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 1999-2014 ImageMagick Studio LLC, a non-profit organization      %
  21 %  dedicated to making software imaging solutions freely available.           %
  22 %                                                                             %
  23 %  You may not use this file except in compliance with the License.  You may  %
  24 %  obtain a copy of the License at                                            %
  25 %                                                                             %
  26 %    http://www.imagemagick.org/script/license.php                            %
  27 %                                                                             %
  28 %  Unless required by applicable law or agreed to in writing, software        %
  29 %  distributed under the License is distributed on an "AS IS" BASIS,          %
  30 %  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   %
  31 %  See the License for the specific language governing permissions and        %
  32 %  limitations under the License.                                             %
  33 %                                                                             %
  34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  35 %
  36 %  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 == BlendPixelTrait ? 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)*image->columns*GetPixelChannels(image);
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 inline ssize_t MagickMax(const ssize_t x,const ssize_t y)
1930 {
1931   if (x > y)
1932     return(x);
1933   return(y);
1934 }
1935
1936 static inline ssize_t MagickMin(const ssize_t x,const ssize_t y)
1937 {
1938   if (x < y)
1939     return(x);
1940   return(y);
1941 }
1942
1943 static MagickBooleanType DitherImage(Image *image,CubeInfo *cube_info,
1944   ExceptionInfo *exception)
1945 {
1946   CacheView
1947     *image_view;
1948
1949   MagickBooleanType
1950     status;
1951
1952   register ssize_t
1953     i;
1954
1955   size_t
1956     depth;
1957
1958   if (cube_info->quantize_info->dither_method != RiemersmaDitherMethod)
1959     return(FloydSteinbergDither(image,cube_info,exception));
1960   /*
1961     Distribute quantization error along a Hilbert curve.
1962   */
1963   (void) ResetMagickMemory(cube_info->error,0,ErrorQueueLength*
1964     sizeof(*cube_info->error));
1965   cube_info->x=0;
1966   cube_info->y=0;
1967   i=MagickMax((ssize_t) image->columns,(ssize_t) image->rows);
1968   for (depth=1; i != 0; depth++)
1969     i>>=1;
1970   if ((ssize_t) (1L << depth) < MagickMax((ssize_t) image->columns,(ssize_t) image->rows))
1971     depth++;
1972   cube_info->offset=0;
1973   cube_info->span=(MagickSizeType) image->columns*image->rows;
1974   image_view=AcquireAuthenticCacheView(image,exception);
1975   if (depth > 1)
1976     Riemersma(image,image_view,cube_info,depth-1,NorthGravity,exception);
1977   status=RiemersmaDither(image,image_view,cube_info,ForgetGravity,exception);
1978   image_view=DestroyCacheView(image_view);
1979   return(status);
1980 }
1981 \f
1982 /*
1983 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1984 %                                                                             %
1985 %                                                                             %
1986 %                                                                             %
1987 +   G e t C u b e I n f o                                                     %
1988 %                                                                             %
1989 %                                                                             %
1990 %                                                                             %
1991 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
1992 %
1993 %  GetCubeInfo() initialize the Cube data structure.
1994 %
1995 %  The format of the GetCubeInfo method is:
1996 %
1997 %      CubeInfo GetCubeInfo(const QuantizeInfo *quantize_info,
1998 %        const size_t depth,const size_t maximum_colors)
1999 %
2000 %  A description of each parameter follows.
2001 %
2002 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
2003 %
2004 %    o depth: Normally, this integer value is zero or one.  A zero or
2005 %      one tells Quantize to choose a optimal tree depth of Log4(number_colors).
2006 %      A tree of this depth generally allows the best representation of the
2007 %      reference image with the least amount of memory and the fastest
2008 %      computational speed.  In some cases, such as an image with low color
2009 %      dispersion (a few number of colors), a value other than
2010 %      Log4(number_colors) is required.  To expand the color tree completely,
2011 %      use a value of 8.
2012 %
2013 %    o maximum_colors: maximum colors.
2014 %
2015 */
2016 static CubeInfo *GetCubeInfo(const QuantizeInfo *quantize_info,
2017   const size_t depth,const size_t maximum_colors)
2018 {
2019   CubeInfo
2020     *cube_info;
2021
2022   double
2023     sum,
2024     weight;
2025
2026   register ssize_t
2027     i;
2028
2029   size_t
2030     length;
2031
2032   /*
2033     Initialize tree to describe color cube_info.
2034   */
2035   cube_info=(CubeInfo *) AcquireMagickMemory(sizeof(*cube_info));
2036   if (cube_info == (CubeInfo *) NULL)
2037     return((CubeInfo *) NULL);
2038   (void) ResetMagickMemory(cube_info,0,sizeof(*cube_info));
2039   cube_info->depth=depth;
2040   if (cube_info->depth > MaxTreeDepth)
2041     cube_info->depth=MaxTreeDepth;
2042   if (cube_info->depth < 2)
2043     cube_info->depth=2;
2044   cube_info->maximum_colors=maximum_colors;
2045   /*
2046     Initialize root node.
2047   */
2048   cube_info->root=GetNodeInfo(cube_info,0,0,(NodeInfo *) NULL);
2049   if (cube_info->root == (NodeInfo *) NULL)
2050     return((CubeInfo *) NULL);
2051   cube_info->root->parent=cube_info->root;
2052   cube_info->quantize_info=CloneQuantizeInfo(quantize_info);
2053   if (cube_info->quantize_info->dither_method == NoDitherMethod)
2054     return(cube_info);
2055   /*
2056     Initialize dither resources.
2057   */
2058   length=(size_t) (1UL << (4*(8-CacheShift)));
2059   cube_info->memory_info=AcquireVirtualMemory(length,sizeof(*cube_info->cache));
2060   if (cube_info->memory_info == (MemoryInfo *) NULL)
2061     return((CubeInfo *) NULL);
2062   cube_info->cache=(ssize_t *) GetVirtualMemoryBlob(cube_info->memory_info);
2063   /*
2064     Initialize color cache.
2065   */
2066   for (i=0; i < (ssize_t) length; i++)
2067     cube_info->cache[i]=(-1);
2068   /*
2069     Distribute weights along a curve of exponential decay.
2070   */
2071   weight=1.0;
2072   for (i=0; i < ErrorQueueLength; i++)
2073   {
2074     cube_info->weights[ErrorQueueLength-i-1]=PerceptibleReciprocal(weight);
2075     weight*=exp(log(((double) QuantumRange+1.0))/(ErrorQueueLength-1.0));
2076   }
2077   /*
2078     Normalize the weighting factors.
2079   */
2080   weight=0.0;
2081   for (i=0; i < ErrorQueueLength; i++)
2082     weight+=cube_info->weights[i];
2083   sum=0.0;
2084   for (i=0; i < ErrorQueueLength; i++)
2085   {
2086     cube_info->weights[i]/=weight;
2087     sum+=cube_info->weights[i];
2088   }
2089   cube_info->weights[0]+=1.0-sum;
2090   return(cube_info);
2091 }
2092 \f
2093 /*
2094 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2095 %                                                                             %
2096 %                                                                             %
2097 %                                                                             %
2098 +   G e t N o d e I n f o                                                     %
2099 %                                                                             %
2100 %                                                                             %
2101 %                                                                             %
2102 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2103 %
2104 %  GetNodeInfo() allocates memory for a new node in the color cube tree and
2105 %  presets all fields to zero.
2106 %
2107 %  The format of the GetNodeInfo method is:
2108 %
2109 %      NodeInfo *GetNodeInfo(CubeInfo *cube_info,const size_t id,
2110 %        const size_t level,NodeInfo *parent)
2111 %
2112 %  A description of each parameter follows.
2113 %
2114 %    o node: The GetNodeInfo method returns a pointer to a queue of nodes.
2115 %
2116 %    o id: Specifies the child number of the node.
2117 %
2118 %    o level: Specifies the level in the storage_class the node resides.
2119 %
2120 */
2121 static NodeInfo *GetNodeInfo(CubeInfo *cube_info,const size_t id,
2122   const size_t level,NodeInfo *parent)
2123 {
2124   NodeInfo
2125     *node_info;
2126
2127   if (cube_info->free_nodes == 0)
2128     {
2129       Nodes
2130         *nodes;
2131
2132       /*
2133         Allocate a new queue of nodes.
2134       */
2135       nodes=(Nodes *) AcquireMagickMemory(sizeof(*nodes));
2136       if (nodes == (Nodes *) NULL)
2137         return((NodeInfo *) NULL);
2138       nodes->nodes=(NodeInfo *) AcquireQuantumMemory(NodesInAList,
2139         sizeof(*nodes->nodes));
2140       if (nodes->nodes == (NodeInfo *) NULL)
2141         return((NodeInfo *) NULL);
2142       nodes->next=cube_info->node_queue;
2143       cube_info->node_queue=nodes;
2144       cube_info->next_node=nodes->nodes;
2145       cube_info->free_nodes=NodesInAList;
2146     }
2147   cube_info->nodes++;
2148   cube_info->free_nodes--;
2149   node_info=cube_info->next_node++;
2150   (void) ResetMagickMemory(node_info,0,sizeof(*node_info));
2151   node_info->parent=parent;
2152   node_info->id=id;
2153   node_info->level=level;
2154   return(node_info);
2155 }
2156 \f
2157 /*
2158 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2159 %                                                                             %
2160 %                                                                             %
2161 %                                                                             %
2162 %  G e t I m a g e Q u a n t i z e E r r o r                                  %
2163 %                                                                             %
2164 %                                                                             %
2165 %                                                                             %
2166 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2167 %
2168 %  GetImageQuantizeError() measures the difference between the original
2169 %  and quantized images.  This difference is the total quantization error.
2170 %  The error is computed by summing over all pixels in an image the distance
2171 %  squared in RGB space between each reference pixel value and its quantized
2172 %  value.  These values are computed:
2173 %
2174 %    o mean_error_per_pixel:  This value is the mean error for any single
2175 %      pixel in the image.
2176 %
2177 %    o normalized_mean_square_error:  This value is the normalized mean
2178 %      quantization error for any single pixel in the image.  This distance
2179 %      measure is normalized to a range between 0 and 1.  It is independent
2180 %      of the range of red, green, and blue values in the image.
2181 %
2182 %    o normalized_maximum_square_error:  Thsi value is the normalized
2183 %      maximum quantization error for any single pixel in the image.  This
2184 %      distance measure is normalized to a range between 0 and 1.  It is
2185 %      independent of the range of red, green, and blue values in your image.
2186 %
2187 %  The format of the GetImageQuantizeError method is:
2188 %
2189 %      MagickBooleanType GetImageQuantizeError(Image *image,
2190 %        ExceptionInfo *exception)
2191 %
2192 %  A description of each parameter follows.
2193 %
2194 %    o image: the image.
2195 %
2196 %    o exception: return any errors or warnings in this structure.
2197 %
2198 */
2199 MagickExport MagickBooleanType GetImageQuantizeError(Image *image,
2200   ExceptionInfo *exception)
2201 {
2202   CacheView
2203     *image_view;
2204
2205   double
2206     alpha,
2207     area,
2208     beta,
2209     distance,
2210     maximum_error,
2211     mean_error,
2212     mean_error_per_pixel;
2213
2214   size_t
2215     index;
2216
2217   ssize_t
2218     y;
2219
2220   assert(image != (Image *) NULL);
2221   assert(image->signature == MagickSignature);
2222   if (image->debug != MagickFalse)
2223     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2224   image->total_colors=GetNumberColors(image,(FILE *) NULL,exception);
2225   (void) ResetMagickMemory(&image->error,0,sizeof(image->error));
2226   if (image->storage_class == DirectClass)
2227     return(MagickTrue);
2228   alpha=1.0;
2229   beta=1.0;
2230   area=3.0*image->columns*image->rows;
2231   maximum_error=0.0;
2232   mean_error_per_pixel=0.0;
2233   mean_error=0.0;
2234   image_view=AcquireVirtualCacheView(image,exception);
2235   for (y=0; y < (ssize_t) image->rows; y++)
2236   {
2237     register const Quantum
2238       *restrict p;
2239
2240     register ssize_t
2241       x;
2242
2243     p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
2244     if (p == (const Quantum *) NULL)
2245       break;
2246     for (x=0; x < (ssize_t) image->columns; x++)
2247     {
2248       index=1UL*GetPixelIndex(image,p);
2249       if (image->alpha_trait == BlendPixelTrait)
2250         {
2251           alpha=(double) (QuantumScale*GetPixelAlpha(image,p));
2252           beta=(double) (QuantumScale*image->colormap[index].alpha);
2253         }
2254       distance=fabs(alpha*GetPixelRed(image,p)-beta*
2255         image->colormap[index].red);
2256       mean_error_per_pixel+=distance;
2257       mean_error+=distance*distance;
2258       if (distance > maximum_error)
2259         maximum_error=distance;
2260       distance=fabs(alpha*GetPixelGreen(image,p)-beta*
2261         image->colormap[index].green);
2262       mean_error_per_pixel+=distance;
2263       mean_error+=distance*distance;
2264       if (distance > maximum_error)
2265         maximum_error=distance;
2266       distance=fabs(alpha*GetPixelBlue(image,p)-beta*
2267         image->colormap[index].blue);
2268       mean_error_per_pixel+=distance;
2269       mean_error+=distance*distance;
2270       if (distance > maximum_error)
2271         maximum_error=distance;
2272       p+=GetPixelChannels(image);
2273     }
2274   }
2275   image_view=DestroyCacheView(image_view);
2276   image->error.mean_error_per_pixel=(double) mean_error_per_pixel/area;
2277   image->error.normalized_mean_error=(double) QuantumScale*QuantumScale*
2278     mean_error/area;
2279   image->error.normalized_maximum_error=(double) QuantumScale*maximum_error;
2280   return(MagickTrue);
2281 }
2282 \f
2283 /*
2284 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2285 %                                                                             %
2286 %                                                                             %
2287 %                                                                             %
2288 %   G e t Q u a n t i z e I n f o                                             %
2289 %                                                                             %
2290 %                                                                             %
2291 %                                                                             %
2292 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2293 %
2294 %  GetQuantizeInfo() initializes the QuantizeInfo structure.
2295 %
2296 %  The format of the GetQuantizeInfo method is:
2297 %
2298 %      GetQuantizeInfo(QuantizeInfo *quantize_info)
2299 %
2300 %  A description of each parameter follows:
2301 %
2302 %    o quantize_info: Specifies a pointer to a QuantizeInfo structure.
2303 %
2304 */
2305 MagickExport void GetQuantizeInfo(QuantizeInfo *quantize_info)
2306 {
2307   (void) LogMagickEvent(TraceEvent,GetMagickModule(),"...");
2308   assert(quantize_info != (QuantizeInfo *) NULL);
2309   (void) ResetMagickMemory(quantize_info,0,sizeof(*quantize_info));
2310   quantize_info->number_colors=256;
2311   quantize_info->dither_method=RiemersmaDitherMethod;
2312   quantize_info->colorspace=UndefinedColorspace;
2313   quantize_info->measure_error=MagickFalse;
2314   quantize_info->signature=MagickSignature;
2315 }
2316 \f
2317 /*
2318 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2319 %                                                                             %
2320 %                                                                             %
2321 %                                                                             %
2322 %     P o s t e r i z e I m a g e                                             %
2323 %                                                                             %
2324 %                                                                             %
2325 %                                                                             %
2326 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2327 %
2328 %  PosterizeImage() reduces the image to a limited number of colors for a
2329 %  "poster" effect.
2330 %
2331 %  The format of the PosterizeImage method is:
2332 %
2333 %      MagickBooleanType PosterizeImage(Image *image,const size_t levels,
2334 %        const DitherMethod dither_method,ExceptionInfo *exception)
2335 %
2336 %  A description of each parameter follows:
2337 %
2338 %    o image: Specifies a pointer to an Image structure.
2339 %
2340 %    o levels: Number of color levels allowed in each channel.  Very low values
2341 %      (2, 3, or 4) have the most visible effect.
2342 %
2343 %    o dither_method: choose from UndefinedDitherMethod, NoDitherMethod,
2344 %      RiemersmaDitherMethod, FloydSteinbergDitherMethod.
2345 %
2346 %    o exception: return any errors or warnings in this structure.
2347 %
2348 */
2349
2350 static inline double MagickRound(double x)
2351 {
2352   /*
2353     Round the fraction to nearest integer.
2354   */
2355   if ((x-floor(x)) < (ceil(x)-x))
2356     return(floor(x));
2357   return(ceil(x));
2358 }
2359
2360 MagickExport MagickBooleanType PosterizeImage(Image *image,const size_t levels,
2361   const DitherMethod dither_method,ExceptionInfo *exception)
2362 {
2363 #define PosterizeImageTag  "Posterize/Image"
2364 #define PosterizePixel(pixel) (Quantum) (QuantumRange*(MagickRound( \
2365   QuantumScale*pixel*(levels-1)))/MagickMax((ssize_t) levels-1,1))
2366
2367   CacheView
2368     *image_view;
2369
2370   MagickBooleanType
2371     status;
2372
2373   MagickOffsetType
2374     progress;
2375
2376   QuantizeInfo
2377     *quantize_info;
2378
2379   register ssize_t
2380     i;
2381
2382   ssize_t
2383     y;
2384
2385   assert(image != (Image *) NULL);
2386   assert(image->signature == MagickSignature);
2387   if (image->debug != MagickFalse)
2388     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2389   if (image->storage_class == PseudoClass)
2390 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2391     #pragma omp parallel for schedule(static,4) shared(progress,status) \
2392       magick_threads(image,image,1,1)
2393 #endif
2394     for (i=0; i < (ssize_t) image->colors; i++)
2395     {
2396       /*
2397         Posterize colormap.
2398       */
2399       if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2400         image->colormap[i].red=(double)
2401           PosterizePixel(image->colormap[i].red);
2402       if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2403         image->colormap[i].green=(double)
2404           PosterizePixel(image->colormap[i].green);
2405       if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2406         image->colormap[i].blue=(double)
2407           PosterizePixel(image->colormap[i].blue);
2408       if ((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0)
2409         image->colormap[i].alpha=(double)
2410           PosterizePixel(image->colormap[i].alpha);
2411     }
2412   /*
2413     Posterize image.
2414   */
2415   status=MagickTrue;
2416   progress=0;
2417   image_view=AcquireAuthenticCacheView(image,exception);
2418 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2419   #pragma omp parallel for schedule(static,4) shared(progress,status) \
2420     magick_threads(image,image,image->rows,1)
2421 #endif
2422   for (y=0; y < (ssize_t) image->rows; y++)
2423   {
2424     register Quantum
2425       *restrict q;
2426
2427     register ssize_t
2428       x;
2429
2430     if (status == MagickFalse)
2431       continue;
2432     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
2433     if (q == (Quantum *) NULL)
2434       {
2435         status=MagickFalse;
2436         continue;
2437       }
2438     for (x=0; x < (ssize_t) image->columns; x++)
2439     {
2440       if ((GetPixelRedTraits(image) & UpdatePixelTrait) != 0)
2441         SetPixelRed(image,PosterizePixel(GetPixelRed(image,q)),q);
2442       if ((GetPixelGreenTraits(image) & UpdatePixelTrait) != 0)
2443         SetPixelGreen(image,PosterizePixel(GetPixelGreen(image,q)),q);
2444       if ((GetPixelBlueTraits(image) & UpdatePixelTrait) != 0)
2445         SetPixelBlue(image,PosterizePixel(GetPixelBlue(image,q)),q);
2446       if (((GetPixelBlackTraits(image) & UpdatePixelTrait) != 0) &&
2447           (image->colorspace == CMYKColorspace))
2448         SetPixelBlack(image,PosterizePixel(GetPixelBlack(image,q)),q);
2449       if (((GetPixelAlphaTraits(image) & UpdatePixelTrait) != 0) &&
2450           (image->alpha_trait == BlendPixelTrait))
2451         SetPixelAlpha(image,PosterizePixel(GetPixelAlpha(image,q)),q);
2452       q+=GetPixelChannels(image);
2453     }
2454     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
2455       status=MagickFalse;
2456     if (image->progress_monitor != (MagickProgressMonitor) NULL)
2457       {
2458         MagickBooleanType
2459           proceed;
2460
2461 #if defined(MAGICKCORE_OPENMP_SUPPORT)
2462         #pragma omp critical (MagickCore_PosterizeImage)
2463 #endif
2464         proceed=SetImageProgress(image,PosterizeImageTag,progress++,
2465           image->rows);
2466         if (proceed == MagickFalse)
2467           status=MagickFalse;
2468       }
2469   }
2470   image_view=DestroyCacheView(image_view);
2471   quantize_info=AcquireQuantizeInfo((ImageInfo *) NULL);
2472   quantize_info->number_colors=(size_t) MagickMin((ssize_t) levels*levels*
2473     levels,MaxColormapSize+1);
2474   quantize_info->dither_method=dither_method;
2475   quantize_info->tree_depth=MaxTreeDepth;
2476   status=QuantizeImage(quantize_info,image,exception);
2477   quantize_info=DestroyQuantizeInfo(quantize_info);
2478   return(status);
2479 }
2480 \f
2481 /*
2482 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2483 %                                                                             %
2484 %                                                                             %
2485 %                                                                             %
2486 +   P r u n e C h i l d                                                       %
2487 %                                                                             %
2488 %                                                                             %
2489 %                                                                             %
2490 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2491 %
2492 %  PruneChild() deletes the given node and merges its statistics into its
2493 %  parent.
2494 %
2495 %  The format of the PruneSubtree method is:
2496 %
2497 %      PruneChild(const Image *image,CubeInfo *cube_info,
2498 %        const NodeInfo *node_info)
2499 %
2500 %  A description of each parameter follows.
2501 %
2502 %    o image: the image.
2503 %
2504 %    o cube_info: A pointer to the Cube structure.
2505 %
2506 %    o node_info: pointer to node in color cube tree that is to be pruned.
2507 %
2508 */
2509 static void PruneChild(const Image *image,CubeInfo *cube_info,
2510   const NodeInfo *node_info)
2511 {
2512   NodeInfo
2513     *parent;
2514
2515   register ssize_t
2516     i;
2517
2518   size_t
2519     number_children;
2520
2521   /*
2522     Traverse any children.
2523   */
2524   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2525   for (i=0; i < (ssize_t) number_children; i++)
2526     if (node_info->child[i] != (NodeInfo *) NULL)
2527       PruneChild(image,cube_info,node_info->child[i]);
2528   /*
2529     Merge color statistics into parent.
2530   */
2531   parent=node_info->parent;
2532   parent->number_unique+=node_info->number_unique;
2533   parent->total_color.red+=node_info->total_color.red;
2534   parent->total_color.green+=node_info->total_color.green;
2535   parent->total_color.blue+=node_info->total_color.blue;
2536   parent->total_color.alpha+=node_info->total_color.alpha;
2537   parent->child[node_info->id]=(NodeInfo *) NULL;
2538   cube_info->nodes--;
2539 }
2540 \f
2541 /*
2542 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2543 %                                                                             %
2544 %                                                                             %
2545 %                                                                             %
2546 +  P r u n e L e v e l                                                        %
2547 %                                                                             %
2548 %                                                                             %
2549 %                                                                             %
2550 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2551 %
2552 %  PruneLevel() deletes all nodes at the bottom level of the color tree merging
2553 %  their color statistics into their parent node.
2554 %
2555 %  The format of the PruneLevel method is:
2556 %
2557 %      PruneLevel(const Image *image,CubeInfo *cube_info,
2558 %        const NodeInfo *node_info)
2559 %
2560 %  A description of each parameter follows.
2561 %
2562 %    o image: the image.
2563 %
2564 %    o cube_info: A pointer to the Cube structure.
2565 %
2566 %    o node_info: pointer to node in color cube tree that is to be pruned.
2567 %
2568 */
2569 static void PruneLevel(const Image *image,CubeInfo *cube_info,
2570   const NodeInfo *node_info)
2571 {
2572   register ssize_t
2573     i;
2574
2575   size_t
2576     number_children;
2577
2578   /*
2579     Traverse any children.
2580   */
2581   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2582   for (i=0; i < (ssize_t) number_children; i++)
2583     if (node_info->child[i] != (NodeInfo *) NULL)
2584       PruneLevel(image,cube_info,node_info->child[i]);
2585   if (node_info->level == cube_info->depth)
2586     PruneChild(image,cube_info,node_info);
2587 }
2588 \f
2589 /*
2590 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2591 %                                                                             %
2592 %                                                                             %
2593 %                                                                             %
2594 +  P r u n e T o C u b e D e p t h                                            %
2595 %                                                                             %
2596 %                                                                             %
2597 %                                                                             %
2598 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2599 %
2600 %  PruneToCubeDepth() deletes any nodes at a depth greater than
2601 %  cube_info->depth while merging their color statistics into their parent
2602 %  node.
2603 %
2604 %  The format of the PruneToCubeDepth method is:
2605 %
2606 %      PruneToCubeDepth(const Image *image,CubeInfo *cube_info,
2607 %        const NodeInfo *node_info)
2608 %
2609 %  A description of each parameter follows.
2610 %
2611 %    o cube_info: A pointer to the Cube structure.
2612 %
2613 %    o node_info: pointer to node in color cube tree that is to be pruned.
2614 %
2615 */
2616 static void PruneToCubeDepth(const Image *image,CubeInfo *cube_info,
2617   const NodeInfo *node_info)
2618 {
2619   register ssize_t
2620     i;
2621
2622   size_t
2623     number_children;
2624
2625   /*
2626     Traverse any children.
2627   */
2628   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2629   for (i=0; i < (ssize_t) number_children; i++)
2630     if (node_info->child[i] != (NodeInfo *) NULL)
2631       PruneToCubeDepth(image,cube_info,node_info->child[i]);
2632   if (node_info->level > cube_info->depth)
2633     PruneChild(image,cube_info,node_info);
2634 }
2635 \f
2636 /*
2637 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2638 %                                                                             %
2639 %                                                                             %
2640 %                                                                             %
2641 %  Q u a n t i z e I m a g e                                                  %
2642 %                                                                             %
2643 %                                                                             %
2644 %                                                                             %
2645 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2646 %
2647 %  QuantizeImage() analyzes the colors within a reference image and chooses a
2648 %  fixed number of colors to represent the image.  The goal of the algorithm
2649 %  is to minimize the color difference between the input and output image while
2650 %  minimizing the processing time.
2651 %
2652 %  The format of the QuantizeImage method is:
2653 %
2654 %      MagickBooleanType QuantizeImage(const QuantizeInfo *quantize_info,
2655 %        Image *image,ExceptionInfo *exception)
2656 %
2657 %  A description of each parameter follows:
2658 %
2659 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
2660 %
2661 %    o image: the image.
2662 %
2663 %    o exception: return any errors or warnings in this structure.
2664 %
2665 */
2666
2667 static MagickBooleanType DirectToColormapImage(Image *image,
2668   ExceptionInfo *exception)
2669 {
2670   CacheView
2671     *image_view;
2672
2673   MagickBooleanType
2674     status;
2675
2676   register ssize_t
2677     i;
2678
2679   size_t
2680     number_colors;
2681
2682   ssize_t
2683     y;
2684
2685   status=MagickTrue;
2686   number_colors=(size_t) (image->columns*image->rows);
2687   if (AcquireImageColormap(image,number_colors,exception) == MagickFalse)
2688     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
2689       image->filename);
2690   if (image->colors != number_colors)
2691     return(MagickFalse);
2692   i=0;
2693   image_view=AcquireAuthenticCacheView(image,exception);
2694   for (y=0; y < (ssize_t) image->rows; y++)
2695   {
2696     MagickBooleanType
2697       proceed;
2698
2699     register Quantum
2700       *restrict q;
2701
2702     register ssize_t
2703       x;
2704
2705     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
2706     if (q == (Quantum *) NULL)
2707       break;
2708     for (x=0; x < (ssize_t) image->columns; x++)
2709     {
2710       image->colormap[i].red=(double) GetPixelRed(image,q);
2711       image->colormap[i].green=(double) GetPixelGreen(image,q);
2712       image->colormap[i].blue=(double) GetPixelBlue(image,q);
2713       image->colormap[i].alpha=(double) GetPixelAlpha(image,q);
2714       SetPixelIndex(image,(Quantum) i,q);
2715       i++;
2716       q+=GetPixelChannels(image);
2717     }
2718     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
2719       break;
2720     proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) y,
2721       image->rows);
2722     if (proceed == MagickFalse)
2723       status=MagickFalse;
2724   }
2725   image_view=DestroyCacheView(image_view);
2726   return(status);
2727 }
2728
2729 MagickExport MagickBooleanType QuantizeImage(const QuantizeInfo *quantize_info,
2730   Image *image,ExceptionInfo *exception)
2731 {
2732   CubeInfo
2733     *cube_info;
2734
2735   MagickBooleanType
2736     status;
2737
2738   size_t
2739     depth,
2740     maximum_colors;
2741
2742   assert(quantize_info != (const QuantizeInfo *) NULL);
2743   assert(quantize_info->signature == MagickSignature);
2744   assert(image != (Image *) NULL);
2745   assert(image->signature == MagickSignature);
2746   if (image->debug != MagickFalse)
2747     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
2748   maximum_colors=quantize_info->number_colors;
2749   if (maximum_colors == 0)
2750     maximum_colors=MaxColormapSize;
2751   if (maximum_colors > MaxColormapSize)
2752     maximum_colors=MaxColormapSize;
2753   if (image->alpha_trait != BlendPixelTrait)
2754     {
2755       if ((image->columns*image->rows) <= maximum_colors)
2756         (void) DirectToColormapImage(image,exception);
2757       if (IsImageGray(image,exception) != MagickFalse)
2758         (void) SetGrayscaleImage(image,exception);
2759     }
2760   if ((image->storage_class == PseudoClass) &&
2761       (image->colors <= maximum_colors))
2762     return(MagickTrue);
2763   depth=quantize_info->tree_depth;
2764   if (depth == 0)
2765     {
2766       size_t
2767         colors;
2768
2769       /*
2770         Depth of color tree is: Log4(colormap size)+2.
2771       */
2772       colors=maximum_colors;
2773       for (depth=1; colors != 0; depth++)
2774         colors>>=2;
2775       if ((quantize_info->dither_method != NoDitherMethod) && (depth > 2))
2776         depth--;
2777       if ((image->alpha_trait == BlendPixelTrait) && (depth > 5))
2778         depth--;
2779       if (IsImageGray(image,exception) != MagickFalse)
2780         depth=MaxTreeDepth;
2781     }
2782   /*
2783     Initialize color cube.
2784   */
2785   cube_info=GetCubeInfo(quantize_info,depth,maximum_colors);
2786   if (cube_info == (CubeInfo *) NULL)
2787     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
2788       image->filename);
2789   status=ClassifyImageColors(cube_info,image,exception);
2790   if (status != MagickFalse)
2791     {
2792       /*
2793         Reduce the number of colors in the image.
2794       */
2795       ReduceImageColors(image,cube_info);
2796       status=AssignImageColors(image,cube_info,exception);
2797     }
2798   DestroyCubeInfo(cube_info);
2799   return(status);
2800 }
2801 \f
2802 /*
2803 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2804 %                                                                             %
2805 %                                                                             %
2806 %                                                                             %
2807 %   Q u a n t i z e I m a g e s                                               %
2808 %                                                                             %
2809 %                                                                             %
2810 %                                                                             %
2811 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2812 %
2813 %  QuantizeImages() analyzes the colors within a set of reference images and
2814 %  chooses a fixed number of colors to represent the set.  The goal of the
2815 %  algorithm is to minimize the color difference between the input and output
2816 %  images while minimizing the processing time.
2817 %
2818 %  The format of the QuantizeImages method is:
2819 %
2820 %      MagickBooleanType QuantizeImages(const QuantizeInfo *quantize_info,
2821 %        Image *images,ExceptionInfo *exception)
2822 %
2823 %  A description of each parameter follows:
2824 %
2825 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
2826 %
2827 %    o images: Specifies a pointer to a list of Image structures.
2828 %
2829 %    o exception: return any errors or warnings in this structure.
2830 %
2831 */
2832 MagickExport MagickBooleanType QuantizeImages(const QuantizeInfo *quantize_info,
2833   Image *images,ExceptionInfo *exception)
2834 {
2835   CubeInfo
2836     *cube_info;
2837
2838   Image
2839     *image;
2840
2841   MagickBooleanType
2842     proceed,
2843     status;
2844
2845   MagickProgressMonitor
2846     progress_monitor;
2847
2848   register ssize_t
2849     i;
2850
2851   size_t
2852     depth,
2853     maximum_colors,
2854     number_images;
2855
2856   assert(quantize_info != (const QuantizeInfo *) NULL);
2857   assert(quantize_info->signature == MagickSignature);
2858   assert(images != (Image *) NULL);
2859   assert(images->signature == MagickSignature);
2860   if (images->debug != MagickFalse)
2861     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
2862   if (GetNextImageInList(images) == (Image *) NULL)
2863     {
2864       /*
2865         Handle a single image with QuantizeImage.
2866       */
2867       status=QuantizeImage(quantize_info,images,exception);
2868       return(status);
2869     }
2870   status=MagickFalse;
2871   maximum_colors=quantize_info->number_colors;
2872   if (maximum_colors == 0)
2873     maximum_colors=MaxColormapSize;
2874   if (maximum_colors > MaxColormapSize)
2875     maximum_colors=MaxColormapSize;
2876   depth=quantize_info->tree_depth;
2877   if (depth == 0)
2878     {
2879       size_t
2880         colors;
2881
2882       /*
2883         Depth of color tree is: Log4(colormap size)+2.
2884       */
2885       colors=maximum_colors;
2886       for (depth=1; colors != 0; depth++)
2887         colors>>=2;
2888       if (quantize_info->dither_method != NoDitherMethod)
2889         depth--;
2890     }
2891   /*
2892     Initialize color cube.
2893   */
2894   cube_info=GetCubeInfo(quantize_info,depth,maximum_colors);
2895   if (cube_info == (CubeInfo *) NULL)
2896     {
2897       (void) ThrowMagickException(exception,GetMagickModule(),
2898         ResourceLimitError,"MemoryAllocationFailed","`%s'",images->filename);
2899       return(MagickFalse);
2900     }
2901   number_images=GetImageListLength(images);
2902   image=images;
2903   for (i=0; image != (Image *) NULL; i++)
2904   {
2905     progress_monitor=SetImageProgressMonitor(image,(MagickProgressMonitor) NULL,
2906       image->client_data);
2907     status=ClassifyImageColors(cube_info,image,exception);
2908     if (status == MagickFalse)
2909       break;
2910     (void) SetImageProgressMonitor(image,progress_monitor,image->client_data);
2911     proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) i,
2912       number_images);
2913     if (proceed == MagickFalse)
2914       break;
2915     image=GetNextImageInList(image);
2916   }
2917   if (status != MagickFalse)
2918     {
2919       /*
2920         Reduce the number of colors in an image sequence.
2921       */
2922       ReduceImageColors(images,cube_info);
2923       image=images;
2924       for (i=0; image != (Image *) NULL; i++)
2925       {
2926         progress_monitor=SetImageProgressMonitor(image,(MagickProgressMonitor)
2927           NULL,image->client_data);
2928         status=AssignImageColors(image,cube_info,exception);
2929         if (status == MagickFalse)
2930           break;
2931         (void) SetImageProgressMonitor(image,progress_monitor,
2932           image->client_data);
2933         proceed=SetImageProgress(image,AssignImageTag,(MagickOffsetType) i,
2934           number_images);
2935         if (proceed == MagickFalse)
2936           break;
2937         image=GetNextImageInList(image);
2938       }
2939     }
2940   DestroyCubeInfo(cube_info);
2941   return(status);
2942 }
2943 \f
2944 /*
2945 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2946 %                                                                             %
2947 %                                                                             %
2948 %                                                                             %
2949 +   Q u a n t i z e E r r o r F l a t t e n                                   %
2950 %                                                                             %
2951 %                                                                             %
2952 %                                                                             %
2953 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
2954 %
2955 %  QuantizeErrorFlatten() traverses the color cube and flattens the quantization
2956 %  error into a sorted 1D array.  This accelerates the color reduction process.
2957 %
2958 %  Contributed by Yoya.
2959 %
2960 %  The format of the QuantizeImages method is:
2961 %
2962 %      size_t QuantizeErrorFlatten(const Image *image,const CubeInfo *cube_info,
2963 %        const NodeInfo *node_info,const ssize_t offset,
2964 %        MagickRealType *quantize_error)
2965 %
2966 %  A description of each parameter follows.
2967 %
2968 %    o image: the image.
2969 %
2970 %    o cube_info: A pointer to the Cube structure.
2971 %
2972 %    o node_info: pointer to node in color cube tree that is current pointer.
2973 %
2974 %    o offset: quantize error offset.
2975 %
2976 %    o quantize_error: the quantization error vector.
2977 %
2978 */
2979 static size_t QuantizeErrorFlatten(const Image *image,const CubeInfo *cube_info,
2980   const NodeInfo *node_info,const ssize_t offset,MagickRealType *quantize_error)
2981 {
2982   register ssize_t
2983     i;
2984
2985   size_t
2986     n,
2987     number_children;
2988
2989   if (offset >= (ssize_t) cube_info->nodes)
2990     return(0);
2991   quantize_error[offset]=node_info->quantize_error;
2992   n=1;
2993   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
2994   for (i=0; i < (ssize_t) number_children ; i++)
2995     if (node_info->child[i] != (NodeInfo *) NULL)
2996       n+=QuantizeErrorFlatten(image,cube_info,node_info->child[i],offset+n,
2997         quantize_error);
2998   return(n);
2999 }
3000 \f
3001 /*
3002 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3003 %                                                                             %
3004 %                                                                             %
3005 %                                                                             %
3006 +   R e d u c e                                                               %
3007 %                                                                             %
3008 %                                                                             %
3009 %                                                                             %
3010 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3011 %
3012 %  Reduce() traverses the color cube tree and prunes any node whose
3013 %  quantization error falls below a particular threshold.
3014 %
3015 %  The format of the Reduce method is:
3016 %
3017 %      Reduce(const Image *image,CubeInfo *cube_info,const NodeInfo *node_info)
3018 %
3019 %  A description of each parameter follows.
3020 %
3021 %    o image: the image.
3022 %
3023 %    o cube_info: A pointer to the Cube structure.
3024 %
3025 %    o node_info: pointer to node in color cube tree that is to be pruned.
3026 %
3027 */
3028 static void Reduce(const Image *image,CubeInfo *cube_info,
3029   const NodeInfo *node_info)
3030 {
3031   register ssize_t
3032     i;
3033
3034   size_t
3035     number_children;
3036
3037   /*
3038     Traverse any children.
3039   */
3040   number_children=cube_info->associate_alpha == MagickFalse ? 8UL : 16UL;
3041   for (i=0; i < (ssize_t) number_children; i++)
3042     if (node_info->child[i] != (NodeInfo *) NULL)
3043       Reduce(image,cube_info,node_info->child[i]);
3044   if (node_info->quantize_error <= cube_info->pruning_threshold)
3045     PruneChild(image,cube_info,node_info);
3046   else
3047     {
3048       /*
3049         Find minimum pruning threshold.
3050       */
3051       if (node_info->number_unique > 0)
3052         cube_info->colors++;
3053       if (node_info->quantize_error < cube_info->next_threshold)
3054         cube_info->next_threshold=node_info->quantize_error;
3055     }
3056 }
3057 \f
3058 /*
3059 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3060 %                                                                             %
3061 %                                                                             %
3062 %                                                                             %
3063 +   R e d u c e I m a g e C o l o r s                                         %
3064 %                                                                             %
3065 %                                                                             %
3066 %                                                                             %
3067 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3068 %
3069 %  ReduceImageColors() repeatedly prunes the tree until the number of nodes
3070 %  with n2 > 0 is less than or equal to the maximum number of colors allowed
3071 %  in the output image.  On any given iteration over the tree, it selects
3072 %  those nodes whose E value is minimal for pruning and merges their
3073 %  color statistics upward. It uses a pruning threshold, Ep, to govern
3074 %  node selection as follows:
3075 %
3076 %    Ep = 0
3077 %    while number of nodes with (n2 > 0) > required maximum number of colors
3078 %      prune all nodes such that E <= Ep
3079 %      Set Ep to minimum E in remaining nodes
3080 %
3081 %  This has the effect of minimizing any quantization error when merging
3082 %  two nodes together.
3083 %
3084 %  When a node to be pruned has offspring, the pruning procedure invokes
3085 %  itself recursively in order to prune the tree from the leaves upward.
3086 %  n2,  Sr, Sg,  and  Sb in a node being pruned are always added to the
3087 %  corresponding data in that node's parent.  This retains the pruned
3088 %  node's color characteristics for later averaging.
3089 %
3090 %  For each node, n2 pixels exist for which that node represents the
3091 %  smallest volume in RGB space containing those pixel's colors.  When n2
3092 %  > 0 the node will uniquely define a color in the output image. At the
3093 %  beginning of reduction,  n2 = 0  for all nodes except a the leaves of
3094 %  the tree which represent colors present in the input image.
3095 %
3096 %  The other pixel count, n1, indicates the total number of colors
3097 %  within the cubic volume which the node represents.  This includes n1 -
3098 %  n2  pixels whose colors should be defined by nodes at a lower level in
3099 %  the tree.
3100 %
3101 %  The format of the ReduceImageColors method is:
3102 %
3103 %      ReduceImageColors(const Image *image,CubeInfo *cube_info)
3104 %
3105 %  A description of each parameter follows.
3106 %
3107 %    o image: the image.
3108 %
3109 %    o cube_info: A pointer to the Cube structure.
3110 %
3111 */
3112
3113 static int MagickRealTypeCompare(const void *error_p,const void *error_q)
3114 {
3115   MagickRealType
3116     *p,
3117     *q;
3118
3119   p=(MagickRealType *) error_p;
3120   q=(MagickRealType *) error_q;
3121   if (*p > *q)
3122     return(1);
3123   if (fabs((double) (*q-*p)) <= MagickEpsilon)
3124     return(0);
3125   return(-1);
3126 }
3127
3128 static void ReduceImageColors(const Image *image,CubeInfo *cube_info)
3129 {
3130 #define ReduceImageTag  "Reduce/Image"
3131
3132   MagickBooleanType
3133     proceed;
3134
3135   MagickOffsetType
3136     offset;
3137
3138   size_t
3139     span;
3140
3141   cube_info->next_threshold=0.0;
3142   if ((cube_info->colors > cube_info->maximum_colors) &&
3143       (cube_info->nodes > 128))
3144     {
3145       MagickRealType
3146         *quantize_error;
3147
3148       /*
3149         Enable rapid reduction of the number of unique colors.
3150       */
3151       quantize_error=(MagickRealType *) AcquireQuantumMemory(cube_info->nodes,
3152         sizeof(*quantize_error));
3153       if (quantize_error != (MagickRealType *) NULL)
3154         {
3155           (void) QuantizeErrorFlatten(image,cube_info,cube_info->root,0,
3156             quantize_error);
3157           qsort(quantize_error,cube_info->nodes,sizeof(MagickRealType),
3158             MagickRealTypeCompare);
3159           cube_info->next_threshold=quantize_error[MagickMax((ssize_t)
3160             cube_info->nodes-110*(cube_info->maximum_colors+1)/100,0)];
3161           quantize_error=(MagickRealType *) RelinquishMagickMemory(
3162             quantize_error);
3163         }
3164   }
3165   for (span=cube_info->colors; cube_info->colors > cube_info->maximum_colors; )
3166   {
3167     cube_info->pruning_threshold=cube_info->next_threshold;
3168     cube_info->next_threshold=cube_info->root->quantize_error-1;
3169     cube_info->colors=0;
3170     Reduce(image,cube_info,cube_info->root);
3171     offset=(MagickOffsetType) span-cube_info->colors;
3172     proceed=SetImageProgress(image,ReduceImageTag,offset,span-
3173       cube_info->maximum_colors+1);
3174     if (proceed == MagickFalse)
3175       break;
3176   }
3177 }
3178 \f
3179 /*
3180 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3181 %                                                                             %
3182 %                                                                             %
3183 %                                                                             %
3184 %   R e m a p I m a g e                                                       %
3185 %                                                                             %
3186 %                                                                             %
3187 %                                                                             %
3188 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3189 %
3190 %  RemapImage() replaces the colors of an image with a dither of the colors
3191 %  provided.
3192 %
3193 %  The format of the RemapImage method is:
3194 %
3195 %      MagickBooleanType RemapImage(const QuantizeInfo *quantize_info,
3196 %        Image *image,const Image *remap_image,ExceptionInfo *exception)
3197 %
3198 %  A description of each parameter follows:
3199 %
3200 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
3201 %
3202 %    o image: the image.
3203 %
3204 %    o remap_image: the reference image.
3205 %
3206 %    o exception: return any errors or warnings in this structure.
3207 %
3208 */
3209 MagickExport MagickBooleanType RemapImage(const QuantizeInfo *quantize_info,
3210   Image *image,const Image *remap_image,ExceptionInfo *exception)
3211 {
3212   CubeInfo
3213     *cube_info;
3214
3215   MagickBooleanType
3216     status;
3217
3218   /*
3219     Initialize color cube.
3220   */
3221   assert(image != (Image *) NULL);
3222   assert(image->signature == MagickSignature);
3223   if (image->debug != MagickFalse)
3224     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",image->filename);
3225   assert(remap_image != (Image *) NULL);
3226   assert(remap_image->signature == MagickSignature);
3227   cube_info=GetCubeInfo(quantize_info,MaxTreeDepth,
3228     quantize_info->number_colors);
3229   if (cube_info == (CubeInfo *) NULL)
3230     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3231       image->filename);
3232   status=ClassifyImageColors(cube_info,remap_image,exception);
3233   if (status != MagickFalse)
3234     {
3235       /*
3236         Classify image colors from the reference image.
3237       */
3238       cube_info->quantize_info->number_colors=cube_info->colors;
3239       status=AssignImageColors(image,cube_info,exception);
3240     }
3241   DestroyCubeInfo(cube_info);
3242   return(status);
3243 }
3244 \f
3245 /*
3246 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3247 %                                                                             %
3248 %                                                                             %
3249 %                                                                             %
3250 %   R e m a p I m a g e s                                                     %
3251 %                                                                             %
3252 %                                                                             %
3253 %                                                                             %
3254 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3255 %
3256 %  RemapImages() replaces the colors of a sequence of images with the
3257 %  closest color from a reference image.
3258 %
3259 %  The format of the RemapImage method is:
3260 %
3261 %      MagickBooleanType RemapImages(const QuantizeInfo *quantize_info,
3262 %        Image *images,Image *remap_image,ExceptionInfo *exception)
3263 %
3264 %  A description of each parameter follows:
3265 %
3266 %    o quantize_info: Specifies a pointer to an QuantizeInfo structure.
3267 %
3268 %    o images: the image sequence.
3269 %
3270 %    o remap_image: the reference image.
3271 %
3272 %    o exception: return any errors or warnings in this structure.
3273 %
3274 */
3275 MagickExport MagickBooleanType RemapImages(const QuantizeInfo *quantize_info,
3276   Image *images,const Image *remap_image,ExceptionInfo *exception)
3277 {
3278   CubeInfo
3279     *cube_info;
3280
3281   Image
3282     *image;
3283
3284   MagickBooleanType
3285     status;
3286
3287   assert(images != (Image *) NULL);
3288   assert(images->signature == MagickSignature);
3289   if (images->debug != MagickFalse)
3290     (void) LogMagickEvent(TraceEvent,GetMagickModule(),"%s",images->filename);
3291   image=images;
3292   if (remap_image == (Image *) NULL)
3293     {
3294       /*
3295         Create a global colormap for an image sequence.
3296       */
3297       status=QuantizeImages(quantize_info,images,exception);
3298       return(status);
3299     }
3300   /*
3301     Classify image colors from the reference image.
3302   */
3303   cube_info=GetCubeInfo(quantize_info,MaxTreeDepth,
3304     quantize_info->number_colors);
3305   if (cube_info == (CubeInfo *) NULL)
3306     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3307       image->filename);
3308   status=ClassifyImageColors(cube_info,remap_image,exception);
3309   if (status != MagickFalse)
3310     {
3311       /*
3312         Classify image colors from the reference image.
3313       */
3314       cube_info->quantize_info->number_colors=cube_info->colors;
3315       image=images;
3316       for ( ; image != (Image *) NULL; image=GetNextImageInList(image))
3317       {
3318         status=AssignImageColors(image,cube_info,exception);
3319         if (status == MagickFalse)
3320           break;
3321       }
3322     }
3323   DestroyCubeInfo(cube_info);
3324   return(status);
3325 }
3326 \f
3327 /*
3328 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3329 %                                                                             %
3330 %                                                                             %
3331 %                                                                             %
3332 %   S e t G r a y s c a l e I m a g e                                         %
3333 %                                                                             %
3334 %                                                                             %
3335 %                                                                             %
3336 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
3337 %
3338 %  SetGrayscaleImage() converts an image to a PseudoClass grayscale image.
3339 %
3340 %  The format of the SetGrayscaleImage method is:
3341 %
3342 %      MagickBooleanType SetGrayscaleImage(Image *image,ExceptionInfo *exeption)
3343 %
3344 %  A description of each parameter follows:
3345 %
3346 %    o image: The image.
3347 %
3348 %    o exception: return any errors or warnings in this structure.
3349 %
3350 */
3351
3352 #if defined(__cplusplus) || defined(c_plusplus)
3353 extern "C" {
3354 #endif
3355
3356 static int IntensityCompare(const void *x,const void *y)
3357 {
3358   PixelInfo
3359     *color_1,
3360     *color_2;
3361
3362   ssize_t
3363     intensity;
3364
3365   color_1=(PixelInfo *) x;
3366   color_2=(PixelInfo *) y;
3367   intensity=(ssize_t) (GetPixelInfoIntensity(color_1)-(ssize_t)
3368     GetPixelInfoIntensity(color_2));
3369   return((int) intensity);
3370 }
3371
3372 #if defined(__cplusplus) || defined(c_plusplus)
3373 }
3374 #endif
3375
3376 static MagickBooleanType SetGrayscaleImage(Image *image,
3377   ExceptionInfo *exception)
3378 {
3379   CacheView
3380     *image_view;
3381
3382   MagickBooleanType
3383     status;
3384
3385   PixelInfo
3386     *colormap;
3387
3388   register ssize_t
3389     i;
3390
3391   ssize_t
3392     *colormap_index,
3393     j,
3394     y;
3395
3396   assert(image != (Image *) NULL);
3397   assert(image->signature == MagickSignature);
3398   if (image->type != GrayscaleType)
3399     (void) TransformImageColorspace(image,GRAYColorspace,exception);
3400   colormap_index=(ssize_t *) AcquireQuantumMemory(MaxMap+1,
3401     sizeof(*colormap_index));
3402   if (colormap_index == (ssize_t *) NULL)
3403     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3404       image->filename);
3405   if (image->storage_class != PseudoClass)
3406     {
3407       for (i=0; i <= (ssize_t) MaxMap; i++)
3408         colormap_index[i]=(-1);
3409       if (AcquireImageColormap(image,MaxMap+1,exception) == MagickFalse)
3410         ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3411           image->filename);
3412       image->colors=0;
3413       status=MagickTrue;
3414       image_view=AcquireAuthenticCacheView(image,exception);
3415 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3416       #pragma omp parallel for schedule(static,4) shared(status) \
3417         magick_threads(image,image,image->rows,1)
3418 #endif
3419       for (y=0; y < (ssize_t) image->rows; y++)
3420       {
3421         register Quantum
3422           *restrict q;
3423
3424         register ssize_t
3425           x;
3426
3427         if (status == MagickFalse)
3428           continue;
3429         q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
3430           exception);
3431         if (q == (Quantum *) NULL)
3432           {
3433             status=MagickFalse;
3434             continue;
3435           }
3436         for (x=0; x < (ssize_t) image->columns; x++)
3437         {
3438           register size_t
3439             intensity;
3440
3441           intensity=ScaleQuantumToMap(GetPixelRed(image,q));
3442           if (colormap_index[intensity] < 0)
3443             {
3444 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3445               #pragma omp critical (MagickCore_SetGrayscaleImage)
3446 #endif
3447               if (colormap_index[intensity] < 0)
3448                 {
3449                   colormap_index[intensity]=(ssize_t) image->colors;
3450                   image->colormap[image->colors].red=(double)
3451                     GetPixelRed(image,q);
3452                   image->colormap[image->colors].green=(double)
3453                     GetPixelGreen(image,q);
3454                   image->colormap[image->colors].blue=(double)
3455                     GetPixelBlue(image,q);
3456                   image->colors++;
3457                }
3458             }
3459           SetPixelIndex(image,(Quantum) colormap_index[intensity],q);
3460           q+=GetPixelChannels(image);
3461         }
3462         if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
3463           status=MagickFalse;
3464       }
3465       image_view=DestroyCacheView(image_view);
3466     }
3467   for (i=0; i < (ssize_t) image->colors; i++)
3468     image->colormap[i].alpha=(double) i;
3469   qsort((void *) image->colormap,image->colors,sizeof(PixelInfo),
3470     IntensityCompare);
3471   colormap=(PixelInfo *) AcquireQuantumMemory(image->colors,sizeof(*colormap));
3472   if (colormap == (PixelInfo *) NULL)
3473     ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
3474       image->filename);
3475   j=0;
3476   colormap[j]=image->colormap[0];
3477   for (i=0; i < (ssize_t) image->colors; i++)
3478   {
3479     if (IsPixelInfoEquivalent(&colormap[j],&image->colormap[i]) == MagickFalse)
3480       {
3481         j++;
3482         colormap[j]=image->colormap[i];
3483       }
3484     colormap_index[(ssize_t) image->colormap[i].alpha]=j;
3485   }
3486   image->colors=(size_t) (j+1);
3487   image->colormap=(PixelInfo *) RelinquishMagickMemory(image->colormap);
3488   image->colormap=colormap;
3489   status=MagickTrue;
3490   image_view=AcquireAuthenticCacheView(image,exception);
3491 #if defined(MAGICKCORE_OPENMP_SUPPORT)
3492   #pragma omp parallel for schedule(static,4) shared(status) \
3493     magick_threads(image,image,image->rows,1)
3494 #endif
3495   for (y=0; y < (ssize_t) image->rows; y++)
3496   {
3497     register Quantum
3498       *restrict q;
3499
3500     register ssize_t
3501       x;
3502
3503     if (status == MagickFalse)
3504       continue;
3505     q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,exception);
3506     if (q == (Quantum *) NULL)
3507       {
3508         status=MagickFalse;
3509         continue;
3510       }
3511     for (x=0; x < (ssize_t) image->columns; x++)
3512     {
3513       SetPixelIndex(image,(Quantum) colormap_index[ScaleQuantumToMap(
3514         GetPixelIndex(image,q))],q);
3515       q+=GetPixelChannels(image);
3516     }
3517     if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
3518       status=MagickFalse;
3519   }
3520   image_view=DestroyCacheView(image_view);
3521   colormap_index=(ssize_t *) RelinquishMagickMemory(colormap_index);
3522   image->type=GrayscaleType;
3523   if (IsImageMonochrome(image,exception) != MagickFalse)
3524     image->type=BilevelType;
3525   return(status);
3526 }