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<p align=center style='text-align:center;line-height:18.0pt'><b><span
style='font-family:宋体;"Times New Roman"'>图</span>6.3
</b><b><span style='font-family:
宋体;"Times New Roman"'>击中</span></b></p>
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<p align=center style='text-align:center;line-height:18.0pt'><span
lang=EN-US> <img width=162 height=66
src="chap06.files/image010.jpg" 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>6.4
</b><b><span style='font-family:
宋体;"Times New Roman"'>不击中</span></b></p>
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<p style='line-height:
18.0pt;'> <b><span
lang=EN-US>5.<span style='font:7.0pt "Times New Roman"'>
</span></span></b> <b><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>补集</span><span
lang=EN-US></span></b></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>设有一幅图象</span><span lang=EN-US>X</span><span
style='font-family:宋体;"Times New Roman"'>，所有</span><span lang=EN-US>X</span><span style='font-family:
宋体;"Times New Roman"'>区域以外的点构成的集合称为</span><span
lang=EN-US>X</span><span style='font-family:宋体;
"Times New Roman"'>的补集，记作</span><span lang=EN-US>X<sup>c</sup></span><span
style='font-family:宋体;"Times New Roman"'>，如图</span><span lang=EN-US>6.5</span><span style='font-family:
宋体;"Times New Roman"'>所示。显然，如果</span><span
lang=EN-US>B</span><span style='font-family:宋体;
"Times New Roman"'>∩</span><span lang=EN-US>X=</span><span
style='font-family:宋体;"Times New Roman"'>Ф，则</span><span lang=EN-US>B</span><span style='font-family:
宋体;"Times New Roman"'>在</span><span
lang=EN-US>X</span><span style='font-family:宋体;
"Times New Roman"'>的补集内，即</span><span lang=EN-US>B<sub> <img width=16 height=13
src="chap06.files/image011.gif" v:shapes="_x0000_i1034"> </sub> X<sup>c</sup></span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>。</span></p>
<p class=a style='line-height:18.0pt'><span lang=EN-US> <img width=192 height=133
src="chap06.files/image013.jpg" v:shapes="_x0000_i1035"> </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>6.5 </b><b><span
style='font-family:宋体;"Times New Roman"'>补集的示意图</span><span lang=EN-US></span></b></p>
<p style='line-height:
18.0pt;'> <b><span
lang=EN-US>6.<span style='font:7.0pt "Times New Roman"'>
</span></span></b> <b><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>结构元素</span><span
lang=EN-US></span></b></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>设有两幅图象</span><span lang=EN-US>B</span><span
style='font-family:宋体;"Times New Roman"'>，</span><span lang=EN-US>X</span><span style='font-family:
宋体;"Times New Roman"'>。若</span><span
lang=EN-US>X</span><span style='font-family:宋体;
"Times New Roman"'>是被处理的对象，而</span><span lang=EN-US>B</span><span
style='font-family:宋体;"Times New Roman"'>是用来处理</span><span lang=EN-US>X</span><span style='font-family:
宋体;"Times New Roman"'>的，则称</span><span
lang=EN-US>B</span><span style='font-family:宋体;
"Times New Roman"'>为结构元素</span><span lang=EN-US>(structure element)</span><span style='font-family:宋体;
"Times New Roman"'>，又被形象地称做刷子。结构元素通常都是一些比较小的图象。</span></p>
<p style='line-height:
18.0pt;'> <b><span
lang=EN-US>7.<span style='font:7.0pt "Times New Roman"'>
</span></span></b> <b><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>对称集</span><span
lang=EN-US></span></b></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>设有一幅图象</span><span lang=EN-US>B</span><span
style='font-family:宋体;"Times New Roman"'>，将</span><span lang=EN-US>B</span><span style='font-family:
宋体;"Times New Roman"'>中所有元素的坐标取反，即令</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"'>变成</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"'>，所有这些点构成的新的集合称为</span><span
lang=EN-US>B</span><span style='font-family:宋体;
"Times New Roman"'>的对称集，记作</span><span lang=EN-US>B<sup>v</sup></span><span
style='font-family:宋体;"Times New Roman"'>，如图</span><span lang=EN-US>6.6</span><span style='font-family:
宋体;"Times New Roman"'>所示。</span></p>
<p style='line-height:
18.0pt;'> <b><span
lang=EN-US>8.<span style='font:7.0pt "Times New Roman"'>
</span></span></b> <b><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>平移</span><span
lang=EN-US></span></b></p>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>设有一幅图象</span><span lang=EN-US>B</span><span
style='font-family:宋体;"Times New Roman"'>，有一个点</span><span lang=EN-US>a(x<sub>0</sub>,y<sub>0</sub>)</span><span
style='font-family:宋体;"Times New Roman"'>，将</span><span lang=EN-US>B</span><span style='font-family:
宋体;"Times New Roman"'>平移</span><span
lang=EN-US>a</span><span style='font-family:宋体;
"Times New Roman"'>后的结果是，把</span><span lang=EN-US>B</span><span
style='font-family:宋体;"Times New Roman"'>中所有元素的横坐标加</span><span lang=EN-US>x<sub>0</sub></span><span
style='font-family:宋体;"Times New Roman"'>，纵坐标加</span><span lang=EN-US>y<sub>0</sub></span><span
style='font-family:宋体;"Times New Roman"'>，即令</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"'>变成</span><span lang=EN-US>(x+x<sub>0</sub></span><span
style='font-family:宋体;"Times New Roman"'>，</span><span lang=EN-US>y+y<sub>0</sub>)</span><span
style='font-family:宋体;"Times New Roman"'>，所有这些点构成的新的集合称为</span><span lang=EN-US>B</span><span
style='font-family:宋体;"Times New Roman"'>的平移，记作</span><span lang=EN-US>B<sub>a</sub></span><span
style='font-family:宋体;"Times New Roman"'>，如图</span><span lang=EN-US>6.7</span><span style='font-family:
宋体;"Times New Roman"'>所示。</span></p>
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<td width=276 valign=top class="Normal">
<p style='line-height:18.0pt'><span lang=EN-US> <img width=272 height=173
src="chap06.files/image015.jpg" v:shapes="_x0000_i1036"> </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>6.6
</b><b><span style='font-family:
宋体;"Times New Roman"'>对称集的示意图</span></b></p>
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<td width=276 valign=top class="Normal">
<p style='line-height:18.0pt'><span lang=EN-US> <img width=234 height=173
src="chap06.files/image017.jpg" v:shapes="_x0000_i1037"> </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>6.7
</b><b><span style='font-family:
宋体;"Times New Roman"'>平移的示意图</span></b></p>
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<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>好了，介绍了这么多基本符号和关系，现在让我们应用这些符号和关系，看一下形态学的基本运算。</span></p>
<h2> <span
lang=EN-US>6.1</span> <span lang=EN-US> </span><a name="_Toc486331892"></a><a
name="_Toc486332892"></a><a name="_Toc486339001"></a><a name="_Toc454810866"></a><a
name="_Toc454856640"><span><span>腐蚀</span></span></a></h2>
<p style='line-height:18.0pt'><span
style='font-family:宋体;"Times New Roman"'>把结构元素</span><span lang=EN-US>B</span><span style='font-family:
宋体;"Times New Roman"'>平移</span><span
lang=EN-US>a</span><span style='font-family:宋体;
"Times New Roman"'>后得到</span><span lang=EN-US>B<sub>a</sub></span><span
style='font-family:宋体;"Times New Roman"'>，若</span><span lang=EN-US>B<sub>a</sub></span><span
style='font-family:宋体;"Times New Roman"'>包含于</span><span lang=EN-US>X</span><span style='font-family:
宋体;"Times New Roman"'>，我们记下这个</span><span
lang=EN-US>a</span><span style='font-family:宋体;
"Times New Roman"'>点，所有满足上述条件的</span><span lang=EN-US>a</span><span
style='font-family:宋体;"Times New Roman"'>点组成的集合称做</span><span lang=EN-US>X</span><span
style='font-family:宋体;"Times New Roman"'>被</span><span lang=EN-US>B</span><span style='font-family:
宋体;"Times New Roman"'>腐蚀</span><span
lang=EN-US>(Erosion)</span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>的结果。用公式表示为：</span><span
lang=EN-US>E(X)={a| B<sub>a</sub><sub> <img width=16 height=13
src="chap06.files/image019.gif" v:shapes="_x0000_i1038"> </sub> X}=X <img width=13 height=13
src="chap06.files/image021.jpg" v:shapes="_x0000_i1039"> B</span><span style='font-family:宋体;"Times New Roman";"Times New Roman"'>，如图</span><span
lang=EN-US>6.8</span><span style='font-family:宋体;
"Times New Roman"'>所示。</span></p>
<p align=center style='text-align:center;line-height:18.0pt'><span
lang=EN-US> <img width=304 height=273
src="chap06.files/image023.jpg" v:shapes="_x0000_i1040"> </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>6.8 </b><b><span
style='font-family:宋体;"Times New Roman"'>腐蚀的示意图</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>6.8</span><span style='font-family:
宋体;"Times New Roman"'>中</span><span
lang=EN-US>X</span><span style='font-family:宋体;
"Times New Roman"'>是被处理的对象，</span><span lang=EN-US>B</span><span
style='font-family:宋体;"Times New Roman"'>是结构元素。不难知道，对于任意一个在阴影部分的点</span><span lang=EN-US>a</span><span
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