Gitiles
Code Review Sign In
gerrit-public.fairphone.software / platform / external / ImageMagick / af8d6655e12345c48d687558c0665070d206a942 / . / www / quantize.html
blob: a39f09b0b016cad13060abf390e1af593f74e1a2 [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"/>
cristyaf8d6652011-02-04 21:57:45 +0000[diff] [blame^]12 <meta name="Description" content="Use ImageMagick to convert, edit, or compose bitmap images in a variety of formats. In addition resize, 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/">
cristyaf8d6652011-02-04 21:57:45 +0000[diff] [blame^]55 <img src="../images/logo.jpg"
56 alt="ImageMagick Logo"
cristy178edaf2011-01-23 03:42:39 +0000[diff] [blame]57 style="width: 123px; height: 118px; border: 0px; float: right;" /></a>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]58<a href="../index.html">
cristyaf8d6652011-02-04 21:57:45 +0000[diff] [blame^]59 <img src="../images/sprite.jpg"
60 alt="ImageMagick Sprite"
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]61 style="width: 114px; height: 118px; border: 0px; float: right;" /></a>
62</div>
63
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]64<div class="westbar">
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]65
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]66<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]67 <a title="About ImageMagick" href="../index.html">About ImageMagick</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]68</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]69<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]70<div class="menu">
cristybb503372010-05-27 20:51:26 +0000[diff] [blame]71 <a title="Binary Releases" href="../www/binary-releases.html">Binary Releases</a>
72</div>
73<div class="sub">
74 <a title="Binary Release: Unix" href="../www/binary-releases.html#unix">Unix</a>
75</div>
76<div class="sub">
77 <a title="Binary Release: MacOS X" href="../www/binary-releases.html#macosx">Mac OS X</a>
78</div>
79<div class="sub">
80 <a title="Binary Release: Windows" href="../www/binary-releases.html#windows">Windows</a>
81</div>
82<div class="sep"></div>
83<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]84 <a title="Command-line Tools" href="../www/command-line-tools.html">Command-line Tools</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]85</div>
86<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]87 <a title="Command-line Tools: Processing" href="../www/command-line-processing.html">Processing</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]88</div>
89<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]90 <a title="Command-line Tools: Options" href="../www/command-line-options.html">Options</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]91</div>
92<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]93 <a title="Command-line Tools: Usage" href="http://www.imagemagick.org/Usage/">Usage</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]94</div>
95<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]96 <a title="Program Interfaces" href="../www/api.html">Program Interfaces</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]97</div>
98<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]99 <a title="Program Interface: MagickWand" href="../www/magick-wand.html">MagickWand</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]100</div>
101<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]102 <a title="Program Interface: MagickCore" href="../www/magick-core.html">MagickCore</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]103</div>
104<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]105 <a title="Program Interface: PerlMagick" href="../www/perl-magick.html">PerlMagick</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]106</div>
107<div class="sub">
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]108 <a title="Program Interface: Magick++" href="../www/magick++.html">Magick++</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]109</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]110<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]111<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]112 <a title="Install from Source" href="../www/install-source.html">Install from Source</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]113</div>
114<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]115 <a title="Install from Source: Unix" href="../www/install-source.html#unix">Unix</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]116</div>
117<div class="sub">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]118 <a title="Install from Source: Windows" href="../www/install-source.html#windows">Windows</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]119 </div>
120<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]121 <a title="Resources" href="../www/resources.html">Resources</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]122</div>
cristybb503372010-05-27 20:51:26 +0000[diff] [blame]123<div class="menu">
124 <a title="Architecture" href="../www/architecture.html">Architecture</a>
125</div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]126<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]127 <a title="Download" href="../www/download.html">Download</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]128</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]129<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]130<div class="menu">
cristy52923442011-01-15 22:54:31 +0000[diff] [blame]131 <a title="Search" href="../www/search.html">Search</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]132</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]133<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]134<div class="menu">
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]135 <a title="Site Map" href="../www/sitemap.html">Site Map</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]136</div>
137<div class="sub">
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]138 <a title="Site Map: Links" href="../www/links.html">Links</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]139</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]140<div class="sep"></div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]141<div class="menu">
cristy83a272e2010-05-07 20:40:35 +0000[diff] [blame]142 <a title="Sponsors" href="../www/sponsors.html">Sponsors:</a>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]143
144<div class="sponsbox">
cristy178edaf2011-01-23 03:42:39 +0000[diff] [blame]145<div class="sponsor">
cristyaf8d6652011-02-04 21:57:45 +0000[diff] [blame^]146 <a title="Sponsor: Best Web Hosting" href="http://webhostinggeeks.com">Best Web Hosting</a><!-- 201110010720 -->
147</div>
148<div class="sponsor">
149 <a title="Sponsor: Web Hosting Ratings" href="http://webhostingrating.com">Web Hosting Ratings</a><!-- 201110010720 -->
150</div>
151<div class="sponsor">
cristy178edaf2011-01-23 03:42:39 +0000[diff] [blame]152 <a title="Sponsor: Druckerei" href="http://www.allesdruck.de">Druckerei</a><!-- 201106010240 -->
153</div>
cristyec6b4752011-01-08 03:16:23 +0000[diff] [blame]154<div class="sponsor">
cristy52923442011-01-15 22:54:31 +0000[diff] [blame]155 <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]156</div>
157<div class="sponsor">
cristyc5baf4f2010-08-31 15:05:33 +0000[diff] [blame]158 <a title="Sponsor: Image Converter" href="http://www.batchphoto.com">Image Converter</a><!-- 201103010900 Bits Coffee-->
159</div>
160<div class="sponsor">
cristy851dbce2010-08-06 21:40:00 +0000[diff] [blame]161 <a title="Sponsor: Flyer drucken" href="http://www.online-druck.biz">Flyer drucken</a><!-- 201109010900 Floeter-->
162</div>
cristyec6b4752011-01-08 03:16:23 +0000[diff] [blame]163<div class="sponsor">
cristy178edaf2011-01-23 03:42:39 +0000[diff] [blame]164 <a title="Sponsor: Druckerei" href="http://print24.com/de/">Druckerei</a><!-- 201110010720 -->
165</div>
166<div class="sponsor">
cristyaf8d6652011-02-04 21:57:45 +0000[diff] [blame^]167 <a title="Sponsor: Custom T-Shirts" href="http://www.ooshirts.com">Custom T-Shirts</a><!-- 2011050100030 ooshirts.com-->
cristyec6b4752011-01-08 03:16:23 +0000[diff] [blame]168</div>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]169</div>
170</div>
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]171</div>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]172
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]173<div class="eastbar">
174 <script type="text/javascript">
175 <!--
176 google_ad_client = "pub-3129977114552745";
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]177 google_ad_slot = "0574824969";
178 google_ad_width = 160;
179 google_ad_height = 600;
180 //-->
181 </script>
182 <script type="text/javascript"
183 src="http://pagead2.googlesyndication.com/pagead/show_ads.js">
184 </script>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]185</div>
186
187<div class="main">
188
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]189<h1>ImageMagick Color Reduction</h1>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]190<p class="navigation-index">[<a href="#describe">Algorithm Description</a> &bull; <a href="#measure">Measuring Color Reduction Error</a>]</p>
191
192<div class="doc-section">
193<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>
194</div>
195
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]196<h2><a id="describe"></a>Algorithm Description</h2>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]197<div class="doc-section">
198
199<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>
200
201<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>
202
203<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>
204
205<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>
206
207<p>The basic algorithm operates in three phases:</p>
208
209<ol>
210 <li>Classification</li>
211 <li>Reduction</li>
212 <li>Assignment</li>
213</ol>
214
215<p><b>Classification</b></p>
216
217<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>
218
219<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>
220
221<pre class="text">
222 total nodes = 1+Sum(8^i), i=1,k
223
224 For k=8,
225 nodes = 1 + (8^1+8^2+....+8^8)
226 = 1 + 8(8^8 - 1)/(8 - 1)
227 = 19,173,961
228</pre>
229
230<p>Therefore, to avoid building a fully populated tree, ImageMagick:</p>
231
232<ol>
233 <li>initializes data structures for nodes only as they are needed;</li>
234 <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>
235</ol>
236
237<pre class="text">
238 For Cmax=255,
239 maximum tree depth = log<sub>2</sub>(256)
240 = 8
241</pre>
242
243<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>
244
245<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>
246
247<dl class="doc">
248<dt class="doc">n1</dt>
249 <dd>number of pixels whose color is contained in the RGB cube which this node represents;</dd>
250<dt class="doc">n2</dt>
251 <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>
252<dt class="doc">Sr,Sg,Sb</dt>
253 <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>
254<dt class="doc">E</dt>
255 <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>
256</dl>
257
258<p><b>Reduction</b></p>
259
260<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>
261
262<pre class="text">
263 Ep = 0
264 while number of nodes with (n2 &gt; 0) &gt; required maximum number of colors
265 prune all nodes such that E &lt;= Ep
266 Set Ep to minimum E in remaining nodes
267</pre>
268
269<p>This has the effect of minimizing any quantization error when merging two nodes together.</p>
270
271<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>
272
273<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>
274
275<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>
276
277<p><b>Assignment</b></p>
278
279<p>Assignment generates the output image from the pruned tree. The output image consists of two parts:</p>
280<ol>
281 <li>A color map, which is an array of color descriptions (RGB triples) for each color present in the output image.</li>
282
283 <li>A pixel array, which represents each pixel as an index into the color map array.</li>
284</ol>
285
286<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>
287
288<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>
289
290<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>
291
292</div>
293
cristydcca3fa2010-12-29 21:50:07 +0000[diff] [blame]294<h2><a id="measure"></a>Measuring Color Reduction Error</h2>
cristy3ed852e2009-09-05 21:47:34 +0000[diff] [blame]295<div class="doc-section">
296
297<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>
298
299<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>
300
301<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>
302
303<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>
304
305<dl class="doc">
306<dt class="doc">mean error per pixel</dt>
307 <dd>is the mean error for any single pixel in the image.</dd>
308<dt class="doc">normalized mean square error</dt>
309 <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>
310<dt class="doc">normalized maximum square error</dt>
311 <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>
312</dl>
313
314</div>
315
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]316
317</div>
318
319<div id="linkbar">
cristyce69bb02010-07-27 19:49:46 +0000[diff] [blame]320 <span id="linkbar-west">&nbsp;</span>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]321 <span id="linkbar-center">
322 <a href="http://www.imagemagick.org/discourse-server/">Discourse Server</a> &bull;
cristya8902942010-07-30 00:49:52 +0000[diff] [blame]323 <a href="http://www.imagemagick.org/MagickStudio/scripts/MagickStudio.cgi">Studio</a>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]324 </span>
325 <span id="linkbar-east">&nbsp;</span>
326 </div>
327 <div class="footer">
cristy7e41fe82010-12-04 23:12:08 +0000[diff] [blame]328 <span id="footer-west">&copy; 1999-2011 ImageMagick Studio LLC</span>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]329 <span id="footer-east"> <a href="http://www.imagemagick.org/script/contact.php">Contact the Wizards</a></span>
330 </div>
331 <div style="clear: both; margin: 0; width: 100%; "></div>
cristya8902942010-07-30 00:49:52 +0000[diff] [blame]332 <script type="text/javascript">
333 var _gaq = _gaq || [];
334 _gaq.push(['_setAccount', 'UA-17690367-1']);
335 _gaq.push(['_trackPageview']);
336
337 (function() {
338 var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
339 ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
340 var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
341 })();
342 </script>
cristy3eaa0ef2010-03-06 20:35:26 +0000[diff] [blame]343</body>
344</html>