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📄 第2章 图象的几何变换.htm

📁 介绍了图像的几何变换的基础教程.包括平移,旋转
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<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>}</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>}</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>hDc=GetDC(hWnd);</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>if(hBitmap!=NULL)</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>DeleteObject(hBitmap); 
//</SPAN><SPAN style="FONT-FAMILY: 宋体">释放原来的位图句柄</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>//</SPAN><SPAN 
style="FONT-FAMILY: 宋体">产生新的位图</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
lang=EN-US>hBitmap=CreateDIBitmap(hDc,(LPBITMAPINFOHEADER)lpTempImgData,</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>(LONG)CBM_INIT,</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>(LPSTR)lpTempImgData+</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>sizeof(BITMAPINFOHEADER) 
+</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
lang=EN-US>NumColors*sizeof(RGBQUAD),</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>(LPBITMAPINFO)lpTempImgData, 
</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>DIB_RGB_COLORS);</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>//</SPAN><SPAN 
style="FONT-FAMILY: 宋体">将平移后的图象存成文件</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
lang=EN-US>hf=_lcreat("c:\\translation.bmp",0);</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
lang=EN-US>_lwrite(hf,(LPSTR)&amp;bf,sizeof(BITMAPFILEHEADER)); </SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
lang=EN-US>_lwrite(hf,(LPSTR)lpTempImgData,BufSize);</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>_lclose(hf);</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>//</SPAN><SPAN 
style="FONT-FAMILY: 宋体">释放资源和内存</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>ReleaseDC(hWnd,hDc);</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
lang=EN-US>LocalUnlock(hTempImgData);</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
lang=EN-US>LocalFree(hTempImgData);</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>GlobalUnlock(hImgData);</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>return TRUE;</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>}</SPAN><SPAN lang=EN-US 
style="FONT-SIZE: 9pt"></SPAN></P>
<H2><SPAN lang=EN-US>2.2</SPAN> <SPAN lang=EN-US></SPAN><A 
name=_Toc486331869></A><A name=_Toc486332869></A><A name=_Toc486338978></A><A 
name=_Toc454810843></A><A 
name=_Toc454856617><SPAN><SPAN>旋转</SPAN></SPAN></A></H2>
<P style="LINE-HEIGHT: 18pt"><SPAN style="FONT-FAMILY: 宋体">旋转</SPAN><SPAN 
lang=EN-US>(rotation)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">有一个绕着什么转的问题，通常的做法是以图象的中心为圆心旋转，举个例子，图</SPAN><SPAN 
lang=EN-US>2.7</SPAN><SPAN style="FONT-FAMILY: 宋体">旋转</SPAN><SPAN 
lang=EN-US>30</SPAN><SPAN style="FONT-FAMILY: 宋体">度</SPAN><SPAN 
lang=EN-US>(</SPAN><SPAN style="FONT-FAMILY: 宋体">顺时针方向</SPAN><SPAN 
lang=EN-US>)</SPAN><SPAN style="FONT-FAMILY: 宋体">后如图</SPAN><SPAN 
lang=EN-US>2.8</SPAN><SPAN style="FONT-FAMILY: 宋体">所示：</SPAN></P>
<TABLE cellSpacing=0 cellPadding=0 border=0>
  <TBODY>
  <TR>
    <TD class=Normal vAlign=bottom width=276>
      <P class=a style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US><IMG height=86 
      src="第2章 图象的几何变换.files/image022.jpg" width=145 v:shapes="_x0000_i1027"> 
      </SPAN></P>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><B><SPAN 
      style="FONT-FAMILY: 宋体">图</SPAN>2.7&nbsp;&nbsp;&nbsp;&nbsp; </B><B><SPAN 
      style="FONT-FAMILY: 宋体">旋转前的图</SPAN><SPAN lang=EN-US></SPAN></B></P></TD>
    <TD class=Normal vAlign=bottom width=276>
      <P class=a style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US><IMG height=147 
      src="第2章 图象的几何变换.files/image023.gif" width=169 v:shapes="_x0000_i1028"> 
      </SPAN></P>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><B><SPAN 
      style="FONT-FAMILY: 宋体">图</SPAN>2.8&nbsp;&nbsp;&nbsp;&nbsp; </B><B><SPAN 
      style="FONT-FAMILY: 宋体">旋转后的图</SPAN><SPAN 
  lang=EN-US></SPAN></B></P></TD></TR></TBODY></TABLE>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">可以看出，旋转后图象变大了。另一种做法是不让图象变大，转出的部分被裁剪掉。如图</SPAN><SPAN 
lang=EN-US>2.9</SPAN><SPAN style="FONT-FAMILY: 宋体">所示。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">我们采用第一种做法，首先给出变换矩阵。在我们熟悉的坐标系中，将一个点顺时针旋转</SPAN><SPAN 
lang=EN-US>a</SPAN><SPAN style="FONT-FAMILY: 宋体">角后的坐标变换公式，如图</SPAN><SPAN 
lang=EN-US>2.10</SPAN><SPAN style="FONT-FAMILY: 宋体">所示，</SPAN><SPAN 
lang=EN-US>r</SPAN><SPAN style="FONT-FAMILY: 宋体">为该点到原点的距离，在旋转过程中，</SPAN><SPAN 
lang=EN-US>r</SPAN><SPAN style="FONT-FAMILY: 宋体">保持不变；</SPAN><SPAN 
lang=EN-US>b</SPAN><SPAN style="FONT-FAMILY: 宋体">为</SPAN><SPAN 
lang=EN-US>r</SPAN><SPAN style="FONT-FAMILY: 宋体">与</SPAN><SPAN 
lang=EN-US>x</SPAN><SPAN style="FONT-FAMILY: 宋体">轴之间的夹角。</SPAN></P>
<TABLE cellSpacing=0 cellPadding=0 border=0>
  <TBODY>
  <TR>
    <TD class=Normal vAlign=bottom width=276>
      <P class=a style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US><IMG height=106 
      src="第2章 图象的几何变换.files/image025.jpg" width=138 v:shapes="_x0000_i1029"> 
      </SPAN></P>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><B><SPAN 
      style="FONT-FAMILY: 宋体">图</SPAN><SPAN lang=EN-US>2.9 </SPAN></B><B><SPAN 
      style="FONT-FAMILY: 宋体">旋转后保持原图大小，</SPAN><SPAN lang=EN-US></SPAN></B></P>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><B><SPAN 
      style="FONT-FAMILY: 宋体">转出的部分被裁掉</SPAN></B></P></TD>
    <TD class=Normal vAlign=bottom width=276>
      <P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US><IMG height=208 
      src="第2章 图象的几何变换.files/image027.jpg" width=235 v:shapes="_x0000_i1030"> 
      </SPAN></P>
      <P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><B><SPAN 
      style="FONT-FAMILY: 宋体">图</SPAN>2.10&nbsp;&nbsp; </B><B><SPAN 
      style="FONT-FAMILY: 宋体">旋转示意图</SPAN><SPAN 
  lang=EN-US></SPAN></B></P></TD></TR></TBODY></TABLE>
<P style="LINE-HEIGHT: 18pt"><SPAN style="FONT-FAMILY: 宋体">旋转前：</SPAN><SPAN 
lang=EN-US>x<SUB>0</SUB>=rcosb</SPAN><SPAN style="FONT-FAMILY: 宋体">；</SPAN><SPAN 
lang=EN-US>y<SUB>0</SUB>=rsinb</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN style="FONT-FAMILY: 宋体">旋转</SPAN><SPAN 
lang=EN-US>a</SPAN><SPAN style="FONT-FAMILY: 宋体">角度后：</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
lang=EN-US>x<SUB>1</SUB>=rcos(b-a)=rcosbcosa+rsinbsina=x<SUB>0</SUB>cosa+y<SUB>0</SUB>sina</SPAN><SPAN 
style="FONT-FAMILY: 宋体">；</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
lang=EN-US>y<SUB>1</SUB>=rsin(b-a)=rsinbcosa-rcosbsina=-x<SUB>0</SUB>sina+y<SUB>0</SUB>cosa</SPAN><SPAN 
style="FONT-FAMILY: 宋体">；</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN style="FONT-FAMILY: 宋体">以矩阵的形式表示：</SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
lang=EN-US><SUB><IMG height=75 src="第2章 图象的几何变换.files/image029.gif" width=292 
v:shapes="_x0000_i1031"> </SUB></SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: right" align=right><SPAN 
lang=EN-US>(2.5)</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">上面的公式中，坐标系</SPAN><SPAN lang=EN-US>xoy</SPAN><SPAN 
style="FONT-FAMILY: 宋体">是以图象的中心为原点，向右为</SPAN><SPAN lang=EN-US>x</SPAN><SPAN 
style="FONT-FAMILY: 宋体">轴正方向，向上为</SPAN><SPAN lang=EN-US>y</SPAN><SPAN 
style="FONT-FAMILY: 宋体">轴正方向。它和以图象左上角点为原点</SPAN><SPAN lang=EN-US>o’</SPAN><SPAN 
style="FONT-FAMILY: 宋体">，向右为</SPAN><SPAN lang=EN-US>x’</SPAN><SPAN 
style="FONT-FAMILY: 宋体">轴正方向，向下为</SPAN><SPAN lang=EN-US>y’</SPAN><SPAN 
style="FONT-FAMILY: 宋体">轴正方向的坐标系</SPAN><SPAN lang=EN-US>x’o’y’</SPAN><SPAN 
style="FONT-FAMILY: 宋体">之间的转换关系如何呢？如图</SPAN><SPAN lang=EN-US>2.11</SPAN><SPAN 
style="FONT-FAMILY: 宋体">所示。</SPAN></P>
<P class=a style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US><IMG height=160 
src="第2章 图象的几何变换.files/image031.jpg" width=207 v:shapes="_x0000_i1032"> 
</SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><B><SPAN 
style="FONT-FAMILY: 宋体">图</SPAN>2.11&nbsp;&nbsp;&nbsp; </B><B><SPAN 
style="FONT-FAMILY: 宋体">两种坐标系间的转换关系</SPAN><SPAN lang=EN-US></SPAN></B></P>
<P style="LINE-HEIGHT: 18pt"><SPAN style="FONT-FAMILY: 宋体">设图象的宽为</SPAN><SPAN 
lang=EN-US>w</SPAN><SPAN style="FONT-FAMILY: 宋体">，高为</SPAN><SPAN 
lang=EN-US>h</SPAN><SPAN style="FONT-FAMILY: 宋体">，容易得到：</SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
lang=EN-US><SUB><IMG height=75 src="第2章 图象的几何变换.files/image033.gif" width=296 
v:shapes="_x0000_i1033"> </SUB></SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: right" align=right><SPAN 
lang=EN-US>(2.6)</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN style="FONT-FAMILY: 宋体">逆变换为：</SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
lang=EN-US><SUB><IMG height=75 src="第2章 图象的几何变换.files/image035.gif" width=284 
v:shapes="_x0000_i1034"> </SUB></SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: right" align=right><SPAN 
lang=EN-US>(2.7)</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">有了上面的公式，我们可以把变换分成三步：</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>1.</SPAN><SPAN 
style="FONT-FAMILY: 宋体">将坐标系</SPAN><SPAN lang=EN-US>o’</SPAN><SPAN 
style="FONT-FAMILY: 宋体">变成</SPAN><SPAN lang=EN-US>o</SPAN><SPAN 
style="FONT-FAMILY: 宋体">；</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>2.</SPAN><SPAN 
style="FONT-FAMILY: 宋体">将该点顺时针旋转</SPAN><SPAN lang=EN-US>a</SPAN><SPAN 
style="FONT-FAMILY: 宋体">角；</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>3.</SPAN><SPAN 
style="FONT-FAMILY: 宋体">将坐标系</SPAN><SPAN lang=EN-US>o</SPAN><SPAN 
style="FONT-FAMILY: 宋体">变回</SPAN><SPAN lang=EN-US>o’</SPAN><SPAN 
style="FONT-FAMILY: 宋体">，这样，我们就得到了变换矩阵，是上面三个矩阵的级联。</SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
lang=EN-US><SUB><IMG height=125 src="第2章 图象的几何变换.files/image037.gif" width=529 
v:shapes="_x0000_i1040"> </SUB></SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: right" align=right><SPAN 
lang=EN-US>(2.8)</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN 
style="FONT-FAMILY: 宋体">要注意的是，因为新图变大，所以上面公式中出现了</SPAN><SPAN 
lang=EN-US>w<SUB>old</SUB></SPAN><SPAN style="FONT-FAMILY: 宋体">，</SPAN><SPAN 
lang=EN-US>h<SUB>old</SUB></SPAN><SPAN style="FONT-FAMILY: 宋体">，</SPAN><SPAN 
lang=EN-US>w<SUB>new</SUB></SPAN><SPAN style="FONT-FAMILY: 宋体">，</SPAN><SPAN 
lang=EN-US>h<SUB>new</SUB></SPAN><SPAN 
style="FONT-FAMILY: 宋体">，它们分别表示原图</SPAN><SPAN lang=EN-US>(old)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">和新图</SPAN><SPAN lang=EN-US>(new)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">的宽、高。我们从图</SPAN><SPAN lang=EN-US>2.8</SPAN><SPAN 
style="FONT-FAMILY: 宋体">中容易看出：</SPAN><SPAN 
lang=EN-US>w<SUB>new</SUB>=max(|x<SUB>4</SUB>-x<SUB>1</SUB>|,|x<SUB>3</SUB>-x<SUB>2</SUB>|) 
</SPAN><SPAN style="FONT-FAMILY: 宋体">；</SPAN><SPAN 
lang=EN-US>h<SUB>new</SUB>=max(|y<SUB>4</SUB>-y<SUB>1</SUB>|,|y<SUB>3</SUB>-y<SUB>2</SUB>|)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">。</SPAN></P>
<P style="LINE-HEIGHT: 18pt"><SPAN lang=EN-US>(2.8)</SPAN><SPAN 
style="FONT-FAMILY: 宋体">的逆变换为</SPAN></P>
<P style="LINE-HEIGHT: 18pt; TEXT-ALIGN: center" align=center><SPAN 
lang=EN-US><SUB><IMG height=125 src="第2章 图象的几何变换.files/image039.gif" width=526
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