Gitiles
Code Review Sign In
gerrit-public.fairphone.software / platform / external / ImageMagick / e6529ff52c05a2d3352d83a429cb69aa15f5b585 / . / www / quantize.html
blob: 6b4afc7e5798863baf68d069d2c46ff579d8fb19 [file] [log] [blame]
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]1<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.1//EN"
2 "http://www.w3.org/TR/xhtml11/DTD/xhtml11.dtd">
3<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en" dir="ltr">
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]4<head>
cristy3c98a4f2010-08-13 20:09:41 +0000[diff] [blame]5 <meta http-equiv="Content-Type" content="text/html; charset=UTF-8"/>
6 <meta name="verify-v1" content="g222frIIxcQTrvDR3NBRUSKP3AnMNoqxOkIniCEkV7U="/>
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]7 <title>ImageMagick: Color Reduction Utilizing Adaptive Spatial Subdivision</title>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]8 <meta http-equiv="Content-Language" content="en-US"/>
9 <meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
10 <meta http-equiv="Reply-to" content="magick-users@imagemagick.org"/>
cristy3c98a4f2010-08-13 20:09:41 +0000[diff] [blame]11 <meta name="Application-name" content="ImageMagick"/>
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]12 <meta name="Description" content="ImageMagick is a software suite to create, edit, compose, or convert bitmap images in a variety of formats. Use ImageMagick to scale, rotate, shear, distort and transform images."/>
cristy3c98a4f2010-08-13 20:09:41 +0000[diff] [blame]13 <meta name="Application-url" content="http://www.imagemagick.org"/>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]14 <meta name="Generator" content="PHP"/>
15 <meta name="Keywords" content="color, reduction, utilizing, adaptive, spatial, subdivision, ImageMagick, ImageMagic, MagickCore, MagickWand, PerlMagick, Magick++, RMagick, PythonMagick, JMagick, TclMagick, Image, Magick, Magic, Wand, ImageMagickObject, Swiss, Army, Knife, Image, Processing"/>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]16 <meta name="Rating" content="GENERAL"/>
17 <meta name="Robots" content="INDEX, FOLLOW"/>
18 <meta name="Generator" content="ImageMagick Studio LLC"/>
19 <meta name="Author" content="ImageMagick Studio LLC"/>
20 <meta name="Revisit-after" content="2 DAYS"/>
21 <meta name="Resource-type" content="document"/>
cristy7e41fe82010-12-04 23:12:08 +0000[diff] [blame]22 <meta name="Copyright" content="Copyright (c) 1999-2011 ImageMagick Studio LLC"/>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]23 <meta name="Distribution" content="Global"/>
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]24 <link rel="icon" href="../images/wand.png"/>
cristy3c98a4f2010-08-13 20:09:41 +0000[diff] [blame]25 <link rel="shortcut icon" href="../images/wand.ico" type="images/x-icon"/>
26 <link rel="meta" type="application/rdf+xml" title="ICI" href="http://imagemagick.org/ici.rdf"/>
cristy7a40ba82011-01-08 20:31:18 +0000[diff] [blame]27 <link rel="stylesheet" href="http://www.google.com/cse/style/look/default.css" type="text/css" />
cristy3c98a4f2010-08-13 20:09:41 +0000[diff] [blame]28 <style type="text/css" media="all">
29 @import url("../www/magick.css");
30 </style>
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]31 <script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.4/jquery.min.js"></script>
cristy361f4662010-12-31 23:02:52 +0000[diff] [blame]32 <script type="text/javascript" src="../fancybox/jquery.fancybox-1.3.4.pack.js"></script>
33 <link rel="stylesheet" type="text/css" href="../fancybox/jquery.fancybox-1.3.4.css" media="screen" />
34 <script type="text/javascript">
35 $(document).ready(function() {
36 $("a[href$=.jpg],a[href$=.png],a[href$=.gif]").fancybox({
37 'transitionIn' : 'elastic',
38 'transitionOut' : 'elastic',
39 'overlayShow' : false,
40 'opacity' : true
41 });
42 });
43 </script>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]44</head>
45
46<body id="www-imagemagick-org">
47<div class="titlebar">
48<a href="../index.html">
49 <img src="../images/script.png" alt="[ImageMagick]"
50 style="width: 350px; height: 60px; margin: 28px auto; float: left;" /></a>
51<a href="http://www.networkredux.com">
52 <img src="../images/networkredux.png" alt="[sponsor]"
cristy52923442011-01-15 22:54:31 +0000[diff] [blame]53 style="margin-top: 42px; border: 0px; float: left;" /></a>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]54<a href="http://www.imagemagick.org/discourse-server/">
55 <img src="../images/logo.jpg" alt=""
cristy178edaf2011-01-23 03:42:39 +0000[diff] [blame]56 style="width: 123px; height: 118px; border: 0px; float: right;" /></a>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]57<a href="../index.html">
58 <img src="../images/sprite.jpg" alt=""
59 style="width: 114px; height: 118px; border: 0px; float: right;" /></a>
60</div>
61
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]62<div class="westbar">
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]63
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]64<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]65 <a title="About ImageMagick" href="../index.html">About ImageMagick</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]66</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]67<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]68<div class="menu">
cristybb503372010-05-27 20:51:26 +0000[diff] [blame]69 <a title="Binary Releases" href="../www/binary-releases.html">Binary Releases</a>
70</div>
71<div class="sub">
72 <a title="Binary Release: Unix" href="../www/binary-releases.html#unix">Unix</a>
73</div>
74<div class="sub">
75 <a title="Binary Release: MacOS X" href="../www/binary-releases.html#macosx">Mac OS X</a>
76</div>
77<div class="sub">
78 <a title="Binary Release: Windows" href="../www/binary-releases.html#windows">Windows</a>
79</div>
80<div class="sep"></div>
81<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]82 <a title="Command-line Tools" href="../www/command-line-tools.html">Command-line Tools</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]83</div>
84<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]85 <a title="Command-line Tools: Processing" href="../www/command-line-processing.html">Processing</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]86</div>
87<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]88 <a title="Command-line Tools: Options" href="../www/command-line-options.html">Options</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]89</div>
90<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]91 <a title="Command-line Tools: Usage" href="http://www.imagemagick.org/Usage/">Usage</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]92</div>
93<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]94 <a title="Program Interfaces" href="../www/api.html">Program Interfaces</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]95</div>
96<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]97 <a title="Program Interface: MagickWand" href="../www/magick-wand.html">MagickWand</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]98</div>
99<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]100 <a title="Program Interface: MagickCore" href="../www/magick-core.html">MagickCore</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]101</div>
102<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]103 <a title="Program Interface: PerlMagick" href="../www/perl-magick.html">PerlMagick</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]104</div>
105<div class="sub">
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]106 <a title="Program Interface: Magick++" href="../www/magick++.html">Magick++</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]107</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]108<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]109<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]110 <a title="Install from Source" href="../www/install-source.html">Install from Source</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]111</div>
112<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]113 <a title="Install from Source: Unix" href="../www/install-source.html#unix">Unix</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]114</div>
115<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]116 <a title="Install from Source: Windows" href="../www/install-source.html#windows">Windows</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]117 </div>
118<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]119 <a title="Resources" href="../www/resources.html">Resources</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]120</div>
cristybb503372010-05-27 20:51:26 +0000[diff] [blame]121<div class="menu">
122 <a title="Architecture" href="../www/architecture.html">Architecture</a>
123</div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]124<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]125 <a title="Download" href="../www/download.html">Download</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]126</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]127<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]128<div class="menu">
cristy52923442011-01-15 22:54:31 +0000[diff] [blame]129 <a title="Search" href="../www/search.html">Search</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]130</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]131<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]132<div class="menu">
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]133 <a title="Site Map" href="../www/sitemap.html">Site Map</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]134</div>
135<div class="sub">
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]136 <a title="Site Map: Links" href="../www/links.html">Links</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]137</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]138<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]139<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]140 <a title="Sponsors" href="../www/sponsors.html">Sponsors:</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]141
142<div class="sponsbox">
cristy178edaf2011-01-23 03:42:39 +0000[diff] [blame]143<div class="sponsor">
144 <a title="Sponsor: Druckerei" href="http://www.allesdruck.de">Druckerei</a><!-- 201106010240 -->
145</div>
cristyec6b4752011-01-08 03:16:23 +0000[diff] [blame]146<div class="sponsor">
cristy52923442011-01-15 22:54:31 +0000[diff] [blame]147 <a title="Sponsor: Web Hosting" href="http://www.bodhost.com/hosting.shtml">Web Hosting</a><!-- 201104010090 -->
cristy7d52cd62010-10-01 17:26:59 +0000[diff] [blame]148</div>
149<div class="sponsor">
cristyc5baf4f2010-08-31 15:05:33 +0000[diff] [blame]150 <a title="Sponsor: Image Converter" href="http://www.batchphoto.com">Image Converter</a><!-- 201103010900 Bits Coffee-->
151</div>
152<div class="sponsor">
cristy851dbce2010-08-06 21:40:00 +0000[diff] [blame]153 <a title="Sponsor: Flyer drucken" href="http://www.online-druck.biz">Flyer drucken</a><!-- 201109010900 Floeter-->
154</div>
cristyec6b4752011-01-08 03:16:23 +0000[diff] [blame]155<div class="sponsor">
cristy178edaf2011-01-23 03:42:39 +0000[diff] [blame]156 <a title="Sponsor: Druckerei" href="http://print24.com/de/">Druckerei</a><!-- 201110010720 -->
157</div>
158<div class="sponsor">
cristyf7964272011-01-30 03:49:12 +0000[diff] [blame]159 <a title="Sponsor: Notebook Reparatur Berlin" href="http://www.notebook-reparaturen-berlin.de">Notebook Reparatur Berlin</a><!-- 2011050100025 gabi.schulze-->
cristyec6b4752011-01-08 03:16:23 +0000[diff] [blame]160</div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]161</div>
162</div>
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]163</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]164
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]165<div class="eastbar">
166 <script type="text/javascript">
167 <!--
168 google_ad_client = "pub-3129977114552745";
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]169 google_ad_slot = "0574824969";
170 google_ad_width = 160;
171 google_ad_height = 600;
172 //-->
173 </script>
174 <script type="text/javascript"
175 src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
176 </script>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]177</div>
178
179<div class="main">
180
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]181<h1>ImageMagick Color Reduction</h1>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]182<p class="navigation-index">[<a href="#describe">Algorithm Description</a> &bull; <a href="#measure">Measuring Color Reduction Error</a>]</p>
183
184<div class="doc-section">
185<p>This document describes how ImageMagick performs color reduction on an image. To fully understand what follows, you should have a knowledge of basic imaging techniques and the tree data structure and terminology.</p>
186</div>
187
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]188<h2><a id="describe"></a>Algorithm Description</h2>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]189<div class="doc-section">
190
191<p>For purposes of color allocation, an image is a set of <em>n</em> pixels, where each pixel is a point in RGB space. RGB space is a 3-dimensional vector space, and each pixel, <em>p(i)</em>, is defined by an ordered triple of red, green, and blue coordinates, (<em>r(i)</em>, <em>g(i)</em>, <em>b(i)</em>).</p>
192
193<p>Each primary color component (<em>red</em>, <em>green</em>, or <em>blue</em>) represents an intensity which varies linearly from 0 to a maximum value, <em>Cmax</em>, 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 (<em>Cmax</em>, <em>Cmax</em>, <em>Cmax</em>). ImageMagick requires <em>Cmax</em>= <em>255</em>.</p>
194
195<p>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.</p>
196
197<p>The tree's root node represents the entire domain, (0,0,0) through (<em>Cmax</em>, <em>Cmax</em>, <em>Cmax</em>). 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.</p>
198
199<p>The basic algorithm operates in three phases:</p>
200
201<ol>
202 <li>Classification</li>
203 <li>Reduction</li>
204 <li>Assignment</li>
205</ol>
206
207<p><b>Classification</b></p>
208
209<p>Classification builds a color description tree for the image. Reduction collapses the tree until the number it represents, at most, is 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. <em>Our goal is to minimize the numerical discrepancies between the original colors and quantized colors</em>. To learn more about quantization error, see <a href="#measure">Measuring Color Reduction Error</a>.</p>
210
211<p>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 <em>Cmax</em>. If color components in the input image are quantized to <em>k</em>-bit precision, so that <em>Cmax</em> = <em>2^k-1</em>, the tree would need <em>k</em> 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:</p>
212
213<pre class="text">
214 total nodes = 1+Sum(8^i), i=1,k
215
216 For k=8,
217 nodes = 1 + (8^1+8^2+....+8^8)
218 = 1 + 8(8^8 - 1)/(8 - 1)
219 = 19,173,961
220</pre>
221
222<p>Therefore, to avoid building a fully populated tree, ImageMagick:</p>
223
224<ol>
225 <li>initializes data structures for nodes only as they are needed;</li>
226 <li>chooses a maximum depth for the tree as a function of the desired number of colors in the output image (currently the <em>base-two</em> logarithm of <em>Cmax</em>).</li>
227</ol>
228
229<pre class="text">
230 For Cmax=255,
231 maximum tree depth = log<sub>2</sub>(256)
232 = 8
233</pre>
234
235<p>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 images. Therefore, the caller can request a specific tree depth.</p>
236
237<p>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 pixels' color. It updates the following data for each such node:</p>
238
239<dl class="doc">
240<dt class="doc">n1</dt>
241 <dd>number of pixels whose color is contained in the RGB cube which this node represents;</dd>
242<dt class="doc">n2</dt>
243 <dd>number of pixels whose color is not represented in a node at lower depth in the tree; initially, <em>n2=0</em> for all nodes except leaves of the tree.</dd>
244<dt class="doc">Sr,Sg,Sb</dt>
245 <dd>sums of the <em>red</em>, <em>green</em>, and <em>blue</em> component values for all pixels not classified at a lower depth. The combination of these sums and <em>n2</em> will ultimately characterize the mean color of a set of pixels represented by this node.</dd>
246<dt class="doc">E</dt>
247 <dd>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.</dd>
248</dl>
249
250<p><b>Reduction</b></p>
251
252<p>Reduction repeatedly prunes the tree until the number of nodes with <em>n2</em> &gt; <em>0</em> 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 <em>E</em> value is minimal for pruning and merges their color statistics upward. It uses a pruning threshold, <em>Ep</em>, to govern node selection as follows:</p>
253
254<pre class="text">
255 Ep = 0
256 while number of nodes with (n2 &gt; 0) &gt; required maximum number of colors
257 prune all nodes such that E &lt;= Ep
258 Set Ep to minimum E in remaining nodes
259</pre>
260
261<p>This has the effect of minimizing any quantization error when merging two nodes together.</p>
262
263<p>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 <em>n2</em>, <em>Sr</em>, <em>Sg</em>, and <em>Sb</em> 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.</p>
264
265<p>For each node, <em>n2</em> pixels exist for which that node represents the smallest volume in RGB space containing those pixel's colors. When <em>n2</em> &gt; <em>0</em> the node will uniquely define a color in the output image. At the beginning of reduction, <em>n2</em> = <em>0</em> for all nodes except the leaves of the tree which represent colors present in the input image.</p>
266
267<p>The other pixel count, <em>n1</em>, indicates the total number of colors within the cubic volume which the node represents. This includes <em>n1</em> - <em>n2</em> pixels whose colors should be defined by nodes at a lower level in the tree.</p>
268
269<p><b>Assignment</b></p>
270
271<p>Assignment generates the output image from the pruned tree. The output image consists of two parts:</p>
272<ol>
273 <li>A color map, which is an array of color descriptions (RGB triples) for each color present in the output image.</li>
274
275 <li>A pixel array, which represents each pixel as an index into the color map array.</li>
276</ol>
277
278<p>First, the assignment phase makes one pass over the pruned color description tree to establish the image's color map. For each node with <em>n2</em> &gt; <em>0</em>, it divides <em>Sr</em>, <em>Sg</em>, and <em>Sb</em> by <em>n2</em>. 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.</p>
279
280<p>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.</p>
281
282<p>Empirical evidence suggests that the 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, <em>Cmax</em>. The color reduction can then proceed as described.</p>
283
284</div>
285
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]286<h2><a id="measure"></a>Measuring Color Reduction Error</h2>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]287<div class="doc-section">
288
289<p>Depending 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 because the high-frequency contour edges introduced by the color reduction process are masked by the high frequencies in the image.</p>
290
291<p>To measure the difference between the original and color reduced images (the total color reduction error), ImageMagick sums over all pixels in 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.</p>
292
293<p>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.</p>
294
295<p>These errors are measured and printed when the <a href="../www/command-line-options.html#colors">-colors</a> and <a href="../www/command-line-options.html#verbose">-verbose</a> options are specified on the <a href="../www/convert.html">convert</a> command line:</p>
296
297<dl class="doc">
298<dt class="doc">mean error per pixel</dt>
299 <dd>is the mean error for any single pixel in the image.</dd>
300<dt class="doc">normalized mean square error</dt>
301 <dd>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.</dd>
302<dt class="doc">normalized maximum square error</dt>
303 <dd>is the largest normalized square quantization error for any single pixel in the image. This distance measure is normalized to a range between of red, green, and blue values in the image.</dd>
304</dl>
305
306</div>
307
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]308
309</div>
310
311<div id="linkbar">
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]312 <span id="linkbar-west">&nbsp;</span>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]313 <span id="linkbar-center">
314 <a href="http://www.imagemagick.org/discourse-server/">Discourse Server</a> &bull;
cristya8902942010-07-30 00:49:52 +0000[diff] [blame]315 <a href="http://www.imagemagick.org/MagickStudio/scripts/MagickStudio.cgi">Studio</a>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]316 </span>
317 <span id="linkbar-east">&nbsp;</span>
318 </div>
319 <div class="footer">
cristy7e41fe82010-12-04 23:12:08 +0000[diff] [blame]320 <span id="footer-west">&copy; 1999-2011 ImageMagick Studio LLC</span>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]321 <span id="footer-east"> <a href="http://www.imagemagick.org/script/contact.php">Contact the Wizards</a></span>
322 </div>
323 <div style="clear: both; margin: 0; width: 100%; "></div>
cristya8902942010-07-30 00:49:52 +0000[diff] [blame]324 <script type="text/javascript">
325 var _gaq = _gaq || [];
326 _gaq.push(['_setAccount', 'UA-17690367-1']);
327 _gaq.push(['_trackPageview']);
328
329 (function() {
330 var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
331 ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
332 var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
333 })();
334 </script>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]335</body>
336</html>