0;
 531   cube_info->transparent_pixels=0;
 532   cube_info->transparent_index=(-1);
 533   (void) DefineImageColormap(image,cube_info,cube_info->root);
 534   /*
 535     Create a reduced color image.
 536   */
 537   if ((cube_info->quantize_info->dither_method != NoDitherMethod) &&
 538       (cube_info->quantize_info->dither_method != NoDitherMethod))
 539     (void) DitherImage(image,cube_info,exception);
 540   else
 541     {
 542       CacheView
 543         *image_view;
 544
 545       MagickBooleanType
 546         status;
 547
 548       status=MagickTrue;
 549       image_view=AcquireAuthenticCacheView(image,exception);
 550 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 551       #pragma omp parallel for schedule(static,4) shared(status) \
 552         magick_threads(image,image,image->rows,1)
 553 #endif
 554       for (y=0; y < (ssize_t) image->rows; y++)
 555       {
 556         CubeInfo
 557           cube;
 558
 559         register Quantum
 560           *restrict q;
 561
 562         register ssize_t
 563           x;
 564
 565         ssize_t
 566           count;
 567
 568         if (status == MagickFalse)
 569           continue;
 570         q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
 571           exception);
 572         if (q == (Quantum *) NULL)
 573           {
 574             status=MagickFalse;
 575             continue;
 576           }
 577         cube=(*cube_info);
 578         for (x=0; x < (ssize_t) image->columns; x+=count)
 579         {
 580           RealPixelInfo
 581             pixel;
 582
 583           register const NodeInfo
 584             *node_info;
 585
 586           register ssize_t
 587             i;
 588
 589           size_t
 590             id,
 591             index;
 592
 593           /*
 594             Identify the deepest node containing the pixel's color.
 595           */
 596           for (count=1; (x+count) < (ssize_t) image->columns; count++)
 597           {
 598             PixelInfo
 599               packet;
 600
 601             GetPixelInfoPixel(image,q+count*GetPixelChannels(image),&packet);
 602             if (IsPixelEquivalent(image,q,&packet) == MagickFalse)
 603               break;
 604           }
 605           AssociateAlphaPixel(image,&cube,q,&pixel);
 606           node_info=cube.root;
 607           for (index=MaxTreeDepth-1; (ssize_t) index > 0; index--)
 608           {
 609             id=ColorToNodeId(&cube,&pixel,index);
 610             if (node_info->child[id] == (NodeInfo *) NULL)
 611               break;
 612             node_info=node_info->child[id];
 613           }
 614           /*
 615             Find closest color among siblings and their children.
 616           */
 617           cube.target=pixel;
 618           cube.distance=(double) (4.0*(QuantumRange+1.0)*
 619             (QuantumRange+1.0)+1.0);
 620           ClosestColor(image,&cube,node_info->parent);
 621           index=cube.color_number;
 622           for (i=0; i < (ssize_t) count; i++)
 623           {
 624             if (image->storage_class == PseudoClass)
 625               SetPixelIndex(image,(Quantum) index,q);
 626             if (cube.quantize_info->measure_error == MagickFalse)
 627               {
 628                 SetPixelRed(image,ClampToQuantum(
 629                   image->colormap[index].red),q);
 630                 SetPixelGreen(image,ClampToQuantum(
 631                   image->colormap[index].green),q);
 632                 SetPixelBlue(image,ClampToQuantum(
 633                   image->colormap[index].blue),q);
 634                 if (cube.associate_alpha != MagickFalse)
 635                   SetPixelAlpha(image,ClampToQuantum(
 636                     image->colormap[index].alpha),q);
 637               }
 638             q+=GetPixelChannels(image);
 639           }
 640         }
 641         if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
 642           status=MagickFalse;
 643         if (image->progress_monitor != (MagickProgressMonitor) NULL)
 644           {
 645             MagickBooleanType
 646               proceed;
 647
 648 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 649             #pragma omp critical (MagickCore_AssignImageColors)
 650 #endif
 651             proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) y,
 652               image->rows);
 653             if (proceed == MagickFalse)
 654               status=MagickFalse;
 655           }
 656       }
 657       image_view=DestroyCacheView(image_view);
 658     }
 659   if (cube_info->quantize_info->measure_error != MagickFalse)
 660     (void) GetImageQuantizeError(image,exception);
 661   if ((cube_info->quantize_info->number_colors == 2) &&
 662       (cube_info->quantize_info->colorspace == GRAYColorspace))
 663     {
 664       double
 665         intensity;
 666
 667       register PixelInfo
 668         *restrict q;
 669
 670       register ssize_t
 671         i;
 672
 673       /*
 674         Monochrome image.
 675       */
 676       q=image->colormap;
 677       for (i=0; i < (ssize_t) image->colors; i++)
 678       {
 679         intensity=(double) ((double) GetPixelInfoIntensity(q) <
 680           ((double) QuantumRange/2.0) ? 0 : QuantumRange);
 681         q->red=intensity;
 682         q->green=intensity;
 683         q->blue=intensity;
 684         q++;
 685       }
 686     }
 687   (void) SyncImage(image,exception);
 688   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
 689       (cube_info->quantize_info->colorspace != CMYKColorspace))
 690     (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
 691   return(MagickTrue);
 692 }
 693 \f
 694 /*
 695 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 696 %                                                                             %
 697 %                                                                             %
 698 %                                                                             %
 699 +   C l a s s i f y I m a g e C o l o r s                                     %
 700 %                                                                             %
 701 %                                                                             %
 702 %                                                                             %
 703 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 704 %
 705 %  ClassifyImageColors() begins by initializing a color description tree
 706 %  of sufficient depth to represent each possible input color in a leaf.
 707 %  However, it is impractical to generate a fully-formed color
 708 %  description tree in the storage_class phase for realistic values of
 709 %  Cmax.  If colors components in the input image are quantized to k-bit
 710 %  precision, so that Cmax= 2k-1, the tree would need k levels below the
 711 %  root node to allow representing each possible input color in a leaf.
 712 %  This becomes prohibitive because the tree's total number of nodes is
 713 %  1 + sum(i=1,k,8k).
 714 %
 715 %  A complete tree would require 19,173,961 nodes for k = 8, Cmax = 255.
 716 %  Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
 717 %  Initializes data structures for nodes only as they are needed;  (2)
 718 %  Chooses a maximum depth for the tree as a function of the desired
 719 %  number of colors in the output image (currently log2(colormap size)).
 720 %
 721 %  For each pixel in the input image, storage_class scans downward from
 722 %  the root of the color description tree.  At each level of the tree it
 723 %  identifies the single node which represents a cube in RGB space
 724 %  containing It updates the following data for each such node:
 725 %
 726 %    n1 : Number of pixels whose color is contained in the RGB cube
 727 %    which this node represents;
 728 %
 729 %    n2 : Number of pixels whose color is not represented in a node at
 730 %    lower depth in the tree;  initially,  n2 = 0 for all nodes except
 731 %    leaves of the tree.
 732 %
 733 %    Sr, Sg, Sb : Sums of the red, green, and blue component values for
 734 %    all pixels not classified at a lower depth. The combination of
 735 %    these sums and n2  will ultimately characterize the mean color of a
 736 %    set of pixels represented by this node.
 737 %
 738 %    E: the distance squared in RGB space between each pixel contained
 739 %    within a node and the nodes' center.  This represents the quantization
 740 %    error for a node.
 741 %
 742 %  The format of the ClassifyImageColors() method is:
 743 %
 744 %      MagickBooleanType ClassifyImageColors(CubeInfo *cube_info,
 745 %        const Image *image,ExceptionInfo *exception)
 746 %
 747 %  A description of each parameter follows.
 748 %
 749 %    o cube_info: A pointer to the Cube structure.
 750 %
 751 %    o image: the image.
 752 %
 753 */
 754
 755 static inline void SetAssociatedAlpha(const Image *image,CubeInfo *cube_info)
 756 {
 757   MagickBooleanType
 758     associate_alpha;
 759
 760   associate_alpha=image->alpha_trait == BlendPixelTrait ? MagickTrue :
 761     MagickFalse;
 762   if (cube_info->quantize_info->colorspace == TransparentColorspace)
 763     associate_alpha=MagickFalse;
 764   if ((cube_info->quantize_info->number_colors == 2) &&
 765       (cube_info->quantize_info->colorspace == GRAYColorspace))
 766     associate_alpha=MagickFalse;
 767   cube_info->associate_alpha=associate_alpha;
 768 }
 769
 770 static MagickBooleanType ClassifyImageColors(CubeInfo *cube_info,
 771   const Image *image,ExceptionInfo *exception)
 772 {
 773 #define ClassifyImageTag  "Classify/Image"
 774
 775   CacheView
 776     *image_view;
 777
 778   MagickBooleanType
 779     proceed;
 780
 781   double
 782     bisect;
 783
 784   NodeInfo
 785     *node_info;
 786
 787   RealPixelInfo
 788     error,
 789     mid,
 790     midpoint,
 791     pixel;
 792
 793   size_t
 794     count,
 795     id,
 796     index,
 797     level;
 798
 799   ssize_t
 800     y;
 801
 802   /*
 803     Classify the first cube_info->maximum_colors colors to a tree depth of 8.
 804   */
 805   SetAssociatedAlpha(image,cube_info);
 806   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
 807       (cube_info->quantize_info->colorspace != CMYKColorspace))
 808     (void) TransformImageColorspace((Image *) image,
 809       cube_info->quantize_info->colorspace,exception);
 810   else
 811     if (IssRGBCompatibleColorspace(image->colorspace) == MagickFalse)
 812       (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
 813   midpoint.red=(double) QuantumRange/2.0;
 814   midpoint.green=(double) QuantumRange/2.0;
 815   midpoint.blue=(double) QuantumRange/2.0;
 816   midpoint.alpha=(double) QuantumRange/2.0;
 817   error.alpha=0.0;
 818   image_view=AcquireVirtualCacheView(image,exception);
 819   for (y=0; y < (ssize_t) image->rows; y++)
 820   {
 821     register const Quantum
 822       *restrict p;
 823
 824     register ssize_t
 825       x;
 826
 827     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 828     if (p == (const Quantum *) NULL)
 829       break;
 830     if (cube_info->nodes > MaxNodes)
 831       {
 832         /*
 833           Prune one level if the color tree is too large.
 834         */
 835         PruneLevel(image,cube_info,cube_info->root);
 836         cube_info->depth--;
 837       }
 838     for (x=0; x < (ssize_t) image->columns; x+=(ssize_t) count)
 839     {
 840       /*
 841         Start at the root and descend the color cube tree.
 842       */
 843       for (count=1; (x+(ssize_t) count) < (ssize_t) image->columns; count++)
 844       {
 845         PixelInfo
 846           packet;
 847
 848         GetPixelInfoPixel(image,p+count*GetPixelChannels(image),&packet);
 849         if (IsPixelEquivalent(image,p,&packet) == MagickFalse)
 850           break;
 851       }
 852       AssociateAlphaPixel(image,cube_info,p,&pixel);
 853       index=MaxTreeDepth-1;
 854       bisect=((double) QuantumRange+1.0)/2.0;
 855       mid=midpoint;
 856       node_info=cube_info->root;
 857       for (level=1; level <= MaxTreeDepth; level++)
 858       {
 859         bisect*=0.5;
 860         id=ColorToNodeId(cube_info,&pixel,index);
 861         mid.red+=(id & 1) != 0 ? bisect : -bisect;
 862         mid.green+=(id & 2) != 0 ? bisect : -bisect;
 863         mid.blue+=(id & 4) != 0 ? bisect : -bisect;
 864         mid.alpha+=(id & 8) != 0 ? bisect : -bisect;
 865         if (node_info->child[id] == (NodeInfo *) NULL)
 866           {
 867             /*
 868               Set colors of new node to contain pixel.
 869             */
 870             node_info->child[id]=GetNodeInfo(cube_info,id,level,node_info);
 871             if (node_info->child[id] == (NodeInfo *) NULL)
 872               (void) ThrowMagickException(exception,GetMagickModule(),
 873                 ResourceLimitError,"MemoryAllocationFailed","`%s'",
 874                 image->filename);
 875             if (level == MaxTreeDepth)
 876               cube_info->colors++;
 877           }
 878         /*
 879           Approximate the quantization error represented by this node.
 880         */
 881         node_info=node_info->child[id];
 882         error.red=QuantumScale*(pixel.red-mid.red);
 883         error.green=QuantumScale*(pixel.green-mid.green);
 884         error.blue=QuantumScale*(pixel.blue-mid.blue);
 885         if (cube_info->associate_alpha != MagickFalse)
 886           error.alpha=QuantumScale*(pixel.alpha-mid.alpha);
 887         node_info->quantize_error+=count*sqrt((double) (error.red*error.red+
 888           error.green*error.green+error.blue*error.blue+
 889           error.alpha*error.alpha));
 890         cube_info->root->quantize_error+=node_info->quantize_error;
 891         index--;
 892       }
 893       /*
 894         Sum RGB for this leaf for later derivation of the mean cube color.
 895       */
 896       node_info->number_unique+=count;
 897       node_info->total_color.red+=count*QuantumScale*ClampPixel(pixel.red);
 898       node_info->total_color.green+=count*QuantumScale*ClampPixel(pixel.green);
 899       node_info->total_color.blue+=count*QuantumScale*ClampPixel(pixel.blue);
 900       if (cube_info->associate_alpha != MagickFalse)
 901         node_info->total_color.alpha+=count*QuantumScale*ClampPixel(
 902           pixel.alpha);
 903       p+=count*GetPixelChannels(image);
 904     }
 905     if (cube_info->colors > cube_info->maximum_colors)
 906       {
 907         PruneToCubeDepth(image,cube_info,cube_info->root);
 908         break;
 909       }
 910     proceed=SetImageProgress(image,ClassifyImageTag,(MagickOffsetType) y,
 911       image->rows);
 912     if (proceed == MagickFalse)
 913       break;
 914   }
 915   for (y++; y < (ssize_t) image->rows; y++)
 916   {
 917     register const Quantum
 918       *restrict p;
 919
 920     register ssize_t
 921       x;
 922
 923     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 924     if (p == (const Quantum *) NULL)
 925       break;
 926     if (cube_info->nodes > MaxNodes)
 927       {
 928         /*
 929           Prune one level if the color tree is too large.
 930         */
 931         PruneLevel(image,cube_info,cube_info->root);
 932         cube_info->depth--;
 933       }
 934     for (x=0; x < (ssize_t) image->columns; x+=(ssize_t) count)
 935     {
 936       /*
 937         Start at the root and descend the color cube tree.
 938       */
 939       for (count=1; (x+(ssize_t) count) < (ssize_t) image->columns; count++)
 940       {
 941         PixelInfo
 942           packet;
 943
 944         GetPixelInfoPixel(image,p+count*GetPixelChannels(image),&packet);
 945         if (IsPixelEquivalent(image,p,&packet) == MagickFalse)
 946           break;
 947       }
 948       AssociateAlphaPixel(image,cube_info,p,&pixel);
 949       index=MaxTreeDepth-1;
 950       bisect=((double) QuantumRange+1.0)/2.0;
 951       mid=midpoint;
 952       node_info=cube_info->root;
 953       for (level=1; level <= cube_info->depth; level++)
 954       {
 955         bisect*=0.5;
 956         id=ColorToNodeId(cube_info,&pixel,index);
 957         mid.red+=(id & 1) != 0 ? bisect : -bisect;
 958         mid.green+=(id & 2) != 0 ? bisect : -bisect;
 959         mid.blue+=(id & 4) != 0 ? bisect : -bisect;
 960         mid.alpha+=(id & 8) != 0 ? bisect : -bisect;
 961         if (node_info->child[id] == (NodeInfo *) NULL)
 962           {
 963             /*
 964               Set colors of new node to contain pixel.
 965             */
 966             node_info->child[id]=GetNodeInfo(cube_info,id,level,node_info);
 967             if (node_info->child[id] == (NodeInfo *) NULL)
 968               (void) ThrowMagickException(exception,GetMagickModule(),
 969                 ResourceLimitError,"MemoryAllocationFailed","%s",
 970                 image->filename);
 971             if (level == cube_info->depth)
 972               cube_info->colors++;
 973           }
 974         /*
 975           Approximate the quantization error represented by this node.
 976         */
 977         node_info=node_info->child[id];
 978         error.red=QuantumScale*(pixel.red-mid.red);
 979         error.green=QuantumScale*(pixel.green-mid.green);
 980         error.blue=QuantumScale*(pixel.blue-mid.blue);
 981         if (cube_info->associate_alpha != MagickFalse)
 982           error.alpha=QuantumScale*(pixel.alpha-mid.alpha);
 983         node_info->quantize_error+=count*sqrt((double) (error.red*error.red+
 984           error.green*error.green+error.blue*error.blue+
 985           error.alpha*error.alpha));
 986         cube_info->root->quantize_error+=node_info->quantize_error;
 987         index--;
 988       }
 989       /*
 990         Sum RGB for this leaf for later derivation of the mean cube color.
 991       */
 992       node_info->number_unique+=count;
 993       node_info->total_color.red+=count*QuantumScale*ClampPixel(pixel.red);
 994       node_info->total_color.green+=count*QuantumScale*ClampPixel(pixel.green);
 995       node_info->total_color.blue+=count*QuantumScale*ClampPixel(pixel.blue);
 996       if (cube_info->associate_alpha != MagickFalse)
 997         node_info->total_color.alpha+=count*QuantumScale*ClampPixel(
 998           pixel.alpha);
 999       p+=count*GetPixelChannels(image);
1000     }
1001     proceed=SetImageProgress(image,ClassifyImageTag,(MagickOffsetType) y,
1002       image->rows);
1003     if (proceed == MagickFalse)
1004       break;
1005   }
1006   image_view=DestroyCacheView(image_view);
1007   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
1008       (cube_info->quantize_info->colorspace != CMYKColorspace))
1009     (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
1010   return(MagickTrue);
1011 }
1012 \f
1013 /*
1014 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1015 %                                                                             %
1016 %                                                                             %
1017 %                                                                             %
1018 %   C l o n e Q u a n t i z e I n f o                                         %
1019 %                                                                             %
1020 %                                                                             %
1021 %                                                                             %
1022 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1023 %
1024 %  CloneQuantizeInfo() makes a duplicate of the given quantize info structure,
1025 %  or if quantize info is NULL, a new one.
1026 %
1027 %  The format of the CloneQuantizeInfo method is:
1028 %
1029 %      QuantizeInfo *CloneQuantizeInfo(const QuantizeInfo *quantize_info)
1030 %
1031 %  A description of each parameter follows:
1032 %
1033 %    o clone_info: Method CloneQuantizeInfo returns a duplicate of the given
1034 %      quantize info, or if image info is NULL a new one.
1035 %
1036 %    o quantize_info: a structure of type info.
1037 %
1038 */
1039 MagickExport QuantizeInfo *CloneQuantizeInfo(const QuantizeInfo *quantize_info)
1040 {
1041   QuantizeInfo
1042     *clone_info;
1043
1044   clone_info=(QuantizeInfo *) AcquireMagickMemory(sizeof(*clone_info));
1045   if (clone_info == (QuantizeInfo *) NULL)
1046     ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
1047   GetQuantizeInfo(clone_info);
1048   if (quantize_info == (QuantizeInfo *) NULL)
1049     return(clone_info);
1050   clone_info->number_colors=quantize_info->number_colors;
1051   clone_info->tree_depth=quantize_info->tree_depth;
1052   clone_info->dither_method=quantize_info->dither_method;
1053   clone_info->colorspace=quantize_info->colorspace;
1054   clone_info->measure_error=quantize_info->measure_error;
1055   return(clone_info);
1056 }
1057 \f
1058 /*
1059 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1060 %                                                                             %
1061 %                                                                             %
1062 %                                                                             %
1063 +   C l o s e s t C o l o r                                                   %
1064 %                                                                             %
1065 %                                                                             %
1066 %                                                                             %
1067 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1068 %
1069 %  ClosestColor() traverses the color cube tree at a particular node and
1070 %  determines which colormap entry best represents the input color.
1071 %
1072 %  The format of the ClosestColor method is:
1073 %
1074 %      void ClosestColor(const Image *image,CubeInfo *cube_info,
1075 %        const NodeInfo *node_info)
1076 %
1077 %  A description of each parameter follows.
1078 %
1079 %    o image: the image.
1080 %
1081 %    o cube_info: A pointer to the Cube structure.
1082 %
1083 %    o node_info: the address of a structure of type NodeInfo which points to a
1084 %      node in the color cube tree that is to be pruned.
1085 %
1086 */
1087 static void ClosestColor(const Image *image,CubeInfo *cube_info,
1088   const NodeInfo *node_info)
1089 {
1090   register ssize_t
1091     i;
1092
1093   size_t
1094     number_children;
1095
1096   /*
1097     Traverse any children.
1098   */
1099   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
1100   for (i=0; i < (ssize_t) number_children; i++)
1101     if (node_info->child[i] != (NodeInfo *) NULL)
1102       ClosestColor(image,cube_info,node_info->child[i]);
1103   if (node_info->number_unique != 0)
1104     {
1105       double
1106         pixel;
1107
1108       register double
1109         alpha,
1110         beta,
1111         distance;
1112
1113       register PixelInfo
1114         *restrict p;
1115
1116       register RealPixelInfo
1117         *restrict q;
1118
1119       /*
1120         Determine if this color is "closest".
1121       */
1122       p=image->colormap+node_info->color_number;
1123       q=(&cube_info->target);
1124       alpha=1.0;
1125       beta=1.0;
1126       if (cube_info->associate_alpha != MagickFalse)
1127         {
1128           alpha=(double) (QuantumScale*p->alpha);
1129           beta=(double) (QuantumScale*q->alpha);
1130         }
1131       pixel=alpha*p->red-beta*q->red;
1132       distance=pixel*pixel;
1133       if (distance <= cube_info->distance)
1134         {
1135           pixel=alpha*p->green-beta*q->green;
1136           distance+=pixel*pixel;
1137           if (distance <= cube_info->distance)
1138             {
1139               pixel=alpha*p->blue-beta*q->blue;
1140               distance+=pixel*pixel;
1141               if (distance <= cube_info->distance)
1142                 {
1143                   pixel=alpha-beta;
1144                   distance+=pixel*pixel;
1145                   if (distance <= cube_info->distance)
1146                     {
1147                       cube_info->distance=distance;
1148                       cube_info->color_number=node_info->color_number;
1149                     }
1150                 }
1151             }
1152         }
1153     }
1154 }
1155 \f
1156 /*
1157 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1158 %                                                                             %
1159 %                                                                             %
1160 %                                                                             %
1161 %   C o m p r e s s I m a g e C o l o r m a p                                 %
1162 %                                                                             %
1163 %                                                                             %
1164 %                                                                             %
1165 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1166 %
1167 %  CompressImageColormap() compresses an image colormap by removing any
1168 %  duplicate or unused color entries.
1169 %
1170 %  The format of the CompressImageColormap method is:
1171 %
1172 %      MagickBooleanType CompressImageColormap(Image *image,
1173 %        ExceptionInfo *exception)
1174 %
1175 %  A description of each parameter follows:
1176 %
1177 %    o image: the image.
1178 %
1179 %    o exception: return any errors or warnings in this structure.
1180 %
1181 */
1182 MagickExport MagickBooleanType CompressImageColormap(Image *image,
1183   ExceptionInfo *exception)
1184 {
1185   QuantizeInfo
1186     quantize_info;
1187
1188   assert(image != (Image *) NULL);
1189   assert(image->signature == MagickSignature);
1190   if (image->debug != MagickFalse)
1191     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1192   if (IsPaletteImage(image,exception) == MagickFalse)
1193     return(MagickFalse);
1194   GetQuantizeInfo(&quantize_info);
1195   quantize_info.number_colors=image->colors;
1196   quantize_info.tree_depth=MaxTreeDepth;
1197   return(QuantizeImage(&quantize_info,image,exception));
1198 }
1199 \f
1200 /*
1201 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1202 %                                                                             %
1203 %                                                                             %
1204 %                                                                             %
1205 +   D e f i n e I m a g e C o l o r m a p                                     %
1206 %                                                                             %
1207 %                                                                             %
1208 %                                                                             %
1209 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1210 %
1211 %  DefineImageColormap() traverses the color cube tree and notes each colormap
1212 %  entry.  A colormap entry is any node in the color cube tree where the
1213 %  of unique colors is not zero.  DefineImageColormap() returns the number of
1214 %  colors in the image colormap.
1215 %
1216 %  The format of the DefineImageColormap method is:
1217 %
1218 %      size_t DefineImageColormap(Image *image,CubeInfo *cube_info,
1219 %        NodeInfo *node_info)
1220 %
1221 %  A description of each parameter follows.
1222 %
1223 %    o image: the image.
1224 %
1225 %    o cube_info: A pointer to the Cube structure.
1226 %
1227 %    o node_info: the address of a structure of type NodeInfo which points to a
1228 %      node in the color cube tree that is to be pruned.
1229 %
1230 */
1231 static size_t DefineImageColormap(Image *image,CubeInfo *cube_info,
1232   NodeInfo *node_info)
1233 {
1234   register ssize_t
1235     i;
1236
1237   size_t
1238     number_children;
1239
1240   /*
1241     Traverse any children.
1242   */
1243   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
1244   for (i=0; i < (ssize_t) number_children; i++)
1245     if (node_info->child[i] != (NodeInfo *) NULL)
1246       (void) DefineImageColormap(image,cube_info,node_info->child[i]);
1247   if (node_info->number_unique != 0)
1248     {
1249       register double
1250         alpha;
1251
1252       register PixelInfo
1253         *restrict q;
1254
1255       /*
1256         Colormap entry is defined by the mean color in this cube.
1257       */
1258       q=image->colormap+image->colors;
1259       alpha=(double) ((MagickOffsetType) node_info->number_unique);
1260       alpha=PerceptibleReciprocal(alpha);
1261       if (cube_info->associate_alpha == MagickFalse)
1262         {
1263           q->red=(double) ClampToQuantum(alpha*QuantumRange*
1264             node_info->total_color.red);
1265           q->green=(double) ClampToQuantum(alpha*QuantumRange*
1266             node_info->total_color.green);
1267           q->blue=(double) ClampToQuantum(alpha*QuantumRange*
1268             node_info->total_color.blue);
1269           q->alpha=(double) OpaqueAlpha;
1270         }
1271       else
1272         {
1273           double
1274             opacity;
1275
1276           opacity=(double) (alpha*QuantumRange*node_info->total_color.alpha);
1277           q->alpha=(double) ClampToQuantum((opacity));
1278           if (q->alpha == OpaqueAlpha)
1279             {
1280               q->red=(double) ClampToQuantum(alpha*QuantumRange*
1281                 node_info->total_color.red);
1282               q->green=(double) ClampToQuantum(alpha*QuantumRange*
1283                 node_info->total_color.green);
1284               q->blue=(double) ClampToQuantum(alpha*QuantumRange*
1285                 node_info->total_color.blue);
1286             }
1287           else
1288             {
1289               double
1290                 gamma;
1291
1292               gamma=(double) (QuantumScale*q->alpha);
1293               gamma=PerceptibleReciprocal(gamma);
1294               q->red=(double) ClampToQuantum(alpha*gamma*QuantumRange*
1295                 node_info->total_color.red);
1296               q->green=(double) ClampToQuantum(alpha*gamma*QuantumRange*
1297                 node_info->total_color.green);
1298               q->blue=(double) ClampToQuantum(alpha*gamma*QuantumRange*
1299                 node_info->total_color.blue);
1300               if (node_info->number_unique > cube_info->transparent_pixels)
1301                 {
1302                   cube_info->transparent_pixels=node_info->number_unique;
1303                   cube_info->transparent_index=(ssize_t) image->colors;
1304                 }
1305             }
1306         }
1307       node_info->color_number=image->colors++;
1308     }
1309   return(image->colors);
1310 }
1311 \f
1312 /*
1313 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1314 %                                                                             %
1315 %                                                                             %
1316 %                                                                             %
1317 +   D e s t r o y C u b e I n f o                                             %
1318 %                                                                             %
1319 %                                                                             %
1320 %                                                                             %
1321 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1322 %
1323 %  DestroyCubeInfo() deallocates memory associated with an image.
1324 %
1325 %  The format of the DestroyCubeInfo method is:
1326 %
1327 %      DestroyCubeInfo(CubeInfo *cube_info)
1328 %
1329 %  A description of each parameter follows:
1330 %
1331 %    o cube_info: the address of a structure of type CubeInfo.
1332 %
1333 */
1334 static void DestroyCubeInfo(CubeInfo *cube_info)
1335 {
1336   register Nodes
1337     *nodes;
1338
1339   /*
1340     Release color cube tree storage.
1341   */
1342   do
1343   {
1344     nodes=cube_info->node_queue->next;
1345     cube_info->node_queue->nodes=(NodeInfo *) RelinquishMagickMemory(
1346       cube_info->node_queue->nodes);
1347     cube_info->node_queue=(Nodes *) RelinquishMagickMemory(
1348       cube_info->node_queue);
1349     cube_info->node_queue=nodes;
1350   } while (cube_info->node_queue != (Nodes *) NULL);
1351   if (cube_info->memory_info != (MemoryInfo *) NULL)
1352     cube_info->memory_info=RelinquishVirtualMemory(cube_info->memory_info);
1353   cube_info->quantize_info=DestroyQuantizeInfo(cube_info->quantize_info);
1354   cube_info=(CubeInfo *) RelinquishMagickMemory(cube_info);
1355 }
1356 \f
1357 /*
1358 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1359 %                                                                             %
1360 %                                                                             %
1361 %                                                                             %
1362 %   D e s t r o y Q u a n t i z e I n f o                                     %
1363 %                                                                             %
1364 %                                                                             %
1365 %                                                                             %
1366 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1367 %
1368 %  DestroyQuantizeInfo() deallocates memory associated with an QuantizeInfo
1369 %  structure.
1370 %
1371 %  The format of the DestroyQuantizeInfo method is:
1372 %
1373 %      QuantizeInfo *DestroyQuantizeInfo(QuantizeInfo *quantize_info)
1374 %
1375 %  A description of each parameter follows:
1376 %
1377 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
1378 %
1379 */
1380 MagickExport QuantizeInfo *DestroyQuantizeInfo(QuantizeInfo *quantize_info)
1381 {
1382   (void) LogMagickEvent(TraceEvent,GetMagickModule(),"...");
1383   assert(quantize_info != (QuantizeInfo *) NULL);
1384   assert(quantize_info->signature == MagickSignature);
1385   quantize_info->signature=(~MagickSignature);
1386   quantize_info=(QuantizeInfo *) RelinquishMagickMemory(quantize_info);
1387   return(quantize_info);
1388 }
1389 \f
1390 /*
1391 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1392 %                                                                             %
1393 %                                                                             %
1394 %                                                                             %
1395 +   D i t h e r I m a g e                                                     %
1396 %                                                                             %
1397 %                                                                             %
1398 %                                                                             %
1399 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1400 %
1401 %  DitherImage() distributes the difference between an original image and
1402 %  the corresponding color reduced algorithm to neighboring pixels using
1403 %  serpentine-scan Floyd-Steinberg error diffusion. DitherImage returns
1404 %  MagickTrue if the image is dithered otherwise MagickFalse.
1405 %
1406 %  The format of the DitherImage method is:
1407 %
1408 %      MagickBooleanType DitherImage(Image *image,CubeInfo *cube_info,
1409 %        ExceptionInfo *exception)
1410 %
1411 %  A description of each parameter follows.
1412 %
1413 %    o image: the image.
1414 %
1415 %    o cube_info: A pointer to the Cube structure.
1416 %
1417 %    o exception: return any errors or warnings in this structure.
1418 %
1419 */
1420
1421 static RealPixelInfo **DestroyPixelThreadSet(RealPixelInfo **pixels)
1422 {
1423   register ssize_t
1424     i;
1425
1426   assert(pixels != (RealPixelInfo **) NULL);
1427   for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
1428     if (pixels[i] != (RealPixelInfo *) NULL)
1429       pixels[i]=(RealPixelInfo *) RelinquishMagickMemory(pixels[i]);
1430   pixels=(RealPixelInfo **) RelinquishMagickMemory(pixels);
1431   return(pixels);
1432 }
1433
1434 static RealPixelInfo **AcquirePixelThreadSet(const size_t count)
1435 {
1436   RealPixelInfo
1437     **pixels;
1438
1439   register ssize_t
1440     i;
1441
1442   size_t
1443     number_threads;
1444
1445   number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
1446   pixels=(RealPixelInfo **) AcquireQuantumMemory(number_threads,
1447     sizeof(*pixels));
1448   if (pixels == (RealPixelInfo **) NULL)
1449     return((RealPixelInfo **) NULL);
1450   (void) ResetMagickMemory(pixels,0,number_threads*sizeof(*pixels));
1451   for (i=0; i < (ssize_t) number_threads; i++)
1452   {
1453     pixels[i]=(RealPixelInfo *) AcquireQuantumMemory(count,2*sizeof(**pixels));
1454     if (pixels[i] == (RealPixelInfo *) NULL)
1455       return(DestroyPixelThreadSet(pixels));
1456   }
1457   return(pixels);
1458 }
1459
1460 static inline ssize_t CacheOffset(CubeInfo *cube_info,
1461   const RealPixelInfo *pixel)
1462 {
1463 #define RedShift(pixel) (((pixel) >> CacheShift) << (0*(8-CacheShift)))
1464 #define GreenShift(pixel) (((pixel) >> CacheShift) << (1*(8-CacheShift)))
1465 #define BlueShift(pixel) (((pixel) >> CacheShift) << (2*(8-CacheShift)))
1466 #define AlphaShift(pixel) (((pixel) >> CacheShift) << (3*(8-CacheShift)))
1467
1468   ssize_t
1469     offset;
1470
1471   offset=(ssize_t) (RedShift(ScaleQuantumToChar(ClampPixel(pixel->red))) |
1472     GreenShift(ScaleQuantumToChar(ClampPixel(pixel->green))) |
1473     BlueShift(ScaleQuantumToChar(ClampPixel(pixel->blue))));
1474   if (cube_info->associate_alpha != MagickFalse)
1475     offset|=AlphaShift(ScaleQuantumToChar(ClampPixel(pixel->alpha)));
1476   return(offset);
1477 }
1478
1479 static MagickBooleanType FloydSteinbergDither(Image *image,CubeInfo *cube_info,
1480   ExceptionInfo *exception)
1481 {
1482 #define DitherImageTag  "Dither/Image"
1483
1484   CacheView
1485     *image_view;
1486
1487   MagickBooleanType
1488     status;
1489
1490   RealPixelInfo
1491     **pixels;
1492
1493   ssize_t
1494     y;
1495
1496   /*
1497     Distribute quantization error using Floyd-Steinberg.
1498   */
1499   pixels=AcquirePixelThreadSet(image->columns);
1500   if (pixels == (RealPixelInfo **) NULL)
1501     return(MagickFalse);
1502   status=MagickTrue;
1503   image_view=AcquireAuthenticCacheView(image,exception);
1504   for (y=0; y < (ssize_t) image->rows; y++)
1505   {
1506     const int
1507       id = GetOpenMPThreadId();
1508
1509     CubeInfo
1510       cube;
1511
1512     RealPixelInfo
1513       *current,
1514       *previous;
1515
1516     register Quantum
1517       *restrict q;
1518
1519     register ssize_t
1520       x;
1521
1522     size_t
1523       index;
1524
1525     ssize_t
1526       v;
1527
1528     if (status == MagickFalse)
1529       continue;
1530     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
1531     if (q == (Quantum *) NULL)
1532       {
1533         status=MagickFalse;
1534         continue;
1535       }
1536     q+=(y & 0x01)*image->columns*GetPixelChannels(image);
1537     cube=(*cube_info);
1538     current=pixels[id]+(y & 0x01)*image->columns;
1539     previous=pixels[id]+((y+1) & 0x01)*image->columns;
1540     v=(ssize_t) ((y & 0x01) != 0 ? -1 : 1);
1541     for (x=0; x < (ssize_t) image->columns; x++)
1542     {
1543       RealPixelInfo
1544         color,
1545         pixel;
1546
1547       register ssize_t
1548         i;
1549
1550       ssize_t
1551         u;
1552
1553       q-=(y & 0x01)*GetPixelChannels(image);
1554       u=(y & 0x01) != 0 ? (ssize_t) image->columns-1-x : x;
1555       AssociateAlphaPixel(image,&cube,q,&pixel);
1556       if (x > 0)
1557         {
1558           pixel.red+=7*current[u-v].red/16;
1559           pixel.green+=7*current[u-v].green/16;
1560           pixel.blue+=7*current[u-v].blue/16;
1561           if (cube.associate_alpha != MagickFalse)
1562             pixel.alpha+=7*current[u-v].alpha/16;
1563         }
1564       if (y > 0)
1565         {
1566           if (x < (ssize_t) (image->columns-1))
1567             {
1568               pixel.red+=previous[u+v].red/16;
1569               pixel.green+=previous[u+v].green/16;
1570               pixel.blue+=previous[u+v].blue/16;
1571               if (cube.associate_alpha != MagickFalse)
1572                 pixel.alpha+=previous[u+v].alpha/16;
1573             }
1574           pixel.red+=5*previous[u].red/16;
1575           pixel.green+=5*previous[u].green/16;
1576           pixel.blue+=5*previous[u].blue/16;
1577           if (cube.associate_alpha != MagickFalse)
1578             pixel.alpha+=5*previous[u].alpha/16;
1579           if (x > 0)
1580             {
1581               pixel.red+=3*previous[u-v].red/16;
1582               pixel.green+=3*previous[u-v].green/16;
1583               pixel.blue+=3*previous[u-v].blue/16;
1584               if (cube.associate_alpha != MagickFalse)
1585                 pixel.alpha+=3*previous[u-v].alpha/16;
1586             }
1587         }
1588       pixel.red=(double) ClampPixel(pixel.red);
1589       pixel.green=(double) ClampPixel(pixel.green);
1590       pixel.blue=(double) ClampPixel(pixel.blue);
1591       if (cube.associate_alpha != MagickFalse)
1592         pixel.alpha=(double) ClampPixel(pixel.alpha);
1593       i=CacheOffset(&cube,&pixel);
1594       if (cube.cache[i] < 0)
1595         {
1596           register NodeInfo
1597             *node_info;
1598
1599           register size_t
1600             id;
1601
1602           /*
1603             Identify the deepest node containing the pixel's color.
1604           */
1605           node_info=cube.root;
1606           for (index=MaxTreeDepth-1; (ssize_t) index > 0; index--)
1607           {
1608             id=ColorToNodeId(&cube,&pixel,index);
1609             if (node_info->child[id] == (NodeInfo *) NULL)
1610               break;
1611             node_info=node_info->child[id];
1612           }
1613           /*
1614             Find closest color among siblings and their children.
1615           */
1616           cube.target=pixel;
1617           cube.distance=(double) (4.0*(QuantumRange+1.0)*(QuantumRange+1.0)+
1618             1.0);
1619           ClosestColor(image,&cube,node_info->parent);
1620           cube.cache[i]=(ssize_t) cube.color_number;
1621         }
1622       /*
1623         Assign pixel to closest colormap entry.
1624       */
1625       index=(size_t) cube.cache[i];
1626       if (image->storage_class == PseudoClass)
1627         SetPixelIndex(image,(Quantum) index,q);
1628       if (cube.quantize_info->measure_error == MagickFalse)
1629         {
1630           SetPixelRed(image,ClampToQuantum(image->colormap[index].red),q);
1631           SetPixelGreen(image,ClampToQuantum(image->colormap[index].green),q);
1632           SetPixelBlue(image,ClampToQuantum(image->colormap[index].blue),q);
1633           if (cube.associate_alpha != MagickFalse)
1634             SetPixelAlpha(image,ClampToQuantum(image->colormap[index].alpha),q);
1635         }
1636       if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1637         status=MagickFalse;
1638       /*
1639         Store the error.
1640       */
1641       AssociateAlphaPixelInfo(&cube,image->colormap+index,&color);
1642       current[u].red=pixel.red-color.red;
1643       current[u].green=pixel.green-color.green;
1644       current[u].blue=pixel.blue-color.blue;
1645       if (cube.associate_alpha != MagickFalse)
1646         current[u].alpha=pixel.alpha-color.alpha;
1647       if (image->progress_monitor != (MagickProgressMonitor) NULL)
1648         {
1649           MagickBooleanType
1650             proceed;
1651
1652 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1653           #pragma omp critical (MagickCore_FloydSteinbergDither)
1654 #endif
1655           proceed=SetImageProgress(image,DitherImageTag,(MagickOffsetType) y,
1656             image->rows);
1657           if (proceed == MagickFalse)
1658             status=MagickFalse;
1659         }
1660       q+=((y+1) & 0x01)*GetPixelChannels(image);
1661     }
1662   }
1663   image_view=DestroyCacheView(image_view);
1664   pixels=DestroyPixelThreadSet(pixels);
1665   return(MagickTrue);
1666 }
1667
1668 static MagickBooleanType
1669   RiemersmaDither(Image *,CacheView *,CubeInfo *,const unsigned int,
1670     ExceptionInfo *exception);
1671
1672 static void Riemersma(Image *image,CacheView *image_view,CubeInfo *cube_info,
1673   const size_t level,const unsigned int direction,ExceptionInfo *exception)
1674 {
1675   if (level == 1)
1676     switch (direction)
1677     {
1678       case WestGravity:
1679       {
1680         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1681           exception);
1682         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1683           exception);
1684         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1685           exception);
1686         break;
1687       }
1688       case EastGravity:
1689       {
1690         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1691           exception);
1692         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1693           exception);
1694         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1695           exception);
1696         break;
1697       }
1698       case NorthGravity:
1699       {
1700         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1701           exception);
1702         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1703           exception);
1704         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1705           exception);
1706         break;
1707       }
1708       case SouthGravity:
1709       {
1710         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1711           exception);
1712         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1713           exception);
1714         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1715           exception);
1716         break;
1717       }
1718       default:
1719         break;
1720     }
1721   else
1722     switch (direction)
1723     {
1724       case WestGravity:
1725       {
1726         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1727           exception);
1728         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1729           exception);
1730         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1731           exception);
1732         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1733           exception);
1734         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1735           exception);
1736         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1737           exception);
1738         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1739           exception);
1740         break;
1741       }
1742       case EastGravity:
1743       {
1744         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1745           exception);
1746         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1747           exception);
1748         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1749           exception);
1750         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1751           exception);
1752         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1753           exception);
1754         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1755           exception);
1756         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1757           exception);
1758         break;
1759       }
1760       case NorthGravity:
1761       {
1762         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1763           exception);
1764         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1765           exception);
1766         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1767           exception);
1768         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1769           exception);
1770         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1771           exception);
1772         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1773           exception);
1774         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1775           exception);
1776         break;
1777       }
1778       case SouthGravity:
1779       {
1780         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1781           exception);
1782         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1783           exception);
1784         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1785           exception);
1786         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1787           exception);
1788         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1789           exception);
1790         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1791           exception);
1792         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1793           exception);
1794         break;
1795       }
1796       default:
1797         break;
1798     }
1799 }
1800
1801 static MagickBooleanType RiemersmaDither(Image *image,CacheView *image_view,
1802   CubeInfo *cube_info,const unsigned int direction,ExceptionInfo *exception)
1803 {
1804 #define DitherImageTag  "Dither/Image"
1805
1806   MagickBooleanType
1807     proceed;
1808
1809   RealPixelInfo
1810     color,
1811     pixel;
1812
1813   register CubeInfo
1814     *p;
1815
1816   size_t
1817     index;
1818
1819   p=cube_info;
1820   if ((p->x >= 0) && (p->x < (ssize_t) image->columns) &&
1821       (p->y >= 0) && (p->y < (ssize_t) image->rows))
1822     {
1823       register Quantum
1824         *restrict q;
1825
1826       register ssize_t
1827         i;
1828
1829       /*
1830         Distribute error.
1831       */
1832       q=GetCacheViewAuthenticPixels(image_view,p->x,p->y,1,1,exception);
1833       if (q == (Quantum *) NULL)
1834         return(MagickFalse);
1835       AssociateAlphaPixel(image,cube_info,q,&pixel);
1836       for (i=0; i < ErrorQueueLength; i++)
1837       {
1838         pixel.red+=p->weights[i]*p->error[i].red;
1839         pixel.green+=p->weights[i]*p->error[i].green;
1840         pixel.blue+=p->weights[i]*p->error[i].blue;
1841         if (cube_info->associate_alpha != MagickFalse)
1842           pixel.alpha+=p->weights[i]*p->error[i].alpha;
1843       }
1844       pixel.red=(double) ClampPixel(pixel.red);
1845       pixel.green=(double) ClampPixel(pixel.green);
1846       pixel.blue=(double) ClampPixel(pixel.blue);
1847       if (cube_info->associate_alpha != MagickFalse)
1848         pixel.alpha=(double) ClampPixel(pixel.alpha);
1849       i=CacheOffset(cube_info,&pixel);
1850       if (p->cache[i] < 0)
1851         {
1852           register NodeInfo
1853             *node_info;
1854
1855           register size_t
1856             id;
1857
1858           /*
1859             Identify the deepest node containing the pixel's color.
1860           */
1861           node_info=p->root;
1862           for (index=MaxTreeDepth-1; (ssize_t) index > 0; index--)
1863           {
1864             id=ColorToNodeId(cube_info,&pixel,index);
1865             if (node_info->child[id] == (NodeInfo *) NULL)
1866               break;
1867             node_info=node_info->child[id];
1868           }
1869           /*
1870             Find closest color among siblings and their children.
1871           */
1872           p->target=pixel;
1873           p->distance=(double) (4.0*(QuantumRange+1.0)*((double)
1874             QuantumRange+1.0)+1.0);
1875           ClosestColor(image,p,node_info->parent);
1876           p->cache[i]=(ssize_t) p->color_number;
1877         }
1878       /*
1879         Assign pixel to closest colormap entry.
1880       */
1881       index=(size_t) p->cache[i];
1882       if (image->storage_class == PseudoClass)
1883         SetPixelIndex(image,(Quantum) index,q);
1884       if (cube_info->quantize_info->measure_error == MagickFalse)
1885         {
1886           SetPixelRed(image,ClampToQuantum(image->colormap[index].red),q);
1887           SetPixelGreen(image,ClampToQuantum(image->colormap[index].green),q);
1888           SetPixelBlue(image,ClampToQuantum(image->colormap[index].blue),q);
1889           if (cube_info->associate_alpha != MagickFalse)
1890             SetPixelAlpha(image,ClampToQuantum(image->colormap[index].alpha),q);
1891         }
1892       if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1893         return(MagickFalse);
1894       /*
1895         Propagate the error as the last entry of the error queue.
1896       */
1897       (void) CopyMagickMemory(p->error,p->error+1,(ErrorQueueLength-1)*
1898         sizeof(p->error[0]));
1899       AssociateAlphaPixelInfo(cube_info,image->colormap+index,&color);
1900       p->error[ErrorQueueLength-1].red=pixel.red-color.red;
1901       p->error[ErrorQueueLength-1].green=pixel.green-color.green;
1902       p->error[ErrorQueueLength-1].blue=pixel.blue-color.blue;
1903       if (cube_info->associate_alpha != MagickFalse)
1904         p->error[ErrorQueueLength-1].alpha=pixel.alpha-color.alpha;
1905       proceed=SetImageProgress(image,DitherImageTag,p->offset,p->span);
1906       if (proceed == MagickFalse)
1907         return(MagickFalse);
1908       p->offset++;
1909     }
1910   switch (direction)
1911   {
1912     case WestGravity: p->x--; break;
1913     case EastGravity: p->x++; break;
1914     case NorthGravity: p->y--; break;
1915     case SouthGravity: p->y++; break;
1916   }
1917   return(MagickTrue);
1918 }
1919
1920 static inline ssize_t MagickMax(const ssize_t x,const ssize_t y)
1921 {
1922   if (x > y)
1923     return(x);
1924   return(y);
1925 }
1926
1927 static inline ssize_t MagickMin(const ssize_t x,const ssize_t y)
1928 {
1929   if (x < y)
1930     return(x);
1931   return(y);
1932 }
1933
1934 static MagickBooleanType DitherImage(Image *image,CubeInfo *cube_info,
1935   ExceptionInfo *exception)
1936 {
1937   CacheView
1938     *image_view;
1939
1940   MagickBooleanType
1941     status;
1942
1943   register ssize_t
1944     i;
1945
1946   size_t
1947     depth;
1948
1949   if (cube_info->quantize_info->dither_method != RiemersmaDitherMethod)
1950     return(FloydSteinbergDither(image,cube_info,exception));
1951   /*
1952     Distribute quantization error along a Hilbert curve.
1953   */
1954   (void) ResetMagickMemory(cube_info->error,0,ErrorQueueLength*
1955     sizeof(*cube_info->error));
1956   cube_info->x=0;
1957   cube_info->y=0;
1958   i=MagickMax((ssize_t) image->columns,(ssize_t) image->rows);
1959   for (depth=1; i != 0; depth++)
1960     i>>=1;
1961   if ((ssize_t) (1L << depth) < MagickMax((ssize_t) image->columns,(ssize_t) image->rows))
1962     depth++;
1963   cube_info->offset=0;
1964   cube_info->span=(MagickSizeType) image->columns*image->rows;
1965   image_view=AcquireAuthenticCacheView(image,exception);
1966   if (depth > 1)
1967     Riemersma(image,image_view,cube_info,depth-1,NorthGravity,exception);
1968   status=RiemersmaDither(image,image_view,cube_info,ForgetGravity,exception);
1969   image_view=DestroyCacheView(image_view);
1970   return(status);
1971 }
1972 \f
1973 /*
1974 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1975 %                                                                             %
1976 %                                                                             %
1977 %                                                                             %
1978 +   G e t C u b e I n f o                                                     %
1979 %                                                                             %
1980 %                                                                             %
1981 %                                                                             %
1982 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1983 %
1984 %  GetCubeInfo() initialize the Cube data structure.
1985 %
1986 %  The format of the GetCubeInfo method is:
1987 %
1988 %      CubeInfo GetCubeInfo(const QuantizeInfo *quantize_info,
1989 %        const size_t depth,const size_t maximum_colors)
1990 %
1991 %  A description of each parameter follows.
1992 %
1993 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
1994 %
1995 %    o depth: Normally, this integer value is zero or one.  A zero or
1996 %      one tells Quantize to choose a optimal tree depth of Log4(number_colors).
1997 %      A tree of this depth generally allows the best representation of the
1998 %      reference image with the least amount of memory and the fastest
1999 %      computational speed.  In some cases, such as an image with low color
2000 %      dispersion (a few number of colors), a value other than
2001 %      Log4(number_colors) is required.  To expand the color tree completely,
2002 %      use a value of 8.
2003 %
2004 %    o maximum_colors: maximum colors.
2005 %
2006 */
2007 static CubeInfo *GetCubeInfo(const QuantizeInfo *quantize_info,
2008   const size_t depth,const size_t maximum_colors)
2009 {
2010   CubeInfo
2011     *cube_info;
2012
2013   double
2014     sum,
2015     weight;
2016
2017   register ssize_t
2018     i;
2019
2020   size_t
2021     length;
2022
2023   /*
2024     Initialize tree to describe color cube_info.
2025   */
2026   cube_info=(CubeInfo *) AcquireMagickMemory(sizeof(*cube_info));
2027   if (cube_info == (CubeInfo *) NULL)
2028     return((CubeInfo *) NULL);
2029   (void) ResetMagickMemory(cube_info,0,sizeof(*cube_info));
2030   cube_info->depth=depth;
2031   if (cube_info->depth > MaxTreeDepth)
2032     cube_info->depth=MaxTreeDepth;
2033   if (cube_info->depth < 2)
2034     cube_info->depth=2;
2035   cube_info->maximum_colors=maximum_colors;
2036   /*
2037     Initialize root node.
2038   */
2039   cube_info->root=GetNodeInfo(cube_info,0,0,(NodeInfo *) NULL);
2040   if (cube_info->root == (NodeInfo *) NULL)
2041     return((CubeInfo *) NULL);
2042   cube_info->root->parent=cube_info->root;
2043   cube_info->quantize_info=CloneQuantizeInfo(quantize_info);
2044   if (cube_info->quantize_info->dither_method == NoDitherMethod)
2045     return(cube_info);
2046   /*
2047     Initialize dither resources.
2048   */
2049   length=(size_t) (1UL << (4*(8-CacheShift)));
2050   cube_info->memory_info=AcquireVirtualMemory(length,sizeof(*cube_info->cache));
2051   if (cube_info->memory_info == (MemoryInfo *) NULL)
2052     return((CubeInfo *) NULL);
2053   cube_info->cache=(ssize_t *) GetVirtualMemoryBlob(cube_info->memory_info);
2054   /*
2055     Initialize color cache.
2056   */
2057   for (i=0; i < (ssize_t) length; i++)
2058     cube_info->cache[i]=(-1);
2059   /*
2060     Distribute weights along a curve of exponential decay.
2061   */
2062   weight=1.0;
2063   for (i=0; i < ErrorQueueLength; i++)
2064   {
2065     cube_info->weights[ErrorQueueLength-i-1]=PerceptibleReciprocal(weight);
2066     weight*=exp(log(((double) QuantumRange+1.0))/(ErrorQueueLength-1.0));
2067   }
2068   /*
2069     Normalize the weighting factors.
2070   */
2071   weight=0.0;
2072   for (i=0; i < ErrorQueueLength; i++)
2073     weight+=cube_info->weights[i];
2074   sum=0.0;
2075   for (i=0; i < ErrorQueueLength; i++)
2076   {
2077     cube_info->weights[i]/=weight;
2078     sum+=cube_info->weights[i];
2079   }
2080   cube_info->weights[0]+=1.0-sum;
2081   return(cube_info);
2082 }
2083 \f
2084 /*
2085 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2086 %                                                                             %
2087 %                                                                             %
2088 %                                                                             %
2089 +   G e t N o d e I n f o                                                     %
2090 %                                                                             %
2091 %                                                                             %
2092 %                                                                             %
2093 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2094 %
2095 %  GetNodeInfo() allocates memory for a new node in the color cube tree and
2096 %  presets all fields to zero.
2097 %
2098 %  The format of the GetNodeInfo method is:
2099 %
2100 %      NodeInfo *GetNodeInfo(CubeInfo *cube_info,const size_t id,
2101 %        const size_t level,NodeInfo *parent)
2102 %
2103 %  A description of each parameter follows.
2104 %
2105 %    o node: The GetNodeInfo method returns a pointer to a queue of nodes.
2106 %
2107 %    o id: Specifies the child number of the node.
2108 %
2109 %    o level: Specifies the level in the storage_class the node resides.
2110 %
2111 */
2112 static NodeInfo *GetNodeInfo(CubeInfo *cube_info,const size_t id,
2113   const size_t level,NodeInfo *parent)
2114 {
2115   NodeInfo
2116     *node_info;
2117
2118   if (cube_info->free_nodes == 0)
2119     {
2120       Nodes
2121         *nodes;
2122
2123       /*
2124         Allocate a new queue of nodes.
2125       */
2126       nodes=(Nodes *) AcquireMagickMemory(sizeof(*nodes));
2127       if (nodes == (Nodes *) NULL)
2128         return((NodeInfo *) NULL);
2129       nodes->nodes=(NodeInfo *) AcquireQuantumMemory(NodesInAList,
2130         sizeof(*nodes->nodes));
2131       if (nodes->nodes == (NodeInfo *) NULL)
2132         return((NodeInfo *) NULL);
2133       nodes->next=cube_info->node_queue;
2134       cube_info->node_queue=nodes;
2135       cube_info->next_node=nodes->nodes;
2136       cube_info->free_nodes=NodesInAList;
2137     }
2138   cube_info->nodes++;
2139   cube_info->free_nodes--;
2140   node_info=cube_info->next_node++;
2141   (void) ResetMagickMemory(node_info,0,sizeof(*node_info));
2142   node_info->parent=parent;
2143   node_info->id=id;
2144   node_info->level=level;
2145   return(node_info);
2146 }
2147 \f
2148 /*
2149 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2150 %                                                                             %
2151 %                                                                             %
2152 %                                                                             %
2153 %  G e t I m a g e Q u a n t i z e E r r o r                                  %
2154 %                                                                             %
2155 %                                                                             %
2156 %                                                                             %
2157 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2158 %
2159 %  GetImageQuantizeError() measures the difference between the original
2160 %  and quantized images.  This difference is the total quantization error.
2161 %  The error is computed by summing over all pixels in an image the distance
2162 %  squared in RGB space between each reference pixel value and its quantized
2163 %  value.  These values are computed:
2164 %
2165 %    o mean_error_per_pixel:  This value is the mean error for any single
2166 %      pixel in the image.
2167 %
2168 %    o normalized_mean_square_error:  This value is the normalized mean
2169 %      quantization error for any single pixel in the image.  This distance
2170 %      measure is normalized to a range between 0 and 1.  It is independent
2171 %      of the range of red, green, and blue values in the image.
2172 %
2173 %    o normalized_maximum_square_error:  Thsi value is the normalized
2174 %      maximum quantization error for any single pixel in the image.  This
2175 %      distance measure is normalized to a range between 0 and 1.  It is
2176 %      independent of the range of red, green, and blue values in your image.
2177 %
2178 %  The format of the GetImageQuantizeError method is:
2179 %
2180 %      MagickBooleanType GetImageQuantizeError(Image *image,
2181 %        ExceptionInfo *exception)
2182 %
2183 %  A description of each parameter follows.
2184 %
2185 %    o image: the image.
2186 %
2187 %    o exception: return any errors or warnings in this structure.
2188 %
2189 */
2190 MagickExport MagickBooleanType GetImageQuantizeError(Image *image,
2191   ExceptionInfo *exception)
2192 {
2193   CacheView
2194     *image_view;
2195
2196   double
2197     alpha,
2198     area,
2199     beta,
2200     distance,
2201     maximum_error,
2202     mean_error,
2203     mean_error_per_pixel;
2204
2205   size_t
2206     index;
2207
2208   ssize_t
2209     y;
2210
2211   assert(image != (Image *) NULL);
2212   assert(image->signature == MagickSignature);
2213   if (image->debug != MagickFalse)
2214     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2215   image->total_colors=GetNumberColors(image,(FILE *) NULL,exception);
2216   (void) ResetMagickMemory(&image->error,0,sizeof(image->error));
2217   if (image->storage_class == DirectClass)
2218     return(MagickTrue);
2219   alpha=1.0;
2220   beta=1.0;
2221   area=3.0*image->columns*image->rows;
2222   maximum_error=0.0;
2223   mean_error_per_pixel=0.0;
2224   mean_error=0.0;
2225   image_view=AcquireVirtualCacheView(image,exception);
2226   for (y=0; y < (ssize_t) image->rows; y++)
2227   {
2228     register const Quantum
2229       *restrict p;
2230
2231     register ssize_t
2232       x;
2233
2234     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
2235     if (p == (const Quantum *) NULL)
2236       break;
2237     for (x=0; x < (ssize_t) image->columns; x++)
2238     {
2239       index=1UL*GetPixelIndex(image,p);
2240       if (image->alpha_trait == BlendPixelTrait)
2241         {
2242           alpha=(double) (QuantumScale*GetPixelAlpha(image,p));
2243           beta=(double) (QuantumScale*image->colormap[index].alpha);
2244         }
2245       distance=fabs(alpha*GetPixelRed(image,p)-beta*
2246         image->colormap[index].red);
2247       mean_error_per_pixel+=distance;
2248       mean_error+=distance*distance;
2249       if (distance > maximum_error)
2250         maximum_error=distance;
2251       distance=fabs(alpha*GetPixelGreen(image,p)-beta*
2252         image->colormap[index].green);
2253       mean_error_per_pixel+=distance;
2254       mean_error+=distance*distance;
2255       if (distance > maximum_error)
2256         maximum_error=distance;
2257       distance=fabs(alpha*GetPixelBlue(image,p)-beta*
2258         image->colormap[index].blue);
2259       mean_error_per_pixel+=distance;
2260       mean_error+=distance*distance;
2261       if (distance > maximum_error)
2262         maximum_error=distance;
2263       p+=GetPixelChannels(image);
2264     }
2265   }
2266   image_view=DestroyCacheView(image_view);
2267   image->error.mean_error_per_pixel=(double) mean_error_per_pixel/area;
2268   image->error.normalized_mean_error=(double) QuantumScale*QuantumScale*
2269     mean_error/area;
2270   image->error.normalized_maximum_error=(double) QuantumScale*maximum_error;
2271   return(MagickTrue);
2272 }
2273 \f
2274 /*
2275 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2276 %                                                                             %
2277 %                                                                             %
2278 %                                                                             %
2279 %   G e t Q u a n t i z e I n f o                                             %
2280 %                                                                             %
2281 %                                                                             %
2282 %                                                                             %
2283 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2284 %
2285 %  GetQuantizeInfo() initializes the QuantizeInfo structure.
2286 %
2287 %  The format of the GetQuantizeInfo method is:
2288 %
2289 %      GetQuantizeInfo(QuantizeInfo *quantize_info)
2290 %
2291 %  A description of each parameter follows:
2292 %
2293 %    o quantize_info: Specifies a pointer to a QuantizeInfo structure.
2294 %
2295 */
2296 MagickExport void GetQuantizeInfo(QuantizeInfo *quantize_info)
2297 {
2298   (void) LogMagickEvent(TraceEvent,GetMagickModule(),"...");
2299   assert(quantize_info != (QuantizeInfo *) NULL);
2300   (void) ResetMagickMemory(quantize_info,0,sizeof(*quantize_info));
2301   quantize_info->number_colors=256;
2302   quantize_info->dither_method=RiemersmaDitherMethod;
2303   quantize_info->colorspace=UndefinedColorspace;
2304   quantize_info->measure_error=MagickFalse;
2305   quantize_info->signature=MagickSignature;
2306 }
2307 \f
2308 /*
2309 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2310 %                                                                             %
2311 %                                                                             %
2312 %                                                                             %
2313 %     P o s t e r i z e I m a g e                                             %
2314 %                                                                             %
2315 %                                                                             %
2316 %                                                                             %
2317 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2318 %
2319 %  PosterizeImage() reduces the image to a limited number of colors for a
2320 %  "poster" effect.
2321 %
2322 %  The format of the PosterizeImage method is:
2323 %
2324 %      MagickBooleanType PosterizeImage(Image *image,const size_t levels,
2325 %        const DitherMethod dither_method,ExceptionInfo *exception)
2326 %
2327 %  A description of each parameter follows:
2328 %
2329 %    o image: Specifies a pointer to an Image structure.
2330 %
2331 %    o levels: Number of color levels allowed in each channel.  Very low values
2332 %      (2, 3, or 4) have the most visible effect.
2333 %
2334 %    o dither_method: choose from UndefinedDitherMethod, NoDitherMethod,
2335 %      RiemersmaDitherMethod, FloydSteinbergDitherMethod.
2336 %
2337 %    o exception: return any errors or warnings in this structure.
2338 %
2339 */
2340
2341 static inline double MagickRound(double x)
2342 {
2343   /*
2344     Round the fraction to nearest integer.
2345   */
2346   if ((x-floor(x)) < (ceil(x)-x))
2347     return(floor(x));
2348   return(ceil(x));
2349 }
2350
2351 MagickExport MagickBooleanType PosterizeImage(Image *image,const size_t levels,
2352   const DitherMethod dither_method,ExceptionInfo *exception)
2353 {
2354 #define PosterizeImageTag  "Posterize/Image"
2355 #define PosterizePixel(pixel) (Quantum) (QuantumRange*(MagickRound( \
2356   QuantumScale*pixel*(levels-1)))/MagickMax((ssize_t) levels-1,1))
2357
2358   CacheView
2359     *image_view;
2360
2361   MagickBooleanType
2362     status;
2363
2364   MagickOffsetType
2365     progress;
2366
2367   QuantizeInfo
2368     *quantize_info;
2369
2370   register ssize_t
2371     i;
2372
2373   ssize_t
2374     y;
2375
2376   assert(image != (Image *) NULL);
2377   assert(image->signature == MagickSignature);
2378   if (image->debug != MagickFalse)
2379     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2380   if (image->storage_class == PseudoClass)
2381 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2382     #pragma omp parallel for schedule(static,4) shared(progress,status) \
2383       magick_threads(image,image,1,1)
2384 #endif
2385     for (i=0; i < (ssize_t) image->colors; i++)
2386     {
2387       /*
2388         Posterize colormap.
2389       */
2390       if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2391         image->colormap[i].red=(double)
2392           PosterizePixel(image->colormap[i].red);
2393       if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2394         image->colormap[i].green=(double)
2395           PosterizePixel(image->colormap[i].green);
2396       if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2397         image->colormap[i].blue=(double)
2398           PosterizePixel(image->colormap[i].blue);
2399       if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
2400         image->colormap[i].alpha=(double)
2401           PosterizePixel(image->colormap[i].alpha);
2402     }
2403   /*
2404     Posterize image.
2405   */
2406   status=MagickTrue;
2407   progress=0;
2408   image_view=AcquireAuthenticCacheView(image,exception);
2409 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2410   #pragma omp parallel for schedule(static,4) shared(progress,status) \
2411     magick_threads(image,image,image->rows,1)
2412 #endif
2413   for (y=0; y < (ssize_t) image->rows; y++)
2414   {
2415     register Quantum
2416       *restrict q;
2417
2418     register ssize_t
2419       x;
2420
2421     if (status == MagickFalse)
2422       continue;
2423     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
2424     if (q == (Quantum *) NULL)
2425       {
2426         status=MagickFalse;
2427         continue;
2428       }
2429     for (x=0; x < (ssize_t) image->columns; x++)
2430     {
2431       if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2432         SetPixelRed(image,PosterizePixel(GetPixelRed(image,q)),q);
2433       if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2434         SetPixelGreen(image,PosterizePixel(GetPixelGreen(image,q)),q);
2435       if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2436         SetPixelBlue(image,PosterizePixel(GetPixelBlue(image,q)),q);
2437       if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
2438           (image->colorspace == CMYKColorspace))
2439         SetPixelBlack(image,PosterizePixel(GetPixelBlack(image,q)),q);
2440       if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
2441           (image->alpha_trait == BlendPixelTrait))
2442         SetPixelAlpha(image,PosterizePixel(GetPixelAlpha(image,q)),q);
2443       q+=GetPixelChannels(image);
2444     }
2445     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
2446       status=MagickFalse;
2447     if (image->progress_monitor != (MagickProgressMonitor) NULL)
2448       {
2449         MagickBooleanType
2450           proceed;
2451
2452 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2453         #pragma omp critical (MagickCore_PosterizeImage)
2454 #endif
2455         proceed=SetImageProgress(image,PosterizeImageTag,progress++,
2456           image->rows);
2457         if (proceed == MagickFalse)
2458           status=MagickFalse;
2459       }
2460   }
2461   image_view=DestroyCacheView(image_view);
2462   quantize_info=AcquireQuantizeInfo((ImageInfo *) NULL);
2463   quantize_info->number_colors=(size_t) MagickMin((ssize_t) levels*levels*
2464     levels,MaxColormapSize+1);
2465   quantize_info->dither_method=dither_method;
2466   quantize_info->tree_depth=MaxTreeDepth;
2467   status=QuantizeImage(quantize_info,image,exception);
2468   quantize_info=DestroyQuantizeInfo(quantize_info);
2469   return(status);
2470 }
2471 \f
2472 /*
2473 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2474 %                                                                             %
2475 %                                                                             %
2476 %                                                                             %
2477 +   P r u n e C h i l d                                                       %
2478 %                                                                             %
2479 %                                                                             %
2480 %                                                                             %
2481 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2482 %
2483 %  PruneChild() deletes the given node and merges its statistics into its
2484 %  parent.
2485 %
2486 %  The format of the PruneSubtree method is:
2487 %
2488 %      PruneChild(const Image *image,CubeInfo *cube_info,
2489 %        const NodeInfo *node_info)
2490 %
2491 %  A description of each parameter follows.
2492 %
2493 %    o image: the image.
2494 %
2495 %    o cube_info: A pointer to the Cube structure.
2496 %
2497 %    o node_info: pointer to node in color cube tree that is to be pruned.
2498 %
2499 */
2500 static void PruneChild(const Image *image,CubeInfo *cube_info,
2501   const NodeInfo *node_info)
2502 {
2503   NodeInfo
2504     *parent;
2505
2506   register ssize_t
2507     i;
2508
2509   size_t
2510     number_children;
2511
2512   /*
2513     Traverse any children.
2514   */
2515   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2516   for (i=0; i < (ssize_t) number_children; i++)
2517     if (node_info->child[i] != (NodeInfo *) NULL)
2518       PruneChild(image,cube_info,node_info->child[i]);
2519   /*
2520     Merge color statistics into parent.
2521   */
2522   parent=node_info->parent;
2523   parent->number_unique+=node_info->number_unique;
2524   parent->total_color.red+=node_info->total_color.red;
2525   parent->total_color.green+=node_info->total_color.green;
2526   parent->total_color.blue+=node_info->total_color.blue;
2527   parent->total_color.alpha+=node_info->total_color.alpha;
2528   parent->child[node_info->id]=(NodeInfo *) NULL;
2529   cube_info->nodes--;
2530 }
2531 \f
2532 /*
2533 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2534 %                                                                             %
2535 %                                                                             %
2536 %                                                                             %
2537 +  P r u n e L e v e l                                                        %
2538 %                                                                             %
2539 %                                                                             %
2540 %                                                                             %
2541 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2542 %
2543 %  PruneLevel() deletes all nodes at the bottom level of the color tree merging
2544 %  their color statistics into their parent node.
2545 %
2546 %  The format of the PruneLevel method is:
2547 %
2548 %      PruneLevel(const Image *image,CubeInfo *cube_info,
2549 %        const NodeInfo *node_info)
2550 %
2551 %  A description of each parameter follows.
2552 %
2553 %    o image: the image.
2554 %
2555 %    o cube_info: A pointer to the Cube structure.
2556 %
2557 %    o node_info: pointer to node in color cube tree that is to be pruned.
2558 %
2559 */
2560 static void PruneLevel(const Image *image,CubeInfo *cube_info,
2561   const NodeInfo *node_info)
2562 {
2563   register ssize_t
2564     i;
2565
2566   size_t
2567     number_children;
2568
2569   /*
2570     Traverse any children.
2571   */
2572   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2573   for (i=0; i < (ssize_t) number_children; i++)
2574     if (node_info->child[i] != (NodeInfo *) NULL)
2575       PruneLevel(image,cube_info,node_info->child[i]);
2576   if (node_info->level == cube_info->depth)
2577     PruneChild(image,cube_info,node_info);
2578 }
2579 \f
2580 /*
2581 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2582 %                                                                             %
2583 %                                                                             %
2584 %                                                                             %
2585 +  P r u n e T o C u b e D e p t h                                            %
2586 %                                                                             %
2587 %                                                                             %
2588 %                                                                             %
2589 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2590 %
2591 %  PruneToCubeDepth() deletes any nodes at a depth greater than
2592 %  cube_info->depth while merging their color statistics into their parent
2593 %  node.
2594 %
2595 %  The format of the PruneToCubeDepth method is:
2596 %
2597 %      PruneToCubeDepth(const Image *image,CubeInfo *cube_info,
2598 %        const NodeInfo *node_info)
2599 %
2600 %  A description of each parameter follows.
2601 %
2602 %    o cube_info: A pointer to the Cube structure.
2603 %
2604 %    o node_info: pointer to node in color cube tree that is to be pruned.
2605 %
2606 */
2607 static void PruneToCubeDepth(const Image *image,CubeInfo *cube_info,
2608   const NodeInfo *node_info)
2609 {
2610   register ssize_t
2611     i;
2612
2613   size_t
2614     number_children;
2615
2616   /*
2617     Traverse any children.
2618   */
2619   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2620   for (i=0; i < (ssize_t) number_children; i++)
2621     if (node_info->child[i] != (NodeInfo *) NULL)
2622       PruneToCubeDepth(image,cube_info,node_info->child[i]);
2623   if (node_info->level > cube_info->depth)
2624     PruneChild(image,cube_info,node_info);
2625 }
2626 \f
2627 /*
2628 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2629 %                                                                             %
2630 %                                                                             %
2631 %                                                                             %
2632 %  Q u a n t i z e I m a g e                                                  %
2633 %                                                                             %
2634 %                                                                             %
2635 %                                                                             %
2636 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2637 %
2638 %  QuantizeImage() analyzes the colors within a reference image and chooses a
2639 %  fixed number of colors to represent the image.  The goal of the algorithm
2640 %  is to minimize the color difference between the input and output image while
2641 %  minimizing the processing time.
2642 %
2643 %  The format of the QuantizeImage method is:
2644 %
2645 %      MagickBooleanType QuantizeImage(const QuantizeInfo *quantize_info,
2646 %        Image *image,ExceptionInfo *exception)
2647 %
2648 %  A description of each parameter follows:
2649 %
2650 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
2651 %
2652 %    o image: the image.
2653 %
2654 %    o exception: return any errors or warnings in this structure.
2655 %
2656 */
2657
2658 static MagickBooleanType DirectToColormapImage(Image *image,
2659   ExceptionInfo *exception)
2660 {
2661   CacheView
2662     *image_view;
2663
2664   MagickBooleanType
2665     status;
2666
2667   register ssize_t
2668     i;
2669
2670   size_t
2671     number_colors;
2672
2673   ssize_t
2674     y;
2675
2676   status=MagickTrue;
2677   number_colors=(size_t) (image->columns*image->rows);
2678   if (AcquireImageColormap(image,number_colors,exception) == MagickFalse)
2679     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
2680       image->filename);
2681   if (image->colors != number_colors)
2682     return(MagickFalse);
2683   i=0;
2684   image_view=AcquireAuthenticCacheView(image,exception);
2685   for (y=0; y < (ssize_t) image->rows; y++)
2686   {
2687     MagickBooleanType
2688       proceed;
2689
2690     register Quantum
2691       *restrict q;
2692
2693     register ssize_t
2694       x;
2695
2696     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
2697     if (q == (Quantum *) NULL)
2698       break;
2699     for (x=0; x < (ssize_t) image->columns; x++)
2700     {
2701       image->colormap[i].red=(double) GetPixelRed(image,q);
2702       image->colormap[i].green=(double) GetPixelGreen(image,q);
2703       image->colormap[i].blue=(double) GetPixelBlue(image,q);
2704       image->colormap[i].alpha=(double) GetPixelAlpha(image,q);
2705       SetPixelIndex(image,(Quantum) i,q);
2706       i++;
2707       q+=GetPixelChannels(image);
2708     }
2709     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
2710       break;
2711     proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) y,
2712       image->rows);
2713     if (proceed == MagickFalse)
2714       status=MagickFalse;
2715   }
2716   image_view=DestroyCacheView(image_view);
2717   return(status);
2718 }
2719
2720 MagickExport MagickBooleanType QuantizeImage(const QuantizeInfo *quantize_info,
2721   Image *image,ExceptionInfo *exception)
2722 {
2723   CubeInfo
2724     *cube_info;
2725
2726   MagickBooleanType
2727     status;
2728
2729   size_t
2730     depth,
2731     maximum_colors;
2732
2733   assert(quantize_info != (const QuantizeInfo *) NULL);
2734   assert(quantize_info->signature == MagickSignature);
2735   assert(image != (Image *) NULL);
2736   assert(image->signature == MagickSignature);
2737   if (image->debug != MagickFalse)
2738     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2739   maximum_colors=quantize_info->number_colors;
2740   if (maximum_colors == 0)
2741     maximum_colors=MaxColormapSize;
2742   if (maximum_colors > MaxColormapSize)
2743     maximum_colors=MaxColormapSize;
2744   if (image->alpha_trait != BlendPixelTrait)
2745     {
2746       if ((image->columns*image->rows) <= maximum_colors)
2747         (void) DirectToColormapImage(image,exception);
2748       if (IsImageGray(image,exception) != MagickFalse)
2749         (void) SetGrayscaleImage(image,exception);
2750     }
2751   if ((image->storage_class == PseudoClass) &&
2752       (image->colors <= maximum_colors))
2753     return(MagickTrue);
2754   depth=quantize_info->tree_depth;
2755   if (depth == 0)
2756     {
2757       size_t
2758         colors;
2759
2760       /*
2761         Depth of color tree is: Log4(colormap size)+2.
2762       */
2763       colors=maximum_colors;
2764       for (depth=1; colors != 0; depth++)
2765         colors>>=2;
2766       if ((quantize_info->dither_method != NoDitherMethod) && (depth > 2))
2767         depth--;
2768       if ((image->alpha_trait == BlendPixelTrait) && (depth > 5))
2769         depth--;
2770     }
2771   /*
2772     Initialize color cube.
2773   */
2774   cube_info=GetCubeInfo(quantize_info,depth,maximum_colors);
2775   if (cube_info == (CubeInfo *) NULL)
2776     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
2777       image->filename);
2778   status=ClassifyImageColors(cube_info,image,exception);
2779   if (status != MagickFalse)
2780     {
2781       /*
2782         Reduce the number of colors in the image.
2783       */
2784       ReduceImageColors(image,cube_info);
2785       status=AssignImageColors(image,cube_info,exception);
2786     }
2787   DestroyCubeInfo(cube_info);
2788   return(status);
2789 }
2790 \f
2791 /*
2792 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2793 %                                                                             %
2794 %                                                                             %
2795 %                                                                             %
2796 %   Q u a n t i z e I m a g e s                                               %
2797 %                                                                             %
2798 %                                                                             %
2799 %                                                                             %
2800 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2801 %
2802 %  QuantizeImages() analyzes the colors within a set of reference images and
2803 %  chooses a fixed number of colors to represent the set.  The goal of the
2804 %  algorithm is to minimize the color difference between the input and output
2805 %  images while minimizing the processing time.
2806 %
2807 %  The format of the QuantizeImages method is:
2808 %
2809 %      MagickBooleanType QuantizeImages(const QuantizeInfo *quantize_info,
2810 %        Image *images,ExceptionInfo *exception)
2811 %
2812 %  A description of each parameter follows:
2813 %
2814 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
2815 %
2816 %    o images: Specifies a pointer to a list of Image structures.
2817 %
2818 %    o exception: return any errors or warnings in this structure.
2819 %
2820 */
2821 MagickExport MagickBooleanType QuantizeImages(const QuantizeInfo *quantize_info,
2822   Image *images,ExceptionInfo *exception)
2823 {
2824   CubeInfo
2825     *cube_info;
2826
2827   Image
2828     *image;
2829
2830   MagickBooleanType
2831     proceed,
2832     status;
2833
2834   MagickProgressMonitor
2835     progress_monitor;
2836
2837   register ssize_t
2838     i;
2839
2840   size_t
2841     depth,
2842     maximum_colors,
2843     number_images;
2844
2845   assert(quantize_info != (const QuantizeInfo *) NULL);
2846   assert(quantize_info->signature == MagickSignature);
2847   assert(images != (Image *) NULL);
2848   assert(images->signature == MagickSignature);
2849   if (images->debug != MagickFalse)
2850     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
2851   if (GetNextImageInList(images) == (Image *) NULL)
2852     {
2853       /*
2854         Handle a single image with QuantizeImage.
2855       */
2856       status=QuantizeImage(quantize_info,images,exception);
2857       return(status);
2858     }
2859   status=MagickFalse;
2860   maximum_colors=quantize_info->number_colors;
2861   if (maximum_colors == 0)
2862     maximum_colors=MaxColormapSize;
2863   if (maximum_colors > MaxColormapSize)
2864     maximum_colors=MaxColormapSize;
2865   depth=quantize_info->tree_depth;
2866   if (depth == 0)
2867     {
2868       size_t
2869         colors;
2870
2871       /*
2872         Depth of color tree is: Log4(colormap size)+2.
2873       */
2874       colors=maximum_colors;
2875       for (depth=1; colors != 0; depth++)
2876         colors>>=2;
2877       if (quantize_info->dither_method != NoDitherMethod)
2878         depth--;
2879     }
2880   /*
2881     Initialize color cube.
2882   */
2883   cube_info=GetCubeInfo(quantize_info,depth,maximum_colors);
2884   if (cube_info == (CubeInfo *) NULL)
2885     {
2886       (void) ThrowMagickException(exception,GetMagickModule(),
2887         ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
2888       return(MagickFalse);
2889     }
2890   number_images=GetImageListLength(images);
2891   image=images;
2892   for (i=0; image != (Image *) NULL; i++)
2893   {
2894     progress_monitor=SetImageProgressMonitor(image,(MagickProgressMonitor) NULL,
2895       image->client_data);
2896     status=ClassifyImageColors(cube_info,image,exception);
2897     if (status == MagickFalse)
2898       break;
2899     (void) SetImageProgressMonitor(image,progress_monitor,image->client_data);
2900     proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) i,
2901       number_images);
2902     if (proceed == MagickFalse)
2903       break;
2904     image=GetNextImageInList(image);
2905   }
2906   if (status != MagickFalse)
2907     {
2908       /*
2909         Reduce the number of colors in an image sequence.
2910       */
2911       ReduceImageColors(images,cube_info);
2912       image=images;
2913       for (i=0; image != (Image *) NULL; i++)
2914       {
2915         progress_monitor=SetImageProgressMonitor(image,(MagickProgressMonitor)
2916           NULL,image->client_data);
2917         status=AssignImageColors(image,cube_info,exception);
2918         if (status == MagickFalse)
2919           break;
2920         (void) SetImageProgressMonitor(image,progress_monitor,
2921           image->client_data);
2922         proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) i,
2923           number_images);
2924         if (proceed == MagickFalse)
2925           break;
2926         image=GetNextImageInList(image);
2927       }
2928     }
2929   DestroyCubeInfo(cube_info);
2930   return(status);
2931 }
2932 \f
2933 /*
2934 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2935 %                                                                             %
2936 %                                                                             %
2937 %                                                                             %
2938 +   Q u a n t i z e E r r o r F l a t t e n                                   %
2939 %                                                                             %
2940 %                                                                             %
2941 %                                                                             %
2942 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2943 %
2944 %  QuantizeErrorFlatten() traverses the color cube and flattens the quantization
2945 %  error into a sorted 1D array.  This accelerates the color reduction process.
2946 %
2947 %  Contributed by Yoya.
2948 %
2949 %  The format of the QuantizeImages method is:
2950 %
2951 %      size_t QuantizeErrorFlatten(const Image *image,const CubeInfo *cube_info,
2952 %        const NodeInfo *node_info,const ssize_t offset,
2953 %        MagickRealType *quantize_error)
2954 %
2955 %  A description of each parameter follows.
2956 %
2957 %    o image: the image.
2958 %
2959 %    o cube_info: A pointer to the Cube structure.
2960 %
2961 %    o node_info: pointer to node in color cube tree that is current pointer.
2962 %
2963 %    o offset: quantize error offset.
2964 %
2965 %    o quantize_error: the quantization error vector.
2966 %
2967 */
2968 static size_t QuantizeErrorFlatten(const Image *image,const CubeInfo *cube_info,
2969   const NodeInfo *node_info,const ssize_t offset,MagickRealType *quantize_error)
2970 {
2971   register ssize_t
2972     i;
2973
2974   size_t
2975     n,
2976     number_children;
2977
2978   if (offset >= (ssize_t) cube_info->nodes)
2979     return(0);
2980   quantize_error[offset]=node_info->quantize_error;
2981   n=1;
2982   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2983   for (i=0; i < (ssize_t) number_children ; i++)
2984     if (node_info->child[i] != (NodeInfo *) NULL)
2985       n+=QuantizeErrorFlatten(image,cube_info,node_info->child[i],offset+n,
2986         quantize_error);
2987   return(n);
2988 }
2989 \f
2990 /*
2991 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2992 %                                                                             %
2993 %                                                                             %
2994 %                                                                             %
2995 +   R e d u c e                                                               %
2996 %                                                                             %
2997 %                                                                             %
2998 %                                                                             %
2999 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3000 %
3001 %  Reduce() traverses the color cube tree and prunes any node whose
3002 %  quantization error falls below a particular threshold.
3003 %
3004 %  The format of the Reduce method is:
3005 %
3006 %      Reduce(const Image *image,CubeInfo *cube_info,const NodeInfo *node_info)
3007 %
3008 %  A description of each parameter follows.
3009 %
3010 %    o image: the image.
3011 %
3012 %    o cube_info: A pointer to the Cube structure.
3013 %
3014 %    o node_info: pointer to node in color cube tree that is to be pruned.
3015 %
3016 */
3017 static void Reduce(const Image *image,CubeInfo *cube_info,
3018   const NodeInfo *node_info)
3019 {
3020   register ssize_t
3021     i;
3022
3023   size_t
3024     number_children;
3025
3026   /*
3027     Traverse any children.
3028   */
3029   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
3030   for (i=0; i < (ssize_t) number_children; i++)
3031     if (node_info->child[i] != (NodeInfo *) NULL)
3032       Reduce(image,cube_info,node_info->child[i]);
3033   if (node_info->quantize_error <= cube_info->pruning_threshold)
3034     PruneChild(image,cube_info,node_info);
3035   else
3036     {
3037       /*
3038         Find minimum pruning threshold.
3039       */
3040       if (node_info->number_unique > 0)
3041         cube_info->colors++;
3042       if (node_info->quantize_error < cube_info->next_threshold)
3043         cube_info->next_threshold=node_info->quantize_error;
3044     }
3045 }
3046 \f
3047 /*
3048 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3049 %                                                                             %
3050 %                                                                             %
3051 %                                                                             %
3052 +   R e d u c e I m a g e C o l o r s                                         %
3053 %                                                                             %
3054 %                                                                             %
3055 %                                                                             %
3056 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3057 %
3058 %  ReduceImageColors() repeatedly prunes the tree until the number of nodes
3059 %  with n2 > 0 is less than or equal to the maximum number of colors allowed
3060 %  in the output image.  On any given iteration over the tree, it selects
3061 %  those nodes whose E value is minimal for pruning and merges their
3062 %  color statistics upward. It uses a pruning threshold, Ep, to govern
3063 %  node selection as follows:
3064 %
3065 %    Ep = 0
3066 %    while number of nodes with (n2 > 0) > required maximum number of colors
3067 %      prune all nodes such that E <= Ep
3068 %      Set Ep to minimum E in remaining nodes
3069 %
3070 %  This has the effect of minimizing any quantization error when merging
3071 %  two nodes together.
3072 %
3073 %  When a node to be pruned has offspring, the pruning procedure invokes
3074 %  itself recursively in order to prune the tree from the leaves upward.
3075 %  n2,  Sr, Sg,  and  Sb in a node being pruned are always added to the
3076 %  corresponding data in that node's parent.  This retains the pruned
3077 %  node's color characteristics for later averaging.
3078 %
3079 %  For each node, n2 pixels exist for which that node represents the
3080 %  smallest volume in RGB space containing those pixel's colors.  When n2
3081 %  > 0 the node will uniquely define a color in the output image. At the
3082 %  beginning of reduction,  n2 = 0  for all nodes except a the leaves of
3083 %  the tree which represent colors present in the input image.
3084 %
3085 %  The other pixel count, n1, indicates the total number of colors
3086 %  within the cubic volume which the node represents.  This includes n1 -
3087 %  n2  pixels whose colors should be defined by nodes at a lower level in
3088 %  the tree.
3089 %
3090 %  The format of the ReduceImageColors method is:
3091 %
3092 %      ReduceImageColors(const Image *image,CubeInfo *cube_info)
3093 %
3094 %  A description of each parameter follows.
3095 %
3096 %    o image: the image.
3097 %
3098 %    o cube_info: A pointer to the Cube structure.
3099 %
3100 */
3101
3102 static int MagickRealTypeCompare(const void *error_p,const void *error_q)
3103 {
3104   MagickRealType
3105     *p,
3106     *q;
3107
3108   p=(MagickRealType *) error_p;
3109   q=(MagickRealType *) error_q;
3110   if (*p > *q)
3111     return(1);
3112   if (fabs((double) (*q-*p)) <= MagickEpsilon)
3113     return(0);
3114   return(-1);
3115 }
3116
3117 static void ReduceImageColors(const Image *image,CubeInfo *cube_info)
3118 {
3119 #define ReduceImageTag  "Reduce/Image"
3120
3121   MagickBooleanType
3122     proceed;
3123
3124   MagickOffsetType
3125     offset;
3126
3127   size_t
3128     span;
3129
3130   cube_info->next_threshold=0.0;
3131   if ((cube_info->colors > cube_info->maximum_colors) && (cube_info->depth > 2))
3132     {
3133       MagickRealType
3134         *quantize_error;
3135
3136       /*
3137         Enable rapid reduction of the number of unique colors.
3138       */
3139       quantize_error=(MagickRealType *) AcquireQuantumMemory(cube_info->nodes,
3140         sizeof(*quantize_error));
3141       if (quantize_error != (MagickRealType *) NULL)
3142         {
3143           (void) QuantizeErrorFlatten(image,cube_info,cube_info->root,0,
3144             quantize_error);
3145           qsort(quantize_error,cube_info->nodes,sizeof(MagickRealType),
3146             MagickRealTypeCompare);
3147           cube_info->next_threshold=quantize_error[cube_info->nodes-
3148             cube_info->maximum_colors];
3149           quantize_error=(MagickRealType *) RelinquishMagickMemory(
3150             quantize_error);
3151         }
3152   }
3153   for (span=cube_info->colors; cube_info->colors > cube_info->maximum_colors; )
3154   {
3155     cube_info->pruning_threshold=cube_info->next_threshold;
3156     cube_info->next_threshold=cube_info->root->quantize_error-1;
3157     cube_info->colors=0;
3158     Reduce(image,cube_info,cube_info->root);
3159     offset=(MagickOffsetType) span-cube_info->colors;
3160     proceed=SetImageProgress(image,ReduceImageTag,offset,span-
3161       cube_info->maximum_colors+1);
3162     if (proceed == MagickFalse)
3163       break;
3164   }
3165 }
3166 \f
3167 /*
3168 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3169 %                                                                             %
3170 %                                                                             %
3171 %                                                                             %
3172 %   R e m a p I m a g e                                                       %
3173 %                                                                             %
3174 %                                                                             %
3175 %                                                                             %
3176 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3177 %
3178 %  RemapImage() replaces the colors of an image with a dither of the colors
3179 %  provided.
3180 %
3181 %  The format of the RemapImage method is:
3182 %
3183 %      MagickBooleanType RemapImage(const QuantizeInfo *quantize_info,
3184 %        Image *image,const Image *remap_image,ExceptionInfo *exception)
3185 %
3186 %  A description of each parameter follows:
3187 %
3188 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
3189 %
3190 %    o image: the image.
3191 %
3192 %    o remap_image: the reference image.
3193 %
3194 %    o exception: return any errors or warnings in this structure.
3195 %
3196 */
3197 MagickExport MagickBooleanType RemapImage(const QuantizeInfo *quantize_info,
3198   Image *image,const Image *remap_image,ExceptionInfo *exception)
3199 {
3200   CubeInfo
3201     *cube_info;
3202
3203   MagickBooleanType
3204     status;
3205
3206   /*
3207     Initialize color cube.
3208   */
3209   assert(image != (Image *) NULL);
3210   assert(image->signature == MagickSignature);
3211   if (image->debug != MagickFalse)
3212     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
3213   assert(remap_image != (Image *) NULL);
3214   assert(remap_image->signature == MagickSignature);
3215   cube_info=GetCubeInfo(quantize_info,MaxTreeDepth,
3216     quantize_info->number_colors);
3217   if (cube_info == (CubeInfo *) NULL)
3218     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3219       image->filename);
3220   status=ClassifyImageColors(cube_info,remap_image,exception);
3221   if (status != MagickFalse)
3222     {
3223       /*
3224         Classify image colors from the reference image.
3225       */
3226       cube_info->quantize_info->number_colors=cube_info->colors;
3227       status=AssignImageColors(image,cube_info,exception);
3228     }
3229   DestroyCubeInfo(cube_info);
3230   return(status);
3231 }
3232 \f
3233 /*
3234 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3235 %                                                                             %
3236 %                                                                             %
3237 %                                                                             %
3238 %   R e m a p I m a g e s                                                     %
3239 %                                                                             %
3240 %                                                                             %
3241 %                                                                             %
3242 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3243 %
3244 %  RemapImages() replaces the colors of a sequence of images with the
3245 %  closest color from a reference image.
3246 %
3247 %  The format of the RemapImage method is:
3248 %
3249 %      MagickBooleanType RemapImages(const QuantizeInfo *quantize_info,
3250 %        Image *images,Image *remap_image,ExceptionInfo *exception)
3251 %
3252 %  A description of each parameter follows:
3253 %
3254 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
3255 %
3256 %    o images: the image sequence.
3257 %
3258 %    o remap_image: the reference image.
3259 %
3260 %    o exception: return any errors or warnings in this structure.
3261 %
3262 */
3263 MagickExport MagickBooleanType RemapImages(const QuantizeInfo *quantize_info,
3264   Image *images,const Image *remap_image,ExceptionInfo *exception)
3265 {
3266   CubeInfo
3267     *cube_info;
3268
3269   Image
3270     *image;
3271
3272   MagickBooleanType
3273     status;
3274
3275   assert(images != (Image *) NULL);
3276   assert(images->signature == MagickSignature);
3277   if (images->debug != MagickFalse)
3278     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
3279   image=images;
3280   if (remap_image == (Image *) NULL)
3281     {
3282       /*
3283         Create a global colormap for an image sequence.
3284       */
3285       status=QuantizeImages(quantize_info,images,exception);
3286       return(status);
3287     }
3288   /*
3289     Classify image colors from the reference image.
3290   */
3291   cube_info=GetCubeInfo(quantize_info,MaxTreeDepth,
3292     quantize_info->number_colors);
3293   if (cube_info == (CubeInfo *) NULL)
3294     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3295       image->filename);
3296   status=ClassifyImageColors(cube_info,remap_image,exception);
3297   if (status != MagickFalse)
3298     {
3299       /*
3300         Classify image colors from the reference image.
3301       */
3302       cube_info->quantize_info->number_colors=cube_info->colors;
3303       image=images;
3304       for ( ; image != (Image *) NULL; image=GetNextImageInList(image))
3305       {
3306         status=AssignImageColors(image,cube_info,exception);
3307         if (status == MagickFalse)
3308           break;
3309       }
3310     }
3311   DestroyCubeInfo(cube_info);
3312   return(status);
3313 }
3314 \f
3315 /*
3316 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3317 %                                                                             %
3318 %                                                                             %
3319 %                                                                             %
3320 %   S e t G r a y s c a l e I m a g e                                         %
3321 %                                                                             %
3322 %                                                                             %
3323 %                                                                             %
3324 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3325 %
3326 %  SetGrayscaleImage() converts an image to a PseudoClass grayscale image.
3327 %
3328 %  The format of the SetGrayscaleImage method is:
3329 %
3330 %      MagickBooleanType SetGrayscaleImage(Image *image,ExceptionInfo *exeption)
3331 %
3332 %  A description of each parameter follows:
3333 %
3334 %    o image: The image.
3335 %
3336 %    o exception: return any errors or warnings in this structure.
3337 %
3338 */
3339
3340 #if defined(__cplusplus) || defined(c_plusplus)
3341 extern "C" {
3342 #endif
3343
3344 static int IntensityCompare(const void *x,const void *y)
3345 {
3346   PixelInfo
3347     *color_1,
3348     *color_2;
3349
3350   ssize_t
3351     intensity;
3352
3353   color_1=(PixelInfo *) x;
3354   color_2=(PixelInfo *) y;
3355   intensity=(ssize_t) (GetPixelInfoIntensity(color_1)-(ssize_t)
3356     GetPixelInfoIntensity(color_2));
3357   return((int) intensity);
3358 }
3359
3360 #if defined(__cplusplus) || defined(c_plusplus)
3361 }
3362 #endif
3363
3364 static MagickBooleanType SetGrayscaleImage(Image *image,
3365   ExceptionInfo *exception)
3366 {
3367   CacheView
3368     *image_view;
3369
3370   MagickBooleanType
3371     status;
3372
3373   PixelInfo
3374     *colormap;
3375
3376   register ssize_t
3377     i;
3378
3379   ssize_t
3380     *colormap_index,
3381     j,
3382     y;
3383
3384   assert(image != (Image *) NULL);
3385   assert(image->signature == MagickSignature);
3386   if (image->type != GrayscaleType)
3387     (void) TransformImageColorspace(image,GRAYColorspace,exception);
3388   colormap_index=(ssize_t *) AcquireQuantumMemory(MaxMap+1,
3389     sizeof(*colormap_index));
3390   if (colormap_index == (ssize_t *) NULL)
3391     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3392       image->filename);
3393   if (image->storage_class != PseudoClass)
3394     {
3395       for (i=0; i <= (ssize_t) MaxMap; i++)
3396         colormap_index[i]=(-1);
3397       if (AcquireImageColormap(image,MaxMap+1,exception) == MagickFalse)
3398         ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3399           image->filename);
3400       image->colors=0;
3401       status=MagickTrue;
3402       image_view=AcquireAuthenticCacheView(image,exception);
3403 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3404       #pragma omp parallel for schedule(static,4) shared(status) \
3405         magick_threads(image,image,image->rows,1)
3406 #endif
3407       for (y=0; y < (ssize_t) image->rows; y++)
3408       {
3409         register Quantum
3410           *restrict q;
3411
3412         register ssize_t
3413           x;
3414
3415         if (status == MagickFalse)
3416           continue;
3417         q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
3418           exception);
3419         if (q == (Quantum *) NULL)
3420           {
3421             status=MagickFalse;
3422             continue;
3423           }
3424         for (x=0; x < (ssize_t) image->columns; x++)
3425         {
3426           register size_t
3427             intensity;
3428
3429           intensity=ScaleQuantumToMap(GetPixelRed(image,q));
3430           if (colormap_index[intensity] < 0)
3431             {
3432 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3433               #pragma omp critical (MagickCore_SetGrayscaleImage)
3434 #endif
3435               if (colormap_index[intensity] < 0)
3436                 {
3437                   colormap_index[intensity]=(ssize_t) image->colors;
3438                   image->colormap[image->colors].red=(double)
3439                     GetPixelRed(image,q);
3440                   image->colormap[image->colors].green=(double)
3441                     GetPixelGreen(image,q);
3442                   image->colormap[image->colors].blue=(double)
3443                     GetPixelBlue(image,q);
3444                   image->colors++;
3445                }
3446             }
3447           SetPixelIndex(image,(Quantum) colormap_index[intensity],q);
3448           q+=GetPixelChannels(image);
3449         }
3450         if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
3451           status=MagickFalse;
3452       }
3453       image_view=DestroyCacheView(image_view);
3454     }
3455   for (i=0; i < (ssize_t) image->colors; i++)
3456     image->colormap[i].alpha=(double) i;
3457   qsort((void *) image->colormap,image->colors,sizeof(PixelInfo),
3458     IntensityCompare);
3459   colormap=(PixelInfo *) AcquireQuantumMemory(image->colors,sizeof(*colormap));
3460   if (colormap == (PixelInfo *) NULL)
3461     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3462       image->filename);
3463   j=0;
3464   colormap[j]=image->colormap[0];
3465   for (i=0; i < (ssize_t) image->colors; i++)
3466   {
3467     if (IsPixelInfoEquivalent(&colormap[j],&image->colormap[i]) == MagickFalse)
3468       {
3469         j++;
3470         colormap[j]=image->colormap[i];
3471       }
3472     colormap_index[(ssize_t) image->colormap[i].alpha]=j;
3473   }
3474   image->colors=(size_t) (j+1);
3475   image->colormap=(PixelInfo *) RelinquishMagickMemory(image->colormap);
3476   image->colormap=colormap;
3477   status=MagickTrue;
3478   image_view=AcquireAuthenticCacheView(image,exception);
3479 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3480   #pragma omp parallel for schedule(static,4) shared(status) \
3481     magick_threads(image,image,image->rows,1)
3482 #endif
3483   for (y=0; y < (ssize_t) image->rows; y++)
3484   {
3485     register Quantum
3486       *restrict q;
3487
3488     register ssize_t
3489       x;
3490
3491     if (status == MagickFalse)
3492       continue;
3493     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
3494     if (q == (Quantum *) NULL)
3495       {
3496         status=MagickFalse;
3497         continue;
3498       }
3499     for (x=0; x < (ssize_t) image->columns; x++)
3500     {
3501       SetPixelIndex(image,(Quantum) colormap_index[ScaleQuantumToMap(
3502         GetPixelIndex(image,q))],q);
3503       q+=GetPixelChannels(image);
3504     }
3505     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
3506       status=MagickFalse;
3507   }
3508   image_view=DestroyCacheView(image_view);
3509   colormap_index=(ssize_t *) RelinquishMagickMemory(colormap_index);
3510   image->type=GrayscaleType;
3511   if (IsImageMonochrome(image,exception) != MagickFalse)
3512     image->type=BilevelType;
3513   return(status);
3514 }