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仿射变换保证物体形状的“平直性”和“平行性”。透视变换不能保证物体形状的“平行性”。仿射变换是透视变换的特殊形式。

将透视变换写成3*3矩阵形式，即为M;

以下面这张图为例，实现仿射变换，包括旋转，平移，缩放，剪切，以图像中心为变换中心；

仿射变换

旋转（逆时针旋转30度）

Mat M=Mat::eye(3,3, CV_32FC1);

float alpha=PI/6; float tx=0; float ty=0; float scale=1;

M.at<float>(0, 0) = cos(alpha);

M.at<float>(0, 1) = sin(alpha); M.at<float>(0, 2) = (1-cos(alpha))*center.x - sin(alpha)* center.y; M.at<float>(1, 0) = -sin(alpha); M.at<float>(1, 1) = cos(alpha); M.at<float>(1, 2) = sin(alpha)* center.x +(1-cos(alpha))*center.y; M.at<float>(2, 0) = 0; M.at<float>(2, 1) = 0; M.at<float>(2, 2) = 1;

 

平移（水平和垂直方向各向右平移20个像素）

Mat M=Mat::eye(3,3, CV_32FC1);    float alpha=0;    float tx=20;    float ty=20;    float scale=0;    M.at
   
    (0, 0) = cos(alpha);    M.at
    
     (0, 1) = sin(alpha);    M.at
     
      (0, 2) = (1-cos(alpha))*center.x - sin(alpha)* center.y + tx;    M.at
      
       (1, 0) = -sin(alpha);    M.at
       
        (1, 1) = cos(alpha);    M.at
        
         (1, 2) = sin(alpha)* center.x +(1-cos(alpha))*center.y + ty; M.at
         
          (2, 0) = 0; M.at
          
           (2, 1) = 0; M.at
           
            (2, 2) = 1;
           
          
         
        
       
      
     
    
   

 

缩放（图像缩小1/2）

Mat M=Mat::eye(3,3, CV_32FC1);    float alpha=0;    float tx=0;    float ty=0;    float scale=0.5;    M.at
   
    (0, 0) = cos(alpha) * scale;    M.at
    
     (0, 1) = sin(alpha) * scale;    M.at
     
      (0, 2) = (1-cos(alpha)* scale)*center.x - sin(alpha)* center.y* scale + tx;    M.at
      
       (1, 0) = -sin(alpha) * scale;    M.at
       
        (1, 1) = cos(alpha)* scale;    M.at
        
         (1, 2) = sin(alpha)* center.x* scale +(1-cos(alpha)* scale)*center.y + ty; M.at
         
          (2, 0) = 0; M.at
          
           (2, 1) = 0; M.at
           
            (2, 2) = 1;
           
          
         
        
       
      
     
    
   

错切变换（剪切变换）：

 

Mat M=Mat::eye(3,3, CV_32FC1);    float alpha=PI/12;    float tx=0;    float ty=0;    float scale=1;    M.at
   
    (0, 0) = 1;    M.at
    
     (0, 1) = sin(alpha);    M.at
     
      (0, 2) = (1-cos(alpha))*center.x - sin(alpha)* center.y;    M.at
      
       (1, 0) = 0;    M.at
       
        (1, 1) = 1;    M.at
        
         (1, 2) = sin(alpha)* center.x +(1-cos(alpha))*center.y; M.at
         
          (2, 0) = 0; M.at
          
           (2, 1) = 0; M.at
           
            (2, 2) = 1;
           
          
         
        
       
      
     
    
   

 

 

透视变换（透视变换不保证平行性）

Mat M=Mat::eye(3,3, CV_32FC1);    float alpha=0;    float tx=0;    float ty=0;    float scale=1;    M.at
   
    (0, 0) = cos(alpha);    M.at
    
     (0, 1) = sin(alpha);    M.at
     
      (0, 2) =(1-cos(alpha))*center.x - sin(alpha)* center.y + tx;    M.at
      
       (1, 0) = -sin(alpha);    M.at
       
        (1, 1) = cos(alpha);    M.at
        
         (1, 2) =sin(alpha)* center.x +(1-cos(alpha))*center.y + ty; M.at
         
          (2, 0) = 0.001; M.at
          
           (2, 1) = 0.001; M.at
           
            (2, 2) = 1;
           
          
         
        
       
      
     
    
   

上述操作使用同一个opencv接口函数：warpPerspective(srcImg, dstImg, M, Size(width, height));

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