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

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