Provided by: graphicsmagick_1.3.12-1build1_i386 bug


       Quantize - ImageMagick's color reduction algorithm.


       #include <magick.h>


       This document describes how ImageMagick performs color reduction on an
       image.  To fully understand this document, you should have a knowledge
       of basic imaging techniques and the tree data structure and

       vector space, and each pixel, pi,  is defined by an ordered triple of
       red, green, and blue coordinates, (ri, gi, bi).

       intensity which varies linearly from 0 to a maximum value, cmax, which
       corresponds to full saturation of that color.  Color allocation is
       vertices at (0,0,0) and (cmax,cmax,cmax).  ImageMagick requires cmax =

       The algorithm maps this domain onto a tree in which each node
       represents a cube within that domain.  In the following discussion,

       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
       image.  Assignment defines the output image's color map and sets each
       minimize the numerical discrepancies between the original colors and
       quantized colors.  To learn more about quantization error, see
       MEASURING COLOR REDUCTION ERROR later in this document.

       Classification begins by initializing a color description tree of
       sufficient depth to represent each possible input color in a leaf.
       tree in the classification phase for realistic values of cmax.  If
       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
               > ki=1 8k

       A complete tree would require 19,173,961 nodes for k = 8, cmax = 255.
       Therefore, to avoid building a fully populated tree, ImageMagick: (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 log4(colormap size)+2).
       A tree of this depth generally allows the best representation of the
       source image with the fastest computational speed and the least amount
       of memory.  However, the default depth is inappropriate for some

       For each pixel in the input image, classification scans downward from
       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
              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
       selection as follows:

         Ep = 0
             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.

       The values of 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.

       smallest volume in RGB space containing those pixel's colors.  When n2
       tree which represent colors present in the input image.


       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
       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
       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
       color in the color map.

       Empirical evidence suggests that distances in color spaces such as YUV,
       or YIQ correspond to perceptual color differences more closely than do
       distances in RGB space.  These color spaces may give better results
       when color reducing an image.  Here the algorithm is as described
       maximum value, cmax.  The color reduction can then proceed as


       invisible.  Images with high spatial frequencies (such as hair or
       grass) will show error much less than pictures with large smoothly
       shaded areas (such as faces).  This is because the high-frequency
       contour edges introduced by the color reduction process are masked by
       the high frequencies in the image.

       To measure the difference between the original and color reduced images
       an image the distance squared in RGB space between each original pixel
       value and its color reduced value. ImageMagick prints several error
       measurements including the mean error per pixel, the normalized mean
       error, and the normalized maximum error.

       The normalized error measurement can be used to compare images.  In
       image resembles the source image.  Ideally, the error should be
       quantization quality.

       These errors are measured and printed when -verbose and -colors are
       specified on the command line:

       mean error per pixel:
              is the mean error for any single pixel in the image.

       normalized mean square error:
              is the normalized mean square quantization error for any single
              pixel in the image.

              the image.

       normalized maximum square error:
              is the largest normalized square quantization error for any
              single pixel in the image.

              the image.


       display(1), animate(1), mogrify(1), import(1), miff(5)


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       Paul Raveling, USC Information Sciences Institute, for the original
       idea of using space subdivision for the color reduction algorithm.
       With Paul's permission, this document is an adaptation from a document
       he wrote.


       John Cristy, ImageMagick Studio