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

   1 /*
   2 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   3 %                                                                             %
   4 %                                                                             %
   5 %                                                                             %
   6 %           QQQ   U   U   AAA   N   N  TTTTT  IIIII   ZZZZZ  EEEEE            %
   7 %          Q   Q  U   U  A   A  NN  N    T      I        ZZ  E                %
   8 %          Q   Q  U   U  AAAAA  N N N    T      I      ZZZ   EEEEE            %
   9 %          Q  QQ  U   U  A   A  N  NN    T      I     ZZ     E                %
  10 %           QQQQ   UUU   A   A  N   N    T    IIIII   ZZZZZ  EEEEE            %
  11 %                                                                             %
  12 %                                                                             %
  13 %    MagickCore Methods to Reduce the Number of Unique Colors in an Image     %
  14 %                                                                             %
  15 %                           Software Design                                   %
  16 %                                Cristy                                       %
  17 %                              July 1992                                      %
  18 %                                                                             %
  19 %                                                                             %
  20 %  Copyright 1999-2015 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 (vertex
  65 %  nearest the origin in RGB space and the vertex farthest from the origin).
  66 %
  67 %  The tree's root node represents the entire domain, (0,0,0) through
  68 %  (Cmax,Cmax,Cmax).  Each lower level in the tree is generated by
  69 %  subdividing one node's cube into eight smaller cubes of equal size.
  70 %  This corresponds to bisecting the parent cube with planes passing
  71 %  through the midpoints of each edge.
  72 %
  73 %  The basic algorithm operates in three phases: Classification,
  74 %  Reduction, and Assignment.  Classification builds a color description
  75 %  tree for the image.  Reduction collapses the tree until the number it
  76 %  represents, at most, the number of colors desired in the output image.
  77 %  Assignment defines the output image's color map and sets each pixel's
  78 %  color by restorage_class in the reduced tree.  Our goal is to minimize
  79 %  the numerical discrepancies between the original colors and quantized
  80 %  colors (quantization error).
  81 %
  82 %  Classification begins by initializing a color description tree of
  83 %  sufficient depth to represent each possible input color in a leaf.
  84 %  However, it is impractical to generate a fully-formed color description
  85 %  tree in the storage_class phase for realistic values of Cmax.  If
  86 %  colors components in the input image are quantized to k-bit precision,
  87 %  so that Cmax= 2k-1, the tree would need k levels below the root node to
  88 %  allow representing each possible input color in a leaf.  This becomes
  89 %  prohibitive because the tree's total number of nodes is 1 +
  90 %  sum(i=1, k, 8k).
  91 %
  92 %  A complete tree would require 19,173,961 nodes for k = 8, Cmax = 255.
  93 %  Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
  94 %  Initializes data structures for nodes only as they are needed;  (2)
  95 %  Chooses a maximum depth for the tree as a function of the desired
  96 %  number of colors in the output image (currently log2(colormap size)).
  97 %
  98 %  For each pixel in the input image, storage_class scans downward from
  99 %  the root of the color description tree.  At each level of the tree it
 100 %  identifies the single node which represents a cube in RGB space
 101 %  containing the pixel's color.  It updates the following data for each
 102 %  such node:
 103 %
 104 %    n1: Number of pixels whose color is contained in the RGB cube which
 105 %    this node represents;
 106 %
 107 %    n2: Number of pixels whose color is not represented in a node at
 108 %    lower depth in the tree;  initially,  n2 = 0 for all nodes except
 109 %    leaves of the tree.
 110 %
 111 %    Sr, Sg, Sb: Sums of the red, green, and blue component values for all
 112 %    pixels not classified at a lower depth. The combination of these sums
 113 %    and n2  will ultimately characterize the mean color of a set of
 114 %    pixels represented by this node.
 115 %
 116 %    E: the distance squared in RGB space between each pixel contained
 117 %    within a node and the nodes' center.  This represents the
 118 %    quantization error for a node.
 119 %
 120 %  Reduction repeatedly prunes the tree until the number of nodes with n2
 121 %  > 0 is less than or equal to the maximum number of colors allowed in
 122 %  the output image.  On any given iteration over the tree, it selects
 123 %  those nodes whose E count is minimal for pruning and merges their color
 124 %  statistics upward. It uses a pruning threshold, Ep, to govern node
 125 %  selection as follows:
 126 %
 127 %    Ep = 0
 128 %    while number of nodes with (n2 > 0) > required maximum number of colors
 129 %      prune all nodes such that E <= Ep
 130 %      Set Ep to minimum E in remaining nodes
 131 %
 132 %  This has the effect of minimizing any quantization error when merging
 133 %  two nodes together.
 134 %
 135 %  When a node to be pruned has offspring, the pruning procedure invokes
 136 %  itself recursively in order to prune the tree from the leaves upward.
 137 %  n2,  Sr, Sg,  and  Sb in a node being pruned are always added to the
 138 %  corresponding data in that node's parent.  This retains the pruned
 139 %  node's color characteristics for later averaging.
 140 %
 141 %  For each node, n2 pixels exist for which that node represents the
 142 %  smallest volume in RGB space containing those pixel's colors.  When n2
 143 %  > 0 the node will uniquely define a color in the output image. At the
 144 %  beginning of reduction,  n2 = 0  for all nodes except a the leaves of
 145 %  the tree which represent colors present in the input image.
 146 %
 147 %  The other pixel count, n1, indicates the total number of colors within
 148 %  the cubic volume which the node represents.  This includes n1 - n2
 149 %  pixels whose colors should be defined by nodes at a lower level in the
 150 %  tree.
 151 %
 152 %  Assignment generates the output image from the pruned tree.  The output
 153 %  image consists of two parts: (1)  A color map, which is an array of
 154 %  color descriptions (RGB triples) for each color present in the output
 155 %  image;  (2)  A pixel array, which represents each pixel as an index
 156 %  into the color map array.
 157 %
 158 %  First, the assignment phase makes one pass over the pruned color
 159 %  description tree to establish the image's color map.  For each node
 160 %  with n2  > 0, it divides Sr, Sg, and Sb by n2 .  This produces the mean
 161 %  color of all pixels that classify no lower than this node.  Each of
 162 %  these colors becomes an entry in the color map.
 163 %
 164 %  Finally,  the assignment phase reclassifies each pixel in the pruned
 165 %  tree to identify the deepest node containing the pixel's color.  The
 166 %  pixel's value in the pixel array becomes the index of this node's mean
 167 %  color in the color map.
 168 %
 169 %  This method is based on a similar algorithm written by Paul Raveling.
 170 %
 171 */
 172 \f
 173 /*
 174   Include declarations.
 175 */
 176 #include "MagickCore/studio.h"
 177 #include "MagickCore/attribute.h"
 178 #include "MagickCore/cache-view.h"
 179 #include "MagickCore/color.h"
 180 #include "MagickCore/color-private.h"
 181 #include "MagickCore/colormap.h"
 182 #include "MagickCore/colorspace.h"
 183 #include "MagickCore/colorspace-private.h"
 184 #include "MagickCore/enhance.h"
 185 #include "MagickCore/exception.h"
 186 #include "MagickCore/exception-private.h"
 187 #include "MagickCore/histogram.h"
 188 #include "MagickCore/image.h"
 189 #include "MagickCore/image-private.h"
 190 #include "MagickCore/list.h"
 191 #include "MagickCore/memory_.h"
 192 #include "MagickCore/monitor.h"
 193 #include "MagickCore/monitor-private.h"
 194 #include "MagickCore/option.h"
 195 #include "MagickCore/pixel-accessor.h"
 196 #include "MagickCore/pixel-private.h"
 197 #include "MagickCore/quantize.h"
 198 #include "MagickCore/quantum.h"
 199 #include "MagickCore/quantum-private.h"
 200 #include "MagickCore/resource_.h"
 201 #include "MagickCore/string_.h"
 202 #include "MagickCore/thread-private.h"
 203 \f
 204 /*
 205   Define declarations.
 206 */
 207 #if !defined(__APPLE__) && !defined(TARGET_OS_IPHONE)
 208 #define CacheShift  2
 209 #else
 210 #define CacheShift  3
 211 #endif
 212 #define ErrorQueueLength  16
 213 #define MaxNodes  266817
 214 #define MaxTreeDepth  8
 215 #define NodesInAList  1920
 216 \f
 217 /*
 218   Typdef declarations.
 219 */
 220 typedef struct _RealPixelInfo
 221 {
 222   double
 223     red,
 224     green,
 225     blue,
 226     alpha;
 227 } RealPixelInfo;
 228
 229 typedef struct _NodeInfo
 230 {
 231   struct _NodeInfo
 232     *parent,
 233     *child[16];
 234
 235   MagickSizeType
 236     number_unique;
 237
 238   RealPixelInfo
 239     total_color;
 240
 241   double
 242     quantize_error;
 243
 244   size_t
 245     color_number,
 246     id,
 247     level;
 248 } NodeInfo;
 249
 250 typedef struct _Nodes
 251 {
 252   NodeInfo
 253     *nodes;
 254
 255   struct _Nodes
 256     *next;
 257 } Nodes;
 258
 259 typedef struct _CubeInfo
 260 {
 261   NodeInfo
 262     *root;
 263
 264   size_t
 265     colors,
 266     maximum_colors;
 267
 268   ssize_t
 269     transparent_index;
 270
 271   MagickSizeType
 272     transparent_pixels;
 273
 274   RealPixelInfo
 275     target;
 276
 277   double
 278     distance,
 279     pruning_threshold,
 280     next_threshold;
 281
 282   size_t
 283     nodes,
 284     free_nodes,
 285     color_number;
 286
 287   NodeInfo
 288     *next_node;
 289
 290   Nodes
 291     *node_queue;
 292
 293   MemoryInfo
 294     *memory_info;
 295
 296   ssize_t
 297     *cache;
 298
 299   RealPixelInfo
 300     error[ErrorQueueLength];
 301
 302   double
 303     weights[ErrorQueueLength];
 304
 305   QuantizeInfo
 306     *quantize_info;
 307
 308   MagickBooleanType
 309     associate_alpha;
 310
 311   ssize_t
 312     x,
 313     y;
 314
 315   size_t
 316     depth;
 317
 318   MagickOffsetType
 319     offset;
 320
 321   MagickSizeType
 322     span;
 323 } CubeInfo;
 324 \f
 325 /*
 326   Method prototypes.
 327 */
 328 static CubeInfo
 329   *GetCubeInfo(const QuantizeInfo *,const size_t,const size_t);
 330
 331 static NodeInfo
 332   *GetNodeInfo(CubeInfo *,const size_t,const size_t,NodeInfo *);
 333
 334 static MagickBooleanType
 335   AssignImageColors(Image *,CubeInfo *,ExceptionInfo *),
 336   ClassifyImageColors(CubeInfo *,const Image *,ExceptionInfo *),
 337   DitherImage(Image *,CubeInfo *,ExceptionInfo *),
 338   SetGrayscaleImage(Image *,ExceptionInfo *);
 339
 340 static size_t
 341   DefineImageColormap(Image *,CubeInfo *,NodeInfo *);
 342
 343 static void
 344   ClosestColor(const Image *,CubeInfo *,const NodeInfo *),
 345   DestroyCubeInfo(CubeInfo *),
 346   PruneLevel(const Image *,CubeInfo *,const NodeInfo *),
 347   PruneToCubeDepth(const Image *,CubeInfo *,const NodeInfo *),
 348   ReduceImageColors(const Image *,CubeInfo *);
 349 \f
 350 /*
 351 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 352 %                                                                             %
 353 %                                                                             %
 354 %                                                                             %
 355 %   A c q u i r e Q u a n t i z e I n f o                                     %
 356 %                                                                             %
 357 %                                                                             %
 358 %                                                                             %
 359 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 360 %
 361 %  AcquireQuantizeInfo() allocates the QuantizeInfo structure.
 362 %
 363 %  The format of the AcquireQuantizeInfo method is:
 364 %
 365 %      QuantizeInfo *AcquireQuantizeInfo(const ImageInfo *image_info)
 366 %
 367 %  A description of each parameter follows:
 368 %
 369 %    o image_info: the image info.
 370 %
 371 */
 372 MagickExport QuantizeInfo *AcquireQuantizeInfo(const ImageInfo *image_info)
 373 {
 374   QuantizeInfo
 375     *quantize_info;
 376
 377   quantize_info=(QuantizeInfo *) AcquireMagickMemory(sizeof(*quantize_info));
 378   if (quantize_info == (QuantizeInfo *) NULL)
 379     ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
 380   GetQuantizeInfo(quantize_info);
 381   if (image_info != (ImageInfo *) NULL)
 382     {
 383       const char
 384         *option;
 385
 386       quantize_info->dither_method=image_info->dither == MagickFalse ?
 387         NoDitherMethod : RiemersmaDitherMethod;
 388       option=GetImageOption(image_info,"dither");
 389       if (option != (const char *) NULL)
 390         quantize_info->dither_method=(DitherMethod) ParseCommandOption(
 391           MagickDitherOptions,MagickFalse,option);
 392       quantize_info->measure_error=image_info->verbose;
 393     }
 394   return(quantize_info);
 395 }
 396 \f
 397 /*
 398 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 399 %                                                                             %
 400 %                                                                             %
 401 %                                                                             %
 402 +   A s s i g n I m a g e C o l o r s                                         %
 403 %                                                                             %
 404 %                                                                             %
 405 %                                                                             %
 406 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 407 %
 408 %  AssignImageColors() generates the output image from the pruned tree.  The
 409 %  output image consists of two parts: (1)  A color map, which is an array
 410 %  of color descriptions (RGB triples) for each color present in the
 411 %  output image;  (2)  A pixel array, which represents each pixel as an
 412 %  index into the color map array.
 413 %
 414 %  First, the assignment phase makes one pass over the pruned color
 415 %  description tree to establish the image's color map.  For each node
 416 %  with n2  > 0, it divides Sr, Sg, and Sb by n2 .  This produces the mean
 417 %  color of all pixels that classify no lower than this node.  Each of
 418 %  these colors becomes an entry in the color map.
 419 %
 420 %  Finally,  the assignment phase reclassifies each pixel in the pruned
 421 %  tree to identify the deepest node containing the pixel's color.  The
 422 %  pixel's value in the pixel array becomes the index of this node's mean
 423 %  color in the color map.
 424 %
 425 %  The format of the AssignImageColors() method is:
 426 %
 427 %      MagickBooleanType AssignImageColors(Image *image,CubeInfo *cube_info)
 428 %
 429 %  A description of each parameter follows.
 430 %
 431 %    o image: the image.
 432 %
 433 %    o cube_info: A pointer to the Cube structure.
 434 %
 435 */
 436
 437 static inline void AssociateAlphaPixel(const Image *image,
 438   const CubeInfo *cube_info,const Quantum *pixel,RealPixelInfo *alpha_pixel)
 439 {
 440   double
 441     alpha;
 442
 443   if ((cube_info->associate_alpha == MagickFalse) ||
 444       (GetPixelAlpha(image,pixel)== OpaqueAlpha))
 445     {
 446       alpha_pixel->red=(double) GetPixelRed(image,pixel);
 447       alpha_pixel->green=(double) GetPixelGreen(image,pixel);
 448       alpha_pixel->blue=(double) GetPixelBlue(image,pixel);
 449       alpha_pixel->alpha=(double) GetPixelAlpha(image,pixel);
 450       return;
 451     }
 452   alpha=(double) (QuantumScale*GetPixelAlpha(image,pixel));
 453   alpha_pixel->red=alpha*GetPixelRed(image,pixel);
 454   alpha_pixel->green=alpha*GetPixelGreen(image,pixel);
 455   alpha_pixel->blue=alpha*GetPixelBlue(image,pixel);
 456   alpha_pixel->alpha=(double) GetPixelAlpha(image,pixel);
 457 }
 458
 459 static inline void AssociateAlphaPixelInfo(const CubeInfo *cube_info,
 460   const PixelInfo *pixel,RealPixelInfo *alpha_pixel)
 461 {
 462   double
 463     alpha;
 464
 465   if ((cube_info->associate_alpha == MagickFalse) ||
 466       (pixel->alpha == OpaqueAlpha))
 467     {
 468       alpha_pixel->red=(double) pixel->red;
 469       alpha_pixel->green=(double) pixel->green;
 470       alpha_pixel->blue=(double) pixel->blue;
 471       alpha_pixel->alpha=(double) pixel->alpha;
 472       return;
 473     }
 474   alpha=(double) (QuantumScale*pixel->alpha);
 475   alpha_pixel->red=alpha*pixel->red;
 476   alpha_pixel->green=alpha*pixel->green;
 477   alpha_pixel->blue=alpha*pixel->blue;
 478   alpha_pixel->alpha=(double) pixel->alpha;
 479 }
 480
 481 static inline Quantum ClampPixel(const MagickRealType value)
 482 {
 483   if (value < 0.0f)
 484     return(0);
 485   if (value >= (MagickRealType) QuantumRange)
 486     return((Quantum) QuantumRange);
 487 #if !defined(MAGICKCORE_HDRI_SUPPORT)
 488   return((Quantum) (value+0.5f));
 489 #else
 490   return(value);
 491 #endif
 492 }
 493
 494 static inline size_t ColorToNodeId(const CubeInfo *cube_info,
 495   const RealPixelInfo *pixel,size_t index)
 496 {
 497   size_t
 498     id;
 499
 500   id=(size_t) (((ScaleQuantumToChar(ClampPixel(pixel->red)) >> index) & 0x01) |
 501     ((ScaleQuantumToChar(ClampPixel(pixel->green)) >> index) & 0x01) << 1 |
 502     ((ScaleQuantumToChar(ClampPixel(pixel->blue)) >> index) & 0x01) << 2);
 503   if (cube_info->associate_alpha != MagickFalse)
 504     id|=((ScaleQuantumToChar(ClampPixel(pixel->alpha)) >> index) & 0x1) << 3;
 505   return(id);
 506 }
 507
 508 static MagickBooleanType AssignImageColors(Image *image,CubeInfo *cube_info,
 509   ExceptionInfo *exception)
 510 {
 511 #define AssignImageTag  "Assign/Image"
 512
 513   ssize_t
 514     y;
 515
 516   /*
 517     Allocate image colormap.
 518   */
 519   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
 520       (cube_info->quantize_info->colorspace != CMYKColorspace))
 521     (void) TransformImageColorspace((Image *) image,
 522       cube_info->quantize_info->colorspace,exception);
 523   else
 524     if (IssRGBCompatibleColorspace(image->colorspace) == MagickFalse)
 525       (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
 526   if (AcquireImageColormap(image,cube_info->colors,exception) == MagickFalse)
 527     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
 528       image->filename);
 529   image->colors=0;
 530   cube_info->transparent_pixels=0;
 531   cube_info->transparent_index=(-1);
 532   (void) DefineImageColormap(image,cube_info,cube_info->root);
 533   /*
 534     Create a reduced color image.
 535   */
 536   if (cube_info->quantize_info->dither_method != NoDitherMethod)
 537     (void) DitherImage(image,cube_info,exception);
 538   else
 539     {
 540       CacheView
 541         *image_view;
 542
 543       MagickBooleanType
 544         status;
 545
 546       status=MagickTrue;
 547       image_view=AcquireAuthenticCacheView(image,exception);
 548 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 549       #pragma omp parallel for schedule(static,4) shared(status) \
 550         magick_threads(image,image,image->rows,1)
 551 #endif
 552       for (y=0; y < (ssize_t) image->rows; y++)
 553       {
 554         CubeInfo
 555           cube;
 556
 557         register Quantum
 558           *restrict q;
 559
 560         register ssize_t
 561           x;
 562
 563         ssize_t
 564           count;
 565
 566         if (status == MagickFalse)
 567           continue;
 568         q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
 569           exception);
 570         if (q == (Quantum *) NULL)
 571           {
 572             status=MagickFalse;
 573             continue;
 574           }
 575         cube=(*cube_info);
 576         for (x=0; x < (ssize_t) image->columns; x+=count)
 577         {
 578           RealPixelInfo
 579             pixel;
 580
 581           register const NodeInfo
 582             *node_info;
 583
 584           register ssize_t
 585             i;
 586
 587           size_t
 588             id,
 589             index;
 590
 591           /*
 592             Identify the deepest node containing the pixel's color.
 593           */
 594           for (count=1; (x+count) < (ssize_t) image->columns; count++)
 595           {
 596             PixelInfo
 597               packet;
 598
 599             GetPixelInfoPixel(image,q+count*GetPixelChannels(image),&packet);
 600             if (IsPixelEquivalent(image,q,&packet) == MagickFalse)
 601               break;
 602           }
 603           AssociateAlphaPixel(image,&cube,q,&pixel);
 604           node_info=cube.root;
 605           for (index=MaxTreeDepth-1; (ssize_t) index > 0; index--)
 606           {
 607             id=ColorToNodeId(&cube,&pixel,index);
 608             if (node_info->child[id] == (NodeInfo *) NULL)
 609               break;
 610             node_info=node_info->child[id];
 611           }
 612           /*
 613             Find closest color among siblings and their children.
 614           */
 615           cube.target=pixel;
 616           cube.distance=(double) (4.0*(QuantumRange+1.0)*
 617             (QuantumRange+1.0)+1.0);
 618           ClosestColor(image,&cube,node_info->parent);
 619           index=cube.color_number;
 620           for (i=0; i < (ssize_t) count; i++)
 621           {
 622             if (image->storage_class == PseudoClass)
 623               SetPixelIndex(image,(Quantum) index,q);
 624             if (cube.quantize_info->measure_error == MagickFalse)
 625               {
 626                 SetPixelRed(image,ClampToQuantum(
 627                   image->colormap[index].red),q);
 628                 SetPixelGreen(image,ClampToQuantum(
 629                   image->colormap[index].green),q);
 630                 SetPixelBlue(image,ClampToQuantum(
 631                   image->colormap[index].blue),q);
 632                 if (cube.associate_alpha != MagickFalse)
 633                   SetPixelAlpha(image,ClampToQuantum(
 634                     image->colormap[index].alpha),q);
 635               }
 636             q+=GetPixelChannels(image);
 637           }
 638         }
 639         if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
 640           status=MagickFalse;
 641         if (image->progress_monitor != (MagickProgressMonitor) NULL)
 642           {
 643             MagickBooleanType
 644               proceed;
 645
 646 #if defined(MAGICKCORE_OPENMP_SUPPORT)
 647             #pragma omp critical (MagickCore_AssignImageColors)
 648 #endif
 649             proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) y,
 650               image->rows);
 651             if (proceed == MagickFalse)
 652               status=MagickFalse;
 653           }
 654       }
 655       image_view=DestroyCacheView(image_view);
 656     }
 657   if (cube_info->quantize_info->measure_error != MagickFalse)
 658     (void) GetImageQuantizeError(image,exception);
 659   if ((cube_info->quantize_info->number_colors == 2) &&
 660       (cube_info->quantize_info->colorspace == GRAYColorspace))
 661     {
 662       double
 663         intensity;
 664
 665       register PixelInfo
 666         *restrict q;
 667
 668       register ssize_t
 669         i;
 670
 671       /*
 672         Monochrome image.
 673       */
 674       q=image->colormap;
 675       for (i=0; i < (ssize_t) image->colors; i++)
 676       {
 677         intensity=(double) (GetPixelInfoLuma(q) < (QuantumRange/2.0) ? 0 :
 678           QuantumRange);
 679         q->red=intensity;
 680         q->green=intensity;
 681         q->blue=intensity;
 682         q++;
 683       }
 684     }
 685   (void) SyncImage(image,exception);
 686   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
 687       (cube_info->quantize_info->colorspace != CMYKColorspace))
 688     (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
 689   return(MagickTrue);
 690 }
 691 \f
 692 /*
 693 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 694 %                                                                             %
 695 %                                                                             %
 696 %                                                                             %
 697 +   C l a s s i f y I m a g e C o l o r s                                     %
 698 %                                                                             %
 699 %                                                                             %
 700 %                                                                             %
 701 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 702 %
 703 %  ClassifyImageColors() begins by initializing a color description tree
 704 %  of sufficient depth to represent each possible input color in a leaf.
 705 %  However, it is impractical to generate a fully-formed color
 706 %  description tree in the storage_class phase for realistic values of
 707 %  Cmax.  If colors components in the input image are quantized to k-bit
 708 %  precision, so that Cmax= 2k-1, the tree would need k levels below the
 709 %  root node to allow representing each possible input color in a leaf.
 710 %  This becomes prohibitive because the tree's total number of nodes is
 711 %  1 + sum(i=1,k,8k).
 712 %
 713 %  A complete tree would require 19,173,961 nodes for k = 8, Cmax = 255.
 714 %  Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
 715 %  Initializes data structures for nodes only as they are needed;  (2)
 716 %  Chooses a maximum depth for the tree as a function of the desired
 717 %  number of colors in the output image (currently log2(colormap size)).
 718 %
 719 %  For each pixel in the input image, storage_class scans downward from
 720 %  the root of the color description tree.  At each level of the tree it
 721 %  identifies the single node which represents a cube in RGB space
 722 %  containing It updates the following data for each such node:
 723 %
 724 %    n1 : Number of pixels whose color is contained in the RGB cube
 725 %    which this node represents;
 726 %
 727 %    n2 : Number of pixels whose color is not represented in a node at
 728 %    lower depth in the tree;  initially,  n2 = 0 for all nodes except
 729 %    leaves of the tree.
 730 %
 731 %    Sr, Sg, Sb : Sums of the red, green, and blue component values for
 732 %    all pixels not classified at a lower depth. The combination of
 733 %    these sums and n2  will ultimately characterize the mean color of a
 734 %    set of pixels represented by this node.
 735 %
 736 %    E: the distance squared in RGB space between each pixel contained
 737 %    within a node and the nodes' center.  This represents the quantization
 738 %    error for a node.
 739 %
 740 %  The format of the ClassifyImageColors() method is:
 741 %
 742 %      MagickBooleanType ClassifyImageColors(CubeInfo *cube_info,
 743 %        const Image *image,ExceptionInfo *exception)
 744 %
 745 %  A description of each parameter follows.
 746 %
 747 %    o cube_info: A pointer to the Cube structure.
 748 %
 749 %    o image: the image.
 750 %
 751 */
 752
 753 static inline void SetAssociatedAlpha(const Image *image,CubeInfo *cube_info)
 754 {
 755   MagickBooleanType
 756     associate_alpha;
 757
 758   associate_alpha=image->alpha_trait != UndefinedPixelTrait ? MagickTrue :
 759     MagickFalse;
 760   if ((cube_info->quantize_info->number_colors == 2) &&
 761       (cube_info->quantize_info->colorspace == GRAYColorspace))
 762     associate_alpha=MagickFalse;
 763   cube_info->associate_alpha=associate_alpha;
 764 }
 765
 766 static MagickBooleanType ClassifyImageColors(CubeInfo *cube_info,
 767   const Image *image,ExceptionInfo *exception)
 768 {
 769 #define ClassifyImageTag  "Classify/Image"
 770
 771   CacheView
 772     *image_view;
 773
 774   MagickBooleanType
 775     proceed;
 776
 777   double
 778     bisect;
 779
 780   NodeInfo
 781     *node_info;
 782
 783   RealPixelInfo
 784     error,
 785     mid,
 786     midpoint,
 787     pixel;
 788
 789   size_t
 790     count,
 791     id,
 792     index,
 793     level;
 794
 795   ssize_t
 796     y;
 797
 798   /*
 799     Classify the first cube_info->maximum_colors colors to a tree depth of 8.
 800   */
 801   SetAssociatedAlpha(image,cube_info);
 802   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
 803       (cube_info->quantize_info->colorspace != CMYKColorspace))
 804     (void) TransformImageColorspace((Image *) image,
 805       cube_info->quantize_info->colorspace,exception);
 806   else
 807     if (IssRGBCompatibleColorspace(image->colorspace) == MagickFalse)
 808       (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
 809   midpoint.red=(double) QuantumRange/2.0;
 810   midpoint.green=(double) QuantumRange/2.0;
 811   midpoint.blue=(double) QuantumRange/2.0;
 812   midpoint.alpha=(double) QuantumRange/2.0;
 813   error.alpha=0.0;
 814   image_view=AcquireVirtualCacheView(image,exception);
 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=((double) QuantumRange+1.0)/2.0;
 851       mid=midpoint;
 852       node_info=cube_info->root;
 853       for (level=1; level <= MaxTreeDepth; level++)
 854       {
 855         double
 856           distance;
 857
 858         bisect*=0.5;
 859         id=ColorToNodeId(cube_info,&pixel,index);
 860         mid.red+=(id & 1) != 0 ? bisect : -bisect;
 861         mid.green+=(id & 2) != 0 ? bisect : -bisect;
 862         mid.blue+=(id & 4) != 0 ? bisect : -bisect;
 863         mid.alpha+=(id & 8) != 0 ? bisect : -bisect;
 864         if (node_info->child[id] == (NodeInfo *) NULL)
 865           {
 866             /*
 867               Set colors of new node to contain pixel.
 868             */
 869             node_info->child[id]=GetNodeInfo(cube_info,id,level,node_info);
 870             if (node_info->child[id] == (NodeInfo *) NULL)
 871               {
 872                 (void) ThrowMagickException(exception,GetMagickModule(),
 873                   ResourceLimitError,"MemoryAllocationFailed","`%s'",
 874                   image->filename);
 875                 continue;
 876               }
 877             if (level == MaxTreeDepth)
 878               cube_info->colors++;
 879           }
 880         /*
 881           Approximate the quantization error represented by this node.
 882         */
 883         node_info=node_info->child[id];
 884         error.red=QuantumScale*(pixel.red-mid.red);
 885         error.green=QuantumScale*(pixel.green-mid.green);
 886         error.blue=QuantumScale*(pixel.blue-mid.blue);
 887         if (cube_info->associate_alpha != MagickFalse)
 888           error.alpha=QuantumScale*(pixel.alpha-mid.alpha);
 889         distance=(double) (error.red*error.red+error.green*error.green+
 890           error.blue*error.blue+error.alpha*error.alpha);
 891         if (IsNaN(distance) != MagickFalse)
 892           distance=0.0;
 893         node_info->quantize_error+=count*sqrt(distance);
 894         cube_info->root->quantize_error+=node_info->quantize_error;
 895         index--;
 896       }
 897       /*
 898         Sum RGB for this leaf for later derivation of the mean cube color.
 899       */
 900       node_info->number_unique+=count;
 901       node_info->total_color.red+=count*QuantumScale*ClampPixel(pixel.red);
 902       node_info->total_color.green+=count*QuantumScale*ClampPixel(pixel.green);
 903       node_info->total_color.blue+=count*QuantumScale*ClampPixel(pixel.blue);
 904       if (cube_info->associate_alpha != MagickFalse)
 905         node_info->total_color.alpha+=count*QuantumScale*ClampPixel(
 906           pixel.alpha);
 907       p+=count*GetPixelChannels(image);
 908     }
 909     if (cube_info->colors > cube_info->maximum_colors)
 910       {
 911         PruneToCubeDepth(image,cube_info,cube_info->root);
 912         break;
 913       }
 914     proceed=SetImageProgress(image,ClassifyImageTag,(MagickOffsetType) y,
 915       image->rows);
 916     if (proceed == MagickFalse)
 917       break;
 918   }
 919   for (y++; y < (ssize_t) image->rows; y++)
 920   {
 921     register const Quantum
 922       *restrict p;
 923
 924     register ssize_t
 925       x;
 926
 927     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
 928     if (p == (const Quantum *) NULL)
 929       break;
 930     if (cube_info->nodes > MaxNodes)
 931       {
 932         /*
 933           Prune one level if the color tree is too large.
 934         */
 935         PruneLevel(image,cube_info,cube_info->root);
 936         cube_info->depth--;
 937       }
 938     for (x=0; x < (ssize_t) image->columns; x+=(ssize_t) count)
 939     {
 940       /*
 941         Start at the root and descend the color cube tree.
 942       */
 943       for (count=1; (x+(ssize_t) count) < (ssize_t) image->columns; count++)
 944       {
 945         PixelInfo
 946           packet;
 947
 948         GetPixelInfoPixel(image,p+count*GetPixelChannels(image),&packet);
 949         if (IsPixelEquivalent(image,p,&packet) == MagickFalse)
 950           break;
 951       }
 952       AssociateAlphaPixel(image,cube_info,p,&pixel);
 953       index=MaxTreeDepth-1;
 954       bisect=((double) QuantumRange+1.0)/2.0;
 955       mid=midpoint;
 956       node_info=cube_info->root;
 957       for (level=1; level <= cube_info->depth; level++)
 958       {
 959         double
 960           distance;
 961
 962         bisect*=0.5;
 963         id=ColorToNodeId(cube_info,&pixel,index);
 964         mid.red+=(id & 1) != 0 ? bisect : -bisect;
 965         mid.green+=(id & 2) != 0 ? bisect : -bisect;
 966         mid.blue+=(id & 4) != 0 ? bisect : -bisect;
 967         mid.alpha+=(id & 8) != 0 ? bisect : -bisect;
 968         if (node_info->child[id] == (NodeInfo *) NULL)
 969           {
 970             /*
 971               Set colors of new node to contain pixel.
 972             */
 973             node_info->child[id]=GetNodeInfo(cube_info,id,level,node_info);
 974             if (node_info->child[id] == (NodeInfo *) NULL)
 975               {
 976                 (void) ThrowMagickException(exception,GetMagickModule(),
 977                   ResourceLimitError,"MemoryAllocationFailed","%s",
 978                   image->filename);
 979                 continue;
 980               }
 981             if (level == cube_info->depth)
 982               cube_info->colors++;
 983           }
 984         /*
 985           Approximate the quantization error represented by this node.
 986         */
 987         node_info=node_info->child[id];
 988         error.red=QuantumScale*(pixel.red-mid.red);
 989         error.green=QuantumScale*(pixel.green-mid.green);
 990         error.blue=QuantumScale*(pixel.blue-mid.blue);
 991         if (cube_info->associate_alpha != MagickFalse)
 992           error.alpha=QuantumScale*(pixel.alpha-mid.alpha);
 993         distance=(double) (error.red*error.red+error.green*error.green+
 994           error.blue*error.blue+error.alpha*error.alpha);
 995         if (IsNaN(distance) != MagickFalse)
 996           distance=0.0;
 997         node_info->quantize_error+=count*sqrt(distance);
 998         cube_info->root->quantize_error+=node_info->quantize_error;
 999         index--;
1000       }
1001       /*
1002         Sum RGB for this leaf for later derivation of the mean cube color.
1003       */
1004       node_info->number_unique+=count;
1005       node_info->total_color.red+=count*QuantumScale*ClampPixel(pixel.red);
1006       node_info->total_color.green+=count*QuantumScale*ClampPixel(pixel.green);
1007       node_info->total_color.blue+=count*QuantumScale*ClampPixel(pixel.blue);
1008       if (cube_info->associate_alpha != MagickFalse)
1009         node_info->total_color.alpha+=count*QuantumScale*ClampPixel(
1010           pixel.alpha);
1011       p+=count*GetPixelChannels(image);
1012     }
1013     proceed=SetImageProgress(image,ClassifyImageTag,(MagickOffsetType) y,
1014       image->rows);
1015     if (proceed == MagickFalse)
1016       break;
1017   }
1018   image_view=DestroyCacheView(image_view);
1019   if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
1020       (cube_info->quantize_info->colorspace != CMYKColorspace))
1021     (void) TransformImageColorspace((Image *) image,sRGBColorspace,exception);
1022   return(y < (ssize_t) image->rows ? MagickFalse : MagickTrue);
1023 }
1024 \f
1025 /*
1026 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1027 %                                                                             %
1028 %                                                                             %
1029 %                                                                             %
1030 %   C l o n e Q u a n t i z e I n f o                                         %
1031 %                                                                             %
1032 %                                                                             %
1033 %                                                                             %
1034 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1035 %
1036 %  CloneQuantizeInfo() makes a duplicate of the given quantize info structure,
1037 %  or if quantize info is NULL, a new one.
1038 %
1039 %  The format of the CloneQuantizeInfo method is:
1040 %
1041 %      QuantizeInfo *CloneQuantizeInfo(const QuantizeInfo *quantize_info)
1042 %
1043 %  A description of each parameter follows:
1044 %
1045 %    o clone_info: Method CloneQuantizeInfo returns a duplicate of the given
1046 %      quantize info, or if image info is NULL a new one.
1047 %
1048 %    o quantize_info: a structure of type info.
1049 %
1050 */
1051 MagickExport QuantizeInfo *CloneQuantizeInfo(const QuantizeInfo *quantize_info)
1052 {
1053   QuantizeInfo
1054     *clone_info;
1055
1056   clone_info=(QuantizeInfo *) AcquireMagickMemory(sizeof(*clone_info));
1057   if (clone_info == (QuantizeInfo *) NULL)
1058     ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
1059   GetQuantizeInfo(clone_info);
1060   if (quantize_info == (QuantizeInfo *) NULL)
1061     return(clone_info);
1062   clone_info->number_colors=quantize_info->number_colors;
1063   clone_info->tree_depth=quantize_info->tree_depth;
1064   clone_info->dither_method=quantize_info->dither_method;
1065   clone_info->colorspace=quantize_info->colorspace;
1066   clone_info->measure_error=quantize_info->measure_error;
1067   return(clone_info);
1068 }
1069 \f
1070 /*
1071 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1072 %                                                                             %
1073 %                                                                             %
1074 %                                                                             %
1075 +   C l o s e s t C o l o r                                                   %
1076 %                                                                             %
1077 %                                                                             %
1078 %                                                                             %
1079 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1080 %
1081 %  ClosestColor() traverses the color cube tree at a particular node and
1082 %  determines which colormap entry best represents the input color.
1083 %
1084 %  The format of the ClosestColor method is:
1085 %
1086 %      void ClosestColor(const Image *image,CubeInfo *cube_info,
1087 %        const NodeInfo *node_info)
1088 %
1089 %  A description of each parameter follows.
1090 %
1091 %    o image: the image.
1092 %
1093 %    o cube_info: A pointer to the Cube structure.
1094 %
1095 %    o node_info: the address of a structure of type NodeInfo which points to a
1096 %      node in the color cube tree that is to be pruned.
1097 %
1098 */
1099 static void ClosestColor(const Image *image,CubeInfo *cube_info,
1100   const NodeInfo *node_info)
1101 {
1102   register ssize_t
1103     i;
1104
1105   size_t
1106     number_children;
1107
1108   /*
1109     Traverse any children.
1110   */
1111   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
1112   for (i=0; i < (ssize_t) number_children; i++)
1113     if (node_info->child[i] != (NodeInfo *) NULL)
1114       ClosestColor(image,cube_info,node_info->child[i]);
1115   if (node_info->number_unique != 0)
1116     {
1117       double
1118         pixel;
1119
1120       register double
1121         alpha,
1122         beta,
1123         distance;
1124
1125       register PixelInfo
1126         *restrict p;
1127
1128       register RealPixelInfo
1129         *restrict q;
1130
1131       /*
1132         Determine if this color is "closest".
1133       */
1134       p=image->colormap+node_info->color_number;
1135       q=(&cube_info->target);
1136       alpha=1.0;
1137       beta=1.0;
1138       if (cube_info->associate_alpha != MagickFalse)
1139         {
1140           alpha=(double) (QuantumScale*p->alpha);
1141           beta=(double) (QuantumScale*q->alpha);
1142         }
1143       pixel=alpha*p->red-beta*q->red;
1144       distance=pixel*pixel;
1145       if (distance <= cube_info->distance)
1146         {
1147           pixel=alpha*p->green-beta*q->green;
1148           distance+=pixel*pixel;
1149           if (distance <= cube_info->distance)
1150             {
1151               pixel=alpha*p->blue-beta*q->blue;
1152               distance+=pixel*pixel;
1153               if (distance <= cube_info->distance)
1154                 {
1155                   pixel=alpha-beta;
1156                   distance+=pixel*pixel;
1157                   if (distance <= cube_info->distance)
1158                     {
1159                       cube_info->distance=distance;
1160                       cube_info->color_number=node_info->color_number;
1161                     }
1162                 }
1163             }
1164         }
1165     }
1166 }
1167 \f
1168 /*
1169 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1170 %                                                                             %
1171 %                                                                             %
1172 %                                                                             %
1173 %   C o m p r e s s I m a g e C o l o r m a p                                 %
1174 %                                                                             %
1175 %                                                                             %
1176 %                                                                             %
1177 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1178 %
1179 %  CompressImageColormap() compresses an image colormap by removing any
1180 %  duplicate or unused color entries.
1181 %
1182 %  The format of the CompressImageColormap method is:
1183 %
1184 %      MagickBooleanType CompressImageColormap(Image *image,
1185 %        ExceptionInfo *exception)
1186 %
1187 %  A description of each parameter follows:
1188 %
1189 %    o image: the image.
1190 %
1191 %    o exception: return any errors or warnings in this structure.
1192 %
1193 */
1194 MagickExport MagickBooleanType CompressImageColormap(Image *image,
1195   ExceptionInfo *exception)
1196 {
1197   QuantizeInfo
1198     quantize_info;
1199
1200   assert(image != (Image *) NULL);
1201   assert(image->signature == MagickSignature);
1202   if (image->debug != MagickFalse)
1203     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
1204   if (IsPaletteImage(image,exception) == MagickFalse)
1205     return(MagickFalse);
1206   GetQuantizeInfo(&quantize_info);
1207   quantize_info.number_colors=image->colors;
1208   quantize_info.tree_depth=MaxTreeDepth;
1209   return(QuantizeImage(&quantize_info,image,exception));
1210 }
1211 \f
1212 /*
1213 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1214 %                                                                             %
1215 %                                                                             %
1216 %                                                                             %
1217 +   D e f i n e I m a g e C o l o r m a p                                     %
1218 %                                                                             %
1219 %                                                                             %
1220 %                                                                             %
1221 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1222 %
1223 %  DefineImageColormap() traverses the color cube tree and notes each colormap
1224 %  entry.  A colormap entry is any node in the color cube tree where the
1225 %  of unique colors is not zero.  DefineImageColormap() returns the number of
1226 %  colors in the image colormap.
1227 %
1228 %  The format of the DefineImageColormap method is:
1229 %
1230 %      size_t DefineImageColormap(Image *image,CubeInfo *cube_info,
1231 %        NodeInfo *node_info)
1232 %
1233 %  A description of each parameter follows.
1234 %
1235 %    o image: the image.
1236 %
1237 %    o cube_info: A pointer to the Cube structure.
1238 %
1239 %    o node_info: the address of a structure of type NodeInfo which points to a
1240 %      node in the color cube tree that is to be pruned.
1241 %
1242 */
1243 static size_t DefineImageColormap(Image *image,CubeInfo *cube_info,
1244   NodeInfo *node_info)
1245 {
1246   register ssize_t
1247     i;
1248
1249   size_t
1250     number_children;
1251
1252   /*
1253     Traverse any children.
1254   */
1255   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
1256   for (i=0; i < (ssize_t) number_children; i++)
1257     if (node_info->child[i] != (NodeInfo *) NULL)
1258       (void) DefineImageColormap(image,cube_info,node_info->child[i]);
1259   if (node_info->number_unique != 0)
1260     {
1261       register double
1262         alpha;
1263
1264       register PixelInfo
1265         *restrict q;
1266
1267       /*
1268         Colormap entry is defined by the mean color in this cube.
1269       */
1270       q=image->colormap+image->colors;
1271       alpha=(double) ((MagickOffsetType) node_info->number_unique);
1272       alpha=PerceptibleReciprocal(alpha);
1273       if (cube_info->associate_alpha == MagickFalse)
1274         {
1275           q->red=(double) ClampToQuantum(alpha*QuantumRange*
1276             node_info->total_color.red);
1277           q->green=(double) ClampToQuantum(alpha*QuantumRange*
1278             node_info->total_color.green);
1279           q->blue=(double) ClampToQuantum(alpha*QuantumRange*
1280             node_info->total_color.blue);
1281           q->alpha=(double) OpaqueAlpha;
1282         }
1283       else
1284         {
1285           double
1286             opacity;
1287
1288           opacity=(double) (alpha*QuantumRange*node_info->total_color.alpha);
1289           q->alpha=(double) ClampToQuantum((opacity));
1290           if (q->alpha == OpaqueAlpha)
1291             {
1292               q->red=(double) ClampToQuantum(alpha*QuantumRange*
1293                 node_info->total_color.red);
1294               q->green=(double) ClampToQuantum(alpha*QuantumRange*
1295                 node_info->total_color.green);
1296               q->blue=(double) ClampToQuantum(alpha*QuantumRange*
1297                 node_info->total_color.blue);
1298             }
1299           else
1300             {
1301               double
1302                 gamma;
1303
1304               gamma=(double) (QuantumScale*q->alpha);
1305               gamma=PerceptibleReciprocal(gamma);
1306               q->red=(double) ClampToQuantum(alpha*gamma*QuantumRange*
1307                 node_info->total_color.red);
1308               q->green=(double) ClampToQuantum(alpha*gamma*QuantumRange*
1309                 node_info->total_color.green);
1310               q->blue=(double) ClampToQuantum(alpha*gamma*QuantumRange*
1311                 node_info->total_color.blue);
1312               if (node_info->number_unique > cube_info->transparent_pixels)
1313                 {
1314                   cube_info->transparent_pixels=node_info->number_unique;
1315                   cube_info->transparent_index=(ssize_t) image->colors;
1316                 }
1317             }
1318         }
1319       node_info->color_number=image->colors++;
1320     }
1321   return(image->colors);
1322 }
1323 \f
1324 /*
1325 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1326 %                                                                             %
1327 %                                                                             %
1328 %                                                                             %
1329 +   D e s t r o y C u b e I n f o                                             %
1330 %                                                                             %
1331 %                                                                             %
1332 %                                                                             %
1333 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1334 %
1335 %  DestroyCubeInfo() deallocates memory associated with an image.
1336 %
1337 %  The format of the DestroyCubeInfo method is:
1338 %
1339 %      DestroyCubeInfo(CubeInfo *cube_info)
1340 %
1341 %  A description of each parameter follows:
1342 %
1343 %    o cube_info: the address of a structure of type CubeInfo.
1344 %
1345 */
1346 static void DestroyCubeInfo(CubeInfo *cube_info)
1347 {
1348   register Nodes
1349     *nodes;
1350
1351   /*
1352     Release color cube tree storage.
1353   */
1354   do
1355   {
1356     nodes=cube_info->node_queue->next;
1357     cube_info->node_queue->nodes=(NodeInfo *) RelinquishMagickMemory(
1358       cube_info->node_queue->nodes);
1359     cube_info->node_queue=(Nodes *) RelinquishMagickMemory(
1360       cube_info->node_queue);
1361     cube_info->node_queue=nodes;
1362   } while (cube_info->node_queue != (Nodes *) NULL);
1363   if (cube_info->memory_info != (MemoryInfo *) NULL)
1364     cube_info->memory_info=RelinquishVirtualMemory(cube_info->memory_info);
1365   cube_info->quantize_info=DestroyQuantizeInfo(cube_info->quantize_info);
1366   cube_info=(CubeInfo *) RelinquishMagickMemory(cube_info);
1367 }
1368 \f
1369 /*
1370 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1371 %                                                                             %
1372 %                                                                             %
1373 %                                                                             %
1374 %   D e s t r o y Q u a n t i z e I n f o                                     %
1375 %                                                                             %
1376 %                                                                             %
1377 %                                                                             %
1378 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1379 %
1380 %  DestroyQuantizeInfo() deallocates memory associated with an QuantizeInfo
1381 %  structure.
1382 %
1383 %  The format of the DestroyQuantizeInfo method is:
1384 %
1385 %      QuantizeInfo *DestroyQuantizeInfo(QuantizeInfo *quantize_info)
1386 %
1387 %  A description of each parameter follows:
1388 %
1389 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
1390 %
1391 */
1392 MagickExport QuantizeInfo *DestroyQuantizeInfo(QuantizeInfo *quantize_info)
1393 {
1394   (void) LogMagickEvent(TraceEvent,GetMagickModule(),"...");
1395   assert(quantize_info != (QuantizeInfo *) NULL);
1396   assert(quantize_info->signature == MagickSignature);
1397   quantize_info->signature=(~MagickSignature);
1398   quantize_info=(QuantizeInfo *) RelinquishMagickMemory(quantize_info);
1399   return(quantize_info);
1400 }
1401 \f
1402 /*
1403 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1404 %                                                                             %
1405 %                                                                             %
1406 %                                                                             %
1407 +   D i t h e r I m a g e                                                     %
1408 %                                                                             %
1409 %                                                                             %
1410 %                                                                             %
1411 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1412 %
1413 %  DitherImage() distributes the difference between an original image and
1414 %  the corresponding color reduced algorithm to neighboring pixels using
1415 %  serpentine-scan Floyd-Steinberg error diffusion. DitherImage returns
1416 %  MagickTrue if the image is dithered otherwise MagickFalse.
1417 %
1418 %  The format of the DitherImage method is:
1419 %
1420 %      MagickBooleanType DitherImage(Image *image,CubeInfo *cube_info,
1421 %        ExceptionInfo *exception)
1422 %
1423 %  A description of each parameter follows.
1424 %
1425 %    o image: the image.
1426 %
1427 %    o cube_info: A pointer to the Cube structure.
1428 %
1429 %    o exception: return any errors or warnings in this structure.
1430 %
1431 */
1432
1433 static RealPixelInfo **DestroyPixelThreadSet(RealPixelInfo **pixels)
1434 {
1435   register ssize_t
1436     i;
1437
1438   assert(pixels != (RealPixelInfo **) NULL);
1439   for (i=0; i < (ssize_t) GetMagickResourceLimit(ThreadResource); i++)
1440     if (pixels[i] != (RealPixelInfo *) NULL)
1441       pixels[i]=(RealPixelInfo *) RelinquishMagickMemory(pixels[i]);
1442   pixels=(RealPixelInfo **) RelinquishMagickMemory(pixels);
1443   return(pixels);
1444 }
1445
1446 static RealPixelInfo **AcquirePixelThreadSet(const size_t count)
1447 {
1448   RealPixelInfo
1449     **pixels;
1450
1451   register ssize_t
1452     i;
1453
1454   size_t
1455     number_threads;
1456
1457   number_threads=(size_t) GetMagickResourceLimit(ThreadResource);
1458   pixels=(RealPixelInfo **) AcquireQuantumMemory(number_threads,
1459     sizeof(*pixels));
1460   if (pixels == (RealPixelInfo **) NULL)
1461     return((RealPixelInfo **) NULL);
1462   (void) ResetMagickMemory(pixels,0,number_threads*sizeof(*pixels));
1463   for (i=0; i < (ssize_t) number_threads; i++)
1464   {
1465     pixels[i]=(RealPixelInfo *) AcquireQuantumMemory(count,2*sizeof(**pixels));
1466     if (pixels[i] == (RealPixelInfo *) NULL)
1467       return(DestroyPixelThreadSet(pixels));
1468   }
1469   return(pixels);
1470 }
1471
1472 static inline ssize_t CacheOffset(CubeInfo *cube_info,
1473   const RealPixelInfo *pixel)
1474 {
1475 #define RedShift(pixel) (((pixel) >> CacheShift) << (0*(8-CacheShift)))
1476 #define GreenShift(pixel) (((pixel) >> CacheShift) << (1*(8-CacheShift)))
1477 #define BlueShift(pixel) (((pixel) >> CacheShift) << (2*(8-CacheShift)))
1478 #define AlphaShift(pixel) (((pixel) >> CacheShift) << (3*(8-CacheShift)))
1479
1480   ssize_t
1481     offset;
1482
1483   offset=(ssize_t) (RedShift(ScaleQuantumToChar(ClampPixel(pixel->red))) |
1484     GreenShift(ScaleQuantumToChar(ClampPixel(pixel->green))) |
1485     BlueShift(ScaleQuantumToChar(ClampPixel(pixel->blue))));
1486   if (cube_info->associate_alpha != MagickFalse)
1487     offset|=AlphaShift(ScaleQuantumToChar(ClampPixel(pixel->alpha)));
1488   return(offset);
1489 }
1490
1491 static MagickBooleanType FloydSteinbergDither(Image *image,CubeInfo *cube_info,
1492   ExceptionInfo *exception)
1493 {
1494 #define DitherImageTag  "Dither/Image"
1495
1496   CacheView
1497     *image_view;
1498
1499   MagickBooleanType
1500     status;
1501
1502   RealPixelInfo
1503     **pixels;
1504
1505   ssize_t
1506     y;
1507
1508   /*
1509     Distribute quantization error using Floyd-Steinberg.
1510   */
1511   pixels=AcquirePixelThreadSet(image->columns);
1512   if (pixels == (RealPixelInfo **) NULL)
1513     return(MagickFalse);
1514   status=MagickTrue;
1515   image_view=AcquireAuthenticCacheView(image,exception);
1516   for (y=0; y < (ssize_t) image->rows; y++)
1517   {
1518     const int
1519       id = GetOpenMPThreadId();
1520
1521     CubeInfo
1522       cube;
1523
1524     RealPixelInfo
1525       *current,
1526       *previous;
1527
1528     register Quantum
1529       *restrict q;
1530
1531     register ssize_t
1532       x;
1533
1534     size_t
1535       index;
1536
1537     ssize_t
1538       v;
1539
1540     if (status == MagickFalse)
1541       continue;
1542     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
1543     if (q == (Quantum *) NULL)
1544       {
1545         status=MagickFalse;
1546         continue;
1547       }
1548     q+=(y & 0x01)*GetPixelChannels(image)*image->columns;
1549     cube=(*cube_info);
1550     current=pixels[id]+(y & 0x01)*image->columns;
1551     previous=pixels[id]+((y+1) & 0x01)*image->columns;
1552     v=(ssize_t) ((y & 0x01) != 0 ? -1 : 1);
1553     for (x=0; x < (ssize_t) image->columns; x++)
1554     {
1555       RealPixelInfo
1556         color,
1557         pixel;
1558
1559       register ssize_t
1560         i;
1561
1562       ssize_t
1563         u;
1564
1565       q-=(y & 0x01)*GetPixelChannels(image);
1566       u=(y & 0x01) != 0 ? (ssize_t) image->columns-1-x : x;
1567       AssociateAlphaPixel(image,&cube,q,&pixel);
1568       if (x > 0)
1569         {
1570           pixel.red+=7*current[u-v].red/16;
1571           pixel.green+=7*current[u-v].green/16;
1572           pixel.blue+=7*current[u-v].blue/16;
1573           if (cube.associate_alpha != MagickFalse)
1574             pixel.alpha+=7*current[u-v].alpha/16;
1575         }
1576       if (y > 0)
1577         {
1578           if (x < (ssize_t) (image->columns-1))
1579             {
1580               pixel.red+=previous[u+v].red/16;
1581               pixel.green+=previous[u+v].green/16;
1582               pixel.blue+=previous[u+v].blue/16;
1583               if (cube.associate_alpha != MagickFalse)
1584                 pixel.alpha+=previous[u+v].alpha/16;
1585             }
1586           pixel.red+=5*previous[u].red/16;
1587           pixel.green+=5*previous[u].green/16;
1588           pixel.blue+=5*previous[u].blue/16;
1589           if (cube.associate_alpha != MagickFalse)
1590             pixel.alpha+=5*previous[u].alpha/16;
1591           if (x > 0)
1592             {
1593               pixel.red+=3*previous[u-v].red/16;
1594               pixel.green+=3*previous[u-v].green/16;
1595               pixel.blue+=3*previous[u-v].blue/16;
1596               if (cube.associate_alpha != MagickFalse)
1597                 pixel.alpha+=3*previous[u-v].alpha/16;
1598             }
1599         }
1600       pixel.red=(double) ClampPixel(pixel.red);
1601       pixel.green=(double) ClampPixel(pixel.green);
1602       pixel.blue=(double) ClampPixel(pixel.blue);
1603       if (cube.associate_alpha != MagickFalse)
1604         pixel.alpha=(double) ClampPixel(pixel.alpha);
1605       i=CacheOffset(&cube,&pixel);
1606       if (cube.cache[i] < 0)
1607         {
1608           register NodeInfo
1609             *node_info;
1610
1611           register size_t
1612             id;
1613
1614           /*
1615             Identify the deepest node containing the pixel's color.
1616           */
1617           node_info=cube.root;
1618           for (index=MaxTreeDepth-1; (ssize_t) index > 0; index--)
1619           {
1620             id=ColorToNodeId(&cube,&pixel,index);
1621             if (node_info->child[id] == (NodeInfo *) NULL)
1622               break;
1623             node_info=node_info->child[id];
1624           }
1625           /*
1626             Find closest color among siblings and their children.
1627           */
1628           cube.target=pixel;
1629           cube.distance=(double) (4.0*(QuantumRange+1.0)*(QuantumRange+1.0)+
1630             1.0);
1631           ClosestColor(image,&cube,node_info->parent);
1632           cube.cache[i]=(ssize_t) cube.color_number;
1633         }
1634       /*
1635         Assign pixel to closest colormap entry.
1636       */
1637       index=(size_t) cube.cache[i];
1638       if (image->storage_class == PseudoClass)
1639         SetPixelIndex(image,(Quantum) index,q);
1640       if (cube.quantize_info->measure_error == MagickFalse)
1641         {
1642           SetPixelRed(image,ClampToQuantum(image->colormap[index].red),q);
1643           SetPixelGreen(image,ClampToQuantum(image->colormap[index].green),q);
1644           SetPixelBlue(image,ClampToQuantum(image->colormap[index].blue),q);
1645           if (cube.associate_alpha != MagickFalse)
1646             SetPixelAlpha(image,ClampToQuantum(image->colormap[index].alpha),q);
1647         }
1648       if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1649         status=MagickFalse;
1650       /*
1651         Store the error.
1652       */
1653       AssociateAlphaPixelInfo(&cube,image->colormap+index,&color);
1654       current[u].red=pixel.red-color.red;
1655       current[u].green=pixel.green-color.green;
1656       current[u].blue=pixel.blue-color.blue;
1657       if (cube.associate_alpha != MagickFalse)
1658         current[u].alpha=pixel.alpha-color.alpha;
1659       if (image->progress_monitor != (MagickProgressMonitor) NULL)
1660         {
1661           MagickBooleanType
1662             proceed;
1663
1664           proceed=SetImageProgress(image,DitherImageTag,(MagickOffsetType) y,
1665             image->rows);
1666           if (proceed == MagickFalse)
1667             status=MagickFalse;
1668         }
1669       q+=((y+1) & 0x01)*GetPixelChannels(image);
1670     }
1671   }
1672   image_view=DestroyCacheView(image_view);
1673   pixels=DestroyPixelThreadSet(pixels);
1674   return(MagickTrue);
1675 }
1676
1677 static MagickBooleanType
1678   RiemersmaDither(Image *,CacheView *,CubeInfo *,const unsigned int,
1679     ExceptionInfo *exception);
1680
1681 static void Riemersma(Image *image,CacheView *image_view,CubeInfo *cube_info,
1682   const size_t level,const unsigned int direction,ExceptionInfo *exception)
1683 {
1684   if (level == 1)
1685     switch (direction)
1686     {
1687       case WestGravity:
1688       {
1689         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1690           exception);
1691         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1692           exception);
1693         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1694           exception);
1695         break;
1696       }
1697       case EastGravity:
1698       {
1699         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1700           exception);
1701         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1702           exception);
1703         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1704           exception);
1705         break;
1706       }
1707       case NorthGravity:
1708       {
1709         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1710           exception);
1711         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1712           exception);
1713         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1714           exception);
1715         break;
1716       }
1717       case SouthGravity:
1718       {
1719         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1720           exception);
1721         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1722           exception);
1723         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1724           exception);
1725         break;
1726       }
1727       default:
1728         break;
1729     }
1730   else
1731     switch (direction)
1732     {
1733       case WestGravity:
1734       {
1735         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1736           exception);
1737         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1738           exception);
1739         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1740           exception);
1741         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1742           exception);
1743         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1744           exception);
1745         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1746           exception);
1747         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1748           exception);
1749         break;
1750       }
1751       case EastGravity:
1752       {
1753         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1754           exception);
1755         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1756           exception);
1757         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1758           exception);
1759         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1760           exception);
1761         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1762           exception);
1763         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1764           exception);
1765         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1766           exception);
1767         break;
1768       }
1769       case NorthGravity:
1770       {
1771         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1772           exception);
1773         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1774           exception);
1775         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1776           exception);
1777         (void) RiemersmaDither(image,image_view,cube_info,EastGravity,
1778           exception);
1779         Riemersma(image,image_view,cube_info,level-1,NorthGravity,
1780           exception);
1781         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1782           exception);
1783         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1784           exception);
1785         break;
1786       }
1787       case SouthGravity:
1788       {
1789         Riemersma(image,image_view,cube_info,level-1,EastGravity,
1790           exception);
1791         (void) RiemersmaDither(image,image_view,cube_info,NorthGravity,
1792           exception);
1793         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1794           exception);
1795         (void) RiemersmaDither(image,image_view,cube_info,WestGravity,
1796           exception);
1797         Riemersma(image,image_view,cube_info,level-1,SouthGravity,
1798           exception);
1799         (void) RiemersmaDither(image,image_view,cube_info,SouthGravity,
1800           exception);
1801         Riemersma(image,image_view,cube_info,level-1,WestGravity,
1802           exception);
1803         break;
1804       }
1805       default:
1806         break;
1807     }
1808 }
1809
1810 static MagickBooleanType RiemersmaDither(Image *image,CacheView *image_view,
1811   CubeInfo *cube_info,const unsigned int direction,ExceptionInfo *exception)
1812 {
1813 #define DitherImageTag  "Dither/Image"
1814
1815   MagickBooleanType
1816     proceed;
1817
1818   RealPixelInfo
1819     color,
1820     pixel;
1821
1822   register CubeInfo
1823     *p;
1824
1825   size_t
1826     index;
1827
1828   p=cube_info;
1829   if ((p->x >= 0) && (p->x < (ssize_t) image->columns) &&
1830       (p->y >= 0) && (p->y < (ssize_t) image->rows))
1831     {
1832       register Quantum
1833         *restrict q;
1834
1835       register ssize_t
1836         i;
1837
1838       /*
1839         Distribute error.
1840       */
1841       q=GetCacheViewAuthenticPixels(image_view,p->x,p->y,1,1,exception);
1842       if (q == (Quantum *) NULL)
1843         return(MagickFalse);
1844       AssociateAlphaPixel(image,cube_info,q,&pixel);
1845       for (i=0; i < ErrorQueueLength; i++)
1846       {
1847         pixel.red+=p->weights[i]*p->error[i].red;
1848         pixel.green+=p->weights[i]*p->error[i].green;
1849         pixel.blue+=p->weights[i]*p->error[i].blue;
1850         if (cube_info->associate_alpha != MagickFalse)
1851           pixel.alpha+=p->weights[i]*p->error[i].alpha;
1852       }
1853       pixel.red=(double) ClampPixel(pixel.red);
1854       pixel.green=(double) ClampPixel(pixel.green);
1855       pixel.blue=(double) ClampPixel(pixel.blue);
1856       if (cube_info->associate_alpha != MagickFalse)
1857         pixel.alpha=(double) ClampPixel(pixel.alpha);
1858       i=CacheOffset(cube_info,&pixel);
1859       if (p->cache[i] < 0)
1860         {
1861           register NodeInfo
1862             *node_info;
1863
1864           register size_t
1865             id;
1866
1867           /*
1868             Identify the deepest node containing the pixel's color.
1869           */
1870           node_info=p->root;
1871           for (index=MaxTreeDepth-1; (ssize_t) index > 0; index--)
1872           {
1873             id=ColorToNodeId(cube_info,&pixel,index);
1874             if (node_info->child[id] == (NodeInfo *) NULL)
1875               break;
1876             node_info=node_info->child[id];
1877           }
1878           /*
1879             Find closest color among siblings and their children.
1880           */
1881           p->target=pixel;
1882           p->distance=(double) (4.0*(QuantumRange+1.0)*((double)
1883             QuantumRange+1.0)+1.0);
1884           ClosestColor(image,p,node_info->parent);
1885           p->cache[i]=(ssize_t) p->color_number;
1886         }
1887       /*
1888         Assign pixel to closest colormap entry.
1889       */
1890       index=(size_t) p->cache[i];
1891       if (image->storage_class == PseudoClass)
1892         SetPixelIndex(image,(Quantum) index,q);
1893       if (cube_info->quantize_info->measure_error == MagickFalse)
1894         {
1895           SetPixelRed(image,ClampToQuantum(image->colormap[index].red),q);
1896           SetPixelGreen(image,ClampToQuantum(image->colormap[index].green),q);
1897           SetPixelBlue(image,ClampToQuantum(image->colormap[index].blue),q);
1898           if (cube_info->associate_alpha != MagickFalse)
1899             SetPixelAlpha(image,ClampToQuantum(image->colormap[index].alpha),q);
1900         }
1901       if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
1902         return(MagickFalse);
1903       /*
1904         Propagate the error as the last entry of the error queue.
1905       */
1906       (void) CopyMagickMemory(p->error,p->error+1,(ErrorQueueLength-1)*
1907         sizeof(p->error[0]));
1908       AssociateAlphaPixelInfo(cube_info,image->colormap+index,&color);
1909       p->error[ErrorQueueLength-1].red=pixel.red-color.red;
1910       p->error[ErrorQueueLength-1].green=pixel.green-color.green;
1911       p->error[ErrorQueueLength-1].blue=pixel.blue-color.blue;
1912       if (cube_info->associate_alpha != MagickFalse)
1913         p->error[ErrorQueueLength-1].alpha=pixel.alpha-color.alpha;
1914       proceed=SetImageProgress(image,DitherImageTag,p->offset,p->span);
1915       if (proceed == MagickFalse)
1916         return(MagickFalse);
1917       p->offset++;
1918     }
1919   switch (direction)
1920   {
1921     case WestGravity: p->x--; break;
1922     case EastGravity: p->x++; break;
1923     case NorthGravity: p->y--; break;
1924     case SouthGravity: p->y++; break;
1925   }
1926   return(MagickTrue);
1927 }
1928
1929 static MagickBooleanType DitherImage(Image *image,CubeInfo *cube_info,
1930   ExceptionInfo *exception)
1931 {
1932   CacheView
1933     *image_view;
1934
1935   MagickBooleanType
1936     status;
1937
1938   register ssize_t
1939     i;
1940
1941   size_t
1942     depth;
1943
1944   if (cube_info->quantize_info->dither_method != RiemersmaDitherMethod)
1945     return(FloydSteinbergDither(image,cube_info,exception));
1946   /*
1947     Distribute quantization error along a Hilbert curve.
1948   */
1949   (void) ResetMagickMemory(cube_info->error,0,ErrorQueueLength*
1950     sizeof(*cube_info->error));
1951   cube_info->x=0;
1952   cube_info->y=0;
1953   i=MagickMax((ssize_t) image->columns,(ssize_t) image->rows);
1954   for (depth=1; i != 0; depth++)
1955     i>>=1;
1956   if ((ssize_t) (1L << depth) < MagickMax((ssize_t) image->columns,(ssize_t) image->rows))
1957     depth++;
1958   cube_info->offset=0;
1959   cube_info->span=(MagickSizeType) image->columns*image->rows;
1960   image_view=AcquireAuthenticCacheView(image,exception);
1961   if (depth > 1)
1962     Riemersma(image,image_view,cube_info,depth-1,NorthGravity,exception);
1963   status=RiemersmaDither(image,image_view,cube_info,ForgetGravity,exception);
1964   image_view=DestroyCacheView(image_view);
1965   return(status);
1966 }
1967 \f
1968 /*
1969 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1970 %                                                                             %
1971 %                                                                             %
1972 %                                                                             %
1973 +   G e t C u b e I n f o                                                     %
1974 %                                                                             %
1975 %                                                                             %
1976 %                                                                             %
1977 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1978 %
1979 %  GetCubeInfo() initialize the Cube data structure.
1980 %
1981 %  The format of the GetCubeInfo method is:
1982 %
1983 %      CubeInfo GetCubeInfo(const QuantizeInfo *quantize_info,
1984 %        const size_t depth,const size_t maximum_colors)
1985 %
1986 %  A description of each parameter follows.
1987 %
1988 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
1989 %
1990 %    o depth: Normally, this integer value is zero or one.  A zero or
1991 %      one tells Quantize to choose a optimal tree depth of Log4(number_colors).
1992 %      A tree of this depth generally allows the best representation of the
1993 %      reference image with the least amount of memory and the fastest
1994 %      computational speed.  In some cases, such as an image with low color
1995 %      dispersion (a few number of colors), a value other than
1996 %      Log4(number_colors) is required.  To expand the color tree completely,
1997 %      use a value of 8.
1998 %
1999 %    o maximum_colors: maximum colors.
2000 %
2001 */
2002 static CubeInfo *GetCubeInfo(const QuantizeInfo *quantize_info,
2003   const size_t depth,const size_t maximum_colors)
2004 {
2005   CubeInfo
2006     *cube_info;
2007
2008   double
2009     sum,
2010     weight;
2011
2012   register ssize_t
2013     i;
2014
2015   size_t
2016     length;
2017
2018   /*
2019     Initialize tree to describe color cube_info.
2020   */
2021   cube_info=(CubeInfo *) AcquireMagickMemory(sizeof(*cube_info));
2022   if (cube_info == (CubeInfo *) NULL)
2023     return((CubeInfo *) NULL);
2024   (void) ResetMagickMemory(cube_info,0,sizeof(*cube_info));
2025   cube_info->depth=depth;
2026   if (cube_info->depth > MaxTreeDepth)
2027     cube_info->depth=MaxTreeDepth;
2028   if (cube_info->depth < 2)
2029     cube_info->depth=2;
2030   cube_info->maximum_colors=maximum_colors;
2031   /*
2032     Initialize root node.
2033   */
2034   cube_info->root=GetNodeInfo(cube_info,0,0,(NodeInfo *) NULL);
2035   if (cube_info->root == (NodeInfo *) NULL)
2036     return((CubeInfo *) NULL);
2037   cube_info->root->parent=cube_info->root;
2038   cube_info->quantize_info=CloneQuantizeInfo(quantize_info);
2039   if (cube_info->quantize_info->dither_method == NoDitherMethod)
2040     return(cube_info);
2041   /*
2042     Initialize dither resources.
2043   */
2044   length=(size_t) (1UL << (4*(8-CacheShift)));
2045   cube_info->memory_info=AcquireVirtualMemory(length,sizeof(*cube_info->cache));
2046   if (cube_info->memory_info == (MemoryInfo *) NULL)
2047     return((CubeInfo *) NULL);
2048   cube_info->cache=(ssize_t *) GetVirtualMemoryBlob(cube_info->memory_info);
2049   /*
2050     Initialize color cache.
2051   */
2052   for (i=0; i < (ssize_t) length; i++)
2053     cube_info->cache[i]=(-1);
2054   /*
2055     Distribute weights along a curve of exponential decay.
2056   */
2057   weight=1.0;
2058   for (i=0; i < ErrorQueueLength; i++)
2059   {
2060     cube_info->weights[ErrorQueueLength-i-1]=PerceptibleReciprocal(weight);
2061     weight*=exp(log(((double) QuantumRange+1.0))/(ErrorQueueLength-1.0));
2062   }
2063   /*
2064     Normalize the weighting factors.
2065   */
2066   weight=0.0;
2067   for (i=0; i < ErrorQueueLength; i++)
2068     weight+=cube_info->weights[i];
2069   sum=0.0;
2070   for (i=0; i < ErrorQueueLength; i++)
2071   {
2072     cube_info->weights[i]/=weight;
2073     sum+=cube_info->weights[i];
2074   }
2075   cube_info->weights[0]+=1.0-sum;
2076   return(cube_info);
2077 }
2078 \f
2079 /*
2080 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2081 %                                                                             %
2082 %                                                                             %
2083 %                                                                             %
2084 +   G e t N o d e I n f o                                                     %
2085 %                                                                             %
2086 %                                                                             %
2087 %                                                                             %
2088 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2089 %
2090 %  GetNodeInfo() allocates memory for a new node in the color cube tree and
2091 %  presets all fields to zero.
2092 %
2093 %  The format of the GetNodeInfo method is:
2094 %
2095 %      NodeInfo *GetNodeInfo(CubeInfo *cube_info,const size_t id,
2096 %        const size_t level,NodeInfo *parent)
2097 %
2098 %  A description of each parameter follows.
2099 %
2100 %    o node: The GetNodeInfo method returns a pointer to a queue of nodes.
2101 %
2102 %    o id: Specifies the child number of the node.
2103 %
2104 %    o level: Specifies the level in the storage_class the node resides.
2105 %
2106 */
2107 static NodeInfo *GetNodeInfo(CubeInfo *cube_info,const size_t id,
2108   const size_t level,NodeInfo *parent)
2109 {
2110   NodeInfo
2111     *node_info;
2112
2113   if (cube_info->free_nodes == 0)
2114     {
2115       Nodes
2116         *nodes;
2117
2118       /*
2119         Allocate a new queue of nodes.
2120       */
2121       nodes=(Nodes *) AcquireMagickMemory(sizeof(*nodes));
2122       if (nodes == (Nodes *) NULL)
2123         return((NodeInfo *) NULL);
2124       nodes->nodes=(NodeInfo *) AcquireQuantumMemory(NodesInAList,
2125         sizeof(*nodes->nodes));
2126       if (nodes->nodes == (NodeInfo *) NULL)
2127         return((NodeInfo *) NULL);
2128       nodes->next=cube_info->node_queue;
2129       cube_info->node_queue=nodes;
2130       cube_info->next_node=nodes->nodes;
2131       cube_info->free_nodes=NodesInAList;
2132     }
2133   cube_info->nodes++;
2134   cube_info->free_nodes--;
2135   node_info=cube_info->next_node++;
2136   (void) ResetMagickMemory(node_info,0,sizeof(*node_info));
2137   node_info->parent=parent;
2138   node_info->id=id;
2139   node_info->level=level;
2140   return(node_info);
2141 }
2142 \f
2143 /*
2144 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2145 %                                                                             %
2146 %                                                                             %
2147 %                                                                             %
2148 %  G e t I m a g e Q u a n t i z e E r r o r                                  %
2149 %                                                                             %
2150 %                                                                             %
2151 %                                                                             %
2152 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2153 %
2154 %  GetImageQuantizeError() measures the difference between the original
2155 %  and quantized images.  This difference is the total quantization error.
2156 %  The error is computed by summing over all pixels in an image the distance
2157 %  squared in RGB space between each reference pixel value and its quantized
2158 %  value.  These values are computed:
2159 %
2160 %    o mean_error_per_pixel:  This value is the mean error for any single
2161 %      pixel in the image.
2162 %
2163 %    o normalized_mean_square_error:  This value is the normalized mean
2164 %      quantization error for any single pixel in the image.  This distance
2165 %      measure is normalized to a range between 0 and 1.  It is independent
2166 %      of the range of red, green, and blue values in the image.
2167 %
2168 %    o normalized_maximum_square_error:  Thsi value is the normalized
2169 %      maximum quantization error for any single pixel in the image.  This
2170 %      distance measure is normalized to a range between 0 and 1.  It is
2171 %      independent of the range of red, green, and blue values in your image.
2172 %
2173 %  The format of the GetImageQuantizeError method is:
2174 %
2175 %      MagickBooleanType GetImageQuantizeError(Image *image,
2176 %        ExceptionInfo *exception)
2177 %
2178 %  A description of each parameter follows.
2179 %
2180 %    o image: the image.
2181 %
2182 %    o exception: return any errors or warnings in this structure.
2183 %
2184 */
2185 MagickExport MagickBooleanType GetImageQuantizeError(Image *image,
2186   ExceptionInfo *exception)
2187 {
2188   CacheView
2189     *image_view;
2190
2191   double
2192     alpha,
2193     area,
2194     beta,
2195     distance,
2196     maximum_error,
2197     mean_error,
2198     mean_error_per_pixel;
2199
2200   size_t
2201     index;
2202
2203   ssize_t
2204     y;
2205
2206   assert(image != (Image *) NULL);
2207   assert(image->signature == MagickSignature);
2208   if (image->debug != MagickFalse)
2209     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2210   image->total_colors=GetNumberColors(image,(FILE *) NULL,exception);
2211   (void) ResetMagickMemory(&image->error,0,sizeof(image->error));
2212   if (image->storage_class == DirectClass)
2213     return(MagickTrue);
2214   alpha=1.0;
2215   beta=1.0;
2216   area=3.0*image->columns*image->rows;
2217   maximum_error=0.0;
2218   mean_error_per_pixel=0.0;
2219   mean_error=0.0;
2220   image_view=AcquireVirtualCacheView(image,exception);
2221   for (y=0; y < (ssize_t) image->rows; y++)
2222   {
2223     register const Quantum
2224       *restrict p;
2225
2226     register ssize_t
2227       x;
2228
2229     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
2230     if (p == (const Quantum *) NULL)
2231       break;
2232     for (x=0; x < (ssize_t) image->columns; x++)
2233     {
2234       index=1UL*GetPixelIndex(image,p);
2235       if (image->alpha_trait != UndefinedPixelTrait)
2236         {
2237           alpha=(double) (QuantumScale*GetPixelAlpha(image,p));
2238           beta=(double) (QuantumScale*image->colormap[index].alpha);
2239         }
2240       distance=fabs((double) (alpha*GetPixelRed(image,p)-beta*
2241         image->colormap[index].red));
2242       mean_error_per_pixel+=distance;
2243       mean_error+=distance*distance;
2244       if (distance > maximum_error)
2245         maximum_error=distance;
2246       distance=fabs((double) (alpha*GetPixelGreen(image,p)-beta*
2247         image->colormap[index].green));
2248       mean_error_per_pixel+=distance;
2249       mean_error+=distance*distance;
2250       if (distance > maximum_error)
2251         maximum_error=distance;
2252       distance=fabs((double) (alpha*GetPixelBlue(image,p)-beta*
2253         image->colormap[index].blue));
2254       mean_error_per_pixel+=distance;
2255       mean_error+=distance*distance;
2256       if (distance > maximum_error)
2257         maximum_error=distance;
2258       p+=GetPixelChannels(image);
2259     }
2260   }
2261   image_view=DestroyCacheView(image_view);
2262   image->error.mean_error_per_pixel=(double) mean_error_per_pixel/area;
2263   image->error.normalized_mean_error=(double) QuantumScale*QuantumScale*
2264     mean_error/area;
2265   image->error.normalized_maximum_error=(double) QuantumScale*maximum_error;
2266   return(MagickTrue);
2267 }
2268 \f
2269 /*
2270 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2271 %                                                                             %
2272 %                                                                             %
2273 %                                                                             %
2274 %   G e t Q u a n t i z e I n f o                                             %
2275 %                                                                             %
2276 %                                                                             %
2277 %                                                                             %
2278 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2279 %
2280 %  GetQuantizeInfo() initializes the QuantizeInfo structure.
2281 %
2282 %  The format of the GetQuantizeInfo method is:
2283 %
2284 %      GetQuantizeInfo(QuantizeInfo *quantize_info)
2285 %
2286 %  A description of each parameter follows:
2287 %
2288 %    o quantize_info: Specifies a pointer to a QuantizeInfo structure.
2289 %
2290 */
2291 MagickExport void GetQuantizeInfo(QuantizeInfo *quantize_info)
2292 {
2293   (void) LogMagickEvent(TraceEvent,GetMagickModule(),"...");
2294   assert(quantize_info != (QuantizeInfo *) NULL);
2295   (void) ResetMagickMemory(quantize_info,0,sizeof(*quantize_info));
2296   quantize_info->number_colors=256;
2297   quantize_info->dither_method=RiemersmaDitherMethod;
2298   quantize_info->colorspace=UndefinedColorspace;
2299   quantize_info->measure_error=MagickFalse;
2300   quantize_info->signature=MagickSignature;
2301 }
2302 \f
2303 /*
2304 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2305 %                                                                             %
2306 %                                                                             %
2307 %                                                                             %
2308 %     P o s t e r i z e I m a g e                                             %
2309 %                                                                             %
2310 %                                                                             %
2311 %                                                                             %
2312 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2313 %
2314 %  PosterizeImage() reduces the image to a limited number of colors for a
2315 %  "poster" effect.
2316 %
2317 %  The format of the PosterizeImage method is:
2318 %
2319 %      MagickBooleanType PosterizeImage(Image *image,const size_t levels,
2320 %        const DitherMethod dither_method,ExceptionInfo *exception)
2321 %
2322 %  A description of each parameter follows:
2323 %
2324 %    o image: Specifies a pointer to an Image structure.
2325 %
2326 %    o levels: Number of color levels allowed in each channel.  Very low values
2327 %      (2, 3, or 4) have the most visible effect.
2328 %
2329 %    o dither_method: choose from UndefinedDitherMethod, NoDitherMethod,
2330 %      RiemersmaDitherMethod, FloydSteinbergDitherMethod.
2331 %
2332 %    o exception: return any errors or warnings in this structure.
2333 %
2334 */
2335
2336 static inline double MagickRound(double x)
2337 {
2338   /*
2339     Round the fraction to nearest integer.
2340   */
2341   if ((x-floor(x)) < (ceil(x)-x))
2342     return(floor(x));
2343   return(ceil(x));
2344 }
2345
2346 MagickExport MagickBooleanType PosterizeImage(Image *image,const size_t levels,
2347   const DitherMethod dither_method,ExceptionInfo *exception)
2348 {
2349 #define PosterizeImageTag  "Posterize/Image"
2350 #define PosterizePixel(pixel) (Quantum) (QuantumRange*(MagickRound( \
2351   QuantumScale*pixel*(levels-1)))/MagickMax((ssize_t) levels-1,1))
2352
2353   CacheView
2354     *image_view;
2355
2356   MagickBooleanType
2357     status;
2358
2359   MagickOffsetType
2360     progress;
2361
2362   QuantizeInfo
2363     *quantize_info;
2364
2365   register ssize_t
2366     i;
2367
2368   ssize_t
2369     y;
2370
2371   assert(image != (Image *) NULL);
2372   assert(image->signature == MagickSignature);
2373   if (image->debug != MagickFalse)
2374     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2375   if (image->storage_class == PseudoClass)
2376 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2377     #pragma omp parallel for schedule(static,4) shared(progress,status) \
2378       magick_threads(image,image,1,1)
2379 #endif
2380     for (i=0; i < (ssize_t) image->colors; i++)
2381     {
2382       /*
2383         Posterize colormap.
2384       */
2385       if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2386         image->colormap[i].red=(double)
2387           PosterizePixel(image->colormap[i].red);
2388       if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2389         image->colormap[i].green=(double)
2390           PosterizePixel(image->colormap[i].green);
2391       if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2392         image->colormap[i].blue=(double)
2393           PosterizePixel(image->colormap[i].blue);
2394       if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
2395         image->colormap[i].alpha=(double)
2396           PosterizePixel(image->colormap[i].alpha);
2397     }
2398   /*
2399     Posterize image.
2400   */
2401   status=MagickTrue;
2402   progress=0;
2403   image_view=AcquireAuthenticCacheView(image,exception);
2404 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2405   #pragma omp parallel for schedule(static,4) shared(progress,status) \
2406     magick_threads(image,image,image->rows,1)
2407 #endif
2408   for (y=0; y < (ssize_t) image->rows; y++)
2409   {
2410     register Quantum
2411       *restrict q;
2412
2413     register ssize_t
2414       x;
2415
2416     if (status == MagickFalse)
2417       continue;
2418     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
2419     if (q == (Quantum *) NULL)
2420       {
2421         status=MagickFalse;
2422         continue;
2423       }
2424     for (x=0; x < (ssize_t) image->columns; x++)
2425     {
2426       if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2427         SetPixelRed(image,PosterizePixel(GetPixelRed(image,q)),q);
2428       if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2429         SetPixelGreen(image,PosterizePixel(GetPixelGreen(image,q)),q);
2430       if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2431         SetPixelBlue(image,PosterizePixel(GetPixelBlue(image,q)),q);
2432       if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
2433           (image->colorspace == CMYKColorspace))
2434         SetPixelBlack(image,PosterizePixel(GetPixelBlack(image,q)),q);
2435       if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
2436           (image->alpha_trait != UndefinedPixelTrait))
2437         SetPixelAlpha(image,PosterizePixel(GetPixelAlpha(image,q)),q);
2438       q+=GetPixelChannels(image);
2439     }
2440     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
2441       status=MagickFalse;
2442     if (image->progress_monitor != (MagickProgressMonitor) NULL)
2443       {
2444         MagickBooleanType
2445           proceed;
2446
2447 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2448         #pragma omp critical (MagickCore_PosterizeImage)
2449 #endif
2450         proceed=SetImageProgress(image,PosterizeImageTag,progress++,
2451           image->rows);
2452         if (proceed == MagickFalse)
2453           status=MagickFalse;
2454       }
2455   }
2456   image_view=DestroyCacheView(image_view);
2457   quantize_info=AcquireQuantizeInfo((ImageInfo *) NULL);
2458   quantize_info->number_colors=(size_t) MagickMin((ssize_t) levels*levels*
2459     levels,MaxColormapSize+1);
2460   quantize_info->dither_method=dither_method;
2461   quantize_info->tree_depth=MaxTreeDepth;
2462   status=QuantizeImage(quantize_info,image,exception);
2463   quantize_info=DestroyQuantizeInfo(quantize_info);
2464   return(status);
2465 }
2466 \f
2467 /*
2468 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2469 %                                                                             %
2470 %                                                                             %
2471 %                                                                             %
2472 +   P r u n e C h i l d                                                       %
2473 %                                                                             %
2474 %                                                                             %
2475 %                                                                             %
2476 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2477 %
2478 %  PruneChild() deletes the given node and merges its statistics into its
2479 %  parent.
2480 %
2481 %  The format of the PruneSubtree method is:
2482 %
2483 %      PruneChild(const Image *image,CubeInfo *cube_info,
2484 %        const NodeInfo *node_info)
2485 %
2486 %  A description of each parameter follows.
2487 %
2488 %    o image: the image.
2489 %
2490 %    o cube_info: A pointer to the Cube structure.
2491 %
2492 %    o node_info: pointer to node in color cube tree that is to be pruned.
2493 %
2494 */
2495 static void PruneChild(const Image *image,CubeInfo *cube_info,
2496   const NodeInfo *node_info)
2497 {
2498   NodeInfo
2499     *parent;
2500
2501   register ssize_t
2502     i;
2503
2504   size_t
2505     number_children;
2506
2507   /*
2508     Traverse any children.
2509   */
2510   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2511   for (i=0; i < (ssize_t) number_children; i++)
2512     if (node_info->child[i] != (NodeInfo *) NULL)
2513       PruneChild(image,cube_info,node_info->child[i]);
2514   /*
2515     Merge color statistics into parent.
2516   */
2517   parent=node_info->parent;
2518   parent->number_unique+=node_info->number_unique;
2519   parent->total_color.red+=node_info->total_color.red;
2520   parent->total_color.green+=node_info->total_color.green;
2521   parent->total_color.blue+=node_info->total_color.blue;
2522   parent->total_color.alpha+=node_info->total_color.alpha;
2523   parent->child[node_info->id]=(NodeInfo *) NULL;
2524   cube_info->nodes--;
2525 }
2526 \f
2527 /*
2528 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2529 %                                                                             %
2530 %                                                                             %
2531 %                                                                             %
2532 +  P r u n e L e v e l                                                        %
2533 %                                                                             %
2534 %                                                                             %
2535 %                                                                             %
2536 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2537 %
2538 %  PruneLevel() deletes all nodes at the bottom level of the color tree merging
2539 %  their color statistics into their parent node.
2540 %
2541 %  The format of the PruneLevel method is:
2542 %
2543 %      PruneLevel(const Image *image,CubeInfo *cube_info,
2544 %        const NodeInfo *node_info)
2545 %
2546 %  A description of each parameter follows.
2547 %
2548 %    o image: the image.
2549 %
2550 %    o cube_info: A pointer to the Cube structure.
2551 %
2552 %    o node_info: pointer to node in color cube tree that is to be pruned.
2553 %
2554 */
2555 static void PruneLevel(const Image *image,CubeInfo *cube_info,
2556   const NodeInfo *node_info)
2557 {
2558   register ssize_t
2559     i;
2560
2561   size_t
2562     number_children;
2563
2564   /*
2565     Traverse any children.
2566   */
2567   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2568   for (i=0; i < (ssize_t) number_children; i++)
2569     if (node_info->child[i] != (NodeInfo *) NULL)
2570       PruneLevel(image,cube_info,node_info->child[i]);
2571   if (node_info->level == cube_info->depth)
2572     PruneChild(image,cube_info,node_info);
2573 }
2574 \f
2575 /*
2576 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2577 %                                                                             %
2578 %                                                                             %
2579 %                                                                             %
2580 +  P r u n e T o C u b e D e p t h                                            %
2581 %                                                                             %
2582 %                                                                             %
2583 %                                                                             %
2584 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2585 %
2586 %  PruneToCubeDepth() deletes any nodes at a depth greater than
2587 %  cube_info->depth while merging their color statistics into their parent
2588 %  node.
2589 %
2590 %  The format of the PruneToCubeDepth method is:
2591 %
2592 %      PruneToCubeDepth(const Image *image,CubeInfo *cube_info,
2593 %        const NodeInfo *node_info)
2594 %
2595 %  A description of each parameter follows.
2596 %
2597 %    o cube_info: A pointer to the Cube structure.
2598 %
2599 %    o node_info: pointer to node in color cube tree that is to be pruned.
2600 %
2601 */
2602 static void PruneToCubeDepth(const Image *image,CubeInfo *cube_info,
2603   const NodeInfo *node_info)
2604 {
2605   register ssize_t
2606     i;
2607
2608   size_t
2609     number_children;
2610
2611   /*
2612     Traverse any children.
2613   */
2614   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2615   for (i=0; i < (ssize_t) number_children; i++)
2616     if (node_info->child[i] != (NodeInfo *) NULL)
2617       PruneToCubeDepth(image,cube_info,node_info->child[i]);
2618   if (node_info->level > cube_info->depth)
2619     PruneChild(image,cube_info,node_info);
2620 }
2621 \f
2622 /*
2623 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2624 %                                                                             %
2625 %                                                                             %
2626 %                                                                             %
2627 %  Q u a n t i z e I m a g e                                                  %
2628 %                                                                             %
2629 %                                                                             %
2630 %                                                                             %
2631 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2632 %
2633 %  QuantizeImage() analyzes the colors within a reference image and chooses a
2634 %  fixed number of colors to represent the image.  The goal of the algorithm
2635 %  is to minimize the color difference between the input and output image while
2636 %  minimizing the processing time.
2637 %
2638 %  The format of the QuantizeImage method is:
2639 %
2640 %      MagickBooleanType QuantizeImage(const QuantizeInfo *quantize_info,
2641 %        Image *image,ExceptionInfo *exception)
2642 %
2643 %  A description of each parameter follows:
2644 %
2645 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
2646 %
2647 %    o image: the image.
2648 %
2649 %    o exception: return any errors or warnings in this structure.
2650 %
2651 */
2652
2653 static MagickBooleanType DirectToColormapImage(Image *image,
2654   ExceptionInfo *exception)
2655 {
2656   CacheView
2657     *image_view;
2658
2659   MagickBooleanType
2660     status;
2661
2662   register ssize_t
2663     i;
2664
2665   size_t
2666     number_colors;
2667
2668   ssize_t
2669     y;
2670
2671   status=MagickTrue;
2672   number_colors=(size_t) (image->columns*image->rows);
2673   if (AcquireImageColormap(image,number_colors,exception) == MagickFalse)
2674     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
2675       image->filename);
2676   if (image->colors != number_colors)
2677     return(MagickFalse);
2678   i=0;
2679   image_view=AcquireAuthenticCacheView(image,exception);
2680   for (y=0; y < (ssize_t) image->rows; y++)
2681   {
2682     MagickBooleanType
2683       proceed;
2684
2685     register Quantum
2686       *restrict q;
2687
2688     register ssize_t
2689       x;
2690
2691     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
2692     if (q == (Quantum *) NULL)
2693       break;
2694     for (x=0; x < (ssize_t) image->columns; x++)
2695     {
2696       image->colormap[i].red=(double) GetPixelRed(image,q);
2697       image->colormap[i].green=(double) GetPixelGreen(image,q);
2698       image->colormap[i].blue=(double) GetPixelBlue(image,q);
2699       image->colormap[i].alpha=(double) GetPixelAlpha(image,q);
2700       SetPixelIndex(image,(Quantum) i,q);
2701       i++;
2702       q+=GetPixelChannels(image);
2703     }
2704     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
2705       break;
2706     proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) y,
2707       image->rows);
2708     if (proceed == MagickFalse)
2709       status=MagickFalse;
2710   }
2711   image_view=DestroyCacheView(image_view);
2712   return(status);
2713 }
2714
2715 MagickExport MagickBooleanType QuantizeImage(const QuantizeInfo *quantize_info,
2716   Image *image,ExceptionInfo *exception)
2717 {
2718   CubeInfo
2719     *cube_info;
2720
2721   MagickBooleanType
2722     status;
2723
2724   size_t
2725     depth,
2726     maximum_colors;
2727
2728   assert(quantize_info != (const QuantizeInfo *) NULL);
2729   assert(quantize_info->signature == MagickSignature);
2730   assert(image != (Image *) NULL);
2731   assert(image->signature == MagickSignature);
2732   if (image->debug != MagickFalse)
2733     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2734   maximum_colors=quantize_info->number_colors;
2735   if (maximum_colors == 0)
2736     maximum_colors=MaxColormapSize;
2737   if (maximum_colors > MaxColormapSize)
2738     maximum_colors=MaxColormapSize;
2739   if (image->alpha_trait == UndefinedPixelTrait)
2740     {
2741       if ((image->columns*image->rows) <= maximum_colors)
2742         (void) DirectToColormapImage(image,exception);
2743       if (IsImageGray(image,exception) != MagickFalse)
2744         (void) SetGrayscaleImage(image,exception);
2745     }
2746   if ((image->storage_class == PseudoClass) &&
2747       (image->colors <= maximum_colors))
2748     return(MagickTrue);
2749   depth=quantize_info->tree_depth;
2750   if (depth == 0)
2751     {
2752       size_t
2753         colors;
2754
2755       /*
2756         Depth of color tree is: Log4(colormap size)+2.
2757       */
2758       colors=maximum_colors;
2759       for (depth=1; colors != 0; depth++)
2760         colors>>=2;
2761       if ((quantize_info->dither_method != NoDitherMethod) && (depth > 2))
2762         depth--;
2763       if ((image->alpha_trait != UndefinedPixelTrait) && (depth > 5))
2764         depth--;
2765       if (IsImageGray(image,exception) != MagickFalse)
2766         depth=MaxTreeDepth;
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_method != NoDitherMethod)
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 +   Q u a n t i z e E r r o r F l a t t e n                                   %
2936 %                                                                             %
2937 %                                                                             %
2938 %                                                                             %
2939 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2940 %
2941 %  QuantizeErrorFlatten() traverses the color cube and flattens the quantization
2942 %  error into a sorted 1D array.  This accelerates the color reduction process.
2943 %
2944 %  Contributed by Yoya.
2945 %
2946 %  The format of the QuantizeImages method is:
2947 %
2948 %      size_t QuantizeErrorFlatten(const Image *image,const CubeInfo *cube_info,
2949 %        const NodeInfo *node_info,const ssize_t offset,
2950 %        MagickRealType *quantize_error)
2951 %
2952 %  A description of each parameter follows.
2953 %
2954 %    o image: the image.
2955 %
2956 %    o cube_info: A pointer to the Cube structure.
2957 %
2958 %    o node_info: pointer to node in color cube tree that is current pointer.
2959 %
2960 %    o offset: quantize error offset.
2961 %
2962 %    o quantize_error: the quantization error vector.
2963 %
2964 */
2965 static size_t QuantizeErrorFlatten(const Image *image,const CubeInfo *cube_info,
2966   const NodeInfo *node_info,const ssize_t offset,MagickRealType *quantize_error)
2967 {
2968   register ssize_t
2969     i;
2970
2971   size_t
2972     n,
2973     number_children;
2974
2975   if (offset >= (ssize_t) cube_info->nodes)
2976     return(0);
2977   quantize_error[offset]=node_info->quantize_error;
2978   n=1;
2979   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2980   for (i=0; i < (ssize_t) number_children ; i++)
2981     if (node_info->child[i] != (NodeInfo *) NULL)
2982       n+=QuantizeErrorFlatten(image,cube_info,node_info->child[i],offset+n,
2983         quantize_error);
2984   return(n);
2985 }
2986 \f
2987 /*
2988 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2989 %                                                                             %
2990 %                                                                             %
2991 %                                                                             %
2992 +   R e d u c e                                                               %
2993 %                                                                             %
2994 %                                                                             %
2995 %                                                                             %
2996 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2997 %
2998 %  Reduce() traverses the color cube tree and prunes any node whose
2999 %  quantization error falls below a particular threshold.
3000 %
3001 %  The format of the Reduce method is:
3002 %
3003 %      Reduce(const Image *image,CubeInfo *cube_info,const NodeInfo *node_info)
3004 %
3005 %  A description of each parameter follows.
3006 %
3007 %    o image: the image.
3008 %
3009 %    o cube_info: A pointer to the Cube structure.
3010 %
3011 %    o node_info: pointer to node in color cube tree that is to be pruned.
3012 %
3013 */
3014 static void Reduce(const Image *image,CubeInfo *cube_info,
3015   const NodeInfo *node_info)
3016 {
3017   register ssize_t
3018     i;
3019
3020   size_t
3021     number_children;
3022
3023   /*
3024     Traverse any children.
3025   */
3026   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
3027   for (i=0; i < (ssize_t) number_children; i++)
3028     if (node_info->child[i] != (NodeInfo *) NULL)
3029       Reduce(image,cube_info,node_info->child[i]);
3030   if (node_info->quantize_error <= cube_info->pruning_threshold)
3031     PruneChild(image,cube_info,node_info);
3032   else
3033     {
3034       /*
3035         Find minimum pruning threshold.
3036       */
3037       if (node_info->number_unique > 0)
3038         cube_info->colors++;
3039       if (node_info->quantize_error < cube_info->next_threshold)
3040         cube_info->next_threshold=node_info->quantize_error;
3041     }
3042 }
3043 \f
3044 /*
3045 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3046 %                                                                             %
3047 %                                                                             %
3048 %                                                                             %
3049 +   R e d u c e I m a g e C o l o r s                                         %
3050 %                                                                             %
3051 %                                                                             %
3052 %                                                                             %
3053 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3054 %
3055 %  ReduceImageColors() repeatedly prunes the tree until the number of nodes
3056 %  with n2 > 0 is less than or equal to the maximum number of colors allowed
3057 %  in the output image.  On any given iteration over the tree, it selects
3058 %  those nodes whose E value is minimal for pruning and merges their
3059 %  color statistics upward. It uses a pruning threshold, Ep, to govern
3060 %  node selection as follows:
3061 %
3062 %    Ep = 0
3063 %    while number of nodes with (n2 > 0) > required maximum number of colors
3064 %      prune all nodes such that E <= Ep
3065 %      Set Ep to minimum E in remaining nodes
3066 %
3067 %  This has the effect of minimizing any quantization error when merging
3068 %  two nodes together.
3069 %
3070 %  When a node to be pruned has offspring, the pruning procedure invokes
3071 %  itself recursively in order to prune the tree from the leaves upward.
3072 %  n2,  Sr, Sg,  and  Sb in a node being pruned are always added to the
3073 %  corresponding data in that node's parent.  This retains the pruned
3074 %  node's color characteristics for later averaging.
3075 %
3076 %  For each node, n2 pixels exist for which that node represents the
3077 %  smallest volume in RGB space containing those pixel's colors.  When n2
3078 %  > 0 the node will uniquely define a color in the output image. At the
3079 %  beginning of reduction,  n2 = 0  for all nodes except a the leaves of
3080 %  the tree which represent colors present in the input image.
3081 %
3082 %  The other pixel count, n1, indicates the total number of colors
3083 %  within the cubic volume which the node represents.  This includes n1 -
3084 %  n2  pixels whose colors should be defined by nodes at a lower level in
3085 %  the tree.
3086 %
3087 %  The format of the ReduceImageColors method is:
3088 %
3089 %      ReduceImageColors(const Image *image,CubeInfo *cube_info)
3090 %
3091 %  A description of each parameter follows.
3092 %
3093 %    o image: the image.
3094 %
3095 %    o cube_info: A pointer to the Cube structure.
3096 %
3097 */
3098
3099 static int MagickRealTypeCompare(const void *error_p,const void *error_q)
3100 {
3101   MagickRealType
3102     *p,
3103     *q;
3104
3105   p=(MagickRealType *) error_p;
3106   q=(MagickRealType *) error_q;
3107   if (*p > *q)
3108     return(1);
3109   if (fabs((double) (*q-*p)) <= MagickEpsilon)
3110     return(0);
3111   return(-1);
3112 }
3113
3114 static void ReduceImageColors(const Image *image,CubeInfo *cube_info)
3115 {
3116 #define ReduceImageTag  "Reduce/Image"
3117
3118   MagickBooleanType
3119     proceed;
3120
3121   MagickOffsetType
3122     offset;
3123
3124   size_t
3125     span;
3126
3127   cube_info->next_threshold=0.0;
3128   if ((cube_info->colors > cube_info->maximum_colors) &&
3129       (cube_info->nodes > 128))
3130     {
3131       MagickRealType
3132         *quantize_error;
3133
3134       /*
3135         Enable rapid reduction of the number of unique colors.
3136       */
3137       quantize_error=(MagickRealType *) AcquireQuantumMemory(cube_info->nodes,
3138         sizeof(*quantize_error));
3139       if (quantize_error != (MagickRealType *) NULL)
3140         {
3141           (void) QuantizeErrorFlatten(image,cube_info,cube_info->root,0,
3142             quantize_error);
3143           qsort(quantize_error,cube_info->nodes,sizeof(MagickRealType),
3144             MagickRealTypeCompare);
3145           cube_info->next_threshold=quantize_error[MagickMax((ssize_t)
3146             cube_info->nodes-110*(cube_info->maximum_colors+1)/100,0)];
3147           quantize_error=(MagickRealType *) RelinquishMagickMemory(
3148             quantize_error);
3149         }
3150   }
3151   for (span=cube_info->colors; cube_info->colors > cube_info->maximum_colors; )
3152   {
3153     cube_info->pruning_threshold=cube_info->next_threshold;
3154     cube_info->next_threshold=cube_info->root->quantize_error-1;
3155     cube_info->colors=0;
3156     Reduce(image,cube_info,cube_info->root);
3157     offset=(MagickOffsetType) span-cube_info->colors;
3158     proceed=SetImageProgress(image,ReduceImageTag,offset,span-
3159       cube_info->maximum_colors+1);
3160     if (proceed == MagickFalse)
3161       break;
3162   }
3163 }
3164 \f
3165 /*
3166 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3167 %                                                                             %
3168 %                                                                             %
3169 %                                                                             %
3170 %   R e m a p I m a g e                                                       %
3171 %                                                                             %
3172 %                                                                             %
3173 %                                                                             %
3174 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3175 %
3176 %  RemapImage() replaces the colors of an image with a dither of the colors
3177 %  provided.
3178 %
3179 %  The format of the RemapImage method is:
3180 %
3181 %      MagickBooleanType RemapImage(const QuantizeInfo *quantize_info,
3182 %        Image *image,const Image *remap_image,ExceptionInfo *exception)
3183 %
3184 %  A description of each parameter follows:
3185 %
3186 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
3187 %
3188 %    o image: the image.
3189 %
3190 %    o remap_image: the reference image.
3191 %
3192 %    o exception: return any errors or warnings in this structure.
3193 %
3194 */
3195 MagickExport MagickBooleanType RemapImage(const QuantizeInfo *quantize_info,
3196   Image *image,const Image *remap_image,ExceptionInfo *exception)
3197 {
3198   CubeInfo
3199     *cube_info;
3200
3201   MagickBooleanType
3202     status;
3203
3204   /*
3205     Initialize color cube.
3206   */
3207   assert(image != (Image *) NULL);
3208   assert(image->signature == MagickSignature);
3209   if (image->debug != MagickFalse)
3210     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
3211   assert(remap_image != (Image *) NULL);
3212   assert(remap_image->signature == MagickSignature);
3213   cube_info=GetCubeInfo(quantize_info,MaxTreeDepth,
3214     quantize_info->number_colors);
3215   if (cube_info == (CubeInfo *) NULL)
3216     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3217       image->filename);
3218   status=ClassifyImageColors(cube_info,remap_image,exception);
3219   if (status != MagickFalse)
3220     {
3221       /*
3222         Classify image colors from the reference image.
3223       */
3224       cube_info->quantize_info->number_colors=cube_info->colors;
3225       status=AssignImageColors(image,cube_info,exception);
3226     }
3227   DestroyCubeInfo(cube_info);
3228   return(status);
3229 }
3230 \f
3231 /*
3232 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3233 %                                                                             %
3234 %                                                                             %
3235 %                                                                             %
3236 %   R e m a p I m a g e s                                                     %
3237 %                                                                             %
3238 %                                                                             %
3239 %                                                                             %
3240 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3241 %
3242 %  RemapImages() replaces the colors of a sequence of images with the
3243 %  closest color from a reference image.
3244 %
3245 %  The format of the RemapImage method is:
3246 %
3247 %      MagickBooleanType RemapImages(const QuantizeInfo *quantize_info,
3248 %        Image *images,Image *remap_image,ExceptionInfo *exception)
3249 %
3250 %  A description of each parameter follows:
3251 %
3252 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
3253 %
3254 %    o images: the image sequence.
3255 %
3256 %    o remap_image: the reference image.
3257 %
3258 %    o exception: return any errors or warnings in this structure.
3259 %
3260 */
3261 MagickExport MagickBooleanType RemapImages(const QuantizeInfo *quantize_info,
3262   Image *images,const Image *remap_image,ExceptionInfo *exception)
3263 {
3264   CubeInfo
3265     *cube_info;
3266
3267   Image
3268     *image;
3269
3270   MagickBooleanType
3271     status;
3272
3273   assert(images != (Image *) NULL);
3274   assert(images->signature == MagickSignature);
3275   if (images->debug != MagickFalse)
3276     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
3277   image=images;
3278   if (remap_image == (Image *) NULL)
3279     {
3280       /*
3281         Create a global colormap for an image sequence.
3282       */
3283       status=QuantizeImages(quantize_info,images,exception);
3284       return(status);
3285     }
3286   /*
3287     Classify image colors from the reference image.
3288   */
3289   cube_info=GetCubeInfo(quantize_info,MaxTreeDepth,
3290     quantize_info->number_colors);
3291   if (cube_info == (CubeInfo *) NULL)
3292     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3293       image->filename);
3294   status=ClassifyImageColors(cube_info,remap_image,exception);
3295   if (status != MagickFalse)
3296     {
3297       /*
3298         Classify image colors from the reference image.
3299       */
3300       cube_info->quantize_info->number_colors=cube_info->colors;
3301       image=images;
3302       for ( ; image != (Image *) NULL; image=GetNextImageInList(image))
3303       {
3304         status=AssignImageColors(image,cube_info,exception);
3305         if (status == MagickFalse)
3306           break;
3307       }
3308     }
3309   DestroyCubeInfo(cube_info);
3310   return(status);
3311 }
3312 \f
3313 /*
3314 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3315 %                                                                             %
3316 %                                                                             %
3317 %                                                                             %
3318 %   S e t G r a y s c a l e I m a g e                                         %
3319 %                                                                             %
3320 %                                                                             %
3321 %                                                                             %
3322 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3323 %
3324 %  SetGrayscaleImage() converts an image to a PseudoClass grayscale image.
3325 %
3326 %  The format of the SetGrayscaleImage method is:
3327 %
3328 %      MagickBooleanType SetGrayscaleImage(Image *image,ExceptionInfo *exeption)
3329 %
3330 %  A description of each parameter follows:
3331 %
3332 %    o image: The image.
3333 %
3334 %    o exception: return any errors or warnings in this structure.
3335 %
3336 */
3337
3338 #if defined(__cplusplus) || defined(c_plusplus)
3339 extern "C" {
3340 #endif
3341
3342 static int IntensityCompare(const void *x,const void *y)
3343 {
3344   PixelInfo
3345     *color_1,
3346     *color_2;
3347
3348   ssize_t
3349     intensity;
3350
3351   color_1=(PixelInfo *) x;
3352   color_2=(PixelInfo *) y;
3353   intensity=(ssize_t) (GetPixelInfoIntensity((const Image *) NULL,color_1)-
3354     (ssize_t) GetPixelInfoIntensity((const Image *) NULL,color_2));
3355   return((int) intensity);
3356 }
3357
3358 #if defined(__cplusplus) || defined(c_plusplus)
3359 }
3360 #endif
3361
3362 static MagickBooleanType SetGrayscaleImage(Image *image,
3363   ExceptionInfo *exception)
3364 {
3365   CacheView
3366     *image_view;
3367
3368   MagickBooleanType
3369     status;
3370
3371   PixelInfo
3372     *colormap;
3373
3374   register ssize_t
3375     i;
3376
3377   ssize_t
3378     *colormap_index,
3379     j,
3380     y;
3381
3382   assert(image != (Image *) NULL);
3383   assert(image->signature == MagickSignature);
3384   if (image->type != GrayscaleType)
3385     (void) TransformImageColorspace(image,GRAYColorspace,exception);
3386   colormap_index=(ssize_t *) AcquireQuantumMemory(MaxMap+1,
3387     sizeof(*colormap_index));
3388   if (colormap_index == (ssize_t *) NULL)
3389     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3390       image->filename);
3391   if (image->storage_class != PseudoClass)
3392     {
3393       for (i=0; i <= (ssize_t) MaxMap; i++)
3394         colormap_index[i]=(-1);
3395       if (AcquireImageColormap(image,MaxMap+1,exception) == MagickFalse)
3396         ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3397           image->filename);
3398       image->colors=0;
3399       status=MagickTrue;
3400       image_view=AcquireAuthenticCacheView(image,exception);
3401 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3402       #pragma omp parallel for schedule(static,4) shared(status) \
3403         magick_threads(image,image,image->rows,1)
3404 #endif
3405       for (y=0; y < (ssize_t) image->rows; y++)
3406       {
3407         register Quantum
3408           *restrict q;
3409
3410         register ssize_t
3411           x;
3412
3413         if (status == MagickFalse)
3414           continue;
3415         q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
3416           exception);
3417         if (q == (Quantum *) NULL)
3418           {
3419             status=MagickFalse;
3420             continue;
3421           }
3422         for (x=0; x < (ssize_t) image->columns; x++)
3423         {
3424           register size_t
3425             intensity;
3426
3427           intensity=ScaleQuantumToMap(GetPixelRed(image,q));
3428           if (colormap_index[intensity] < 0)
3429             {
3430 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3431               #pragma omp critical (MagickCore_SetGrayscaleImage)
3432 #endif
3433               if (colormap_index[intensity] < 0)
3434                 {
3435                   colormap_index[intensity]=(ssize_t) image->colors;
3436                   image->colormap[image->colors].red=(double)
3437                     GetPixelRed(image,q);
3438                   image->colormap[image->colors].green=(double)
3439                     GetPixelGreen(image,q);
3440                   image->colormap[image->colors].blue=(double)
3441                     GetPixelBlue(image,q);
3442                   image->colors++;
3443                }
3444             }
3445           SetPixelIndex(image,(Quantum) colormap_index[intensity],q);
3446           q+=GetPixelChannels(image);
3447         }
3448         if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
3449           status=MagickFalse;
3450       }
3451       image_view=DestroyCacheView(image_view);
3452     }
3453   for (i=0; i < (ssize_t) image->colors; i++)
3454     image->colormap[i].alpha=(double) i;
3455   qsort((void *) image->colormap,image->colors,sizeof(PixelInfo),
3456     IntensityCompare);
3457   colormap=(PixelInfo *) AcquireQuantumMemory(image->colors,sizeof(*colormap));
3458   if (colormap == (PixelInfo *) NULL)
3459     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3460       image->filename);
3461   j=0;
3462   colormap[j]=image->colormap[0];
3463   for (i=0; i < (ssize_t) image->colors; i++)
3464   {
3465     if (IsPixelInfoEquivalent(&colormap[j],&image->colormap[i]) == MagickFalse)
3466       {
3467         j++;
3468         colormap[j]=image->colormap[i];
3469       }
3470     colormap_index[(ssize_t) image->colormap[i].alpha]=j;
3471   }
3472   image->colors=(size_t) (j+1);
3473   image->colormap=(PixelInfo *) RelinquishMagickMemory(image->colormap);
3474   image->colormap=colormap;
3475   status=MagickTrue;
3476   image_view=AcquireAuthenticCacheView(image,exception);
3477 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3478   #pragma omp parallel for schedule(static,4) shared(status) \
3479     magick_threads(image,image,image->rows,1)
3480 #endif
3481   for (y=0; y < (ssize_t) image->rows; y++)
3482   {
3483     register Quantum
3484       *restrict q;
3485
3486     register ssize_t
3487       x;
3488
3489     if (status == MagickFalse)
3490       continue;
3491     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
3492     if (q == (Quantum *) NULL)
3493       {
3494         status=MagickFalse;
3495         continue;
3496       }
3497     for (x=0; x < (ssize_t) image->columns; x++)
3498     {
3499       SetPixelIndex(image,(Quantum) colormap_index[ScaleQuantumToMap(
3500         GetPixelIndex(image,q))],q);
3501       q+=GetPixelChannels(image);
3502     }
3503     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
3504       status=MagickFalse;
3505   }
3506   image_view=DestroyCacheView(image_view);
3507   colormap_index=(ssize_t *) RelinquishMagickMemory(colormap_index);
3508   image->type=GrayscaleType;
3509   if (IsImageMonochrome(image,exception) != MagickFalse)
3510     image->type=BilevelType;
3511   return(status);
3512 }