initializes data structures for nodes only as they are needed.Therefore, to avoid building a fully populated tree, ImageMagick: This becomes prohibitive because the tree's total number of nodes: total nodes = 1+Sum(8^i), i=1,k If color components in the input image are quantized to k-bit precision, so that Cmax = 2^k-1, the tree would need k levels below the root node to allow representing 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. To learn more about quantization error, see Measuring Color Reduction Error.Ĭlassification begins by initializing a color description tree of sufficient depth to represent each possible input color in a leaf. Our goal is to minimize the numerical discrepancies between the original colors and quantized colors.
Assignment defines the output image's color map and sets each pixel's color by reclassification in the reduced tree. Reduction collapses the tree until the number it represents, at most, is the number of colors desired in the output image. The basic algorithm operates in three phases:Ĭlassification builds a color description tree for the image. This corresponds to bisecting the parent cube with planes passing through the midpoints of each edge.
Each lower level in the tree is generated by subdividing one node's cube into eight smaller cubes of equal size. The tree's root node represents the entire domain, (0,0,0) through ( Cmax, Cmax, Cmax). 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 algorithm maps this domain onto a tree in which each node represents a cube within that domain. 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).
IMAGEMAGICK COLORS FULL
RGB space is a 3-dimensional vector space, and each pixel, p(i), is defined by an ordered triple of red, green, and blue coordinates, ( r(i), g(i), b(i)).Įach 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. Algorithm Descriptionįor purposes of color allocation, an image is a set of n pixels, where each pixel is a point in RGB space. To fully understand what follows, you should have a knowledge of basic imaging techniques and the tree data structure and terminology. This document describes how ImageMagick performs color reduction on an image.
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