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                %
  10 %           QQQQ   UUU   A   A  N   N    T    IIIII   ZZZZZ  EEEEE            %
  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   ssize_t
 295     *cache;
 296
 297   RealPixelInfo
 298     error[ErrorQueueLength];
 299
 300   double
 301     weights[ErrorQueueLength];
 302
 303   QuantizeInfo
 304     *quantize_info;
 305
 306   MagickBooleanType
 307     associate_alpha;
 308
 309   ssize_t
 310     x,
 311     y;
 312
 313   size_t
 314     depth;
 315
 316   MagickOffsetType
 317     offset;
 318
 319   MagickSizeType
 320     span;
 321 } CubeInfo;
 322 \f
 323 /*
 324   Method prototypes.
 325 */
 326 static CubeInfo
 327   *GetCubeInfo(const QuantizeInfo *,const size_t,const size_t);
 328
 329 static NodeInfo
 330   *GetNodeInfo(CubeInfo *,const size_t,const size_t,NodeInfo *);
 331
 332 static MagickBooleanType
 333   AssignImageColors(Image *,CubeInfo *,ExceptionInfo *),
 334   ClassifyImageColors(CubeInfo *,const Image *,ExceptionInfo *),
 335   DitherImage(Image *,CubeInfo *,ExceptionInfo *),
 336   SetGrayscaleImage(Image *,ExceptionInfo *);
 337
 338 static size_t
 339   DefineImageColormap(Image *,CubeInfo *,NodeInfo *);
 340
 341 static void
 342   ClosestColor(const Image *,CubeInfo *,const NodeInfo *),
 343   DestroyCubeInfo(CubeInfo *),
 344   PruneLevel(const Image *,CubeInfo *,const NodeInfo *),
 345   PruneToCubeDepth(const Image *,CubeInfo *,const NodeInfo *),
 346   ReduceImageColors(const Image *,CubeInfo *);
 347 \f
 348 /*
 349 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 350 %                                                                             %
 351 %                                                                             %
 352 %                                                                             %
 353 %   A c q u i r e Q u a n t i z e I n f o                                     %
 354 %                                                                             %
 355 %                                                                             %
 356 %                                                                             %
 357 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 358 %
 359 %  AcquireQuantizeInfo() allocates the QuantizeInfo structure.
 360 %
 361 %  The format of the AcquireQuantizeInfo method is:
 362 %
 363 %      QuantizeInfo *AcquireQuantizeInfo(const ImageInfo *image_info)
 364 %
 365 %  A description of each parameter follows:
 366 %
 367 %    o image_info: the image info.
 368 %
 369 */
 370 MagickExport QuantizeInfo *AcquireQuantizeInfo(const ImageInfo *image_info)
 371 {
 372   QuantizeInfo
 373     *quantize_info;
 374
 375   quantize_info=(QuantizeInfo *) AcquireMagickMemory(sizeof(*quantize_info));
 376   if (quantize_info == (QuantizeInfo *) NULL)
 377     ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
 378   GetQuantizeInfo(quantize_info);
 379   if (image_info != (ImageInfo *) NULL)
 380     {
 381       const char
 382         *option;
 383
 384       quantize_info->dither_method=image_info->dither == MagickFalse ?
 385         NoDitherMethod : RiemersmaDitherMethod;
 386       option=GetImageOption(image_info,"dither");
 387       if (option != (const char *) NULL)
 388         quantize_info->dither_method=(DitherMethod) ParseCommandOption(
 389           MagickDitherOptions,MagickFalse,option);
 390       quantize_info->measure_error=image_info->verbose;
 391     }
 392   return(quantize_info);
 393 }
 394 \f
 395 /*
 396 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 397 %                                                                             %
 398 %                                                                             %
 399 %                                                                             %
 400 +   A s s i g n I m a g e C o l o r s                                         %
 401 %                                                                             %
 402 %                                                                             %
 403 %                                                                             %
 404 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 405 %
 406 %  AssignImageColors() generates the output image from the pruned tree.  The
 407 %  output image consists of two parts: (1)  A color map, which is an array
 408 %  of color descriptions (RGB triples) for each color present in the
 409 %  output image;  (2)  A pixel array, which represents each pixel as an
 410 %  index into the color map array.
 411 %
 412 %  First, the assignment phase makes one pass over the pruned color
 413 %  description tree to establish the image's color map.  For each node
 414 %  with n2  > 0, it divides Sr, Sg, and Sb by n2 .  This produces the mean
 415 %  color of all pixels that classify no lower than this node.  Each of
 416 %  these colors becomes an entry in the color map.
 417 %
 418 %  Finally,  the assignment phase reclassifies each pixel in the pruned
 419 %  tree to identify the deepest node containing the pixel's color.  The
 420 %  pixel's value in the pixel array becomes the index of this node's mean
 421 %  color in the color map.
 422 %
 423 %  The format of the AssignImageColors() method is:
 424 %
 425 %      MagickBooleanType AssignImageColors(Image *image,CubeInfo *cube_info)
 426 %
 427 %  A description of each parameter follows.
 428 %
 429 %    o image: the image.
 430 %
 431 %    o cube_info: A pointer to the Cube structure.
 432 %
 433 */
 434
 435 static inline void AssociateAlphaPixel(const Image *image,
 436   const CubeInfo *cube_info,const Quantum *pixel,RealPixelInfo *alpha_pixel)
 437 {
 438   double
 439     alpha;
 440
 441   if ((cube_info->associate_alpha == MagickFalse) ||
 442       (GetPixelAlpha(image,pixel)== OpaqueAlpha))
 443     {
 444       alpha_pixel->red=(double) GetPixelRed(image,pixel);
 445       alpha_pixel->green=(double) GetPixelGreen(image,pixel);
 446       alpha_pixel->blue=(double) GetPixelBlue(image,pixel);
 447       alpha_pixel->alpha=(double) GetPixelAlpha(image,pixel);
 448       return;
 449     }
 450   alpha=(double) (QuantumScale*GetPixelAlpha(image,pixel));
 451   alpha_pixel->red=alpha*GetPixelRed(image,pixel);
 452   alpha_pixel->green=alpha*GetPixelGreen(image,pixel);
 453   alpha_pixel->blue=alpha*GetPixelBlue(image,pixel);
 454   alpha_pixel->alpha=(double) GetPixelAlpha(image,pixel);
 455 }
 456
 457 static inline void AssociateAlphaPixelInfo(const Image *image,
 458   const CubeInfo *cube_info,const PixelInfo *pixel,
 459   RealPixelInfo *alpha_pixel)
 460 {
 461   double
 462     alpha;
 463
 464   if ((cube_info->associate_alpha == MagickFalse) ||
 465       (pixel->alpha == OpaqueAlpha))
 466     {
 467       alpha_pixel->red=(double) pixel->red;
 468       alpha_pixel->green=(double) pixel->green;
 469       alpha_pixel->blue=(double) pixel->blue;
 470       alpha_pixel->alpha=(double) pixel->alpha;
 471       return;
 472     }
 473   alpha=(double) (QuantumScale*pixel->alpha);
 474   alpha_pixel->red=alpha*pixel->red;
 475   alpha_pixel->green=alpha*pixel->green;
 476   alpha_pixel->blue=alpha*pixel->blue;
 477   alpha_pixel->alpha=(double) pixel->alpha;
 478 }
 479
 480 static inline Quantum ClampPixel(const MagickRealType value)
 481 {
 482   if (value < 0.0f)
 483     return(0);
 484   if (value >= (MagickRealType) QuantumRange)
 485     return((Quantum) QuantumRange);
 486 #if !defined(MAGICKCORE_HDRI_SUPPORT)
 487   return((Quantum) (value+0.5f));
 488 #else
 489   return(value);
 490 #endif
 491 }
 492
 493 static inline size_t ColorToNodeId(const CubeInfo *cube_info,
 494   const RealPixelInfo *pixel,size_t index)
 495 {
 496   size_t
 497     id;
 498
 499   id=(size_t) (((ScaleQuantumToChar(ClampPixel(pixel->red)) >> index) & 0x01) |
 500     ((ScaleQuantumToChar(ClampPixel(pixel->green)) >> index) & 0x01) << 1 |
 501     ((ScaleQuantumToChar(ClampPixel(pixel->blue)) >> index) & 0x01) << 2);
 502   if (cube_info->associate_alpha != MagickFalse)
 503     id|=((ScaleQuantumToChar(ClampPixel(pixel->alpha)) >> index) & 0x1) << 3;
 504   return(id);
 505 }
 506
 507 static MagickBooleanType AssignImageColors(Image *image,CubeInfo *cube_info,
 508   ExceptionInfo *exception)
 509 {
 510 #define AssignImageTag  "Assign/Image"
 511
 512   ssize_t
 513     y;
 514
 515   /*
 516     Allocate image colormap.
 517   */
 518   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
 519       (cube_info->quantize_info->colorspace != CMYKColorspace))
 520     (void) TransformImageColorspace((Image *) image,
 521       cube_info->quantize_info->colorspace,exception);
 522   else
 523     if (IssRGBCompatibleColorspace(image->colorspace) == MagickFalse)
 524       (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
 525   if (AcquireImageColormap(image,cube_info->colors,exception) == MagickFalse)
 526     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 527       image->filename);
 528   image->colors=0;
 529   cube_info->transparent_pixels=0;
 530   cube_info->transparent_index=(-1);
 531   (void) DefineImageColormap(image,cube_info,cube_info->root);
 532   /*
 533     Create a reduced color image.
 534   */
 535   if ((cube_info->quantize_info->dither_method != NoDitherMethod) &&
 536       (cube_info->quantize_info->dither_method != NoDitherMethod))
 537     (void) DitherImage(image,cube_info,exception);
 538   else
 539     {
 540       CacheView
 541         *image_view;
 542
 543       MagickBooleanType
 544         status;
 545
 546       status=MagickTrue;
 547       image_view=AcquireAuthenticCacheView(image,exception);
 548 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 549       #pragma omp parallel for schedule(static,4) shared(status) \
 550         magick_threads(image,image,image->rows,1)
 551 #endif
 552       for (y=0; y < (ssize_t) image->rows; y++)
 553       {
 554         CubeInfo
 555           cube;
 556
 557         register Quantum
 558           *restrict q;
 559
 560         register ssize_t
 561           x;
 562
 563         ssize_t
 564           count;
 565
 566         if (status == MagickFalse)
 567           continue;
 568         q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
 569           exception);
 570         if (q == (Quantum *) NULL)
 571           {
 572             status=MagickFalse;
 573             continue;
 574           }
 575         cube=(*cube_info);
 576         for (x=0; x < (ssize_t) image->columns; x+=count)
 577         {
 578           RealPixelInfo
 579             pixel;
 580
 581           register const NodeInfo
 582             *node_info;
 583
 584           register ssize_t
 585             i;
 586
 587           size_t
 588             id,
 589             index;
 590
 591           /*
 592             Identify the deepest node containing the pixel's color.
 593           */
 594           for (count=1; (x+count) < (ssize_t) image->columns; count++)
 595           {
 596             PixelInfo
 597               packet;
 598
 599             GetPixelInfoPixel(image,q+count*GetPixelChannels(image),&packet);
 600             if (IsPixelEquivalent(image,q,&packet) == MagickFalse)
 601               break;
 602           }
 603           AssociateAlphaPixel(image,&cube,q,&pixel);
 604           node_info=cube.root;
 605           for (index=MaxTreeDepth-1; (ssize_t) index > 0; index--)
 606           {
 607             id=ColorToNodeId(&cube,&pixel,index);
 608             if (node_info->child[id] == (NodeInfo *) NULL)
 609               break;
 610             node_info=node_info->child[id];
 611           }
 612           /*
 613             Find closest color among siblings and their children.
 614           */
 615           cube.target=pixel;
 616           cube.distance=(double) (4.0*(QuantumRange+1.0)*
 617             (QuantumRange+1.0)+1.0);
 618           ClosestColor(image,&cube,node_info->parent);
 619           index=cube.color_number;
 620           for (i=0; i < (ssize_t) count; i++)
 621           {
 622             if (image->storage_class == PseudoClass)
 623               SetPixelIndex(image,(Quantum) index,q);
 624             if (cube.quantize_info->measure_error == MagickFalse)
 625               {
 626                 SetPixelRed(image,ClampToQuantum(
 627                   image->colormap[index].red),q);
 628                 SetPixelGreen(image,ClampToQuantum(
 629                   image->colormap[index].green),q);
 630                 SetPixelBlue(image,ClampToQuantum(
 631                   image->colormap[index].blue),q);
 632                 if (cube.associate_alpha != MagickFalse)
 633                   SetPixelAlpha(image,ClampToQuantum(
 634                     image->colormap[index].alpha),q);
 635               }
 636             q+=GetPixelChannels(image);
 637           }
 638         }
 639         if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
 640           status=MagickFalse;
 641         if (image->progress_monitor != (MagickProgressMonitor) NULL)
 642           {
 643             MagickBooleanType
 644               proceed;
 645
 646 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 647             #pragma omp critical (MagickCore_AssignImageColors)
 648 #endif
 649             proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) y,
 650               image->rows);
 651             if (proceed == MagickFalse)
 652               status=MagickFalse;
 653           }
 654       }
 655       image_view=DestroyCacheView(image_view);
 656     }
 657   if (cube_info->quantize_info->measure_error != MagickFalse)
 658     (void) GetImageQuantizeError(image,exception);
 659   if ((cube_info->quantize_info->number_colors == 2) &&
 660       (cube_info->quantize_info->colorspace == GRAYColorspace))
 661     {
 662       double
 663         intensity;
 664
 665       register PixelInfo
 666         *restrict q;
 667
 668       register ssize_t
 669         i;
 670
 671       /*
 672         Monochrome image.
 673       */
 674       q=image->colormap;
 675       for (i=0; i < (ssize_t) image->colors; i++)
 676       {
 677         intensity=(double) ((double) GetPixelInfoIntensity(q) <
 678           ((double) QuantumRange/2.0) ? 0 : QuantumRange);
 679         q->red=intensity;
 680         q->green=intensity;
 681         q->blue=intensity;
 682         q++;
 683       }
 684     }
 685   (void) SyncImage(image,exception);
 686   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
 687       (cube_info->quantize_info->colorspace != CMYKColorspace))
 688     (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
 689   return(MagickTrue);
 690 }
 691 \f
 692 /*
 693 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 694 %                                                                             %
 695 %                                                                             %
 696 %                                                                             %
 697 +   C l a s s i f y I m a g e C o l o r s                                     %
 698 %                                                                             %
 699 %                                                                             %
 700 %                                                                             %
 701 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 702 %
 703 %  ClassifyImageColors() begins by initializing a color description tree
 704 %  of sufficient depth to represent each possible input color in a leaf.
 705 %  However, it is impractical to generate a fully-formed color
 706 %  description tree in the storage_class phase for realistic values of
 707 %  Cmax.  If colors components in the input image are quantized to k-bit
 708 %  precision, so that Cmax= 2k-1, the tree would need k levels below the
 709 %  root node to allow representing each possible input color in a leaf.
 710 %  This becomes prohibitive because the tree's total number of nodes is
 711 %  1 + sum(i=1,k,8k).
 712 %
 713 %  A complete tree would require 19,173,961 nodes for k = 8, Cmax = 255.
 714 %  Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
 715 %  Initializes data structures for nodes only as they are needed;  (2)
 716 %  Chooses a maximum depth for the tree as a function of the desired
 717 %  number of colors in the output image (currently log2(colormap size)).
 718 %
 719 %  For each pixel in the input image, storage_class scans downward from
 720 %  the root of the color description tree.  At each level of the tree it
 721 %  identifies the single node which represents a cube in RGB space
 722 %  containing It updates the following data for each such node:
 723 %
 724 %    n1 : Number of pixels whose color is contained in the RGB cube
 725 %    which this node represents;
 726 %
 727 %    n2 : Number of pixels whose color is not represented in a node at
 728 %    lower depth in the tree;  initially,  n2 = 0 for all nodes except
 729 %    leaves of the tree.
 730 %
 731 %    Sr, Sg, Sb : Sums of the red, green, and blue component values for
 732 %    all pixels not classified at a lower depth. The combination of
 733 %    these sums and n2  will ultimately characterize the mean color of a
 734 %    set of pixels represented by this node.
 735 %
 736 %    E: the distance squared in RGB space between each pixel contained
 737 %    within a node and the nodes' center.  This represents the quantization
 738 %    error for a node.
 739 %
 740 %  The format of the ClassifyImageColors() method is:
 741 %
 742 %      MagickBooleanType ClassifyImageColors(CubeInfo *cube_info,
 743 %        const Image *image,ExceptionInfo *exception)
 744 %
 745 %  A description of each parameter follows.
 746 %
 747 %    o cube_info: A pointer to the Cube structure.
 748 %
 749 %    o image: the image.
 750 %
 751 */
 752
 753 static inline void SetAssociatedAlpha(const Image *image,CubeInfo *cube_info)
 754 {
 755   MagickBooleanType
 756     associate_alpha;
 757
 758   associate_alpha=image->alpha_trait == BlendPixelTrait ? MagickTrue :
 759     MagickFalse;
 760   if (cube_info->quantize_info->colorspace == TransparentColorspace)
 761     associate_alpha=MagickFalse;
 762   if ((cube_info->quantize_info->number_colors == 2) &&
 763       (cube_info->quantize_info->colorspace == GRAYColorspace))
 764     associate_alpha=MagickFalse;
 765   cube_info->associate_alpha=associate_alpha;
 766 }
 767
 768 static MagickBooleanType ClassifyImageColors(CubeInfo *cube_info,
 769   const Image *image,ExceptionInfo *exception)
 770 {
 771 #define ClassifyImageTag  "Classify/Image"
 772
 773   CacheView
 774     *image_view;
 775
 776   MagickBooleanType
 777     proceed;
 778
 779   double
 780     bisect;
 781
 782   NodeInfo
 783     *node_info;
 784
 785   RealPixelInfo
 786     error,
 787     mid,
 788     midpoint,
 789     pixel;
 790
 791   size_t
 792     count,
 793     id,
 794     index,
 795     level;
 796
 797   ssize_t
 798     y;
 799
 800   /*
 801     Classify the first cube_info->maximum_colors colors to a tree depth of 8.
 802   */
 803   SetAssociatedAlpha(image,cube_info);
 804   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
 805       (cube_info->quantize_info->colorspace != CMYKColorspace))
 806     (void) TransformImageColorspace((Image *) image,
 807       cube_info->quantize_info->colorspace,exception);
 808   else
 809     if (IssRGBCompatibleColorspace(image->colorspace) == MagickFalse)
 810       (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
 811   midpoint.red=(double) QuantumRange/2.0;
 812   midpoint.green=(double) QuantumRange/2.0;
 813   midpoint.blue=(double) QuantumRange/2.0;
 814   midpoint.alpha=(double) QuantumRange/2.0;
 815   error.alpha=0.0;
 816   image_view=AcquireVirtualCacheView(image,exception);
 817   for (y=0; y < (ssize_t) image->rows; y++)
 818   {
 819     register const Quantum
 820       *restrict p;
 821
 822     register ssize_t
 823       x;
 824
 825     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 826     if (p == (const Quantum *) NULL)
 827       break;
 828     if (cube_info->nodes > MaxNodes)
 829       {
 830         /*
 831           Prune one level if the color tree is too large.
 832         */
 833         PruneLevel(image,cube_info,cube_info->root);
 834         cube_info->depth--;
 835       }
 836     for (x=0; x < (ssize_t) image->columns; x+=(ssize_t) count)
 837     {
 838       /*
 839         Start at the root and descend the color cube tree.
 840       */
 841       for (count=1; (x+(ssize_t) count) < (ssize_t) image->columns; count++)
 842       {
 843         PixelInfo
 844           packet;
 845
 846         GetPixelInfoPixel(image,p+count*GetPixelChannels(image),&packet);
 847         if (IsPixelEquivalent(image,p,&packet) == MagickFalse)
 848           break;
 849       }
 850       AssociateAlphaPixel(image,cube_info,p,&pixel);
 851       index=MaxTreeDepth-1;
 852       bisect=((double) QuantumRange+1.0)/2.0;
 853       mid=midpoint;
 854       node_info=cube_info->root;
 855       for (level=1; level <= MaxTreeDepth; level++)
 856       {
 857         bisect*=0.5;
 858         id=ColorToNodeId(cube_info,&pixel,index);
 859         mid.red+=(id & 1) != 0 ? bisect : -bisect;
 860         mid.green+=(id & 2) != 0 ? bisect : -bisect;
 861         mid.blue+=(id & 4) != 0 ? bisect : -bisect;
 862         mid.alpha+=(id & 8) != 0 ? bisect : -bisect;
 863         if (node_info->child[id] == (NodeInfo *) NULL)
 864           {
 865             /*
 866               Set colors of new node to contain pixel.
 867             */
 868             node_info->child[id]=GetNodeInfo(cube_info,id,level,node_info);
 869             if (node_info->child[id] == (NodeInfo *) NULL)
 870               (void) ThrowMagickException(exception,GetMagickModule(),
 871                 ResourceLimitError,"MemoryAllocationFailed","`%s'",
 872                 image->filename);
 873             if (level == MaxTreeDepth)
 874               cube_info->colors++;
 875           }
 876         /*
 877           Approximate the quantization error represented by this node.
 878         */
 879         node_info=node_info->child[id];
 880         error.red=QuantumScale*(pixel.red-mid.red);
 881         error.green=QuantumScale*(pixel.green-mid.green);
 882         error.blue=QuantumScale*(pixel.blue-mid.blue);
 883         if (cube_info->associate_alpha != MagickFalse)
 884           error.alpha=QuantumScale*(pixel.alpha-mid.alpha);
 885         node_info->quantize_error+=sqrt((double) (count*error.red*error.red+
 886           count*error.green*error.green+count*error.blue*error.blue+count*
 887           error.alpha*error.alpha));
 888         cube_info->root->quantize_error+=node_info->quantize_error;
 889         index--;
 890       }
 891       /*
 892         Sum RGB for this leaf for later derivation of the mean cube color.
 893       */
 894       node_info->number_unique+=count;
 895       node_info->total_color.red+=count*QuantumScale*ClampPixel(pixel.red);
 896       node_info->total_color.green+=count*QuantumScale*ClampPixel(pixel.green);
 897       node_info->total_color.blue+=count*QuantumScale*ClampPixel(pixel.blue);
 898       if (cube_info->associate_alpha != MagickFalse)
 899         node_info->total_color.alpha+=count*QuantumScale*ClampPixel(
 900           pixel.alpha);
 901       p+=count*GetPixelChannels(image);
 902     }
 903     if (cube_info->colors > cube_info->maximum_colors)
 904       {
 905         PruneToCubeDepth(image,cube_info,cube_info->root);
 906         break;
 907       }
 908     proceed=SetImageProgress(image,ClassifyImageTag,(MagickOffsetType) y,
 909       image->rows);
 910     if (proceed == MagickFalse)
 911       break;
 912   }
 913   for (y++; y < (ssize_t) image->rows; y++)
 914   {
 915     register const Quantum
 916       *restrict p;
 917
 918     register ssize_t
 919       x;
 920
 921     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 922     if (p == (const Quantum *) NULL)
 923       break;
 924     if (cube_info->nodes > MaxNodes)
 925       {
 926         /*
 927           Prune one level if the color tree is too large.
 928         */
 929         PruneLevel(image,cube_info,cube_info->root);
 930         cube_info->depth--;
 931       }
 932     for (x=0; x < (ssize_t) image->columns; x+=(ssize_t) count)
 933     {
 934       /*
 935         Start at the root and descend the color cube tree.
 936       */
 937       for (count=1; (x+(ssize_t) count) < (ssize_t) image->columns; count++)
 938       {
 939         PixelInfo
 940           packet;
 941
 942         GetPixelInfoPixel(image,p+count*GetPixelChannels(image),&packet);
 943         if (IsPixelEquivalent(image,p,&packet) == MagickFalse)
 944           break;
 945       }
 946       AssociateAlphaPixel(image,cube_info,p,&pixel);
 947       index=MaxTreeDepth-1;
 948       bisect=((double) QuantumRange+1.0)/2.0;
 949       mid=midpoint;
 950       node_info=cube_info->root;
 951       for (level=1; level <= cube_info->depth; level++)
 952       {
 953         bisect*=0.5;
 954         id=ColorToNodeId(cube_info,&pixel,index);
 955         mid.red+=(id & 1) != 0 ? bisect : -bisect;
 956         mid.green+=(id & 2) != 0 ? bisect : -bisect;
 957         mid.blue+=(id & 4) != 0 ? bisect : -bisect;
 958         mid.alpha+=(id & 8) != 0 ? bisect : -bisect;
 959         if (node_info->child[id] == (NodeInfo *) NULL)
 960           {
 961             /*
 962               Set colors of new node to contain pixel.
 963             */
 964             node_info->child[id]=GetNodeInfo(cube_info,id,level,node_info);
 965             if (node_info->child[id] == (NodeInfo *) NULL)
 966               (void) ThrowMagickException(exception,GetMagickModule(),
 967                 ResourceLimitError,"MemoryAllocationFailed","%s",
 968                 image->filename);
 969             if (level == cube_info->depth)
 970               cube_info->colors++;
 971           }
 972         /*
 973           Approximate the quantization error represented by this node.
 974         */
 975         node_info=node_info->child[id];
 976         error.red=QuantumScale*(pixel.red-mid.red);
 977         error.green=QuantumScale*(pixel.green-mid.green);
 978         error.blue=QuantumScale*(pixel.blue-mid.blue);
 979         if (cube_info->associate_alpha != MagickFalse)
 980           error.alpha=QuantumScale*(pixel.alpha-mid.alpha);
 981         node_info->quantize_error+=sqrt((double) (count*error.red*error.red+
 982           count*error.green*error.green+count*error.blue*error.blue+count*
 983           error.alpha*error.alpha));
 984         cube_info->root->quantize_error+=node_info->quantize_error;
 985         index--;
 986       }
 987       /*
 988         Sum RGB for this leaf for later derivation of the mean cube color.
 989       */
 990       node_info->number_unique+=count;
 991       node_info->total_color.red+=count*QuantumScale*ClampPixel(pixel.red);
 992       node_info->total_color.green+=count*QuantumScale*ClampPixel(pixel.green);
 993       node_info->total_color.blue+=count*QuantumScale*ClampPixel(pixel.blue);
 994       if (cube_info->associate_alpha != MagickFalse)
 995         node_info->total_color.alpha+=count*QuantumScale*ClampPixel(
 996           pixel.alpha);
 997       p+=count*GetPixelChannels(image);
 998     }
 999     proceed=SetImageProgress(image,ClassifyImageTag,(MagickOffsetType) y,
1000       image->rows);
1001     if (proceed == MagickFalse)
1002       break;
1003   }
1004   image_view=DestroyCacheView(image_view);
1005   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
1006       (cube_info->quantize_info->colorspace != CMYKColorspace))
1007     (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
1008   return(MagickTrue);
1009 }
1010 \f
1011 /*
1012 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1013 %                                                                             %
1014 %                                                                             %
1015 %                                                                             %
1016 %   C l o n e Q u a n t i z e I n f o                                         %
1017 %                                                                             %
1018 %                                                                             %
1019 %                                                                             %
1020 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1021 %
1022 %  CloneQuantizeInfo() makes a duplicate of the given quantize info structure,
1023 %  or if quantize info is NULL, a new one.
1024 %
1025 %  The format of the CloneQuantizeInfo method is:
1026 %
1027 %      QuantizeInfo *CloneQuantizeInfo(const QuantizeInfo *quantize_info)
1028 %
1029 %  A description of each parameter follows:
1030 %
1031 %    o clone_info: Method CloneQuantizeInfo returns a duplicate of the given
1032 %      quantize info, or if image info is NULL a new one.
1033 %
1034 %    o quantize_info: a structure of type info.
1035 %
1036 */
1037 MagickExport QuantizeInfo *CloneQuantizeInfo(const QuantizeInfo *quantize_info)
1038 {
1039   QuantizeInfo
1040     *clone_info;
1041
1042   clone_info=(QuantizeInfo *) AcquireMagickMemory(sizeof(*clone_info));
1043   if (clone_info == (QuantizeInfo *) NULL)
1044     ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
1045   GetQuantizeInfo(clone_info);
1046   if (quantize_info == (QuantizeInfo *) NULL)
1047     return(clone_info);
1048   clone_info->number_colors=quantize_info->number_colors;
1049   clone_info->tree_depth=quantize_info->tree_depth;
1050   clone_info->dither_method=quantize_info->dither_method;
1051   clone_info->colorspace=quantize_info->colorspace;
1052   clone_info->measure_error=quantize_info->measure_error;
1053   return(clone_info);
1054 }
1055 \f
1056 /*
1057 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1058 %                                                                             %
1059 %                                                                             %
1060 %                                                                             %
1061 +   C l o s e s t C o l o r                                                   %
1062 %                                                                             %
1063 %                                                                             %
1064 %                                                                             %
1065 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1066 %
1067 %  ClosestColor() traverses the color cube tree at a particular node and
1068 %  determines which colormap entry best represents the input color.
1069 %
1070 %  The format of the ClosestColor method is:
1071 %
1072 %      void ClosestColor(const Image *image,CubeInfo *cube_info,
1073 %        const NodeInfo *node_info)
1074 %
1075 %  A description of each parameter follows.
1076 %
1077 %    o image: the image.
1078 %
1079 %    o cube_info: A pointer to the Cube structure.
1080 %
1081 %    o node_info: the address of a structure of type NodeInfo which points to a
1082 %      node in the color cube tree that is to be pruned.
1083 %
1084 */
1085 static void ClosestColor(const Image *image,CubeInfo *cube_info,
1086   const NodeInfo *node_info)
1087 {
1088   register ssize_t
1089     i;
1090
1091   size_t
1092     number_children;
1093
1094   /*
1095     Traverse any children.
1096   */
1097   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
1098   for (i=0; i < (ssize_t) number_children; i++)
1099     if (node_info->child[i] != (NodeInfo *) NULL)
1100       ClosestColor(image,cube_info,node_info->child[i]);
1101   if (node_info->number_unique != 0)
1102     {
1103       double
1104         pixel;
1105
1106       register double
1107         alpha,
1108         beta,
1109         distance;
1110
1111       register PixelInfo
1112         *restrict p;
1113
1114       register RealPixelInfo
1115         *restrict q;
1116
1117       /*
1118         Determine if this color is "closest".
1119       */
1120       p=image->colormap+node_info->color_number;
1121       q=(&cube_info->target);
1122       alpha=1.0;
1123       beta=1.0;
1124       if (cube_info->associate_alpha != MagickFalse)
1125         {
1126           alpha=(double) (QuantumScale*p->alpha);
1127           beta=(double) (QuantumScale*q->alpha);
1128         }
1129       pixel=alpha*p->red-beta*q->red;
1130       distance=pixel*pixel;
1131       if (distance <= cube_info->distance)
1132         {
1133           pixel=alpha*p->green-beta*q->green;
1134           distance+=pixel*pixel;
1135           if (distance <= cube_info->distance)
1136             {
1137               pixel=alpha*p->blue-beta*q->blue;
1138               distance+=pixel*pixel;
1139               if (distance <= cube_info->distance)
1140                 {
1141                   pixel=alpha-beta;
1142                   distance+=pixel*pixel;
1143                   if (distance <= cube_info->distance)
1144                     {
1145                       cube_info->distance=distance;
1146                       cube_info->color_number=node_info->color_number;
1147                     }
1148                 }
1149             }
1150         }
1151     }
1152 }
1153 \f
1154 /*
1155 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1156 %                                                                             %
1157 %                                                                             %
1158 %                                                                             %
1159 %   C o m p r e s s I m a g e C o l o r m a p                                 %
1160 %                                                                             %
1161 %                                                                             %
1162 %                                                                             %
1163 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1164 %
1165 %  CompressImageColormap() compresses an image colormap by removing any
1166 %  duplicate or unused color entries.
1167 %
1168 %  The format of the CompressImageColormap method is:
1169 %
1170 %      MagickBooleanType CompressImageColormap(Image *image,
1171 %        ExceptionInfo *exception)
1172 %
1173 %  A description of each parameter follows:
1174 %
1175 %    o image: the image.
1176 %
1177 %    o exception: return any errors or warnings in this structure.
1178 %
1179 */
1180 MagickExport MagickBooleanType CompressImageColormap(Image *image,
1181   ExceptionInfo *exception)
1182 {
1183   QuantizeInfo
1184     quantize_info;
1185
1186   assert(image != (Image *) NULL);
1187   assert(image->signature == MagickSignature);
1188   if (image->debug != MagickFalse)
1189     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1190   if (IsPaletteImage(image,exception) == MagickFalse)
1191     return(MagickFalse);
1192   GetQuantizeInfo(&quantize_info);
1193   quantize_info.number_colors=image->colors;
1194   quantize_info.tree_depth=MaxTreeDepth;
1195   return(QuantizeImage(&quantize_info,image,exception));
1196 }
1197 \f
1198 /*
1199 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1200 %                                                                             %
1201 %                                                                             %
1202 %                                                                             %
1203 +   D e f i n e I m a g e C o l o r m a p                                     %
1204 %                                                                             %
1205 %                                                                             %
1206 %                                                                             %
1207 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1208 %
1209 %  DefineImageColormap() traverses the color cube tree and notes each colormap
1210 %  entry.  A colormap entry is any node in the color cube tree where the
1211 %  of unique colors is not zero.  DefineImageColormap() returns the number of
1212 %  colors in the image colormap.
1213 %
1214 %  The format of the DefineImageColormap method is:
1215 %
1216 %      size_t DefineImageColormap(Image *image,CubeInfo *cube_info,
1217 %        NodeInfo *node_info)
1218 %
1219 %  A description of each parameter follows.
1220 %
1221 %    o image: the image.
1222 %
1223 %    o cube_info: A pointer to the Cube structure.
1224 %
1225 %    o node_info: the address of a structure of type NodeInfo which points to a
1226 %      node in the color cube tree that is to be pruned.
1227 %
1228 */
1229 static size_t DefineImageColormap(Image *image,CubeInfo *cube_info,
1230   NodeInfo *node_info)
1231 {
1232   register ssize_t
1233     i;
1234
1235   size_t
1236     number_children;
1237
1238   /*
1239     Traverse any children.
1240   */
1241   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
1242   for (i=0; i < (ssize_t) number_children; i++)
1243     if (node_info->child[i] != (NodeInfo *) NULL)
1244       (void) DefineImageColormap(image,cube_info,node_info->child[i]);
1245   if (node_info->number_unique != 0)
1246     {
1247       register double
1248         alpha;
1249
1250       register PixelInfo
1251         *restrict q;
1252
1253       /*
1254         Colormap entry is defined by the mean color in this cube.
1255       */
1256       q=image->colormap+image->colors;
1257       alpha=(double) ((MagickOffsetType) node_info->number_unique);
1258       alpha=PerceptibleReciprocal(alpha);
1259       if (cube_info->associate_alpha == MagickFalse)
1260         {
1261           q->red=(double) ClampToQuantum(alpha*QuantumRange*
1262             node_info->total_color.red);
1263           q->green=(double) ClampToQuantum(alpha*QuantumRange*
1264             node_info->total_color.green);
1265           q->blue=(double) ClampToQuantum(alpha*QuantumRange*
1266             node_info->total_color.blue);
1267           q->alpha=(double) OpaqueAlpha;
1268         }
1269       else
1270         {
1271           double
1272             opacity;
1273
1274           opacity=(double) (alpha*QuantumRange*node_info->total_color.alpha);
1275           q->alpha=(double) ClampToQuantum((opacity));
1276           if (q->alpha == OpaqueAlpha)
1277             {
1278               q->red=(double) ClampToQuantum(alpha*QuantumRange*
1279                 node_info->total_color.red);
1280               q->green=(double) ClampToQuantum(alpha*QuantumRange*
1281                 node_info->total_color.green);
1282               q->blue=(double) ClampToQuantum(alpha*QuantumRange*
1283                 node_info->total_color.blue);
1284             }
1285           else
1286             {
1287               double
1288                 gamma;
1289
1290               gamma=(double) (QuantumScale*q->alpha);
1291               gamma=PerceptibleReciprocal(gamma);
1292               q->red=(double) ClampToQuantum(alpha*gamma*QuantumRange*
1293                 node_info->total_color.red);
1294               q->green=(double) ClampToQuantum(alpha*gamma*QuantumRange*
1295                 node_info->total_color.green);
1296               q->blue=(double) ClampToQuantum(alpha*gamma*QuantumRange*
1297                 node_info->total_color.blue);
1298               if (node_info->number_unique > cube_info->transparent_pixels)
1299                 {
1300                   cube_info->transparent_pixels=node_info->number_unique;
1301                   cube_info->transparent_index=(ssize_t) image->colors;
1302                 }
1303             }
1304         }
1305       node_info->color_number=image->colors++;
1306     }
1307   return(image->colors);
1308 }
1309 \f
1310 /*
1311 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1312 %                                                                             %
1313 %                                                                             %
1314 %                                                                             %
1315 +   D e s t r o y C u b e I n f o                                             %
1316 %                                                                             %
1317 %                                                                             %
1318 %                                                                             %
1319 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1320 %
1321 %  DestroyCubeInfo() deallocates memory associated with an image.
1322 %
1323 %  The format of the DestroyCubeInfo method is:
1324 %
1325 %      DestroyCubeInfo(CubeInfo *cube_info)
1326 %
1327 %  A description of each parameter follows:
1328 %
1329 %    o cube_info: the address of a structure of type CubeInfo.
1330 %
1331 */
1332 static void DestroyCubeInfo(CubeInfo *cube_info)
1333 {
1334   register Nodes
1335     *nodes;
1336
1337   /*
1338     Release color cube tree storage.
1339   */
1340   do
1341   {
1342     nodes=cube_info->node_queue->next;
1343     cube_info->node_queue->nodes=(NodeInfo *) RelinquishMagickMemory(
1344       cube_info->node_queue->nodes);
1345     cube_info->node_queue=(Nodes *) RelinquishMagickMemory(
1346       cube_info->node_queue);
1347     cube_info->node_queue=nodes;
1348   } while (cube_info->node_queue != (Nodes *) NULL);
1349   if (cube_info->cache != (ssize_t *) NULL)
1350     cube_info->cache=(ssize_t *) RelinquishMagickMemory(cube_info->cache);
1351   cube_info->quantize_info=DestroyQuantizeInfo(cube_info->quantize_info);
1352   cube_info=(CubeInfo *) RelinquishMagickMemory(cube_info);
1353 }
1354 \f
1355 /*
1356 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1357 %                                                                             %
1358 %                                                                             %
1359 %                                                                             %
1360 %   D e s t r o y Q u a n t i z e I n f o                                     %
1361 %                                                                             %
1362 %                                                                             %
1363 %                                                                             %
1364 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1365 %
1366 %  DestroyQuantizeInfo() deallocates memory associated with an QuantizeInfo
1367 %  structure.
1368 %
1369 %  The format of the DestroyQuantizeInfo method is:
1370 %
1371 %      QuantizeInfo *DestroyQuantizeInfo(QuantizeInfo *quantize_info)
1372 %
1373 %  A description of each parameter follows:
1374 %
1375 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
1376 %
1377 */
1378 MagickExport QuantizeInfo *DestroyQuantizeInfo(QuantizeInfo *quantize_info)
1379 {
1380   (void) LogMagickEvent(TraceEvent,GetMagickModule(),"...");
1381   assert(quantize_info != (QuantizeInfo *) NULL);
1382   assert(quantize_info->signature == MagickSignature);
1383   quantize_info->signature=(~MagickSignature);
1384   quantize_info=(QuantizeInfo *) RelinquishMagickMemory(quantize_info);
1385   return(quantize_info);
1386 }
1387 \f
1388 /*
1389 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1390 %                                                                             %
1391 %                                                                             %
1392 %                                                                             %
1393 +   D i t h e r I m a g e                                                     %
1394 %                                                                             %
1395 %                                                                             %
1396 %                                                                             %
1397 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1398 %
1399 %  DitherImage() distributes the difference between an original image and
1400 %  the corresponding color reduced algorithm to neighboring pixels using
1401 %  serpentine-scan Floyd-Steinberg error diffusion. DitherImage returns
1402 %  MagickTrue if the image is dithered otherwise MagickFalse.
1403 %
1404 %  The format of the DitherImage method is:
1405 %
1406 %      MagickBooleanType DitherImage(Image *image,CubeInfo *cube_info,
1407 %        ExceptionInfo *exception)
1408 %
1409 %  A description of each parameter follows.
1410 %
1411 %    o image: the image.
1412 %
1413 %    o cube_info: A pointer to the Cube structure.
1414 %
1415 %    o exception: return any errors or warnings in this structure.
1416 %
1417 */
1418
1419 static RealPixelInfo **DestroyPixelThreadSet(RealPixelInfo **pixels)
1420 {
1421   register ssize_t
1422     i;
1423
1424   assert(pixels != (RealPixelInfo **) NULL);
1425   for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
1426     if (pixels[i] != (RealPixelInfo *) NULL)
1427       pixels[i]=(RealPixelInfo *) RelinquishMagickMemory(pixels[i]);
1428   pixels=(RealPixelInfo **) RelinquishMagickMemory(pixels);
1429   return(pixels);
1430 }
1431
1432 static RealPixelInfo **AcquirePixelThreadSet(const size_t count)
1433 {
1434   RealPixelInfo
1435     **pixels;
1436
1437   register ssize_t
1438     i;
1439
1440   size_t
1441     number_threads;
1442
1443   number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
1444   pixels=(RealPixelInfo **) AcquireQuantumMemory(number_threads,
1445     sizeof(*pixels));
1446   if (pixels == (RealPixelInfo **) NULL)
1447     return((RealPixelInfo **) NULL);
1448   (void) ResetMagickMemory(pixels,0,number_threads*sizeof(*pixels));
1449   for (i=0; i < (ssize_t) number_threads; i++)
1450   {
1451     pixels[i]=(RealPixelInfo *) AcquireQuantumMemory(count,2*sizeof(**pixels));
1452     if (pixels[i] == (RealPixelInfo *) NULL)
1453       return(DestroyPixelThreadSet(pixels));
1454   }
1455   return(pixels);
1456 }
1457
1458 static inline ssize_t CacheOffset(CubeInfo *cube_info,
1459   const RealPixelInfo *pixel)
1460 {
1461 #define RedShift(pixel) (((pixel) >> CacheShift) << (0*(8-CacheShift)))
1462 #define GreenShift(pixel) (((pixel) >> CacheShift) << (1*(8-CacheShift)))
1463 #define BlueShift(pixel) (((pixel) >> CacheShift) << (2*(8-CacheShift)))
1464 #define AlphaShift(pixel) (((pixel) >> CacheShift) << (3*(8-CacheShift)))
1465
1466   ssize_t
1467     offset;
1468
1469   offset=(ssize_t) (RedShift(ScaleQuantumToChar(ClampPixel(pixel->red))) |
1470     GreenShift(ScaleQuantumToChar(ClampPixel(pixel->green))) |
1471     BlueShift(ScaleQuantumToChar(ClampPixel(pixel->blue))));
1472   if (cube_info->associate_alpha != MagickFalse)
1473     offset|=AlphaShift(ScaleQuantumToChar(ClampPixel(pixel->alpha)));
1474   return(offset);
1475 }
1476
1477 static MagickBooleanType FloydSteinbergDither(Image *image,CubeInfo *cube_info,
1478   ExceptionInfo *exception)
1479 {
1480 #define DitherImageTag  "Dither/Image"
1481
1482   CacheView
1483     *image_view;
1484
1485   MagickBooleanType
1486     status;
1487
1488   RealPixelInfo
1489     **pixels;
1490
1491   ssize_t
1492     y;
1493
1494   /*
1495     Distribute quantization error using Floyd-Steinberg.
1496   */
1497   pixels=AcquirePixelThreadSet(image->columns);
1498   if (pixels == (RealPixelInfo **) NULL)
1499     return(MagickFalse);
1500   status=MagickTrue;
1501   image_view=AcquireAuthenticCacheView(image,exception);
1502   for (y=0; y < (ssize_t) image->rows; y++)
1503   {
1504     const int
1505       id = GetOpenMPThreadId();
1506
1507     CubeInfo
1508       cube;
1509
1510     RealPixelInfo
1511       *current,
1512       *previous;
1513
1514     register Quantum
1515       *restrict q;
1516
1517     register ssize_t
1518       x;
1519
1520     size_t
1521       index;
1522
1523     ssize_t
1524       v;
1525
1526     if (status == MagickFalse)
1527       continue;
1528     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
1529     if (q == (Quantum *) NULL)
1530       {
1531         status=MagickFalse;
1532         continue;
1533       }
1534     q+=(y & 0x01)*image->columns*GetPixelChannels(image);
1535     cube=(*cube_info);
1536     current=pixels[id]+(y & 0x01)*image->columns;
1537     previous=pixels[id]+((y+1) & 0x01)*image->columns;
1538     v=(ssize_t) ((y & 0x01) != 0 ? -1 : 1);
1539     for (x=0; x < (ssize_t) image->columns; x++)
1540     {
1541       RealPixelInfo
1542         color,
1543         pixel;
1544
1545       register ssize_t
1546         i;
1547
1548       ssize_t
1549         u;
1550
1551       q-=(y & 0x01)*GetPixelChannels(image);
1552       u=(y & 0x01) != 0 ? (ssize_t) image->columns-1-x : x;
1553       AssociateAlphaPixel(image,&cube,q,&pixel);
1554       if (x > 0)
1555         {
1556           pixel.red+=7*current[u-v].red/16;
1557           pixel.green+=7*current[u-v].green/16;
1558           pixel.blue+=7*current[u-v].blue/16;
1559           if (cube.associate_alpha != MagickFalse)
1560             pixel.alpha+=7*current[u-v].alpha/16;
1561         }
1562       if (y > 0)
1563         {
1564           if (x < (ssize_t) (image->columns-1))
1565             {
1566               pixel.red+=previous[u+v].red/16;
1567               pixel.green+=previous[u+v].green/16;
1568               pixel.blue+=previous[u+v].blue/16;
1569               if (cube.associate_alpha != MagickFalse)
1570                 pixel.alpha+=previous[u+v].alpha/16;
1571             }
1572           pixel.red+=5*previous[u].red/16;
1573           pixel.green+=5*previous[u].green/16;
1574           pixel.blue+=5*previous[u].blue/16;
1575           if (cube.associate_alpha != MagickFalse)
1576             pixel.alpha+=5*previous[u].alpha/16;
1577           if (x > 0)
1578             {
1579               pixel.red+=3*previous[u-v].red/16;
1580               pixel.green+=3*previous[u-v].green/16;
1581               pixel.blue+=3*previous[u-v].blue/16;
1582               if (cube.associate_alpha != MagickFalse)
1583                 pixel.alpha+=3*previous[u-v].alpha/16;
1584             }
1585         }
1586       pixel.red=(double) ClampPixel(pixel.red);
1587       pixel.green=(double) ClampPixel(pixel.green);
1588       pixel.blue=(double) ClampPixel(pixel.blue);
1589       if (cube.associate_alpha != MagickFalse)
1590         pixel.alpha=(double) ClampPixel(pixel.alpha);
1591       i=CacheOffset(&cube,&pixel);
1592       if (cube.cache[i] < 0)
1593         {
1594           register NodeInfo
1595             *node_info;
1596
1597           register size_t
1598             id;
1599
1600           /*
1601             Identify the deepest node containing the pixel's color.
1602           */
1603           node_info=cube.root;
1604           for (index=MaxTreeDepth-1; (ssize_t) index > 0; index--)
1605           {
1606             id=ColorToNodeId(&cube,&pixel,index);
1607             if (node_info->child[id] == (NodeInfo *) NULL)
1608               break;
1609             node_info=node_info->child[id];
1610           }
1611           /*
1612             Find closest color among siblings and their children.
1613           */
1614           cube.target=pixel;
1615           cube.distance=(double) (4.0*(QuantumRange+1.0)*(QuantumRange+1.0)+
1616             1.0);
1617           ClosestColor(image,&cube,node_info->parent);
1618           cube.cache[i]=(ssize_t) cube.color_number;
1619         }
1620       /*
1621         Assign pixel to closest colormap entry.
1622       */
1623       index=(size_t) cube.cache[i];
1624       if (image->storage_class == PseudoClass)
1625         SetPixelIndex(image,(Quantum) index,q);
1626       if (cube.quantize_info->measure_error == MagickFalse)
1627         {
1628           SetPixelRed(image,ClampToQuantum(image->colormap[index].red),q);
1629           SetPixelGreen(image,ClampToQuantum(image->colormap[index].green),q);
1630           SetPixelBlue(image,ClampToQuantum(image->colormap[index].blue),q);
1631           if (cube.associate_alpha != MagickFalse)
1632             SetPixelAlpha(image,ClampToQuantum(image->colormap[index].alpha),q);
1633         }
1634       if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1635         status=MagickFalse;
1636       /*
1637         Store the error.
1638       */
1639       AssociateAlphaPixelInfo(image,&cube,image->colormap+index,&color);
1640       current[u].red=pixel.red-color.red;
1641       current[u].green=pixel.green-color.green;
1642       current[u].blue=pixel.blue-color.blue;
1643       if (cube.associate_alpha != MagickFalse)
1644         current[u].alpha=pixel.alpha-color.alpha;
1645       if (image->progress_monitor != (MagickProgressMonitor) NULL)
1646         {
1647           MagickBooleanType
1648             proceed;
1649
1650 #if defined(MAGICKCORE_OPENMP_SUPPORT)
1651           #pragma omp critical (MagickCore_FloydSteinbergDither)
1652 #endif
1653           proceed=SetImageProgress(image,DitherImageTag,(MagickOffsetType) y,
1654             image->rows);
1655           if (proceed == MagickFalse)
1656             status=MagickFalse;
1657         }
1658       q+=((y+1) & 0x01)*GetPixelChannels(image);
1659     }
1660   }
1661   image_view=DestroyCacheView(image_view);
1662   pixels=DestroyPixelThreadSet(pixels);
1663   return(MagickTrue);
1664 }
1665
1666 static MagickBooleanType
1667   RiemersmaDither(Image *,CacheView *,CubeInfo *,const unsigned int,
1668     ExceptionInfo *exception);
1669
1670 static void Riemersma(Image *image,CacheView *image_view,CubeInfo *cube_info,
1671   const size_t level,const unsigned int direction,ExceptionInfo *exception)
1672 {
1673   if (level == 1)
1674     switch (direction)
1675     {
1676       case WestGravity:
1677       {
1678         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1679           exception);
1680         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1681           exception);
1682         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1683           exception);
1684         break;
1685       }
1686       case EastGravity:
1687       {
1688         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1689           exception);
1690         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1691           exception);
1692         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1693           exception);
1694         break;
1695       }
1696       case NorthGravity:
1697       {
1698         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1699           exception);
1700         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1701           exception);
1702         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1703           exception);
1704         break;
1705       }
1706       case SouthGravity:
1707       {
1708         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1709           exception);
1710         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1711           exception);
1712         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1713           exception);
1714         break;
1715       }
1716       default:
1717         break;
1718     }
1719   else
1720     switch (direction)
1721     {
1722       case WestGravity:
1723       {
1724         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1725           exception);
1726         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1727           exception);
1728         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1729           exception);
1730         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1731           exception);
1732         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1733           exception);
1734         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1735           exception);
1736         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1737           exception);
1738         break;
1739       }
1740       case EastGravity:
1741       {
1742         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1743           exception);
1744         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1745           exception);
1746         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1747           exception);
1748         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1749           exception);
1750         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1751           exception);
1752         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1753           exception);
1754         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1755           exception);
1756         break;
1757       }
1758       case NorthGravity:
1759       {
1760         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1761           exception);
1762         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1763           exception);
1764         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1765           exception);
1766         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1767           exception);
1768         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1769           exception);
1770         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1771           exception);
1772         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1773           exception);
1774         break;
1775       }
1776       case SouthGravity:
1777       {
1778         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1779           exception);
1780         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1781           exception);
1782         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1783           exception);
1784         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1785           exception);
1786         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1787           exception);
1788         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1789           exception);
1790         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1791           exception);
1792         break;
1793       }
1794       default:
1795         break;
1796     }
1797 }
1798
1799 static MagickBooleanType RiemersmaDither(Image *image,CacheView *image_view,
1800   CubeInfo *cube_info,const unsigned int direction,ExceptionInfo *exception)
1801 {
1802 #define DitherImageTag  "Dither/Image"
1803
1804   MagickBooleanType
1805     proceed;
1806
1807   RealPixelInfo
1808     color,
1809     pixel;
1810
1811   register CubeInfo
1812     *p;
1813
1814   size_t
1815     index;
1816
1817   p=cube_info;
1818   if ((p->x >= 0) && (p->x < (ssize_t) image->columns) &&
1819       (p->y >= 0) && (p->y < (ssize_t) image->rows))
1820     {
1821       register Quantum
1822         *restrict q;
1823
1824       register ssize_t
1825         i;
1826
1827       /*
1828         Distribute error.
1829       */
1830       q=GetCacheViewAuthenticPixels(image_view,p->x,p->y,1,1,exception);
1831       if (q == (Quantum *) NULL)
1832         return(MagickFalse);
1833       AssociateAlphaPixel(image,cube_info,q,&pixel);
1834       for (i=0; i < ErrorQueueLength; i++)
1835       {
1836         pixel.red+=p->weights[i]*p->error[i].red;
1837         pixel.green+=p->weights[i]*p->error[i].green;
1838         pixel.blue+=p->weights[i]*p->error[i].blue;
1839         if (cube_info->associate_alpha != MagickFalse)
1840           pixel.alpha+=p->weights[i]*p->error[i].alpha;
1841       }
1842       pixel.red=(double) ClampPixel(pixel.red);
1843       pixel.green=(double) ClampPixel(pixel.green);
1844       pixel.blue=(double) ClampPixel(pixel.blue);
1845       if (cube_info->associate_alpha != MagickFalse)
1846         pixel.alpha=(double) ClampPixel(pixel.alpha);
1847       i=CacheOffset(cube_info,&pixel);
1848       if (p->cache[i] < 0)
1849         {
1850           register NodeInfo
1851             *node_info;
1852
1853           register size_t
1854             id;
1855
1856           /*
1857             Identify the deepest node containing the pixel's color.
1858           */
1859           node_info=p->root;
1860           for (index=MaxTreeDepth-1; (ssize_t) index > 0; index--)
1861           {
1862             id=ColorToNodeId(cube_info,&pixel,index);
1863             if (node_info->child[id] == (NodeInfo *) NULL)
1864               break;
1865             node_info=node_info->child[id];
1866           }
1867           node_info=node_info->parent;
1868           /*
1869             Find closest color among siblings and their children.
1870           */
1871           p->target=pixel;
1872           p->distance=(double) (4.0*(QuantumRange+1.0)*((double)
1873             QuantumRange+1.0)+1.0);
1874           ClosestColor(image,p,node_info->parent);
1875           p->cache[i]=(ssize_t) p->color_number;
1876         }
1877       /*
1878         Assign pixel to closest colormap entry.
1879       */
1880       index=(size_t) p->cache[i];
1881       if (image->storage_class == PseudoClass)
1882         SetPixelIndex(image,(Quantum) index,q);
1883       if (cube_info->quantize_info->measure_error == MagickFalse)
1884         {
1885           SetPixelRed(image,ClampToQuantum(image->colormap[index].red),q);
1886           SetPixelGreen(image,ClampToQuantum(image->colormap[index].green),q);
1887           SetPixelBlue(image,ClampToQuantum(image->colormap[index].blue),q);
1888           if (cube_info->associate_alpha != MagickFalse)
1889             SetPixelAlpha(image,ClampToQuantum(image->colormap[index].alpha),q);
1890         }
1891       if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1892         return(MagickFalse);
1893       /*
1894         Propagate the error as the last entry of the error queue.
1895       */
1896       (void) CopyMagickMemory(p->error,p->error+1,(ErrorQueueLength-1)*
1897         sizeof(p->error[0]));
1898       AssociateAlphaPixelInfo(image,cube_info,image->colormap+index,&color);
1899       p->error[ErrorQueueLength-1].red=pixel.red-color.red;
1900       p->error[ErrorQueueLength-1].green=pixel.green-color.green;
1901       p->error[ErrorQueueLength-1].blue=pixel.blue-color.blue;
1902       if (cube_info->associate_alpha != MagickFalse)
1903         p->error[ErrorQueueLength-1].alpha=pixel.alpha-color.alpha;
1904       proceed=SetImageProgress(image,DitherImageTag,p->offset,p->span);
1905       if (proceed == MagickFalse)
1906         return(MagickFalse);
1907       p->offset++;
1908     }
1909   switch (direction)
1910   {
1911     case WestGravity: p->x--; break;
1912     case EastGravity: p->x++; break;
1913     case NorthGravity: p->y--; break;
1914     case SouthGravity: p->y++; break;
1915   }
1916   return(MagickTrue);
1917 }
1918
1919 static inline ssize_t MagickMax(const ssize_t x,const ssize_t y)
1920 {
1921   if (x > y)
1922     return(x);
1923   return(y);
1924 }
1925
1926 static inline ssize_t MagickMin(const ssize_t x,const ssize_t y)
1927 {
1928   if (x < y)
1929     return(x);
1930   return(y);
1931 }
1932
1933 static MagickBooleanType DitherImage(Image *image,CubeInfo *cube_info,
1934   ExceptionInfo *exception)
1935 {
1936   CacheView
1937     *image_view;
1938
1939   MagickBooleanType
1940     status;
1941
1942   register ssize_t
1943     i;
1944
1945   size_t
1946     depth;
1947
1948   if (cube_info->quantize_info->dither_method != RiemersmaDitherMethod)
1949     return(FloydSteinbergDither(image,cube_info,exception));
1950   /*
1951     Distribute quantization error along a Hilbert curve.
1952   */
1953   (void) ResetMagickMemory(cube_info->error,0,ErrorQueueLength*
1954     sizeof(*cube_info->error));
1955   cube_info->x=0;
1956   cube_info->y=0;
1957   i=MagickMax((ssize_t) image->columns,(ssize_t) image->rows);
1958   for (depth=1; i != 0; depth++)
1959     i>>=1;
1960   if ((ssize_t) (1L << depth) < MagickMax((ssize_t) image->columns,(ssize_t) image->rows))
1961     depth++;
1962   cube_info->offset=0;
1963   cube_info->span=(MagickSizeType) image->columns*image->rows;
1964   image_view=AcquireAuthenticCacheView(image,exception);
1965   if (depth > 1)
1966     Riemersma(image,image_view,cube_info,depth-1,NorthGravity,exception);
1967   status=RiemersmaDither(image,image_view,cube_info,ForgetGravity,exception);
1968   image_view=DestroyCacheView(image_view);
1969   return(status);
1970 }
1971 \f
1972 /*
1973 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1974 %                                                                             %
1975 %                                                                             %
1976 %                                                                             %
1977 +   G e t C u b e I n f o                                                     %
1978 %                                                                             %
1979 %                                                                             %
1980 %                                                                             %
1981 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1982 %
1983 %  GetCubeInfo() initialize the Cube data structure.
1984 %
1985 %  The format of the GetCubeInfo method is:
1986 %
1987 %      CubeInfo GetCubeInfo(const QuantizeInfo *quantize_info,
1988 %        const size_t depth,const size_t maximum_colors)
1989 %
1990 %  A description of each parameter follows.
1991 %
1992 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
1993 %
1994 %    o depth: Normally, this integer value is zero or one.  A zero or
1995 %      one tells Quantize to choose a optimal tree depth of Log4(number_colors).
1996 %      A tree of this depth generally allows the best representation of the
1997 %      reference image with the least amount of memory and the fastest
1998 %      computational speed.  In some cases, such as an image with low color
1999 %      dispersion (a few number of colors), a value other than
2000 %      Log4(number_colors) is required.  To expand the color tree completely,
2001 %      use a value of 8.
2002 %
2003 %    o maximum_colors: maximum colors.
2004 %
2005 */
2006 static CubeInfo *GetCubeInfo(const QuantizeInfo *quantize_info,
2007   const size_t depth,const size_t maximum_colors)
2008 {
2009   CubeInfo
2010     *cube_info;
2011
2012   double
2013     sum,
2014     weight;
2015
2016   register ssize_t
2017     i;
2018
2019   size_t
2020     length;
2021
2022   /*
2023     Initialize tree to describe color cube_info.
2024   */
2025   cube_info=(CubeInfo *) AcquireMagickMemory(sizeof(*cube_info));
2026   if (cube_info == (CubeInfo *) NULL)
2027     return((CubeInfo *) NULL);
2028   (void) ResetMagickMemory(cube_info,0,sizeof(*cube_info));
2029   cube_info->depth=depth;
2030   if (cube_info->depth > MaxTreeDepth)
2031     cube_info->depth=MaxTreeDepth;
2032   if (cube_info->depth < 2)
2033     cube_info->depth=2;
2034   cube_info->maximum_colors=maximum_colors;
2035   /*
2036     Initialize root node.
2037   */
2038   cube_info->root=GetNodeInfo(cube_info,0,0,(NodeInfo *) NULL);
2039   if (cube_info->root == (NodeInfo *) NULL)
2040     return((CubeInfo *) NULL);
2041   cube_info->root->parent=cube_info->root;
2042   cube_info->quantize_info=CloneQuantizeInfo(quantize_info);
2043   if (cube_info->quantize_info->dither_method == NoDitherMethod)
2044     return(cube_info);
2045   /*
2046     Initialize dither resources.
2047   */
2048   length=(size_t) (1UL << (4*(8-CacheShift)));
2049   cube_info->cache=(ssize_t *) AcquireQuantumMemory(length,
2050     sizeof(*cube_info->cache));
2051   if (cube_info->cache == (ssize_t *) NULL)
2052     return((CubeInfo *) NULL);
2053   /*
2054     Initialize color cache.
2055   */
2056   for (i=0; i < (ssize_t) length; i++)
2057     cube_info->cache[i]=(-1);
2058   /*
2059     Distribute weights along a curve of exponential decay.
2060   */
2061   weight=1.0;
2062   for (i=0; i < ErrorQueueLength; i++)
2063   {
2064     cube_info->weights[ErrorQueueLength-i-1]=PerceptibleReciprocal(weight);
2065     weight*=exp(log(((double) QuantumRange+1.0))/(ErrorQueueLength-1.0));
2066   }
2067   /*
2068     Normalize the weighting factors.
2069   */
2070   weight=0.0;
2071   for (i=0; i < ErrorQueueLength; i++)
2072     weight+=cube_info->weights[i];
2073   sum=0.0;
2074   for (i=0; i < ErrorQueueLength; i++)
2075   {
2076     cube_info->weights[i]/=weight;
2077     sum+=cube_info->weights[i];
2078   }
2079   cube_info->weights[0]+=1.0-sum;
2080   return(cube_info);
2081 }
2082 \f
2083 /*
2084 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2085 %                                                                             %
2086 %                                                                             %
2087 %                                                                             %
2088 +   G e t N o d e I n f o                                                     %
2089 %                                                                             %
2090 %                                                                             %
2091 %                                                                             %
2092 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2093 %
2094 %  GetNodeInfo() allocates memory for a new node in the color cube tree and
2095 %  presets all fields to zero.
2096 %
2097 %  The format of the GetNodeInfo method is:
2098 %
2099 %      NodeInfo *GetNodeInfo(CubeInfo *cube_info,const size_t id,
2100 %        const size_t level,NodeInfo *parent)
2101 %
2102 %  A description of each parameter follows.
2103 %
2104 %    o node: The GetNodeInfo method returns a pointer to a queue of nodes.
2105 %
2106 %    o id: Specifies the child number of the node.
2107 %
2108 %    o level: Specifies the level in the storage_class the node resides.
2109 %
2110 */
2111 static NodeInfo *GetNodeInfo(CubeInfo *cube_info,const size_t id,
2112   const size_t level,NodeInfo *parent)
2113 {
2114   NodeInfo
2115     *node_info;
2116
2117   if (cube_info->free_nodes == 0)
2118     {
2119       Nodes
2120         *nodes;
2121
2122       /*
2123         Allocate a new queue of nodes.
2124       */
2125       nodes=(Nodes *) AcquireMagickMemory(sizeof(*nodes));
2126       if (nodes == (Nodes *) NULL)
2127         return((NodeInfo *) NULL);
2128       nodes->nodes=(NodeInfo *) AcquireQuantumMemory(NodesInAList,
2129         sizeof(*nodes->nodes));
2130       if (nodes->nodes == (NodeInfo *) NULL)
2131         return((NodeInfo *) NULL);
2132       nodes->next=cube_info->node_queue;
2133       cube_info->node_queue=nodes;
2134       cube_info->next_node=nodes->nodes;
2135       cube_info->free_nodes=NodesInAList;
2136     }
2137   cube_info->nodes++;
2138   cube_info->free_nodes--;
2139   node_info=cube_info->next_node++;
2140   (void) ResetMagickMemory(node_info,0,sizeof(*node_info));
2141   node_info->parent=parent;
2142   node_info->id=id;
2143   node_info->level=level;
2144   return(node_info);
2145 }
2146 \f
2147 /*
2148 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2149 %                                                                             %
2150 %                                                                             %
2151 %                                                                             %
2152 %  G e t I m a g e Q u a n t i z e E r r o r                                  %
2153 %                                                                             %
2154 %                                                                             %
2155 %                                                                             %
2156 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2157 %
2158 %  GetImageQuantizeError() measures the difference between the original
2159 %  and quantized images.  This difference is the total quantization error.
2160 %  The error is computed by summing over all pixels in an image the distance
2161 %  squared in RGB space between each reference pixel value and its quantized
2162 %  value.  These values are computed:
2163 %
2164 %    o mean_error_per_pixel:  This value is the mean error for any single
2165 %      pixel in the image.
2166 %
2167 %    o normalized_mean_square_error:  This value is the normalized mean
2168 %      quantization error for any single pixel in the image.  This distance
2169 %      measure is normalized to a range between 0 and 1.  It is independent
2170 %      of the range of red, green, and blue values in the image.
2171 %
2172 %    o normalized_maximum_square_error:  Thsi value is the normalized
2173 %      maximum quantization error for any single pixel in the image.  This
2174 %      distance measure is normalized to a range between 0 and 1.  It is
2175 %      independent of the range of red, green, and blue values in your image.
2176 %
2177 %  The format of the GetImageQuantizeError method is:
2178 %
2179 %      MagickBooleanType GetImageQuantizeError(Image *image,
2180 %        ExceptionInfo *exception)
2181 %
2182 %  A description of each parameter follows.
2183 %
2184 %    o image: the image.
2185 %
2186 %    o exception: return any errors or warnings in this structure.
2187 %
2188 */
2189 MagickExport MagickBooleanType GetImageQuantizeError(Image *image,
2190   ExceptionInfo *exception)
2191 {
2192   CacheView
2193     *image_view;
2194
2195   double
2196     alpha,
2197     area,
2198     beta,
2199     distance,
2200     maximum_error,
2201     mean_error,
2202     mean_error_per_pixel;
2203
2204   size_t
2205     index;
2206
2207   ssize_t
2208     y;
2209
2210   assert(image != (Image *) NULL);
2211   assert(image->signature == MagickSignature);
2212   if (image->debug != MagickFalse)
2213     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2214   image->total_colors=GetNumberColors(image,(FILE *) NULL,exception);
2215   (void) ResetMagickMemory(&image->error,0,sizeof(image->error));
2216   if (image->storage_class == DirectClass)
2217     return(MagickTrue);
2218   alpha=1.0;
2219   beta=1.0;
2220   area=3.0*image->columns*image->rows;
2221   maximum_error=0.0;
2222   mean_error_per_pixel=0.0;
2223   mean_error=0.0;
2224   image_view=AcquireVirtualCacheView(image,exception);
2225   for (y=0; y < (ssize_t) image->rows; y++)
2226   {
2227     register const Quantum
2228       *restrict p;
2229
2230     register ssize_t
2231       x;
2232
2233     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
2234     if (p == (const Quantum *) NULL)
2235       break;
2236     for (x=0; x < (ssize_t) image->columns; x++)
2237     {
2238       index=1UL*GetPixelIndex(image,p);
2239       if (image->alpha_trait == BlendPixelTrait)
2240         {
2241           alpha=(double) (QuantumScale*GetPixelAlpha(image,p));
2242           beta=(double) (QuantumScale*image->colormap[index].alpha);
2243         }
2244       distance=fabs(alpha*GetPixelRed(image,p)-beta*
2245         image->colormap[index].red);
2246       mean_error_per_pixel+=distance;
2247       mean_error+=distance*distance;
2248       if (distance > maximum_error)
2249         maximum_error=distance;
2250       distance=fabs(alpha*GetPixelGreen(image,p)-beta*
2251         image->colormap[index].green);
2252       mean_error_per_pixel+=distance;
2253       mean_error+=distance*distance;
2254       if (distance > maximum_error)
2255         maximum_error=distance;
2256       distance=fabs(alpha*GetPixelBlue(image,p)-beta*
2257         image->colormap[index].blue);
2258       mean_error_per_pixel+=distance;
2259       mean_error+=distance*distance;
2260       if (distance > maximum_error)
2261         maximum_error=distance;
2262       p+=GetPixelChannels(image);
2263     }
2264   }
2265   image_view=DestroyCacheView(image_view);
2266   image->error.mean_error_per_pixel=(double) mean_error_per_pixel/area;
2267   image->error.normalized_mean_error=(double) QuantumScale*QuantumScale*
2268     mean_error/area;
2269   image->error.normalized_maximum_error=(double) QuantumScale*maximum_error;
2270   return(MagickTrue);
2271 }
2272 \f
2273 /*
2274 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2275 %                                                                             %
2276 %                                                                             %
2277 %                                                                             %
2278 %   G e t Q u a n t i z e I n f o                                             %
2279 %                                                                             %
2280 %                                                                             %
2281 %                                                                             %
2282 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2283 %
2284 %  GetQuantizeInfo() initializes the QuantizeInfo structure.
2285 %
2286 %  The format of the GetQuantizeInfo method is:
2287 %
2288 %      GetQuantizeInfo(QuantizeInfo *quantize_info)
2289 %
2290 %  A description of each parameter follows:
2291 %
2292 %    o quantize_info: Specifies a pointer to a QuantizeInfo structure.
2293 %
2294 */
2295 MagickExport void GetQuantizeInfo(QuantizeInfo *quantize_info)
2296 {
2297   (void) LogMagickEvent(TraceEvent,GetMagickModule(),"...");
2298   assert(quantize_info != (QuantizeInfo *) NULL);
2299   (void) ResetMagickMemory(quantize_info,0,sizeof(*quantize_info));
2300   quantize_info->number_colors=256;
2301   quantize_info->dither_method=RiemersmaDitherMethod;
2302   quantize_info->colorspace=UndefinedColorspace;
2303   quantize_info->measure_error=MagickFalse;
2304   quantize_info->signature=MagickSignature;
2305 }
2306 \f
2307 /*
2308 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2309 %                                                                             %
2310 %                                                                             %
2311 %                                                                             %
2312 %     P o s t e r i z e I m a g e                                             %
2313 %                                                                             %
2314 %                                                                             %
2315 %                                                                             %
2316 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2317 %
2318 %  PosterizeImage() reduces the image to a limited number of colors for a
2319 %  "poster" effect.
2320 %
2321 %  The format of the PosterizeImage method is:
2322 %
2323 %      MagickBooleanType PosterizeImage(Image *image,const size_t levels,
2324 %        const DitherMethod dither_method,ExceptionInfo *exception)
2325 %
2326 %  A description of each parameter follows:
2327 %
2328 %    o image: Specifies a pointer to an Image structure.
2329 %
2330 %    o levels: Number of color levels allowed in each channel.  Very low values
2331 %      (2, 3, or 4) have the most visible effect.
2332 %
2333 %    o dither_method: choose from UndefinedDitherMethod, NoDitherMethod,
2334 %      RiemersmaDitherMethod, FloydSteinbergDitherMethod.
2335 %
2336 %    o exception: return any errors or warnings in this structure.
2337 %
2338 */
2339
2340 static inline ssize_t MagickRound(double x)
2341 {
2342   /*
2343     Round the fraction to nearest integer.
2344   */
2345   if (x >= 0.0)
2346     return((ssize_t) (x+0.5));
2347   return((ssize_t) (x-0.5));
2348 }
2349
2350 MagickExport MagickBooleanType PosterizeImage(Image *image,const size_t levels,
2351   const DitherMethod dither_method,ExceptionInfo *exception)
2352 {
2353 #define PosterizeImageTag  "Posterize/Image"
2354 #define PosterizePixel(pixel) (Quantum) (QuantumRange*(MagickRound( \
2355   QuantumScale*pixel*(levels-1)))/MagickMax((ssize_t) levels-1,1))
2356
2357   CacheView
2358     *image_view;
2359
2360   MagickBooleanType
2361     status;
2362
2363   MagickOffsetType
2364     progress;
2365
2366   QuantizeInfo
2367     *quantize_info;
2368
2369   register ssize_t
2370     i;
2371
2372   ssize_t
2373     y;
2374
2375   assert(image != (Image *) NULL);
2376   assert(image->signature == MagickSignature);
2377   if (image->debug != MagickFalse)
2378     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2379   if (image->storage_class == PseudoClass)
2380 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2381     #pragma omp parallel for schedule(static,4) shared(progress,status) \
2382       magick_threads(image,image,1,1)
2383 #endif
2384     for (i=0; i < (ssize_t) image->colors; i++)
2385     {
2386       /*
2387         Posterize colormap.
2388       */
2389       if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2390         image->colormap[i].red=(double)
2391           PosterizePixel(image->colormap[i].red);
2392       if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2393         image->colormap[i].green=(double)
2394           PosterizePixel(image->colormap[i].green);
2395       if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2396         image->colormap[i].blue=(double)
2397           PosterizePixel(image->colormap[i].blue);
2398       if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
2399         image->colormap[i].alpha=(double)
2400           PosterizePixel(image->colormap[i].alpha);
2401     }
2402   /*
2403     Posterize image.
2404   */
2405   status=MagickTrue;
2406   progress=0;
2407   image_view=AcquireAuthenticCacheView(image,exception);
2408 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2409   #pragma omp parallel for schedule(static,4) shared(progress,status) \
2410     magick_threads(image,image,image->rows,1)
2411 #endif
2412   for (y=0; y < (ssize_t) image->rows; y++)
2413   {
2414     register Quantum
2415       *restrict q;
2416
2417     register ssize_t
2418       x;
2419
2420     if (status == MagickFalse)
2421       continue;
2422     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
2423     if (q == (Quantum *) NULL)
2424       {
2425         status=MagickFalse;
2426         continue;
2427       }
2428     for (x=0; x < (ssize_t) image->columns; x++)
2429     {
2430       if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2431         SetPixelRed(image,PosterizePixel(GetPixelRed(image,q)),q);
2432       if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2433         SetPixelGreen(image,PosterizePixel(GetPixelGreen(image,q)),q);
2434       if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2435         SetPixelBlue(image,PosterizePixel(GetPixelBlue(image,q)),q);
2436       if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
2437           (image->colorspace == CMYKColorspace))
2438         SetPixelBlack(image,PosterizePixel(GetPixelBlack(image,q)),q);
2439       if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
2440           (image->alpha_trait == BlendPixelTrait))
2441         SetPixelAlpha(image,PosterizePixel(GetPixelAlpha(image,q)),q);
2442       q+=GetPixelChannels(image);
2443     }
2444     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
2445       status=MagickFalse;
2446     if (image->progress_monitor != (MagickProgressMonitor) NULL)
2447       {
2448         MagickBooleanType
2449           proceed;
2450
2451 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2452         #pragma omp critical (MagickCore_PosterizeImage)
2453 #endif
2454         proceed=SetImageProgress(image,PosterizeImageTag,progress++,
2455           image->rows);
2456         if (proceed == MagickFalse)
2457           status=MagickFalse;
2458       }
2459   }
2460   image_view=DestroyCacheView(image_view);
2461   quantize_info=AcquireQuantizeInfo((ImageInfo *) NULL);
2462   quantize_info->number_colors=(size_t) MagickMin((ssize_t) levels*levels*
2463     levels,MaxColormapSize+1);
2464   quantize_info->dither_method=dither_method;
2465   quantize_info->tree_depth=MaxTreeDepth;
2466   status=QuantizeImage(quantize_info,image,exception);
2467   quantize_info=DestroyQuantizeInfo(quantize_info);
2468   return(status);
2469 }
2470 \f
2471 /*
2472 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2473 %                                                                             %
2474 %                                                                             %
2475 %                                                                             %
2476 +   P r u n e C h i l d                                                       %
2477 %                                                                             %
2478 %                                                                             %
2479 %                                                                             %
2480 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2481 %
2482 %  PruneChild() deletes the given node and merges its statistics into its
2483 %  parent.
2484 %
2485 %  The format of the PruneSubtree method is:
2486 %
2487 %      PruneChild(const Image *image,CubeInfo *cube_info,
2488 %        const NodeInfo *node_info)
2489 %
2490 %  A description of each parameter follows.
2491 %
2492 %    o image: the image.
2493 %
2494 %    o cube_info: A pointer to the Cube structure.
2495 %
2496 %    o node_info: pointer to node in color cube tree that is to be pruned.
2497 %
2498 */
2499 static void PruneChild(const Image *image,CubeInfo *cube_info,
2500   const NodeInfo *node_info)
2501 {
2502   NodeInfo
2503     *parent;
2504
2505   register ssize_t
2506     i;
2507
2508   size_t
2509     number_children;
2510
2511   /*
2512     Traverse any children.
2513   */
2514   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2515   for (i=0; i < (ssize_t) number_children; i++)
2516     if (node_info->child[i] != (NodeInfo *) NULL)
2517       PruneChild(image,cube_info,node_info->child[i]);
2518   /*
2519     Merge color statistics into parent.
2520   */
2521   parent=node_info->parent;
2522   parent->number_unique+=node_info->number_unique;
2523   parent->total_color.red+=node_info->total_color.red;
2524   parent->total_color.green+=node_info->total_color.green;
2525   parent->total_color.blue+=node_info->total_color.blue;
2526   parent->total_color.alpha+=node_info->total_color.alpha;
2527   parent->child[node_info->id]=(NodeInfo *) NULL;
2528   cube_info->nodes--;
2529 }
2530 \f
2531 /*
2532 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2533 %                                                                             %
2534 %                                                                             %
2535 %                                                                             %
2536 +  P r u n e L e v e l                                                        %
2537 %                                                                             %
2538 %                                                                             %
2539 %                                                                             %
2540 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2541 %
2542 %  PruneLevel() deletes all nodes at the bottom level of the color tree merging
2543 %  their color statistics into their parent node.
2544 %
2545 %  The format of the PruneLevel method is:
2546 %
2547 %      PruneLevel(const Image *image,CubeInfo *cube_info,
2548 %        const NodeInfo *node_info)
2549 %
2550 %  A description of each parameter follows.
2551 %
2552 %    o image: the image.
2553 %
2554 %    o cube_info: A pointer to the Cube structure.
2555 %
2556 %    o node_info: pointer to node in color cube tree that is to be pruned.
2557 %
2558 */
2559 static void PruneLevel(const Image *image,CubeInfo *cube_info,
2560   const NodeInfo *node_info)
2561 {
2562   register ssize_t
2563     i;
2564
2565   size_t
2566     number_children;
2567
2568   /*
2569     Traverse any children.
2570   */
2571   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2572   for (i=0; i < (ssize_t) number_children; i++)
2573     if (node_info->child[i] != (NodeInfo *) NULL)
2574       PruneLevel(image,cube_info,node_info->child[i]);
2575   if (node_info->level == cube_info->depth)
2576     PruneChild(image,cube_info,node_info);
2577 }
2578 \f
2579 /*
2580 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2581 %                                                                             %
2582 %                                                                             %
2583 %                                                                             %
2584 +  P r u n e T o C u b e D e p t h                                            %
2585 %                                                                             %
2586 %                                                                             %
2587 %                                                                             %
2588 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2589 %
2590 %  PruneToCubeDepth() deletes any nodes at a depth greater than
2591 %  cube_info->depth while merging their color statistics into their parent
2592 %  node.
2593 %
2594 %  The format of the PruneToCubeDepth method is:
2595 %
2596 %      PruneToCubeDepth(const Image *image,CubeInfo *cube_info,
2597 %        const NodeInfo *node_info)
2598 %
2599 %  A description of each parameter follows.
2600 %
2601 %    o cube_info: A pointer to the Cube structure.
2602 %
2603 %    o node_info: pointer to node in color cube tree that is to be pruned.
2604 %
2605 */
2606 static void PruneToCubeDepth(const Image *image,CubeInfo *cube_info,
2607   const NodeInfo *node_info)
2608 {
2609   register ssize_t
2610     i;
2611
2612   size_t
2613     number_children;
2614
2615   /*
2616     Traverse any children.
2617   */
2618   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2619   for (i=0; i < (ssize_t) number_children; i++)
2620     if (node_info->child[i] != (NodeInfo *) NULL)
2621       PruneToCubeDepth(image,cube_info,node_info->child[i]);
2622   if (node_info->level > cube_info->depth)
2623     PruneChild(image,cube_info,node_info);
2624 }
2625 \f
2626 /*
2627 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2628 %                                                                             %
2629 %                                                                             %
2630 %                                                                             %
2631 %  Q u a n t i z e I m a g e                                                  %
2632 %                                                                             %
2633 %                                                                             %
2634 %                                                                             %
2635 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2636 %
2637 %  QuantizeImage() analyzes the colors within a reference image and chooses a
2638 %  fixed number of colors to represent the image.  The goal of the algorithm
2639 %  is to minimize the color difference between the input and output image while
2640 %  minimizing the processing time.
2641 %
2642 %  The format of the QuantizeImage method is:
2643 %
2644 %      MagickBooleanType QuantizeImage(const QuantizeInfo *quantize_info,
2645 %        Image *image,ExceptionInfo *exception)
2646 %
2647 %  A description of each parameter follows:
2648 %
2649 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
2650 %
2651 %    o image: the image.
2652 %
2653 %    o exception: return any errors or warnings in this structure.
2654 %
2655 */
2656
2657 static MagickBooleanType DirectToColormapImage(Image *image,
2658   ExceptionInfo *exception)
2659 {
2660   CacheView
2661     *image_view;
2662
2663   MagickBooleanType
2664     status;
2665
2666   register ssize_t
2667     i;
2668
2669   size_t
2670     number_colors;
2671
2672   ssize_t
2673     y;
2674
2675   status=MagickTrue;
2676   number_colors=(size_t) (image->columns*image->rows);
2677   if (AcquireImageColormap(image,number_colors,exception) == MagickFalse)
2678     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
2679       image->filename);
2680   if (image->colors != number_colors)
2681     return(MagickFalse);
2682   i=0;
2683   image_view=AcquireAuthenticCacheView(image,exception);
2684   for (y=0; y < (ssize_t) image->rows; y++)
2685   {
2686     MagickBooleanType
2687       proceed;
2688
2689     register Quantum
2690       *restrict q;
2691
2692     register ssize_t
2693       x;
2694
2695     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
2696     if (q == (Quantum *) NULL)
2697       break;
2698     for (x=0; x < (ssize_t) image->columns; x++)
2699     {
2700       image->colormap[i].red=(double) GetPixelRed(image,q);
2701       image->colormap[i].green=(double) GetPixelGreen(image,q);
2702       image->colormap[i].blue=(double) GetPixelBlue(image,q);
2703       image->colormap[i].alpha=(double) GetPixelAlpha(image,q);
2704       SetPixelIndex(image,(Quantum) i,q);
2705       i++;
2706       q+=GetPixelChannels(image);
2707     }
2708     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
2709       break;
2710     proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) y,
2711       image->rows);
2712     if (proceed == MagickFalse)
2713       status=MagickFalse;
2714   }
2715   image_view=DestroyCacheView(image_view);
2716   return(status);
2717 }
2718
2719 MagickExport MagickBooleanType QuantizeImage(const QuantizeInfo *quantize_info,
2720   Image *image,ExceptionInfo *exception)
2721 {
2722   CubeInfo
2723     *cube_info;
2724
2725   MagickBooleanType
2726     status;
2727
2728   size_t
2729     depth,
2730     maximum_colors;
2731
2732   assert(quantize_info != (const QuantizeInfo *) NULL);
2733   assert(quantize_info->signature == MagickSignature);
2734   assert(image != (Image *) NULL);
2735   assert(image->signature == MagickSignature);
2736   if (image->debug != MagickFalse)
2737     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2738   maximum_colors=quantize_info->number_colors;
2739   if (maximum_colors == 0)
2740     maximum_colors=MaxColormapSize;
2741   if (maximum_colors > MaxColormapSize)
2742     maximum_colors=MaxColormapSize;
2743   if (image->alpha_trait != BlendPixelTrait)
2744     {
2745       if ((image->columns*image->rows) <= maximum_colors)
2746         (void) DirectToColormapImage(image,exception);
2747       if (IsImageGray(image,exception) != MagickFalse)
2748         (void) SetGrayscaleImage(image,exception);
2749     }
2750   if ((image->storage_class == PseudoClass) &&
2751       (image->colors <= maximum_colors))
2752     return(MagickTrue);
2753   depth=quantize_info->tree_depth;
2754   if (depth == 0)
2755     {
2756       size_t
2757         colors;
2758
2759       /*
2760         Depth of color tree is: Log4(colormap size)+2.
2761       */
2762       colors=maximum_colors;
2763       for (depth=1; colors != 0; depth++)
2764         colors>>=2;
2765       if ((quantize_info->dither_method != NoDitherMethod) && (depth > 2))
2766         depth--;
2767       if ((image->alpha_trait == BlendPixelTrait) && (depth > 5))
2768         depth--;
2769     }
2770   /*
2771     Initialize color cube.
2772   */
2773   cube_info=GetCubeInfo(quantize_info,depth,maximum_colors);
2774   if (cube_info == (CubeInfo *) NULL)
2775     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
2776       image->filename);
2777   status=ClassifyImageColors(cube_info,image,exception);
2778   if (status != MagickFalse)
2779     {
2780       /*
2781         Reduce the number of colors in the image.
2782       */
2783       ReduceImageColors(image,cube_info);
2784       status=AssignImageColors(image,cube_info,exception);
2785     }
2786   DestroyCubeInfo(cube_info);
2787   return(status);
2788 }
2789 \f
2790 /*
2791 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2792 %                                                                             %
2793 %                                                                             %
2794 %                                                                             %
2795 %   Q u a n t i z e I m a g e s                                               %
2796 %                                                                             %
2797 %                                                                             %
2798 %                                                                             %
2799 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2800 %
2801 %  QuantizeImages() analyzes the colors within a set of reference images and
2802 %  chooses a fixed number of colors to represent the set.  The goal of the
2803 %  algorithm is to minimize the color difference between the input and output
2804 %  images while minimizing the processing time.
2805 %
2806 %  The format of the QuantizeImages method is:
2807 %
2808 %      MagickBooleanType QuantizeImages(const QuantizeInfo *quantize_info,
2809 %        Image *images,ExceptionInfo *exception)
2810 %
2811 %  A description of each parameter follows:
2812 %
2813 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
2814 %
2815 %    o images: Specifies a pointer to a list of Image structures.
2816 %
2817 %    o exception: return any errors or warnings in this structure.
2818 %
2819 */
2820 MagickExport MagickBooleanType QuantizeImages(const QuantizeInfo *quantize_info,
2821   Image *images,ExceptionInfo *exception)
2822 {
2823   CubeInfo
2824     *cube_info;
2825
2826   Image
2827     *image;
2828
2829   MagickBooleanType
2830     proceed,
2831     status;
2832
2833   MagickProgressMonitor
2834     progress_monitor;
2835
2836   register ssize_t
2837     i;
2838
2839   size_t
2840     depth,
2841     maximum_colors,
2842     number_images;
2843
2844   assert(quantize_info != (const QuantizeInfo *) NULL);
2845   assert(quantize_info->signature == MagickSignature);
2846   assert(images != (Image *) NULL);
2847   assert(images->signature == MagickSignature);
2848   if (images->debug != MagickFalse)
2849     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
2850   if (GetNextImageInList(images) == (Image *) NULL)
2851     {
2852       /*
2853         Handle a single image with QuantizeImage.
2854       */
2855       status=QuantizeImage(quantize_info,images,exception);
2856       return(status);
2857     }
2858   status=MagickFalse;
2859   maximum_colors=quantize_info->number_colors;
2860   if (maximum_colors == 0)
2861     maximum_colors=MaxColormapSize;
2862   if (maximum_colors > MaxColormapSize)
2863     maximum_colors=MaxColormapSize;
2864   depth=quantize_info->tree_depth;
2865   if (depth == 0)
2866     {
2867       size_t
2868         colors;
2869
2870       /*
2871         Depth of color tree is: Log4(colormap size)+2.
2872       */
2873       colors=maximum_colors;
2874       for (depth=1; colors != 0; depth++)
2875         colors>>=2;
2876       if (quantize_info->dither_method != NoDitherMethod)
2877         depth--;
2878     }
2879   /*
2880     Initialize color cube.
2881   */
2882   cube_info=GetCubeInfo(quantize_info,depth,maximum_colors);
2883   if (cube_info == (CubeInfo *) NULL)
2884     {
2885       (void) ThrowMagickException(exception,GetMagickModule(),
2886         ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
2887       return(MagickFalse);
2888     }
2889   number_images=GetImageListLength(images);
2890   image=images;
2891   for (i=0; image != (Image *) NULL; i++)
2892   {
2893     progress_monitor=SetImageProgressMonitor(image,(MagickProgressMonitor) NULL,
2894       image->client_data);
2895     status=ClassifyImageColors(cube_info,image,exception);
2896     if (status == MagickFalse)
2897       break;
2898     (void) SetImageProgressMonitor(image,progress_monitor,image->client_data);
2899     proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) i,
2900       number_images);
2901     if (proceed == MagickFalse)
2902       break;
2903     image=GetNextImageInList(image);
2904   }
2905   if (status != MagickFalse)
2906     {
2907       /*
2908         Reduce the number of colors in an image sequence.
2909       */
2910       ReduceImageColors(images,cube_info);
2911       image=images;
2912       for (i=0; image != (Image *) NULL; i++)
2913       {
2914         progress_monitor=SetImageProgressMonitor(image,(MagickProgressMonitor)
2915           NULL,image->client_data);
2916         status=AssignImageColors(image,cube_info,exception);
2917         if (status == MagickFalse)
2918           break;
2919         (void) SetImageProgressMonitor(image,progress_monitor,
2920           image->client_data);
2921         proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) i,
2922           number_images);
2923         if (proceed == MagickFalse)
2924           break;
2925         image=GetNextImageInList(image);
2926       }
2927     }
2928   DestroyCubeInfo(cube_info);
2929   return(status);
2930 }
2931 \f
2932 /*
2933 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2934 %                                                                             %
2935 %                                                                             %
2936 %                                                                             %
2937 +   R e d u c e                                                               %
2938 %                                                                             %
2939 %                                                                             %
2940 %                                                                             %
2941 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2942 %
2943 %  Reduce() traverses the color cube tree and prunes any node whose
2944 %  quantization error falls below a particular threshold.
2945 %
2946 %  The format of the Reduce method is:
2947 %
2948 %      Reduce(const Image *image,CubeInfo *cube_info,const NodeInfo *node_info)
2949 %
2950 %  A description of each parameter follows.
2951 %
2952 %    o image: the image.
2953 %
2954 %    o cube_info: A pointer to the Cube structure.
2955 %
2956 %    o node_info: pointer to node in color cube tree that is to be pruned.
2957 %
2958 */
2959 static void Reduce(const Image *image,CubeInfo *cube_info,
2960   const NodeInfo *node_info)
2961 {
2962   register ssize_t
2963     i;
2964
2965   size_t
2966     number_children;
2967
2968   /*
2969     Traverse any children.
2970   */
2971   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2972   for (i=0; i < (ssize_t) number_children; i++)
2973     if (node_info->child[i] != (NodeInfo *) NULL)
2974       Reduce(image,cube_info,node_info->child[i]);
2975   if (node_info->quantize_error <= cube_info->pruning_threshold)
2976     PruneChild(image,cube_info,node_info);
2977   else
2978     {
2979       /*
2980         Find minimum pruning threshold.
2981       */
2982       if (node_info->number_unique > 0)
2983         cube_info->colors++;
2984       if (node_info->quantize_error < cube_info->next_threshold)
2985         cube_info->next_threshold=node_info->quantize_error;
2986     }
2987 }
2988 \f
2989 /*
2990 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2991 %                                                                             %
2992 %                                                                             %
2993 %                                                                             %
2994 +   R e d u c e I m a g e C o l o r s                                         %
2995 %                                                                             %
2996 %                                                                             %
2997 %                                                                             %
2998 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2999 %
3000 %  ReduceImageColors() repeatedly prunes the tree until the number of nodes
3001 %  with n2 > 0 is less than or equal to the maximum number of colors allowed
3002 %  in the output image.  On any given iteration over the tree, it selects
3003 %  those nodes whose E value is minimal for pruning and merges their
3004 %  color statistics upward. It uses a pruning threshold, Ep, to govern
3005 %  node selection as follows:
3006 %
3007 %    Ep = 0
3008 %    while number of nodes with (n2 > 0) > required maximum number of colors
3009 %      prune all nodes such that E <= Ep
3010 %      Set Ep to minimum E in remaining nodes
3011 %
3012 %  This has the effect of minimizing any quantization error when merging
3013 %  two nodes together.
3014 %
3015 %  When a node to be pruned has offspring, the pruning procedure invokes
3016 %  itself recursively in order to prune the tree from the leaves upward.
3017 %  n2,  Sr, Sg,  and  Sb in a node being pruned are always added to the
3018 %  corresponding data in that node's parent.  This retains the pruned
3019 %  node's color characteristics for later averaging.
3020 %
3021 %  For each node, n2 pixels exist for which that node represents the
3022 %  smallest volume in RGB space containing those pixel's colors.  When n2
3023 %  > 0 the node will uniquely define a color in the output image. At the
3024 %  beginning of reduction,  n2 = 0  for all nodes except a the leaves of
3025 %  the tree which represent colors present in the input image.
3026 %
3027 %  The other pixel count, n1, indicates the total number of colors
3028 %  within the cubic volume which the node represents.  This includes n1 -
3029 %  n2  pixels whose colors should be defined by nodes at a lower level in
3030 %  the tree.
3031 %
3032 %  The format of the ReduceImageColors method is:
3033 %
3034 %      ReduceImageColors(const Image *image,CubeInfo *cube_info)
3035 %
3036 %  A description of each parameter follows.
3037 %
3038 %    o image: the image.
3039 %
3040 %    o cube_info: A pointer to the Cube structure.
3041 %
3042 */
3043 static void ReduceImageColors(const Image *image,CubeInfo *cube_info)
3044 {
3045 #define ReduceImageTag  "Reduce/Image"
3046
3047   MagickBooleanType
3048     proceed;
3049
3050   MagickOffsetType
3051     offset;
3052
3053   size_t
3054     span;
3055
3056   cube_info->next_threshold=0.0;
3057   for (span=cube_info->colors; cube_info->colors > cube_info->maximum_colors; )
3058   {
3059     cube_info->pruning_threshold=cube_info->next_threshold;
3060     cube_info->next_threshold=cube_info->root->quantize_error-1;
3061     cube_info->colors=0;
3062     Reduce(image,cube_info,cube_info->root);
3063     offset=(MagickOffsetType) span-cube_info->colors;
3064     proceed=SetImageProgress(image,ReduceImageTag,offset,span-
3065       cube_info->maximum_colors+1);
3066     if (proceed == MagickFalse)
3067       break;
3068   }
3069 }
3070 \f
3071 /*
3072 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3073 %                                                                             %
3074 %                                                                             %
3075 %                                                                             %
3076 %   R e m a p I m a g e                                                       %
3077 %                                                                             %
3078 %                                                                             %
3079 %                                                                             %
3080 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3081 %
3082 %  RemapImage() replaces the colors of an image with a dither of the colors
3083 %  provided.
3084 %
3085 %  The format of the RemapImage method is:
3086 %
3087 %      MagickBooleanType RemapImage(const QuantizeInfo *quantize_info,
3088 %        Image *image,const Image *remap_image,ExceptionInfo *exception)
3089 %
3090 %  A description of each parameter follows:
3091 %
3092 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
3093 %
3094 %    o image: the image.
3095 %
3096 %    o remap_image: the reference image.
3097 %
3098 %    o exception: return any errors or warnings in this structure.
3099 %
3100 */
3101 MagickExport MagickBooleanType RemapImage(const QuantizeInfo *quantize_info,
3102   Image *image,const Image *remap_image,ExceptionInfo *exception)
3103 {
3104   CubeInfo
3105     *cube_info;
3106
3107   MagickBooleanType
3108     status;
3109
3110   /*
3111     Initialize color cube.
3112   */
3113   assert(image != (Image *) NULL);
3114   assert(image->signature == MagickSignature);
3115   if (image->debug != MagickFalse)
3116     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
3117   assert(remap_image != (Image *) NULL);
3118   assert(remap_image->signature == MagickSignature);
3119   cube_info=GetCubeInfo(quantize_info,MaxTreeDepth,
3120     quantize_info->number_colors);
3121   if (cube_info == (CubeInfo *) NULL)
3122     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3123       image->filename);
3124   status=ClassifyImageColors(cube_info,remap_image,exception);
3125   if (status != MagickFalse)
3126     {
3127       /*
3128         Classify image colors from the reference image.
3129       */
3130       cube_info->quantize_info->number_colors=cube_info->colors;
3131       status=AssignImageColors(image,cube_info,exception);
3132     }
3133   DestroyCubeInfo(cube_info);
3134   return(status);
3135 }
3136 \f
3137 /*
3138 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3139 %                                                                             %
3140 %                                                                             %
3141 %                                                                             %
3142 %   R e m a p I m a g e s                                                     %
3143 %                                                                             %
3144 %                                                                             %
3145 %                                                                             %
3146 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3147 %
3148 %  RemapImages() replaces the colors of a sequence of images with the
3149 %  closest color from a reference image.
3150 %
3151 %  The format of the RemapImage method is:
3152 %
3153 %      MagickBooleanType RemapImages(const QuantizeInfo *quantize_info,
3154 %        Image *images,Image *remap_image,ExceptionInfo *exception)
3155 %
3156 %  A description of each parameter follows:
3157 %
3158 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
3159 %
3160 %    o images: the image sequence.
3161 %
3162 %    o remap_image: the reference image.
3163 %
3164 %    o exception: return any errors or warnings in this structure.
3165 %
3166 */
3167 MagickExport MagickBooleanType RemapImages(const QuantizeInfo *quantize_info,
3168   Image *images,const Image *remap_image,ExceptionInfo *exception)
3169 {
3170   CubeInfo
3171     *cube_info;
3172
3173   Image
3174     *image;
3175
3176   MagickBooleanType
3177     status;
3178
3179   assert(images != (Image *) NULL);
3180   assert(images->signature == MagickSignature);
3181   if (images->debug != MagickFalse)
3182     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
3183   image=images;
3184   if (remap_image == (Image *) NULL)
3185     {
3186       /*
3187         Create a global colormap for an image sequence.
3188       */
3189       status=QuantizeImages(quantize_info,images,exception);
3190       return(status);
3191     }
3192   /*
3193     Classify image colors from the reference image.
3194   */
3195   cube_info=GetCubeInfo(quantize_info,MaxTreeDepth,
3196     quantize_info->number_colors);
3197   if (cube_info == (CubeInfo *) NULL)
3198     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3199       image->filename);
3200   status=ClassifyImageColors(cube_info,remap_image,exception);
3201   if (status != MagickFalse)
3202     {
3203       /*
3204         Classify image colors from the reference image.
3205       */
3206       cube_info->quantize_info->number_colors=cube_info->colors;
3207       image=images;
3208       for ( ; image != (Image *) NULL; image=GetNextImageInList(image))
3209       {
3210         status=AssignImageColors(image,cube_info,exception);
3211         if (status == MagickFalse)
3212           break;
3213       }
3214     }
3215   DestroyCubeInfo(cube_info);
3216   return(status);
3217 }
3218 \f
3219 /*
3220 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3221 %                                                                             %
3222 %                                                                             %
3223 %                                                                             %
3224 %   S e t G r a y s c a l e I m a g e                                         %
3225 %                                                                             %
3226 %                                                                             %
3227 %                                                                             %
3228 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3229 %
3230 %  SetGrayscaleImage() converts an image to a PseudoClass grayscale image.
3231 %
3232 %  The format of the SetGrayscaleImage method is:
3233 %
3234 %      MagickBooleanType SetGrayscaleImage(Image *image,ExceptionInfo *exeption)
3235 %
3236 %  A description of each parameter follows:
3237 %
3238 %    o image: The image.
3239 %
3240 %    o exception: return any errors or warnings in this structure.
3241 %
3242 */
3243
3244 #if defined(__cplusplus) || defined(c_plusplus)
3245 extern "C" {
3246 #endif
3247
3248 static int IntensityCompare(const void *x,const void *y)
3249 {
3250   PixelInfo
3251     *color_1,
3252     *color_2;
3253
3254   ssize_t
3255     intensity;
3256
3257   color_1=(PixelInfo *) x;
3258   color_2=(PixelInfo *) y;
3259   intensity=(ssize_t) (GetPixelInfoIntensity(color_1)-(ssize_t)
3260     GetPixelInfoIntensity(color_2));
3261   return((int) intensity);
3262 }
3263
3264 #if defined(__cplusplus) || defined(c_plusplus)
3265 }
3266 #endif
3267
3268 static MagickBooleanType SetGrayscaleImage(Image *image,
3269   ExceptionInfo *exception)
3270 {
3271   CacheView
3272     *image_view;
3273
3274   MagickBooleanType
3275     status;
3276
3277   PixelInfo
3278     *colormap;
3279
3280   register ssize_t
3281     i;
3282
3283   ssize_t
3284     *colormap_index,
3285     j,
3286     y;
3287
3288   assert(image != (Image *) NULL);
3289   assert(image->signature == MagickSignature);
3290   if (image->type != GrayscaleType)
3291     (void) TransformImageColorspace(image,GRAYColorspace,exception);
3292   colormap_index=(ssize_t *) AcquireQuantumMemory(MaxMap+1,
3293     sizeof(*colormap_index));
3294   if (colormap_index == (ssize_t *) NULL)
3295     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3296       image->filename);
3297   if (image->storage_class != PseudoClass)
3298     {
3299       for (i=0; i <= (ssize_t) MaxMap; i++)
3300         colormap_index[i]=(-1);
3301       if (AcquireImageColormap(image,MaxMap+1,exception) == MagickFalse)
3302         ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3303           image->filename);
3304       image->colors=0;
3305       status=MagickTrue;
3306       image_view=AcquireAuthenticCacheView(image,exception);
3307 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3308       #pragma omp parallel for schedule(static,4) shared(status) \
3309         magick_threads(image,image,image->rows,1)
3310 #endif
3311       for (y=0; y < (ssize_t) image->rows; y++)
3312       {
3313         register Quantum
3314           *restrict q;
3315
3316         register ssize_t
3317           x;
3318
3319         if (status == MagickFalse)
3320           continue;
3321         q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
3322           exception);
3323         if (q == (Quantum *) NULL)
3324           {
3325             status=MagickFalse;
3326             continue;
3327           }
3328         for (x=0; x < (ssize_t) image->columns; x++)
3329         {
3330           register size_t
3331             intensity;
3332
3333           intensity=ScaleQuantumToMap(GetPixelRed(image,q));
3334           if (colormap_index[intensity] < 0)
3335             {
3336 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3337               #pragma omp critical (MagickCore_SetGrayscaleImage)
3338 #endif
3339               if (colormap_index[intensity] < 0)
3340                 {
3341                   colormap_index[intensity]=(ssize_t) image->colors;
3342                   image->colormap[image->colors].red=(double)
3343                     GetPixelRed(image,q);
3344                   image->colormap[image->colors].green=(double)
3345                     GetPixelGreen(image,q);
3346                   image->colormap[image->colors].blue=(double)
3347                     GetPixelBlue(image,q);
3348                   image->colors++;
3349                }
3350             }
3351           SetPixelIndex(image,(Quantum) colormap_index[intensity],q);
3352           q+=GetPixelChannels(image);
3353         }
3354         if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
3355           status=MagickFalse;
3356       }
3357       image_view=DestroyCacheView(image_view);
3358     }
3359   for (i=0; i < (ssize_t) image->colors; i++)
3360     image->colormap[i].alpha=(double) i;
3361   qsort((void *) image->colormap,image->colors,sizeof(PixelInfo),
3362     IntensityCompare);
3363   colormap=(PixelInfo *) AcquireQuantumMemory(image->colors,
3364     sizeof(*colormap));
3365   if (colormap == (PixelInfo *) NULL)
3366     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3367       image->filename);
3368   j=0;
3369   colormap[j]=image->colormap[0];
3370   for (i=0; i < (ssize_t) image->colors; i++)
3371   {
3372     if (IsPixelInfoEquivalent(&colormap[j],&image->colormap[i]) == MagickFalse)
3373       {
3374         j++;
3375         colormap[j]=image->colormap[i];
3376       }
3377     colormap_index[(ssize_t) image->colormap[i].alpha]=j;
3378   }
3379   image->colors=(size_t) (j+1);
3380   image->colormap=(PixelInfo *) RelinquishMagickMemory(image->colormap);
3381   image->colormap=colormap;
3382   status=MagickTrue;
3383   image_view=AcquireAuthenticCacheView(image,exception);
3384 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3385   #pragma omp parallel for schedule(static,4) shared(status) \
3386     magick_threads(image,image,image->rows,1)
3387 #endif
3388   for (y=0; y < (ssize_t) image->rows; y++)
3389   {
3390     register Quantum
3391       *restrict q;
3392
3393     register ssize_t
3394       x;
3395
3396     if (status == MagickFalse)
3397       continue;
3398     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
3399     if (q == (Quantum *) NULL)
3400       {
3401         status=MagickFalse;
3402         continue;
3403       }
3404     for (x=0; x < (ssize_t) image->columns; x++)
3405     {
3406       SetPixelIndex(image,(Quantum) colormap_index[ScaleQuantumToMap(
3407         GetPixelIndex(image,q))],q);
3408       q+=GetPixelChannels(image);
3409     }
3410     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
3411       status=MagickFalse;
3412   }
3413   image_view=DestroyCacheView(image_view);
3414   colormap_index=(ssize_t *) RelinquishMagickMemory(colormap_index);
3415   image->type=GrayscaleType;
3416   if (IsImageMonochrome(image,exception) != MagickFalse)
3417     image->type=BilevelType;
3418   return(status);
3419 }