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<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><b><span style='font-size:10.5pt;
font-family:"Times New Roman"'>5.</span></b><b><span style='font-size:7.0pt;
font-family:"Times New Roman"'>
</span></b><b><span lang=ZH-CN style='font-size:10.5pt'>补集</span></b><span
style='font-size:10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><span lang=ZH-CN style='font-size:10.5pt'>设有一幅图象</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>X</span><span
lang=ZH-CN style='font-size:10.5pt'>，所有</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>X</span><span lang=ZH-CN style='font-size:10.5pt'>区域以外的点构成的集合称为</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>X</span><span
lang=ZH-CN style='font-size:10.5pt'>的补集，记作</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>X<sup>c</sup></span><span lang=ZH-CN
style='font-size:10.5pt'>，如图</span><span style='font-size:10.5pt;font-family:
"Times New Roman"'>6.5</span><span lang=ZH-CN style='font-size:10.5pt'>所示。显然，如果</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>∩</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>X=</span><span lang=ZH-CN style='font-size:10.5pt'>Ф，则</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>在</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>X</span><span lang=ZH-CN style='font-size:10.5pt'>的补集内，即</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B<sub> <!--[if gte vml 1]><v:shape
id="_x0000_i1030" type="#_x0000_t75" alt="" style='width:12pt;height:9.75pt'>
<v:imagedata src="./chp6.files/image001.gif" o:href="http://www-scf.usc.edu/~flv/ipbook/chap06.files/image011.gif"/>
</v:shape><![endif]--><![if !vml]><img width=16 height=13
src="./chp6.files/image001.gif" v:shapes="_x0000_i1030"><![endif]></sub>X<sup>c</sup></span><span
lang=ZH-CN style='font-size:10.5pt'>。</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'><o:p></o:p></span></p>
<p class=a style='margin:0cm;margin-bottom:.0001pt;line-height:18.0pt'><!--[if gte vml 1]><v:shape
id="_x0000_i1031" type="#_x0000_t75" alt="" style='width:2in;height:99.75pt'>
<v:imagedata src="./chp6.files/image006.jpg" o:href="http://www-scf.usc.edu/~flv/ipbook/chap06.files/image013.jpg"/>
</v:shape><![endif]--><![if !vml]><img width=192 height=133
src="./chp6.files/image006.jpg" v:shapes="_x0000_i1031"><![endif]></p>
<p align=center style='margin:0cm;margin-bottom:.0001pt;text-align:center;
line-height:18.0pt'><b><span lang=ZH-CN style='font-size:10.5pt'>图</span></b><b><span
style='font-size:10.5pt;font-family:"Times New Roman"'>6.5
</span></b><b><span lang=ZH-CN style='font-size:10.5pt'>补集的示意图</span></b><span
style='font-size:10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><b><span style='font-size:10.5pt;
font-family:"Times New Roman"'>6.</span></b><b><span style='font-size:7.0pt;
font-family:"Times New Roman"'>
</span></b><b><span lang=ZH-CN style='font-size:10.5pt'>结构元素</span></b><span
style='font-size:10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><span lang=ZH-CN style='font-size:10.5pt'>设有两幅图象</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>，</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>X</span><span lang=ZH-CN style='font-size:10.5pt'>。若</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>X</span><span
lang=ZH-CN style='font-size:10.5pt'>是被处理的对象，而</span><span style='font-size:
10.5pt;font-family:"Times New Roman"'>B</span><span lang=ZH-CN
style='font-size:10.5pt'>是用来处理</span><span style='font-size:10.5pt;font-family:
"Times New Roman"'>X</span><span lang=ZH-CN style='font-size:10.5pt'>的，则称</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>为结构元素</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>(structure element)</span><span lang=ZH-CN
style='font-size:10.5pt'>，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><span
style='font-size:10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><b><span style='font-size:10.5pt;
font-family:"Times New Roman"'>7.</span></b><b><span style='font-size:7.0pt;
font-family:"Times New Roman"'>
</span></b><b><span lang=ZH-CN style='font-size:10.5pt'>对称集</span></b><span
style='font-size:10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><span lang=ZH-CN style='font-size:10.5pt'>设有一幅图象</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>，将</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>B</span><span lang=ZH-CN style='font-size:10.5pt'>中所有元素的坐标取反，即令</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>(x</span><span
lang=ZH-CN style='font-size:10.5pt'>，</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>y)</span><span lang=ZH-CN style='font-size:10.5pt'>变成</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>(-x</span><span
lang=ZH-CN style='font-size:10.5pt'>，</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>-y)</span><span lang=ZH-CN style='font-size:
10.5pt'>，所有这些点构成的新的集合称为</span><span style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>的对称集，记作</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>B<sup>v</sup></span><span lang=ZH-CN
style='font-size:10.5pt'>，如图</span><span style='font-size:10.5pt;font-family:
"Times New Roman"'>6.6</span><span lang=ZH-CN style='font-size:10.5pt'>所示。</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><b><span style='font-size:10.5pt;
font-family:"Times New Roman"'>8.</span></b><b><span style='font-size:7.0pt;
font-family:"Times New Roman"'>
</span></b><b><span lang=ZH-CN style='font-size:10.5pt'>平移</span></b><span
style='font-size:10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><span lang=ZH-CN style='font-size:10.5pt'>设有一幅图象</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>，有一个点</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>a(x<sub>0</sub>,y<sub>0</sub>)</span><span
lang=ZH-CN style='font-size:10.5pt'>，将</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>B</span><span lang=ZH-CN style='font-size:10.5pt'>平移</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>a</span><span
lang=ZH-CN style='font-size:10.5pt'>后的结果是，把</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>B</span><span lang=ZH-CN style='font-size:10.5pt'>中所有元素的横坐标加</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>x<sub>0</sub></span><span
lang=ZH-CN style='font-size:10.5pt'>，纵坐标加</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>y<sub>0</sub></span><span lang=ZH-CN
style='font-size:10.5pt'>，即令</span><span style='font-size:10.5pt;font-family:
"Times New Roman"'>(x</span><span lang=ZH-CN style='font-size:10.5pt'>，</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>y)</span><span
lang=ZH-CN style='font-size:10.5pt'>变成</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>(x+x<sub>0</sub></span><span lang=ZH-CN
style='font-size:10.5pt'>，</span><span style='font-size:10.5pt;font-family:
"Times New Roman"'>y+y<sub>0</sub>)</span><span lang=ZH-CN style='font-size:
10.5pt'>，所有这些点构成的新的集合称为</span><span style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>的平移，记作</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>B<sub>a</sub></span><span lang=ZH-CN
style='font-size:10.5pt'>，如图</span><span style='font-size:10.5pt;font-family:
"Times New Roman"'>6.7</span><span lang=ZH-CN style='font-size:10.5pt'>所示。</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
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<p style='text-align:justify;text-justify:inter-ideograph;line-height:18.0pt'><span
style='font-size:10.5pt;font-family:"Times New Roman"'><!--[if gte vml 1]><v:shape
id="_x0000_i1032" type="#_x0000_t75" alt="" style='width:204pt;height:129.75pt'>
<v:imagedata src="./chp6.files/image007.jpg" o:href="http://www-scf.usc.edu/~flv/ipbook/chap06.files/image015.jpg"/>
</v:shape><![endif]--><![if !vml]><img width=272 height=173
src="./chp6.files/image007.jpg" v:shapes="_x0000_i1032"><![endif]><o:p></o:p></span></p>
<p align=center style='text-align:center;line-height:18.0pt'><b><span
lang=ZH-CN style='font-size:10.5pt'>图</span></b><b><span style='font-size:
10.5pt;font-family:"Times New Roman"'>6.6 </span></b><b><span
lang=ZH-CN style='font-size:10.5pt'>对称集的示意图</span></b><span style='font-size:
10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
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<td width=276 valign=top style='width:207.0pt;padding:0cm 0cm 0cm 0cm'>
<p style='text-align:justify;text-justify:inter-ideograph;line-height:18.0pt'><span
style='font-size:10.5pt;font-family:"Times New Roman"'><!--[if gte vml 1]><v:shape
id="_x0000_i1033" type="#_x0000_t75" alt="" style='width:175.5pt;height:129.75pt'>
<v:imagedata src="./chp6.files/image008.jpg" o:href="http://www-scf.usc.edu/~flv/ipbook/chap06.files/image017.jpg"/>
</v:shape><![endif]--><![if !vml]><img width=234 height=173
src="./chp6.files/image008.jpg" v:shapes="_x0000_i1033"><![endif]><o:p></o:p></span></p>
<p align=center style='text-align:center;line-height:18.0pt'><b><span
lang=ZH-CN style='font-size:10.5pt'>图</span></b><b><span style='font-size:
10.5pt;font-family:"Times New Roman"'>6.7 </span></b><b><span
lang=ZH-CN style='font-size:10.5pt'>平移的示意图</span></b><span style='font-size:
10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
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<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><span lang=ZH-CN style='font-size:10.5pt'>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><span
style='font-size:10.5pt;font-family:"Times New Roman"'><o:p></o:p></span></p>
<h2 style='text-align:justify;text-justify:inter-ideograph'><span
style='font-family:"Times New Roman"'>6.1 </span><span lang=ZH-CN
style='mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"'>腐蚀</span><span
style='font-family:"Times New Roman"'><o:p></o:p></span></h2>
<p style='margin:0cm;margin-bottom:.0001pt;text-align:justify;text-justify:
inter-ideograph;line-height:18.0pt'><span lang=ZH-CN style='font-size:10.5pt'>把结构元素</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>平移</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>a</span><span lang=ZH-CN style='font-size:10.5pt'>后得到</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B<sub>a</sub></span><span
lang=ZH-CN style='font-size:10.5pt'>，若</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>B<sub>a</sub></span><span lang=ZH-CN
style='font-size:10.5pt'>包含于</span><span style='font-size:10.5pt;font-family:
"Times New Roman"'>X</span><span lang=ZH-CN style='font-size:10.5pt'>，我们记下这个</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>a</span><span
lang=ZH-CN style='font-size:10.5pt'>点，所有满足上述条件的</span><span style='font-size:
10.5pt;font-family:"Times New Roman"'>a</span><span lang=ZH-CN
style='font-size:10.5pt'>点组成的集合称做</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>X</span><span lang=ZH-CN style='font-size:10.5pt'>被</span><span
style='font-size:10.5pt;font-family:"Times New Roman"'>B</span><span
lang=ZH-CN style='font-size:10.5pt'>腐蚀</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>(Erosion)</span><span lang=ZH-CN
style='font-size:10.5pt'>的结果。用公式表示为：</span><span style='font-size:10.5pt;
font-family:"Times New Roman"'>E(X)={a| B<sub>a <!--[if gte vml 1]><v:shape
id="_x0000_i1034" type="#_x0000_t75" alt="" style='width:12pt;height:9.75pt'>
<v:imagedata src="./chp6.files/image001.gif" o:href="http://www-scf.usc.edu/~flv/ipbook/chap06.files/image019.gif"/>
</v:shape><![endif]--><![if !vml]><img width=16 height=13
src="./chp6.files/image001.gif" v:shapes="_x0000_i1034"><![endif]></sub>X}=X <!--[if gte vml 1]><v:shape
id="_x0000_i1035" type="#_x0000_t75" alt="" style='width:9.75pt;height:9.75pt'>
<v:imagedata src="./chp6.files/image009.jpg" o:href="http://www-scf.usc.edu/~flv/ipbook/chap06.files/image021.jpg"/>
</v:shape><![endif]--><![if !vml]><img width=13 height=13
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