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<title>第4章 图象的半影调和抖动技术</title>
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<h1><a name="_Toc486331877"></a><a name="_Toc486332877"></a><a
name="_Toc486338986"></a><a name="_Toc454810851"></a><a name="_Toc454856625"><span><span>第<span
lang=EN-US>4</span></span></span></a><span><span><span style='font-family:黑体;"Times New Roman"'>章</span>
</span></span><span><span><span
style='font-family:黑体;"Times New Roman"'>图象的半影调和抖动技术</span></span></span></h1>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>在介绍本章内容之前，先提出一个问题？普通的黑白针式打印机能打出灰度图来吗？如果说能，从针式打印机的打印原理来分析，似乎是不可能的。因为针打是靠撞针击打色带在纸上形成黑点的，不可能打出灰色的点来；如果说不能，可是我们的确见过用针式打印机打印出来的灰色图象。到底是怎么回事呢？</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>你再仔细看看那些打印出来的所谓的灰色图象，最好用放大镜看。你会发现，原来这些灰色图象都是由一些黑点组成的，黑点多一些，图象就暗一些；黑点少一些，图案就亮一些。下面这几张图就很能说明这一点。</span></p>
<p align=center style='text-align:center;line-height:18.0pt'><span
lang=EN-US> <img width=259 height=56
src="chap04.files/image001.gif" v:shapes="_x0000_i1025"> </span></p>
<p align=center style='text-align:center;line-height:18.0pt'><b><span
style='font-family:宋体;"Times New Roman"'>图</span><span lang=EN-US>4.1 </span></b><b><span
style='font-family:宋体;"Times New Roman"'>用黑白两种颜色打印出灰度效果</span><span lang=EN-US></span></b></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>图</span><span lang=EN-US>4.1</span><span style='font-family:
宋体;"Times New Roman"'>中最左边的是原图，是一幅真正的灰度图，另外三张图都是黑白二值图。容易看出，最左的那幅和原图最接近。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>由二值图象显示出灰度效果的方法，就是我们今天要讲的半影调</span><span lang=EN-US>(halftone)</span><span
style='font-family:宋体;"Times New Roman"'>技术，它的一个主要用途就是在只有二值输出的打印机上打印图象。我们介绍两种方法：图案法和抖动法。</span></p>
<h2> <span
lang=EN-US>4.1</span> <span lang=EN-US> </span><a name="_Toc486331878"></a><a
name="_Toc486332878"></a><a name="_Toc486338987"></a><a name="_Toc454810852"></a><a
name="_Toc454856626"><span><span>图案法</span></span></a></h2>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>图案法</span><span lang=EN-US>(patterning)</span><span
style='font-family:宋体;"Times New Roman"'>是指灰度可以用一定比例的黑白点组成的区域表示，从而达到整体图象的灰度感。黑白点的位置选择称为图案化。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>在具体介绍图案法之前，先介绍一下分辨率的概念。计算机显示器，打印机，扫描仪等设备的一个重要指标就是分辨率，单位是</span><span
lang=EN-US>dpi(dot per inch)</span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>，即每英寸点数，点数越多，分辨率就越高，图象就越清晰。让我们来计算一下，计算机显示器的分辨率有多高。设显示器为</span><span
lang=EN-US>15</span><span style='font-family:宋体;
"Times New Roman"'>英寸</span><span lang=EN-US>(</span><span
style='font-family:宋体;"Times New Roman"'>指对角线长度</span><span lang=EN-US>)</span><span
style='font-family:宋体;"Times New Roman"'>，最多显示</span><span lang=EN-US>1280</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>1024</span><span style='font-family:
宋体;"Times New Roman"'>个点。因为宽高比为</span><span
lang=EN-US>4</span><span style='font-family:宋体;
"Times New Roman"'>：</span><span lang=EN-US>3</span><span
style='font-family:宋体;"Times New Roman"'>，所以宽有</span><span lang=EN-US>12</span><span
style='font-family:宋体;"Times New Roman"'>英寸，高有</span><span lang=EN-US>9</span><span style='font-family:
宋体;"Times New Roman"'>英寸，则该显示器的水平分辨率为</span><span
lang=EN-US>106dpi</span><span style='font-family:宋体;
"Times New Roman"'>，垂直分辨率为</span><span lang=EN-US>113.8dpi</span><span
style='font-family:宋体;"Times New Roman"'>。一般的激光打印机的分辨率有</span><span lang=EN-US>300dpi</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>300dpi</span><span
style='font-family:宋体;"Times New Roman"'>，</span><span lang=EN-US>600dpi</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>600dpi</span><span
style='font-family:宋体;"Times New Roman"'>，</span><span lang=EN-US>720dpi</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>720dpi</span><span
style='font-family:宋体;"Times New Roman"'>。所以打出来的图象要比计算机显示出来的清晰的多。扫描仪的分辨率要高一些，数码相机的分辨率更高。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>言归正传，前面讲了，图案化使用图案来表示象素的灰度，那么我们来做一道计算题。假设有一幅</span><span
lang=EN-US>240</span><span style='font-family:宋体;
"Times New Roman"'>×</span><span lang=EN-US>180</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>8bit</span><span style='font-family:
宋体;"Times New Roman"'>的灰度图，当用分辨率为</span><span
lang=EN-US>300dpi</span><span style='font-family:宋体;
"Times New Roman"'>×</span><span lang=EN-US>300dpi</span><span
style='font-family:宋体;"Times New Roman"'>的激光打印机将其打印到</span><span lang=EN-US>12.8</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>9.6</span><span style='font-family:
宋体;"Times New Roman"'>英寸的纸上时，每个象素的图案有多大？</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>这道题很简单，这张纸最多可以打</span><span lang=EN-US>(300</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>12.8) </span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>(300</span><span style='font-family:
宋体;"Times New Roman"'>×</span><span
lang=EN-US>9.6)=3840</span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>×</span><span
lang=EN-US>2880</span><span style='font-family:宋体;
"Times New Roman"'>个点，所以每个象素可以用</span><span lang=EN-US>(3840/240)</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>(2880/180)=16</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>16</span><span style='font-family:
宋体;"Times New Roman"'>个点大小的图案来表示，即一个象素</span><span
lang=EN-US>256</span><span style='font-family:宋体;
"Times New Roman"'>个点。如果这</span><span lang=EN-US>16</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>16</span><span style='font-family:
宋体;"Times New Roman"'>的方块中一个黑点也没有，就可以表示灰度</span><span
lang=EN-US>256</span><span style='font-family:宋体;
"Times New Roman"'>；有一个黑点，就表示灰度</span><span lang=EN-US>255</span><span
style='font-family:宋体;"Times New Roman"'>；依次类推，当都是黑点时，表示灰度</span><span lang=EN-US>0</span><span
style='font-family:宋体;"Times New Roman"'>。这样，</span><span lang=EN-US>16</span><span style='font-family:
宋体;"Times New Roman"'>×</span><span
lang=EN-US>16</span><span style='font-family:宋体;
"Times New Roman"'>的方块可以表示</span><span lang=EN-US>257</span><span
style='font-family:宋体;"Times New Roman"'>级灰度，比要求的</span><span lang=EN-US>8bit</span><span
style='font-family:宋体;"Times New Roman"'>共</span><span lang=EN-US>256</span><span style='font-family:
宋体;"Times New Roman"'>级灰度还多了一个。所以上面的那幅图的灰度级别完全能够打印出来。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>这里有一个图案构成的问题，即黑点打在哪里？比如说，只有一个黑点时，我们可以打在正中央，也可以打</span><span
lang=EN-US>16</span><span style='font-family:宋体;
"Times New Roman"'>×</span><span lang=EN-US>16</span><span
style='font-family:宋体;"Times New Roman"'>的左上角。图案可以是规则的，也可以是不规则的。一般情况下，有规则的图案比随即图案能够避免点的丛集，但有时会导致图象中有明显的线条。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>如图</span><span lang=EN-US>4.1</span><span style='font-family:
宋体;"Times New Roman"'>中，</span><span
lang=EN-US>2</span><span style='font-family:宋体;
"Times New Roman"'>×</span><span lang=EN-US>2</span><span
style='font-family:宋体;"Times New Roman"'>的图案可以表示</span><span lang=EN-US>5</span><span
style='font-family:宋体;"Times New Roman"'>级灰度，当图象中有一片灰度为的</span><span lang=EN-US>1</span><span
style='font-family:宋体;"Times New Roman"'>的区域时，如图</span><span lang=EN-US>4.2</span><span
style='font-family:宋体;"Times New Roman"'>所示，有明显的水平和垂直线条。</span></p>
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<td width=276 valign=bottom class="Normal">
<p align=center style='text-align:center;line-height:18.0pt'><b><span
lang=EN-US> <img width=316 height=89
src="chap04.files/image002.gif" v:shapes="_x0000_i1027"> </span></b></p>
<p align=center style='text-align:center;line-height:18.0pt'><b><span
style='font-family:宋体;"Times New Roman"'>图</span>4.2
2</b><b><span style='font-family:
宋体;"Times New Roman"'>×</span><span
lang=EN-US>2</span></b><b><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>的图案</span><span
lang=EN-US></span></b></p>
</td>
<td width=276 valign=bottom class="Normal">
<p align=center style='text-align:center;line-height:18.0pt'><b><span
lang=EN-US> <img width=162 height=98
src="chap04.files/image003.gif" v:shapes="_x0000_i1028"> </span></b></p>
<p align=center style='text-align:center;line-height:18.0pt'><b><span
style='font-family:宋体;"Times New Roman"'>图</span>4.3
</b><b><span style='font-family:
宋体;"Times New Roman"'>规则图案导致线条</span><span
lang=EN-US></span></b></p>
</td>
</tr>
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</div>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>如果想存储</span><span lang=EN-US>256</span><span
style='font-family:宋体;"Times New Roman"'>级灰度的图案，就需要</span><span lang=EN-US>256</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>16</span><span style='font-family:
宋体;"Times New Roman"'>×</span><span
lang=EN-US>16</span><span style='font-family:宋体;
"Times New Roman"'>的二值点阵，占用的空间还是相当可观的。有一个更好的办法是：只存储一个整数矩阵，称为标准图案，其中的每个值从</span><span
lang=EN-US>0</span><span style='font-family:宋体;
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