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

 package com.gurge.amd;

/**
 * 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 {

/*
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                                             %
%                                                                             %
%                                                                             %
%           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);
            }
        }
    }
}
