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📄 第3章 图象的平滑(去噪声)、锐化.htm

📁 介绍了图像的一些基本处理,如平滑,锐化
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lang=EN-US><SUB> <IMG height=75 src="第3章 图象的平滑(去噪声)、锐化.files/image027.gif" 
width=107 v:shapes="_x0000_i1077"> </SUB></SPAN><SPAN 
style="FONT-FAMILY: 宋体">，可以看出，距离越近的点，加权系数越大。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">新的模板也是一个常用的平滑模板，称为高斯</SPAN><SPAN 
lang=EN-US>(Gauss)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">模板。为什么叫这个名字，这是因为这个模板是通过采样</SPAN><SPAN 
lang=EN-US>2</SPAN><SPAN style="FONT-FAMILY: 宋体">维高斯函数得到的。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN style="FONT-FAMILY: 宋体">设图象为</SPAN><SPAN 
lang=EN-US><SUB> <IMG height=96 src="第3章 图象的平滑(去噪声)、锐化.files/image028.gif" 
width=96 v:shapes="_x0000_i1078"> </SUB></SPAN><SPAN 
style="FONT-FAMILY: 宋体">，分别用两种平滑模板处理</SPAN><SPAN lang=EN-US>(</SPAN><SPAN 
style="FONT-FAMILY: 宋体">周围一圈象素直接从原图拷贝</SPAN><SPAN lang=EN-US>)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">。采用</SPAN><SPAN lang=EN-US>Box</SPAN><SPAN 
style="FONT-FAMILY: 宋体">模板的结果为</SPAN><SPAN lang=EN-US><SUB> <IMG height=96 
src="第3章 图象的平滑(去噪声)、锐化.files/image030.gif" width=135 v:shapes="_x0000_i1079"> 
</SUB></SPAN><SPAN style="FONT-FAMILY: 宋体">，采用高斯模板的结果为</SPAN><SPAN 
lang=EN-US><SUB> <IMG height=96 src="第3章 图象的平滑(去噪声)、锐化.files/image032.gif" 
width=136 v:shapes="_x0000_i1080"> </SUB></SPAN><SPAN 
style="FONT-FAMILY: 宋体">。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">可以看到，原图中出现噪声的区域是第</SPAN><SPAN lang=EN-US>2</SPAN><SPAN 
style="FONT-FAMILY: 宋体">行第</SPAN><SPAN lang=EN-US>2</SPAN><SPAN 
style="FONT-FAMILY: 宋体">列和第</SPAN><SPAN lang=EN-US>3</SPAN><SPAN 
style="FONT-FAMILY: 宋体">行第</SPAN><SPAN lang=EN-US>2</SPAN><SPAN 
style="FONT-FAMILY: 宋体">列，灰度从</SPAN><SPAN lang=EN-US>2</SPAN><SPAN 
style="FONT-FAMILY: 宋体">一下子跳到了</SPAN><SPAN lang=EN-US>6</SPAN><SPAN 
style="FONT-FAMILY: 宋体">，用</SPAN><SPAN lang=EN-US>Box</SPAN><SPAN 
style="FONT-FAMILY: 宋体">模板处理后，灰度从</SPAN><SPAN lang=EN-US>3.11</SPAN><SPAN 
style="FONT-FAMILY: 宋体">跳到</SPAN><SPAN lang=EN-US>4.33</SPAN><SPAN 
style="FONT-FAMILY: 宋体">；用高斯模板处理后，灰度从</SPAN><SPAN lang=EN-US>3.</SPAN><SPAN 
style="FONT-FAMILY: 宋体">跳到</SPAN><SPAN lang=EN-US>4.56,</SPAN><SPAN 
style="FONT-FAMILY: 宋体">都缓和了跳变的幅度，从这一点上看，两者都达到了平滑的目的。但是，原图中的第</SPAN><SPAN 
lang=EN-US>3</SPAN><SPAN style="FONT-FAMILY: 宋体">，第</SPAN><SPAN 
lang=EN-US>4</SPAN><SPAN style="FONT-FAMILY: 宋体">行总的来说，灰度值是比较高的，经模板</SPAN><SPAN 
lang=EN-US>1</SPAN><SPAN style="FONT-FAMILY: 宋体">处理后，第</SPAN><SPAN 
lang=EN-US>3</SPAN><SPAN style="FONT-FAMILY: 宋体">行第</SPAN><SPAN 
lang=EN-US>2</SPAN><SPAN style="FONT-FAMILY: 宋体">列元素的灰度变成了</SPAN><SPAN 
lang=EN-US>4.33</SPAN><SPAN style="FONT-FAMILY: 宋体">，与第</SPAN><SPAN 
lang=EN-US>3</SPAN><SPAN style="FONT-FAMILY: 宋体">，第</SPAN><SPAN 
lang=EN-US>4</SPAN><SPAN style="FONT-FAMILY: 宋体">行的总体灰度相比偏小，另外，原图中第</SPAN><SPAN 
lang=EN-US>3</SPAN><SPAN style="FONT-FAMILY: 宋体">行第</SPAN><SPAN 
lang=EN-US>2</SPAN><SPAN style="FONT-FAMILY: 宋体">列元素的灰度为</SPAN><SPAN 
lang=EN-US>6</SPAN><SPAN style="FONT-FAMILY: 宋体">，第</SPAN><SPAN 
lang=EN-US>3</SPAN><SPAN style="FONT-FAMILY: 宋体">行第</SPAN><SPAN 
lang=EN-US>3</SPAN><SPAN style="FONT-FAMILY: 宋体">列元素的灰度为</SPAN><SPAN 
lang=EN-US>4</SPAN><SPAN style="FONT-FAMILY: 宋体">，变换后，后者</SPAN><SPAN 
lang=EN-US>4.56</SPAN><SPAN style="FONT-FAMILY: 宋体">反而比前者</SPAN><SPAN 
lang=EN-US>4.33</SPAN><SPAN 
style="FONT-FAMILY: 宋体">大了。而采用高斯模板没有出现这些问题，究其原因，就是因为它考虑了位置的影响。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">举个实际的例子：下图中，从左到右分别是原图，用高斯模板处理的图，用</SPAN><SPAN 
lang=EN-US>Box</SPAN><SPAN 
style="FONT-FAMILY: 宋体">模板处理的图，可以看出，采用高斯模板，在实现平滑效果的同时，要比</SPAN><SPAN 
lang=EN-US>Box</SPAN><SPAN style="FONT-FAMILY: 宋体">模板清晰一些。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">在学习锐化后，我们将给出一个通用的</SPAN><SPAN lang=EN-US>3</SPAN><SPAN 
style="FONT-FAMILY: 宋体">×</SPAN><SPAN lang=EN-US>3</SPAN><SPAN 
style="FONT-FAMILY: 宋体">模板操作的程序。</SPAN></P>
<P class=a style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US><IMG height=193 
src="第3章 图象的平滑(去噪声)、锐化.files/image033.gif" width=537 v:shapes="_x0000_i1039"> 
</SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><B><SPAN 
style="FONT-FAMILY: 宋体">图</SPAN>3.3&nbsp;&nbsp;&nbsp;&nbsp; </B><B><SPAN 
style="FONT-FAMILY: 宋体">高斯模板和</SPAN><SPAN lang=EN-US>Box</SPAN></B><B><SPAN 
style="FONT-FAMILY: 宋体">模板的对比图</SPAN><SPAN lang=EN-US></SPAN></B></P>
<H2><SPAN lang=EN-US>3.2</SPAN> <SPAN lang=EN-US></SPAN><A 
name=_Toc486331875></A><A name=_Toc486332875></A><A name=_Toc486338984></A><A 
name=_Toc454810849></A><A 
name=_Toc454856623><SPAN><SPAN>中值滤波</SPAN></SPAN></A></H2>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">中值滤波也是一种典型的低通滤波器，它的目的是保护图象边缘的同时去除噪声。所谓中值滤波，是指把以某点</SPAN><SPAN 
lang=EN-US>(x,y)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">为中心的小窗口内的所有象素的灰度按从大到小的顺序排列，将中间值作为</SPAN><SPAN 
lang=EN-US>(x,y)</SPAN><SPAN style="FONT-FAMILY: 宋体">处的灰度值</SPAN><SPAN 
lang=EN-US>(</SPAN><SPAN 
style="FONT-FAMILY: 宋体">若窗口中有偶数个象素，则取两个中间值的平均</SPAN><SPAN 
lang=EN-US>)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">。中值滤波是如何去除噪声的呢？举个例子就很容易明白了。</SPAN></P>
<TABLE cellSpacing=0 cellPadding=0 border=0>
  <TBODY>
  <TR>
    <TD class=Normal vAlign=top width=276>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">原图</SPAN></P></TD>
    <TD class=Normal vAlign=top width=276>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">处理后的图</SPAN></P></TD></TR>
  <TR>
    <TD class=Normal vAlign=top width=276>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      lang=EN-US><SUB><IMG height=141 src="第3章 图象的平滑(去噪声)、锐化.files/image035.gif" 
      width=149 v:shapes="_x0000_i1040"> </SUB></SPAN></P></TD>
    <TD class=Normal vAlign=top width=276>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      lang=EN-US><SUB><IMG height=141 src="第3章 图象的平滑(去噪声)、锐化.files/image037.gif" 
      width=104 v:shapes="_x0000_i1041"> </SUB></SPAN></P></TD></TR></TBODY></TABLE>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">图中数字代表该处的灰度。可以看出原图中间的</SPAN><SPAN 
lang=EN-US>6</SPAN><SPAN 
style="FONT-FAMILY: 宋体">和周围的灰度相差很大，是一个噪声点。经过</SPAN><SPAN 
lang=EN-US>3</SPAN><SPAN style="FONT-FAMILY: 宋体">×</SPAN><SPAN 
lang=EN-US>1</SPAN><SPAN style="FONT-FAMILY: 宋体">窗口</SPAN><SPAN 
lang=EN-US>(</SPAN><SPAN style="FONT-FAMILY: 宋体">即水平</SPAN><SPAN 
lang=EN-US>3</SPAN><SPAN style="FONT-FAMILY: 宋体">个象素取中间值</SPAN><SPAN 
lang=EN-US>)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">的中值滤波，得到右边那幅图，可以看出，噪声点被去除了。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">下面将中值滤波和上面介绍的两种平滑模板作个比较，看看中值滤波有什么特点。我们以一维模板为例，只考虑水平方向，大小为</SPAN><SPAN 
lang=EN-US>3</SPAN><SPAN style="FONT-FAMILY: 宋体">×</SPAN><SPAN 
lang=EN-US>1(</SPAN><SPAN style="FONT-FAMILY: 宋体">宽×高</SPAN><SPAN 
lang=EN-US>)</SPAN><SPAN style="FONT-FAMILY: 宋体">。</SPAN><SPAN 
lang=EN-US>Box</SPAN><SPAN style="FONT-FAMILY: 宋体">模板为</SPAN><SPAN 
lang=EN-US><SUB> <IMG height=41 src="第3章 图象的平滑(去噪声)、锐化.files/image039.gif" 
width=85 v:shapes="_x0000_i1033"> </SUB></SPAN><SPAN 
style="FONT-FAMILY: 宋体">，高斯模板为</SPAN><SPAN lang=EN-US><SUB> <IMG height=41 
src="第3章 图象的平滑(去噪声)、锐化.files/image041.gif" width=88 v:shapes="_x0000_i1034"> 
</SUB></SPAN><SPAN style="FONT-FAMILY: 宋体">。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN style="FONT-FAMILY: 宋体">先考察第一幅图：</SPAN></P>
<TABLE cellSpacing=0 cellPadding=0 border=0>
  <TBODY>
  <TR>
    <TD class=Normal vAlign=top width=141>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">原图</SPAN></P></TD>
    <TD class=Normal vAlign=top width=137>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">经</SPAN><SPAN lang=EN-US>Box</SPAN><SPAN 
      style="FONT-FAMILY: 宋体">模板处理后</SPAN></P></TD>
    <TD class=Normal vAlign=top width=137>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">经</SPAN><SPAN lang=EN-US>Gauss</SPAN><SPAN 
      style="FONT-FAMILY: 宋体">模板处理后</SPAN></P></TD>
    <TD class=Normal vAlign=top width=136>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">经中值滤波处理后</SPAN></P></TD></TR>
  <TR>
    <TD class=Normal width=141>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      lang=EN-US><SUB><IMG height=112 src="第3章 图象的平滑(去噪声)、锐化.files/image043.gif" 
      width=127 v:shapes="_x0000_i1035"> </SUB></SPAN></P></TD>
    <TD class=Normal width=137>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      lang=EN-US><SUB><IMG height=155 src="第3章 图象的平滑(去噪声)、锐化.files/image045.gif" 
      width=104 v:shapes="_x0000_i1036"> </SUB></SPAN></P></TD>
    <TD class=Normal width=137>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      lang=EN-US><SUB><IMG height=155 src="第3章 图象的平滑(去噪声)、锐化.files/image047.gif" 
      width=117 v:shapes="_x0000_i1037"> </SUB></SPAN></P></TD>
    <TD class=Normal width=136>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      lang=EN-US><SUB><IMG height=112 src="第3章 图象的平滑(去噪声)、锐化.files/image049.gif" 
      width=84 v:shapes="_x0000_i1038"> </SUB></SPAN></P></TD></TR></TBODY></TABLE>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">从原图中不难看出左边区域灰度值低，右边区域灰度值高，中间有一条明显的边界</SPAN><SPAN 
lang=EN-US>,</SPAN><SPAN style="FONT-FAMILY: 宋体">这一类图象称之为</SPAN><SPAN 
lang=EN-US>“step”(</SPAN><SPAN style="FONT-FAMILY: 宋体">就象灰度上了个台阶</SPAN><SPAN 
lang=EN-US>)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">。应用平滑模板后，图象平滑了，但是也使边界模糊了。应用中值滤波，就能很好地保持原来的边界。所以说，中值滤波的特点是保护图象边缘的同时去除噪声。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN style="FONT-FAMILY: 宋体">再看第二幅图：</SPAN></P>
<TABLE cellSpacing=0 cellPadding=0 border=0>
  <TBODY>
  <TR>
    <TD class=Normal vAlign=top width=138>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">原图</SPAN></P></TD>
    <TD class=Normal vAlign=top width=138>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">经</SPAN><SPAN lang=EN-US>Box</SPAN><SPAN 
      style="FONT-FAMILY: 宋体">模板处理后</SPAN></P></TD>
    <TD class=Normal vAlign=top width=138>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">经</SPAN><SPAN lang=EN-US>Gauss</SPAN><SPAN 
      style="FONT-FAMILY: 宋体">模板处理后</SPAN></P></TD>
    <TD class=Normal vAlign=top width=138>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
      style="FONT-FAMILY: 宋体">经中值滤波处理后</SPAN></P></TD></TR>
  <TR>
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