Quantize.java

/*
 * @(#)Quantize.java    0.90 9/19/00 Adam Doppelt
 */


/**
 * An efficient color quantization algorithm, adapted from the C++
 * implementation quantize.c in <a
 * href="http://www.imagemagick.org/">ImageMagick</a>. The pixels for
 * an image are placed into an oct tree. The oct tree is reduced in
 * size, and the pixels from the original image are reassigned to the
 * nodes in the reduced tree.<p>
 *
 * Here is the copyright notice from ImageMagick:
 * 
 * <pre>
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %  Permission is hereby granted, free of charge, to any person obtaining a    %
 %  copy of this software and associated documentation files ("ImageMagick"),  %
 %  to deal in ImageMagick without restriction, including without limitation   %
 %  the rights to use, copy, modify, merge, publish, distribute, sublicense,   %
 %  and/or sell copies of ImageMagick, and to permit persons to whom the       %
 %  ImageMagick is furnished to do so, subject to the following conditions:    %
 %                                                                             %
 %  The above copyright notice and this permission notice shall be included in %
 %  all copies or substantial portions of ImageMagick.                         %
 %                                                                             %
 %  The software is provided "as is", without warranty of any kind, express or %
 %  implied, including but not limited to the warranties of merchantability,   %
 %  fitness for a particular purpose and noninfringement.  In no event shall   %
 %  E. I. du Pont de Nemours and Company be liable for any claim, damages or   %
 %  other liability, whether in an action of contract, tort or otherwise,      %
 %  arising from, out of or in connection with ImageMagick or the use or other %
 %  dealings in ImageMagick.                                                   %
 %                                                                             %
 %  Except as contained in this notice, the name of the E. I. du Pont de       %
 %  Nemours and Company shall not be used in advertising or otherwise to       %
 %  promote the sale, use or other dealings in ImageMagick without prior       %
 %  written authorization from the E. I. du Pont de Nemours and Company.       %
 %                                                                             %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 </pre>
 *
 *
 * @version 0.90 19 Sep 2000
 * @author <a href="http://www.gurge.com/amd/">Adam Doppelt</a>
 */
public class Quantize {

  /*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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   %           QQQ   U   U   AAA   N   N  TTTTT  IIIII   ZZZZZ  EEEEE            %
   %          Q   Q  U   U  A   A  NN  N    T      I        ZZ  E                %
   %          Q   Q  U   U  AAAAA  N N N    T      I      ZZZ   EEEEE            %
   %          Q  QQ  U   U  A   A  N  NN    T      I     ZZ     E                %
   %           QQQQ   UUU   A   A  N   N    T    IIIII   ZZZZZ  EEEEE            %
   %                                                                             %
   %                                                                             %
   %              Reduce the Number of Unique Colors in an Image                 %
   %                                                                             %
   %                                                                             %
   %                           Software Design                                   %
   %                             John Cristy                                     %
   %                              July 1992                                      %
   %                                                                             %
   %                                                                             %
   %  Copyright 1998 E. I. du Pont de Nemours and Company                        %
   %                                                                             %
   %  Permission is hereby granted, free of charge, to any person obtaining a    %
   %  copy of this software and associated documentation files ("ImageMagick"),  %
   %  to deal in ImageMagick without restriction, including without limitation   %
   %  the rights to use, copy, modify, merge, publish, distribute, sublicense,   %
   %  and/or sell copies of ImageMagick, and to permit persons to whom the       %
   %  ImageMagick is furnished to do so, subject to the following conditions:    %
   %                                                                             %
   %  The above copyright notice and this permission notice shall be included in %
   %  all copies or substantial portions of ImageMagick.                         %
   %                                                                             %
   %  The software is provided "as is", without warranty of any kind, express or %
   %  implied, including but not limited to the warranties of merchantability,   %
   %  fitness for a particular purpose and noninfringement.  In no event shall   %
   %  E. I. du Pont de Nemours and Company be liable for any claim, damages or   %
   %  other liability, whether in an action of contract, tort or otherwise,      %
   %  arising from, out of or in connection with ImageMagick or the use or other %
   %  dealings in ImageMagick.                                                   %
   %                                                                             %
   %  Except as contained in this notice, the name of the E. I. du Pont de       %
   %  Nemours and Company shall not be used in advertising or otherwise to       %
   %  promote the sale, use or other dealings in ImageMagick without prior       %
   %  written authorization from the E. I. du Pont de Nemours and Company.       %
   %                                                                             %
   %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
   %
   %  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 program 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.
   %
   %  Function Quantize 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 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 reclassification 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 classification 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, classification 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.
   %
   %  With the permission of USC Information Sciences Institute, 4676 Admiralty
   %  Way, Marina del Rey, California  90292, this code was adapted from module
   %  ALCOLS written by Paul Raveling.
   %
   %  The names of ISI and USC are not used in advertising or publicity
   %  pertaining to distribution of the software without prior specific
   %  written permission from ISI.
   %
   */

  final static boolean QUICK = true;

  final static int MAX_RGB = 255;
  final static int MAX_NODES = 266817;
  final static int MAX_TREE_DEPTH = 8;

  // these are precomputed in advance
  static int SQUARES[];
  static int SHIFT[];

  static {
    SQUARES = new int[MAX_RGB + MAX_RGB + 1];
    for (int i= -MAX_RGB; i <= MAX_RGB; i++) {
      SQUARES[i + MAX_RGB] = i * i;
    }

    SHIFT = new int[MAX_TREE_DEPTH + 1];
    for (int i = 0; i < MAX_TREE_DEPTH + 1; ++i) {
      SHIFT[i] = 1 << (15 - i);
    }
  }


  /**
   * Reduce the image to the given number of colors. The pixels are
   * reduced in place.
   * @return The new color palette.
   */
  public static int[] quantizeImage(int pixels[][], int max_colors) {
    Cube cube = new Cube(pixels, max_colors);
    cube.classification();
    cube.reduction();
    cube.assignment();
    return cube.colormap;
  }

  static class Cube {
    int pixels[][];
    int max_colors;
    int colormap[];

    Node root;
    int depth;

    // counter for the number of colors in the cube. this gets
    // recalculated often.
    int colors;

    // counter for the number of nodes in the tree
    int nodes;

    Cube(int pixels[][], int max_colors) {
      this.pixels = pixels;
      this.max_colors = max_colors;

      int i = max_colors;
      // tree_depth = log max_colors
      //                 4
      for (depth = 1; i != 0; depth++) {
        i /= 4;
      }
      if (depth > 1) {
        --depth;
      }
      if (depth > MAX_TREE_DEPTH) {
        depth = MAX_TREE_DEPTH;
      } else if (depth < 2) {
        depth = 2;
      }

      root = new Node(this);
    }

    /*
         * Procedure 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
     * classification 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, classification 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:
     *
     *   number_pixels : Number of pixels whose color is contained
     *   in the RGB cube which this node represents;
     *
     *   unique : 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.
     *
     *   total_red/green/blue : 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.
     */
    void classification() {
      int pixels[][] = this.pixels;

      int width = pixels.length;
      int height = pixels[0].length;

      // convert to indexed color
      for (int x = width; x-- > 0; ) {
        for (int y = height; y-- > 0; ) {
          int pixel = pixels[x][y];
          int red   = (pixel >> 16) & 0xFF;
          int green = (pixel >>  8) & 0xFF;
          int blue  = (pixel >>  0) & 0xFF;

          // a hard limit on the number of nodes in the tree
          if (nodes > MAX_NODES) {
            System.out.println("pruning");
            root.pruneLevel();
            --depth;
          }

          // walk the tree to depth, increasing the
          // number_pixels count for each node
          Node node = root;
          for (int level = 1; level <= depth; ++level) {
            int id = (((red   > node.mid_red   ? 1 : 0) << 0) |
              ((green > node.mid_green ? 1 : 0) << 1) |
              ((blue  > node.mid_blue  ? 1 : 0) << 2));
            if (node.child[id] == null) {
              new Node(node, id, level);
            }
            node = node.child[id];
            node.number_pixels += SHIFT[level];
          }

          ++node.unique;
          node.total_red   += red;
          node.total_green += green;
          node.total_blue  += blue;
        }
      }
    }

    /*
         * reduction repeatedly prunes the tree until the number of
     * nodes with unique > 0 is less than or equal to the maximum
     * number of colors allowed in the output image.
     *
     * When a node to be pruned has offspring, the pruning
     * procedure invokes itself recursively in order to prune the
     * tree from the leaves upward.  The statistics of the 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.
     */
    void reduction() {
      int threshold = 1;
      while (colors > max_colors) {
        colors = 0;
        threshold = root.reduce(threshold, Integer.MAX_VALUE);
      }
    }

    /**
     * The result of a closest color search.
     */
    static class Search {
      int distance;
      int color_number;
    }

    /*
         * Procedure 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.
     */
    void assignment() {
      colormap = new int[colors];

      colors = 0;
      root.colormap();

      int pixels[][] = this.pixels;

      int width = pixels.length;
      int height = pixels[0].length;

      Search search = new Search();

      // convert to indexed color
      for (int x = width; x-- > 0; ) {
        for (int y = height; y-- > 0; ) {
          int pixel = pixels[x][y];
          int red   = (pixel >> 16) & 0xFF;
          int green = (pixel >>  8) & 0xFF;
          int blue  = (pixel >>  0) & 0xFF;

          // walk the tree to find the cube containing that color
          Node node = root;
          for (;; ) {
            int id = (((red   > node.mid_red   ? 1 : 0) << 0) |
              ((green > node.mid_green ? 1 : 0) << 1) |
              ((blue  > node.mid_blue  ? 1 : 0) << 2)  );
            if (node.child[id] == null) {
              break;
            }
            node = node.child[id];
          }

          if (QUICK) {
            // if QUICK is set, just use that
            // node. Strictly speaking, this isn't
            // necessarily best match.
            pixels[x][y] = node.color_number;
          } else {
            // Find the closest color.
            search.distance = Integer.MAX_VALUE;
            node.parent.closestColor(red, green, blue, search);
            pixels[x][y] = search.color_number;
          }
        }
      }
    }

    /**
     * A single Node in the tree.
     */
    static class Node {
      Cube cube;

      // parent node
      Node parent;

      // child nodes
      Node child[];
      int nchild;

      // our index within our parent
      int id;
      // our level within the tree
      int level;
      // our color midpoint
      int mid_red;
      int mid_green;
      int mid_blue;

      // the pixel count for this node and all children
      int number_pixels;

      // the pixel count for this node
      int unique;
      // the sum of all pixels contained in this node
      int total_red;
      int total_green;
      int total_blue;

      // used to build the colormap
      int color_number;

      Node(Cube cube) {
        this.cube = cube;
        this.parent = this;
        this.child = new Node[8];
        this.id = 0;
        this.level = 0;

        this.number_pixels = Integer.MAX_VALUE;

        this.mid_red   = (MAX_RGB + 1) >> 1;
        this.mid_green = (MAX_RGB + 1) >> 1;
        this.mid_blue  = (MAX_RGB + 1) >> 1;
      }

      Node(Node parent, int id, int level) {
        this.cube = parent.cube;
        this.parent = parent;
        this.child = new Node[8];
        this.id = id;
        this.level = level;

        // add to the cube
        ++cube.nodes;
        if (level == cube.depth) {
          ++cube.colors;
        }

        // add to the parent
        ++parent.nchild;
        parent.child[id] = this;

        // figure out our midpoint
        int bi = (1 << (MAX_TREE_DEPTH - level)) >> 1;
        mid_red   = parent.mid_red   + ((id & 1) > 0 ? bi : -bi);
        mid_green = parent.mid_green + ((id & 2) > 0 ? bi : -bi);
        mid_blue  = parent.mid_blue  + ((id & 4) > 0 ? bi : -bi);
      }

      /**
       * Remove this child node, and make sure our parent
       * absorbs our pixel statistics.
       */
      void pruneChild() {
        --parent.nchild;
        parent.unique += unique;
        parent.total_red     += total_red;
        parent.total_green   += total_green;
        parent.total_blue    += total_blue;
        parent.child[id] = null;
        --cube.nodes;
        cube = null;
        parent = null;
      }

      /**
       * Prune the lowest layer of the tree.
       */
      void pruneLevel() {
        if (nchild != 0) {
          for (int id = 0; id < 8; id++) {
            if (child[id] != null) {
              child[id].pruneLevel();
            }
          }
        }
        if (level == cube.depth) {
          pruneChild();
        }
      }

      /**
       * Remove any nodes that have fewer than threshold
       * pixels. Also, as long as we're walking the tree:
       *
       *  - figure out the color with the fewest pixels
       *  - recalculate the total number of colors in the tree
       */
      int reduce(int threshold, int next_threshold) {
        if (nchild != 0) {
          for (int id = 0; id < 8; id++) {
            if (child[id] != null) {
              next_threshold = child[id].reduce(threshold, next_threshold);
            }
          }
        }
        if (number_pixels <= threshold) {
          pruneChild();
        } else {
          if (unique != 0) {
            cube.colors++;
          }
          if (number_pixels < next_threshold) {
            next_threshold = number_pixels;
          }
        }
        return next_threshold;
      }

      /*
       * colormap traverses the color cube tree and notes each
       * colormap entry. A colormap entry is any node in the
       * color cube tree where the number of unique colors is
       * not zero.
       */
      void colormap() {
        if (nchild != 0) {
          for (int id = 0; id < 8; id++) {
            if (child[id] != null) {
              child[id].colormap();
            }
          }
        }
        if (unique != 0) {
          int r = ((total_red   + (unique >> 1)) / unique);
          int g = ((total_green + (unique >> 1)) / unique);
          int b = ((total_blue  + (unique >> 1)) / unique);
          cube.colormap[cube.colors] = (((    0xFF) << 24) |
            ((r & 0xFF) << 16) |
            ((g & 0xFF) <<  8) |
            ((b & 0xFF) <<  0));
          color_number = cube.colors++;
        }
      }

      /* ClosestColor traverses the color cube tree at a
       * particular node and determines which colormap entry
       * best represents the input color.
       */
      void closestColor(int red, int green, int blue, Search search) {
        if (nchild != 0) {
          for (int id = 0; id < 8; id++) {
            if (child[id] != null) {
              child[id].closestColor(red, green, blue, search);
            }
          }
        }

        if (unique != 0) {
          int color = cube.colormap[color_number];
          int distance = distance(color, red, green, blue);
          if (distance < search.distance) {
            search.distance = distance;
            search.color_number = color_number;
          }
        }
      }

      /**
       * Figure out the distance between this node and som color.
       */
      final static int distance(int color, int r, int g, int b) {
        return (SQUARES[((color >> 16) & 0xFF) - r + MAX_RGB] +
          SQUARES[((color >>  8) & 0xFF) - g + MAX_RGB] +
          SQUARES[((color >>  0) & 0xFF) - b + MAX_RGB]);
      }

      public String toString() {
        StringBuffer buf = new StringBuffer();
        if (parent == this) {
          buf.append("root");
        } else {
          buf.append("node");
        }
        buf.append(' ');
        buf.append(level);
        buf.append(" [");
        buf.append(mid_red);
        buf.append(',');
        buf.append(mid_green);
        buf.append(',');
        buf.append(mid_blue);
        buf.append(']');
        return new String(buf);
      }
    }
  }
}