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"Times New Roman"'>到</span><span lang=EN-US>255</span><span
style='font-family:宋体;"Times New Roman"'>。图象的实际灰度和阵列中的每个值比较，当该值大于等于灰度时，对应点打一黑点。下面举一个</span><span
lang=EN-US>25</span><span style='font-family:宋体;
"Times New Roman"'>级灰度的例子加以说明。</span></p>
<p class=a style='line-height:18.0pt'><span lang=EN-US> <img width=285 height=124
src="chap04.files/image005.jpg" v:shapes="_x0000_i1029"> </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>4.4 </b><b><span
style='font-family:宋体;"Times New Roman"'>标准图案举例</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>4.4</span><span style='font-family:
宋体;"Times New Roman"'>中，左边为标准图案，右边为灰度为</span><span
lang=EN-US>15</span><span style='font-family:宋体;
"Times New Roman"'>的图案，共有</span><span lang=EN-US>10</span><span
style='font-family:宋体;"Times New Roman"'>个黑点，</span><span lang=EN-US>15</span><span style='font-family:
宋体;"Times New Roman"'>个白点。其实道理很简单，灰度为</span><span
lang=EN-US>0</span><span style='font-family:宋体;
"Times New Roman"'>时全是黑点，灰度每增加</span><span lang=EN-US>1</span><span
style='font-family:宋体;"Times New Roman"'>，减少一个黑点。要注意的是，</span><span lang=EN-US>5</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>5</span><span style='font-family:
宋体;"Times New Roman"'>的图案可以表示</span><span
lang=EN-US>26</span><span style='font-family:宋体;
"Times New Roman"'>种灰度，当灰度是</span><span lang=EN-US>25</span><span
style='font-family:宋体;"Times New Roman"'>才是全白点，而不是灰度为</span><span lang=EN-US>24</span><span
style='font-family:宋体;"Times New Roman"'>时。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>下面介绍一种设计标准图案的算法，是由</span><span lang=EN-US>Limb</span><span
style='font-family:宋体;"Times New Roman"'>在</span><span lang=EN-US>1969</span><span style='font-family:
宋体;"Times New Roman"'>年提出的。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>先以一个</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"'>的矩阵开始：设</span><span lang=EN-US>M<sub>1</sub>=<sub>
<img width=49 height=48
src="chap04.files/image007.gif" v:shapes="_x0000_i1030"> </sub> </span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>，通过递归关系有</span><span
lang=EN-US>M<sub>n+1</sub>=<sub> <img width=181 height=51
src="chap04.files/image009.gif" v:shapes="_x0000_i1031"> </sub> </span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>，其中</span><span
lang=EN-US>M<sub>n</sub></span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>和</span><span
lang=EN-US>U<sub>n</sub></span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>均为</span><span
lang=EN-US>2<sup>n</sup></span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>×</span><span
lang=EN-US>2<sup>n</sup></span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>的方阵，</span><span
lang=EN-US>U<sub>n</sub></span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>的所有元素都是</span><span
lang=EN-US>1</span><span style='font-family:宋体;
"Times New Roman"'>。根据这个算法，可以得到</span><span lang=EN-US>M<sub>2</sub>=<sub>
<img width=120 height=96
src="chap04.files/image011.gif" v:shapes="_x0000_i1032"> </sub> </span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>，为</span><span
lang=EN-US>16</span><span style='font-family:宋体;
"Times New Roman"'>级灰度的标准图案。</span></p>
<p style='line-height:18.0pt'><span
lang=EN-US>M<sub>3</sub>(8</span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>×</span><span
lang=EN-US>8</span><span style='font-family:宋体;
"Times New Roman"'>阵</span><span lang=EN-US>)</span><span
style='font-family:宋体;"Times New Roman"'>比较特殊，称为</span><span lang=EN-US>Bayer</span><span
style='font-family:宋体;"Times New Roman"'>抖动表。</span><span lang=EN-US>M<sub>4</sub></span><span
style='font-family:宋体;"Times New Roman"'>是一个</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"'>的矩阵。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>根据上面的算法，如果利用</span><span lang=EN-US>M<sub>3</sub></span><span
style='font-family:宋体;"Times New Roman"'>一个象素要用</span><span lang=EN-US>8</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>8</span><span style='font-family:
宋体;"Times New Roman"'>的图案表示，则一幅</span><span
lang=EN-US>N</span><span style='font-family:宋体;
"Times New Roman"'>×</span><span lang=EN-US>N</span><span
style='font-family:宋体;"Times New Roman"'>的图将变成</span><span lang=EN-US>8N</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>8N</span><span style='font-family:
宋体;"Times New Roman"'>大小。如果利用</span><span
lang=EN-US>M<sub>4</sub></span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>，就更不得了，变成</span><span
lang=EN-US>16N</span><span style='font-family:宋体;
"Times New Roman"'>×</span><span lang=EN-US>16N</span><span
style='font-family:宋体;"Times New Roman"'>了。能不能在保持原图大小的情况下利用图案化技术呢？一种很自然的想法是：如果用</span><span
lang=EN-US>M<sub>2</sub></span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>阵，则将原图中每</span><span
lang=EN-US>8</span><span style='font-family:宋体;
"Times New Roman"'>×</span><span lang=EN-US>8</span><span
style='font-family:宋体;"Times New Roman"'>个点中取一点，即重新采样，然后再应用图案化技术，就能够保持原图大小。实际上，这种方法并不可行。首先，你不知道这</span><span
lang=EN-US>8</span><span style='font-family:宋体;
"Times New Roman"'>×</span><span lang=EN-US>8</span><span
style='font-family:宋体;"Times New Roman"'>个点中找哪一点比较合适，另外，</span><span lang=EN-US>8</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>8</span><span style='font-family:
宋体;"Times New Roman"'>的间隔实在太大了，生成的图象和原图肯定相差很大，就象图</span><span
lang=EN-US>4.1</span><span style='font-family:宋体;
"Times New Roman"'>最右边的那幅图一样。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>我们可以采用这样的做法：假设原图是</span><span lang=EN-US>256</span><span
style='font-family:宋体;"Times New Roman"'>级灰度，利用</span><span lang=EN-US>Bayer</span><span
style='font-family:宋体;"Times New Roman"'>抖动表，做如下处理</span></p>
<p align=center style='text-align:center;line-height:18.0pt'><span
lang=EN-US>if (g[y][x]>>2) > bayer[y&7][x&7] then </span><span
style='font-family:宋体;"Times New Roman"'>打一白点</span><span lang=EN-US> else </span><span
style='font-family:宋体;"Times New Roman"'>打一黑点</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>其中，</span><span lang=EN-US>x,y</span><span style='font-family:
宋体;"Times New Roman"'>代表原图的象素坐标，</span><span
lang=EN-US>g[y][x]</span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>代表该点灰度。首先将灰度右移两位，变成</span><span
lang=EN-US>64</span><span style='font-family:宋体;
"Times New Roman"'>级，然后将</span><span lang=EN-US>x</span><span
style='font-family:宋体;"Times New Roman"'>，</span><span lang=EN-US>y</span><span style='font-family:
宋体;"Times New Roman"'>做模</span><span
lang=EN-US>8</span><span style='font-family:宋体;
"Times New Roman"'>运算，找到</span><span lang=EN-US>Bayer</span><span
style='font-family:宋体;"Times New Roman"'>表中的对应点，两者做比较，根据上面给出的判据做处理。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>我们可以看到，模</span><span lang=EN-US>8</span><span
style='font-family:宋体;"Times New Roman"'>运算使得原图分成了一个个</span><span lang=EN-US>8</span><span
style='font-family:宋体;"Times New Roman"'>×</span><span lang=EN-US>8</span><span style='font-family:
宋体;"Times New Roman"'>的小块，每个小块和</span><span
lang=EN-US>8</span><span style='font-family:宋体;
"Times New Roman"'>×</span><span lang=EN-US>8</span><span
style='font-family:宋体;"Times New Roman"'>的</span><span lang=EN-US>Bayer</span><span style='font-family:
宋体;"Times New Roman"'>表相对应。小块中的每个点都参与了比较，这样就避免了上面提到的选点和块划分过大的问题。模</span><span
lang=EN-US>8</span><span style='font-family:宋体;
"Times New Roman"'>运算实质上是引入了随机成分，这就是我们下面要讲到的抖动技术。</span></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>图</span><span lang=EN-US>4.5</span><span style='font-family:
宋体;"Times New Roman"'>就是利用了这个算法，使用</span><span
lang=EN-US>M<sub>3</sub>(Bayer</span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>抖动表</span><span
lang=EN-US>)</span><span style='font-family:宋体;
"Times New Roman"'>阵得到的；图</span><span lang=EN-US>6</span><span
style='font-family:宋体;"Times New Roman"'>是使用</span><span lang=EN-US>M<sub>4</sub></span><span
style='font-family:宋体;"Times New Roman"'>阵得到的，可见两者的差别并不是很大，所以一般用</span><span lang=EN-US>Bayer</span><span
style='font-family:宋体;"Times New Roman"'>表就可以了。</span></p>
<p align=center style='text-align:center;line-height:18.0pt'><span
lang=EN-US> <img width=409 height=259
src="chap04.files/image012.gif" v:shapes="_x0000_i1033"> </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>4.5 </b><b><span
style='font-family:宋体;"Times New Roman"'>利用</span><span lang=EN-US>M3</span></b><b><span
style='font-family:宋体;"Times New Roman"'>抖动生成的图</span><span lang=EN-US></span></b></p>
<p align=center style='text-align:center;line-height:18.0pt'><b><span
lang=EN-US> <img width=409 height=259
src="chap04.files/image013.gif" v:shapes="_x0000_i1034"> </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>4.6 </b><b><span
style='font-family:宋体;"Times New Roman"'>利用</span><span lang=EN-US>M4</span></b><b><span
style='font-family:宋体;"Times New Roman"'>抖动生成的图</span><span lang=EN-US></span></b></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>下面是算法的源程序，是针对</span><span lang=EN-US>Bayer</span><span
style='font-family:宋体;"Times New Roman"'>表的。因为它是个常用的表，我们不再利用</span><span lang=EN-US>Limb</span><span
style='font-family:宋体;"Times New Roman"'>公式，而是直接给出。针对</span><span lang=EN-US>M<sub>4</sub></span><span
style='font-family:宋体;"Times New Roman"'>阵的算法是类似的，不同的地方在于，要用</span><span lang=EN-US>Limb</span><span
style='font-family:宋体;"Times New Roman"'>公式得到</span><span lang=EN-US>M<sub>4</sub></span><span
style='font-family:宋体;"Times New Roman"'>阵，灰度也不用右移</span><span lang=EN-US>2</span><span
style='font-family:宋体;"Times New Roman"'>位。要注意的是，为了处理的方便，我们的结果图仍采用</span><span lang=EN-US>256</span><span
style='font-family:宋体;"Times New Roman"'>级灰度图，不过只用到了</span><span lang=EN-US>0</span><span
style='font-family:宋体;"Times New Roman"'>和</span><span lang=EN-US>255</span><span style='font-family:
宋体;"Times New Roman"'>两种灰度。</span></p>
<p style='line-height:18.0pt'>BYTE BayerPattern[8][8]={ 0,32,8,40,2,34,10,42,</p>
<p style='line-height:
18.0pt'><span lang=EN-US>48,16,56,24,50,18,58,26,</span></p>
<p style='line-height:18.0pt'><span>
</span>
12,44,4,36,14,46,6,38,</p>
<p style='line-height:18.0pt'><span>
</span>
60,28,52,20,62,30,54,22,</p>
<p style='line-height:18.0pt'><span>
</span>
3,35,11,43,1,33,9,41,</p>
<p style='line-height:18.0pt'><span>
</span>
51,19,59,27,49,17,57,25,</p>
<p style='line-height:18.0pt'><span>
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