quantize.c

Go to the documentation of this file.

/*
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%                                                                             %
%    MagickCore Methods to Reduce the Number of Unique Colors in an Image     %
%                                                                             %
%                           Software Design                                   %
%                             John Cristy                                     %
%                              July 1992                                      %
%                                                                             %
%                                                                             %
%  Copyright 1999-2008 ImageMagick Studio LLC, a non-profit organization      %
%  dedicated to making software imaging solutions freely available.           %
%                                                                             %
%  You may not use this file except in compliance with the License.  You may  %
%  obtain a copy of the License at                                            %
%                                                                             %
%    http://www.imagemagick.org/script/license.php                            %
%                                                                             %
%  Unless required by applicable law or agreed to in writing, software        %
%  distributed under the License is distributed on an "AS IS" BASIS,          %
%  WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.   %
%  See the License for the specific language governing permissions and        %
%  limitations under the License.                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  Realism in computer graphics typically requires using 24 bits/pixel to
%  generate an image.  Yet many graphic display devices do not contain the
%  amount of memory necessary to match the spatial and color resolution of
%  the human eye.  The Quantize methods takes a 24 bit image and reduces
%  the number of colors so it can be displayed on raster device with less
%  bits per pixel.  In most instances, the quantized image closely
%  resembles the original reference image.
%
%  A reduction of colors in an image is also desirable for image
%  transmission and real-time animation.
%
%  QuantizeImage() takes a standard RGB or monochrome images and quantizes
%  them down to some fixed number of colors.
%
%  For purposes of color allocation, an image is a set of n pixels, where
%  each pixel is a point in RGB space.  RGB space is a 3-dimensional
%  vector space, and each pixel, Pi,  is defined by an ordered triple of
%  red, green, and blue coordinates, (Ri, Gi, Bi).
%
%  Each primary color component (red, green, or blue) represents an
%  intensity which varies linearly from 0 to a maximum value, Cmax, which
%  corresponds to full saturation of that color.  Color allocation is
%  defined over a domain consisting of the cube in RGB space with opposite
%  vertices at (0,0,0) and (Cmax, Cmax, Cmax).  QUANTIZE requires Cmax =
%  255.
%
%  The algorithm maps this domain onto a tree in which each node
%  represents a cube within that domain.  In the following discussion
%  these cubes are defined by the coordinate of two opposite vertices:
%  The vertex nearest the origin in RGB space and the vertex farthest from
%  the origin.
%
%  The tree's root node represents the entire domain, (0,0,0) through
%  (Cmax,Cmax,Cmax).  Each lower level in the tree is generated by
%  subdividing one node's cube into eight smaller cubes of equal size.
%  This corresponds to bisecting the parent cube with planes passing
%  through the midpoints of each edge.
%
%  The basic algorithm operates in three phases: Classification,
%  Reduction, and Assignment.  Classification builds a color description
%  tree for the image.  Reduction collapses the tree until the number it
%  represents, at most, the number of colors desired in the output image.
%  Assignment defines the output image's color map and sets each pixel's
%  color by restorage_class in the reduced tree.  Our goal is to minimize
%  the numerical discrepancies between the original colors and quantized
%  colors (quantization error).
%
%  Classification begins by initializing a color description tree of
%  sufficient depth to represent each possible input color in a leaf.
%  However, it is impractical to generate a fully-formed color description
%  tree in the storage_class phase for realistic values of Cmax.  If
%  colors components in the input image are quantized to k-bit precision,
%  so that Cmax= 2k-1, the tree would need k levels below the root node to
%  allow representing each possible input color in a leaf.  This becomes
%  prohibitive because the tree's total number of nodes is 1 +
%  sum(i=1, k, 8k).
%
%  A complete tree would require 19,173,961 nodes for k = 8, Cmax = 255.
%  Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
%  Initializes data structures for nodes only as they are needed;  (2)
%  Chooses a maximum depth for the tree as a function of the desired
%  number of colors in the output image (currently log2(colormap size)).
%
%  For each pixel in the input image, storage_class scans downward from
%  the root of the color description tree.  At each level of the tree it
%  identifies the single node which represents a cube in RGB space
%  containing the pixel's color.  It updates the following data for each
%  such node:
%
%    n1: Number of pixels whose color is contained in the RGB cube which
%    this node represents;
%
%    n2: Number of pixels whose color is not represented in a node at
%    lower depth in the tree;  initially,  n2 = 0 for all nodes except
%    leaves of the tree.
%
%    Sr, Sg, Sb: Sums of the red, green, and blue component values for all
%    pixels not classified at a lower depth. The combination of these sums
%    and n2  will ultimately characterize the mean color of a set of
%    pixels represented by this node.
%
%    E: the distance squared in RGB space between each pixel contained
%    within a node and the nodes' center.  This represents the
%    quantization error for a node.
%
%  Reduction repeatedly prunes the tree until the number of nodes with n2
%  > 0 is less than or equal to the maximum number of colors allowed in
%  the output image.  On any given iteration over the tree, it selects
%  those nodes whose E count is minimal for pruning and merges their color
%  statistics upward. It uses a pruning threshold, Ep, to govern node
%  selection as follows:
%
%    Ep = 0
%    while number of nodes with (n2 > 0) > required maximum number of colors
%      prune all nodes such that E <= Ep
%      Set Ep to minimum E in remaining nodes
%
%  This has the effect of minimizing any quantization error when merging
%  two nodes together.
%
%  When a node to be pruned has offspring, the pruning procedure invokes
%  itself recursively in order to prune the tree from the leaves upward.
%  n2,  Sr, Sg,  and  Sb in a node being pruned are always added to the
%  corresponding data in that node's parent.  This retains the pruned
%  node's color characteristics for later averaging.
%
%  For each node, n2 pixels exist for which that node represents the
%  smallest volume in RGB space containing those pixel's colors.  When n2
%  > 0 the node will uniquely define a color in the output image. At the
%  beginning of reduction,  n2 = 0  for all nodes except a the leaves of
%  the tree which represent colors present in the input image.
%
%  The other pixel count, n1, indicates the total number of colors within
%  the cubic volume which the node represents.  This includes n1 - n2
%  pixels whose colors should be defined by nodes at a lower level in the
%  tree.
%
%  Assignment generates the output image from the pruned tree.  The output
%  image consists of two parts: (1)  A color map, which is an array of
%  color descriptions (RGB triples) for each color present in the output
%  image;  (2)  A pixel array, which represents each pixel as an index
%  into the color map array.
%
%  First, the assignment phase makes one pass over the pruned color
%  description tree to establish the image's color map.  For each node
%  with n2  > 0, it divides Sr, Sg, and Sb by n2 .  This produces the mean
%  color of all pixels that classify no lower than this node.  Each of
%  these colors becomes an entry in the color map.
%
%  Finally,  the assignment phase reclassifies each pixel in the pruned
%  tree to identify the deepest node containing the pixel's color.  The
%  pixel's value in the pixel array becomes the index of this node's mean
%  color in the color map.
%
%  This method is based on a similar algorithm written by Paul Raveling.
%
*/

/*
  Include declarations.
*/
#include "magick/studio.h"
#include "magick/cache-view.h"
#include "magick/color.h"
#include "magick/color-private.h"
#include "magick/colorspace.h"
#include "magick/enhance.h"
#include "magick/exception.h"
#include "magick/exception-private.h"
#include "magick/image.h"
#include "magick/image-private.h"
#include "magick/list.h"
#include "magick/memory_.h"
#include "magick/monitor.h"
#include "magick/monitor-private.h"
#include "magick/option.h"
#include "magick/pixel-private.h"
#include "magick/quantize.h"
#include "magick/quantum.h"
#include "magick/string_.h"

/*
  Define declarations.
*/
#define CacheShift  2
#define ErrorQueueLength  16
#define MaxNodes  266817
#define MaxTreeDepth  8
#define NodesInAList  1920

/*
  Typdef declarations.
*/
typedef struct _RealPixelPacket
{
  MagickRealLongType
    red,
    green,
    blue,
    opacity;
} RealPixelPacket;

typedef struct _NodeInfo
{
  struct _NodeInfo
    *parent,
    *child[16];

  MagickSizeType
    number_unique;

  RealPixelPacket
    total_color;

  MagickRealType
    quantize_error;

  unsigned long
    color_number,
    id,
    level;
} NodeInfo;

typedef struct _Nodes
{
  NodeInfo
    *nodes;

  struct _Nodes
    *next;
} Nodes;

typedef struct _CubeInfo
{
  NodeInfo
    *root;

  unsigned long
    colors,
    maximum_colors;

  long
    transparent_index;

  MagickSizeType
    transparent_pixels;

  RealPixelPacket
    target;

  MagickRealType
    distance,
    pruning_threshold,
    next_threshold;

  unsigned long
    nodes,
    free_nodes,
    color_number;

  NodeInfo
    *next_node;

  Nodes
    *node_queue;

  long
    *cache;

  RealPixelPacket
    error[ErrorQueueLength];

  MagickRealType
    weights[ErrorQueueLength];

  QuantizeInfo
    *quantize_info;

  MagickBooleanType
    associate_alpha;

  long
    x,
    y;

  unsigned long
    depth;

  MagickOffsetType
    offset;

  MagickSizeType
    span;
} CubeInfo;

/*
  Method prototypes.
*/
static CubeInfo
   *GetCubeInfo(const QuantizeInfo *,const unsigned long,const unsigned long);

static NodeInfo
  *GetNodeInfo(CubeInfo *,const unsigned long,const unsigned long,NodeInfo *);

static MagickBooleanType
  AssignImageColors(Image *,CubeInfo *),
  ClassifyImageColors(CubeInfo *,const Image *,ExceptionInfo *),
  DitherImage(Image *,CubeInfo *),
  SetGrayscaleImage(Image *);

static unsigned long
  DefineImageColormap(Image *,CubeInfo *,NodeInfo *);

static void
  ClosestColor(const Image *,CubeInfo *,const NodeInfo *),
  DestroyCubeInfo(CubeInfo *),
  PruneLevel(const Image *,CubeInfo *,const NodeInfo *),
  PruneToCubeDepth(const Image *,CubeInfo *,const NodeInfo *),
  ReduceImageColors(const Image *,CubeInfo *);

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%   A c q u i r e Q u a n t i z e I n f o                                     %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  AcquireQuantizeInfo() allocates the QuantizeInfo structure.
%
%  The format of the AcquireQuantizeInfo method is:
%
%      QuantizeInfo *AcquireQuantizeInfo(const ImageInfo *image_info)
%
%  A description of each parameter follows:
%
%    o image_info: the image info.
%
*/
MagickExport QuantizeInfo *AcquireQuantizeInfo(const ImageInfo *image_info)
{
  QuantizeInfo
    *quantize_info;

  quantize_info=(QuantizeInfo *) AcquireMagickMemory(sizeof(*quantize_info));
  if (quantize_info == (QuantizeInfo *) NULL)
    ThrowFatalException(ResourceLimitFatalError,"MemoryAllocationFailed");
  GetQuantizeInfo(quantize_info);
  if (image_info != (ImageInfo *) NULL)
    {
      const char
        *option;

      quantize_info->dither=image_info->dither;
      option=GetImageOption(image_info,"dither");
      if (option != (const char *) NULL)
        quantize_info->dither_method=(DitherMethod) ParseMagickOption(
          MagickDitherOptions,MagickFalse,option);
      quantize_info->measure_error=image_info->verbose;
    }
  return(quantize_info);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
+   A s s i g n I m a g e C o l o r s                                         %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  AssignImageColors() generates the output image from the pruned tree.  The
%  output image consists of two parts: (1)  A color map, which is an array
%  of color descriptions (RGB triples) for each color present in the
%  output image;  (2)  A pixel array, which represents each pixel as an
%  index into the color map array.
%
%  First, the assignment phase makes one pass over the pruned color
%  description tree to establish the image's color map.  For each node
%  with n2  > 0, it divides Sr, Sg, and Sb by n2 .  This produces the mean
%  color of all pixels that classify no lower than this node.  Each of
%  these colors becomes an entry in the color map.
%
%  Finally,  the assignment phase reclassifies each pixel in the pruned
%  tree to identify the deepest node containing the pixel's color.  The
%  pixel's value in the pixel array becomes the index of this node's mean
%  color in the color map.
%
%  The format of the AssignImageColors() method is:
%
%      MagickBooleanType AssignImageColors(Image *image,CubeInfo *cube_info)
%
%  A description of each parameter follows.
%
%    o image: the image.
%
%    o cube_info: A pointer to the Cube structure.
%
*/

static inline void AssociateAlphaPixel(const CubeInfo *cube_info,
  const PixelPacket *pixel,RealPixelPacket *alpha_pixel)
{
  MagickRealType
    alpha;

  if ((cube_info->associate_alpha == MagickFalse) ||
      (pixel->opacity == OpaqueOpacity))
    {
      alpha_pixel->red=(MagickRealType) pixel->red;
      alpha_pixel->green=(MagickRealType) pixel->green;
      alpha_pixel->blue=(MagickRealType) pixel->blue;
      alpha_pixel->opacity=(MagickRealType) pixel->opacity;
      return;
    }
  alpha=(MagickRealType) (QuantumScale*(QuantumRange-pixel->opacity));
  alpha_pixel->red=alpha*pixel->red;
  alpha_pixel->green=alpha*pixel->green;
  alpha_pixel->blue=alpha*pixel->blue;
  alpha_pixel->opacity=(MagickRealType) pixel->opacity;
}

static inline Quantum ClipToQuantum(const MagickRealType value)
{
  if (value <= 0.0)
    return((Quantum) 0);
  if (value >= QuantumRange)
    return((Quantum) QuantumRange);
  return((Quantum) (value+0.5));
}

static inline unsigned long ColorToNodeId(const CubeInfo *cube_info,
  const RealPixelPacket *pixel,unsigned long index)
{
  unsigned long
    id;

  id=(unsigned long) (
    ((ScaleQuantumToChar(ClipToQuantum(pixel->red)) >> index) & 0x1) |
    ((ScaleQuantumToChar(ClipToQuantum(pixel->green)) >> index) & 0x1) << 1 |
    ((ScaleQuantumToChar(ClipToQuantum(pixel->blue)) >> index) & 0x1) << 2);
  if (cube_info->associate_alpha != MagickFalse)
    id|=((ScaleQuantumToChar(ClipToQuantum(pixel->opacity)) >> index) & 0x1)
      << 3;
  return(id);
}

static inline MagickBooleanType IsSameColor(const Image *image,
  const PixelPacket *p,const PixelPacket *q)
{
  if ((p->red != q->red) || (p->green != q->green) || (p->blue != q->blue))
    return(MagickFalse);
  if ((image->matte != MagickFalse) && (p->opacity != q->opacity))
    return(MagickFalse);
  return(MagickTrue);
}

static MagickBooleanType AssignImageColors(Image *image,CubeInfo *cube_info)
{
#define AssignImageTag  "Assign/Image"

  long
    y;

  MagickBooleanType
    proceed;

  RealPixelPacket
    pixel;

  register IndexPacket
    *indexes;

  register long
    i,
    x;

  register const NodeInfo
    *node_info;

  register PixelPacket
    *q;

  ssize_t
    count;

  unsigned long
    id,
    index;

  /*
    Allocate image colormap.
  */
  if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
      (cube_info->quantize_info->colorspace != CMYKColorspace))
    (void) SetImageColorspace((Image *) image,
      cube_info->quantize_info->colorspace);
  else
    if ((image->colorspace != GRAYColorspace) &&
        (image->colorspace != RGBColorspace) &&
        (image->colorspace != CMYColorspace))
      (void) SetImageColorspace((Image *) image,RGBColorspace);
  if (AcquireImageColormap(image,cube_info->colors) == MagickFalse)
    ThrowBinaryException(ResourceLimitError,"MemoryAllocationFailed",
      image->filename);
  image->colors=0;
  cube_info->transparent_pixels=0;
  cube_info->transparent_index=(-1);
  (void) DefineImageColormap(image,cube_info,cube_info->root);
  /*
    Create a reduced color image.
  */
  if ((cube_info->quantize_info->dither != MagickFalse) &&
      (cube_info->quantize_info->dither_method != NoDitherMethod))
    (void) DitherImage(image,cube_info);
  else
    {
      ExceptionInfo
        *exception;

      ViewInfo
        *image_view;

      exception=(&image->exception);
      image_view=AcquireCacheView(image);
      for (y=0; y < (long) image->rows; y++)
      {

        q=GetCacheViewAuthenticPixels(image_view,0,y,image->columns,1,
          exception);
        if (q == (PixelPacket *) NULL)
          break;
        indexes=GetCacheViewAuthenticIndexQueue(image_view);
        for (x=0; x < (long) image->columns; x+=count)
        {
          /*
            Identify the deepest node containing the pixel's color.
          */
          for (count=1; (x+count) < (long) image->columns; count++)
            if (IsSameColor(image,q,q+count) == MagickFalse)
              break;
          AssociateAlphaPixel(cube_info,q,&pixel);
          node_info=cube_info->root;
          for (index=MaxTreeDepth-1; (long) index > 0; index--)
          {
            id=ColorToNodeId(cube_info,&pixel,index);
            if (node_info->child[id] == (NodeInfo *) NULL)
              break;
            node_info=node_info->child[id];
          }
          /*
            Find closest color among siblings and their children.
          */
          cube_info->target=pixel;
          cube_info->distance=(MagickRealType) (4.0*(QuantumRange+1.0)*
            (QuantumRange+1.0)+1.0);
          ClosestColor(image,cube_info,node_info->parent);
          index=cube_info->color_number;
          for (i=0; i < (long) count; i++)
          {
            if (image->storage_class == PseudoClass)
              indexes[x+i]=(IndexPacket) index;
            if (cube_info->quantize_info->measure_error == MagickFalse)
              {
                q->red=image->colormap[index].red;
                q->green=image->colormap[index].green;
                q->blue=image->colormap[index].blue;
                if (cube_info->associate_alpha != MagickFalse)
                  q->opacity=image->colormap[index].opacity;
              }
            q++;
          }
        }
        if (SyncCacheViewAuthenticPixels(image_view,exception) == MagickFalse)
          break;
        proceed=SetImageProgress(image,AssignImageTag,y,image->rows);
        if (proceed == MagickFalse)
          break;
      }
      image_view=DestroyCacheView(image_view);
    }
  if (cube_info->quantize_info->measure_error != MagickFalse)
    (void) GetImageQuantizeError(image);
  if ((cube_info->quantize_info->number_colors == 2) &&
      (cube_info->quantize_info->colorspace == GRAYColorspace))
    {
      Quantum
        intensity;

      /*
        Monochrome image.
      */
      q=image->colormap;
      for (i=0; i < (long) image->colors; i++)
      {
        intensity=(Quantum) (PixelIntensity(q) < ((MagickRealType)
          QuantumRange/2.0) ? 0 : QuantumRange);
        q->red=intensity;
        q->green=intensity;
        q->blue=intensity;
        q++;
      }
    }
  (void) SyncImage(image);
  if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
      (cube_info->quantize_info->colorspace != CMYKColorspace))
    (void) SetImageColorspace((Image *) image,RGBColorspace);
  return(MagickTrue);
}

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
+   C l a s s i f y I m a g e C o l o r s                                     %
%                                                                             %
%                                                                             %
%                                                                             %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%  ClassifyImageColors() begins by initializing a color description tree
%  of sufficient depth to represent each possible input color in a leaf.
%  However, it is impractical to generate a fully-formed color
%  description tree in the storage_class phase for realistic values of
%  Cmax.  If colors components in the input image are quantized to k-bit
%  precision, so that Cmax= 2k-1, the tree would need k levels below the
%  root node to allow representing each possible input color in a leaf.
%  This becomes prohibitive because the tree's total number of nodes is
%  1 + sum(i=1,k,8k).
%
%  A complete tree would require 19,173,961 nodes for k = 8, Cmax = 255.
%  Therefore, to avoid building a fully populated tree, QUANTIZE: (1)
%  Initializes data structures for nodes only as they are needed;  (2)
%  Chooses a maximum depth for the tree as a function of the desired
%  number of colors in the output image (currently log2(colormap size)).
%
%  For each pixel in the input image, storage_class scans downward from
%  the root of the color description tree.  At each level of the tree it
%  identifies the single node which represents a cube in RGB space
%  containing It updates the following data for each such node:
%
%    n1 : Number of pixels whose color is contained in the RGB cube
%    which this node represents;
%
%    n2 : Number of pixels whose color is not represented in a node at
%    lower depth in the tree;  initially,  n2 = 0 for all nodes except
%    leaves of the tree.
%
%    Sr, Sg, Sb : Sums of the red, green, and blue component values for
%    all pixels not classified at a lower depth. The combination of
%    these sums and n2  will ultimately characterize the mean color of a
%    set of pixels represented by this node.
%
%    E: the distance squared in RGB space between each pixel contained
%    within a node and the nodes' center.  This represents the quantization
%    error for a node.
%
%  The format of the ClassifyImageColors() method is:
%
%      MagickBooleanType ClassifyImageColors(CubeInfo *cube_info,
%        const Image *image,ExceptionInfo *exception)
%
%  A description of each parameter follows.
%
%    o cube_info: A pointer to the Cube structure.
%
%    o image: the image.
%
*/

static inline void SetAssociatedAlpha(const Image *image,CubeInfo *cube_info)
{
  MagickBooleanType
    associate_alpha;

  associate_alpha=image->matte;
  if (cube_info->quantize_info->colorspace == TransparentColorspace)
    associate_alpha=MagickFalse;
  if ((cube_info->quantize_info->number_colors == 2) &&
      (cube_info->quantize_info->colorspace == GRAYColorspace))
    associate_alpha=MagickFalse;
  cube_info->associate_alpha=associate_alpha;
}

static MagickBooleanType ClassifyImageColors(CubeInfo *cube_info,
  const Image *image,ExceptionInfo *exception)
{
#define ClassifyImageTag  "Classify/Image"

  long
    y;

  MagickBooleanType
    proceed;

  MagickRealType
    bisect;

  NodeInfo
    *node_info;

  RealPixelPacket
    error,
    mid,
    midpoint,
    pixel;

  register long
    x;

  register const PixelPacket
    *p;

  size_t
    count;

  unsigned long
    id,
    index,
    level;

  ViewInfo
    *image_view;

  /*
    Classify the first cube_info->maximum_colors colors to a tree depth of 8.
  */
  SetAssociatedAlpha(image,cube_info);
  if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
      (cube_info->quantize_info->colorspace != CMYKColorspace))
    (void) SetImageColorspace((Image *) image,
      cube_info->quantize_info->colorspace);
  else
    if ((image->colorspace != GRAYColorspace) &&
        (image->colorspace != CMYColorspace) &&
        (image->colorspace != RGBColorspace))
      (void) SetImageColorspace((Image *) image,RGBColorspace);
  midpoint.red=(MagickRealType) QuantumRange/2.0;
  midpoint.green=(MagickRealType) QuantumRange/2.0;
  midpoint.blue=(MagickRealType) QuantumRange/2.0;
  midpoint.opacity=(MagickRealType) QuantumRange/2.0;
  error.opacity=0.0;
  image_view=AcquireCacheView(image);
  for (y=0; y < (long) image->rows; y++)
  {
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      break;
    if (cube_info->nodes > MaxNodes)
      {
        /*
          Prune one level if the color tree is too large.
        */
        PruneLevel(image,cube_info,cube_info->root);
        cube_info->depth--;
      }
    for (x=0; x < (long) image->columns; x+=(long) count)
    {
      /*
        Start at the root and descend the color cube tree.
      */
      for (count=1; (x+count) < image->columns; count++)
        if (IsSameColor(image,p,p+count) == MagickFalse)
          break;
      AssociateAlphaPixel(cube_info,p,&pixel);
      index=MaxTreeDepth-1;
      bisect=((MagickRealType) QuantumRange+1.0)/2.0;
      mid=midpoint;
      node_info=cube_info->root;
      for (level=1; level <= MaxTreeDepth; level++)
      {
        bisect*=0.5;
        id=ColorToNodeId(cube_info,&pixel,index);
        mid.red+=(id & 1) != 0 ? bisect : -bisect;
        mid.green+=(id & 2) != 0 ? bisect : -bisect;
        mid.blue+=(id & 4) != 0 ? bisect : -bisect;
        mid.opacity+=(id & 8) != 0 ? bisect : -bisect;
        if (node_info->child[id] == (NodeInfo *) NULL)
          {
            /*
              Set colors of new node to contain pixel.
            */
            node_info->child[id]=GetNodeInfo(cube_info,id,level,node_info);
            if (node_info->child[id] == (NodeInfo *) NULL)
              (void) ThrowMagickException(exception,GetMagickModule(),
                ResourceLimitError,"MemoryAllocationFailed","`%s'",
                image->filename);
            if (level == MaxTreeDepth)
              cube_info->colors++;
          }
        /*
          Approximate the quantization error represented by this node.
        */
        node_info=node_info->child[id];
        error.red=QuantumScale*(pixel.red-mid.red);
        error.green=QuantumScale*(pixel.green-mid.green);
        error.blue=QuantumScale*(pixel.blue-mid.blue);
        if (cube_info->associate_alpha != MagickFalse)
          error.opacity=QuantumScale*(pixel.opacity-mid.opacity);
        node_info->quantize_error+=sqrt((double) (count*error.red*error.red+
          count*error.green*error.green+count*error.blue*error.blue+
          count*error.opacity*error.opacity));
        cube_info->root->quantize_error+=node_info->quantize_error;
        index--;
      }
      /*
        Sum RGB for this leaf for later derivation of the mean cube color.
      */
      node_info->number_unique+=count;
      node_info->total_color.red+=count*QuantumScale*pixel.red;
      node_info->total_color.green+=count*QuantumScale*pixel.green;
      node_info->total_color.blue+=count*QuantumScale*pixel.blue;
      if (cube_info->associate_alpha != MagickFalse)
        node_info->total_color.opacity+=count*QuantumScale*pixel.opacity;
      p+=count;
    }
    if (cube_info->colors > cube_info->maximum_colors)
      {
        PruneToCubeDepth(image,cube_info,cube_info->root);
        break;
      }
    proceed=SetImageProgress(image,ClassifyImageTag,y,image->rows);
    if (proceed == MagickFalse)
      break;
  }
  for (y++; y < (long) image->rows; y++)
  {
    p=GetCacheViewVirtualPixels(image_view,0,y,image->columns,1,exception);
    if (p == (const PixelPacket *) NULL)
      break;
    if (cube_info->nodes > MaxNodes)
      {
        /*
          Prune one level if the color tree is too large.
        */
        PruneLevel(image,cube_info,cube_info->root);
        cube_info->depth--;
      }
    for (x=0; x < (long) image->columns; x+=(long) count)
    {
      /*
        Start at the root and descend the color cube tree.
      */
      for (count=1; (x+count) < image->columns; count++)
        if (IsSameColor(image,p,p+count) == MagickFalse)
          break;
      AssociateAlphaPixel(cube_info,p,&pixel);
      index=MaxTreeDepth-1;
      bisect=((MagickRealType) QuantumRange+1.0)/2.0;
      mid=midpoint;
      node_info=cube_info->root;
      for (level=1; level <= cube_info->depth; level++)
      {
        bisect*=0.5;
        id=ColorToNodeId(cube_info,&pixel,index);
        mid.red+=(id & 1) != 0 ? bisect : -bisect;
        mid.green+=(id & 2) != 0 ? bisect : -bisect;
        mid.blue+=(id & 4) != 0 ? bisect : -bisect;
        mid.opacity+=(id & 8) != 0 ? bisect : -bisect;
        if (node_info->child[id] == (NodeInfo *) NULL)
          {
            /*
              Set colors of new node to contain pixel.
            */
            node_info->child[id]=GetNodeInfo(cube_info,id,level,node_info);
            if (node_info->child[id] == (NodeInfo *) NULL)
              (void) ThrowMagickException(exception,GetMagickModule(),
                ResourceLimitError,"MemoryAllocationFailed",image->filename);
            if (level == cube_info->depth)
              cube_info->colors++;
          }
        /*
          Approximate the quantization error represented by this node.
        */
        node_info=node_info->child[id];
        error.red=QuantumScale*(pixel.red-mid.red);
        error.green=QuantumScale*(pixel.green-mid.green);
        error.blue=QuantumScale*(pixel.blue-mid.blue);
        if (cube_info->associate_alpha != MagickFalse)
          error.opacity=QuantumScale*(pixel.opacity-mid.opacity);
        node_info->quantize_error+=sqrt((double) (count*error.red*error.red+
          count*error.green*error.green+error.blue*error.blue+
          count*error.opacity*error.opacity));
        cube_info->root->quantize_error+=node_info->quantize_error;
        index--;
      }
      /*
        Sum RGB for this leaf for later derivation of the mean cube color.
      */
      node_info->number_unique+=count;
      node_info->total_color.red+=count*QuantumScale*pixel.red;
      node_info->total_color.green+=count*QuantumScale*pixel.green;
      node_info->total_color.blue+=count*QuantumScale*pixel.blue;
      if (cube_info->associate_alpha != MagickFalse)
        node_info->total_color.opacity+=count*QuantumScale*pixel.opacity;
      p+=count;
    }
    proceed=SetImageProgress(image,ClassifyImageTag,y,image->rows);
    if (proceed == MagickFalse)
      break;
  }
  image_view=DestroyCacheView(image_view);
  if ((cube_info->quantize_info->colorspace != UndefinedColorspace) &&
      (cube_info->quantize_info->colorspace != CMYKColorspace))
    (void) SetImageColorspace((Image *) image,RGBColorspace);
  return(MagickTrue);
}

/*
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