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Manpages ## quantizeSection: File Formats (5)Updated: $Date: 2003/12/29 00:03:12 $ Index Return to Main Contents ## NAMEQuantize - ImageMagick's color reduction algorithm.## SYNOPSIS#include <magick.h>
## DESCRIPTIONThis document describes howImageMagick 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 terminology.
For purposes of color allocation, an image is a set of
Each primary color component (red, green, or blue) represents an
intensity which varies linearly from 0 to a maximum value,
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
(
The basic algorithm operates in three phases:
Sigma ki=1 8k
A complete tree would require 19,173,961 nodes for 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: **n****1****:**- Number of pixels whose color is contained in the RGB cube which this node represents;
**n****2****:**-
Number of pixels whose color is not represented in a node at lower
depth in the tree; initially,
*n**2**= 0*for all nodes except leaves of the tree. **S****r****, S****g****, S****b****:**-
Sums of the red, green, and blue component values for all pixels not
classified at a lower depth. The combination of these sums and
*n**2*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.
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.
The values of
For each node,
The other pixel count,
First, the assignment phase makes one pass over the pruned color
description tree to establish the image's color map. For each node
with 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.
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
except each pixel is a point in the alternate color space. For convenience,
the color components are normalized to the range 0 to a maximum value,
## MEASURING COLOR REDUCTION ERRORDepending on the image, the color reduction error may be obvious or 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
(the total color reduction error), The normalized error measurement can be used to compare images. In general, the closer the mean error is to zero the more the quantized image resembles the source image. Ideally, the error should be perceptually-based, since the human eye is the final judge of quantization quality.
These errors are measured and printed when **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.
This distance measure is normalized to a range between 0 and 1. It is independent of the range of red, green, and blue values in the image. **normalized maximum square error:**-
is the largest normalized quantization error for any single
pixel in the image.
This distance measure is normalized to a range between 0 and 1. It is independent of the range of red, green, and blue values in the image.
## SEE ALSOdisplay(1), animate(1), mogrify(1), import(1), miff(5)
## COPYRIGHTCopyright (C) 2003 ImageMagick Studio LLC, a non-profit organization dedicated to making software imaging solutions freely available.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 ImageMagick Studio 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 ImageMagick Studio shall not be used in advertising or otherwise to promote the sale, use or other dealings in ImageMagick without prior written authorization from the ImageMagick Studio. ## ACKNOWLEDGEMENTSPaul 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.## AUTHORSJohn Cristy, ImageMagick Studio
## Index- NAME
- SYNOPSIS
- DESCRIPTION
- MEASURING COLOR REDUCTION ERROR
- SEE ALSO
- COPYRIGHT
- ACKNOWLEDGEMENTS
- AUTHORS
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