Shear

Detail

在二维图像处理中，shear操作是指将图像沿水平或垂直方向进行错切，从而改变图像的形状。shear操作可以用仿射变换矩阵来表示，如下所示为一个Horizontal Shear：

$$\left[\begin{array}{cc}1& \tan (\theta )\\ 0& 1\end{array}\right]$$ $$\left[\begin{array}{c}{x}^{\prime }\\ y^{\prime }\end{array}\right]=\left[\begin{array}{c}x+my\\ y\end{array}\right]=\left[\begin{array}{cc}1& m\\ 0& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]$$

上述矩阵的效果如图：

同时还有Vertical Shear

$$\left[\begin{array}{cc}1& 0\\ \tan (\theta )& 1\end{array}\right]$$ $$\left[\begin{array}{c}{x}^{\prime }\\ y^{\prime }\end{array}\right]=\left[\begin{array}{c}x\\ mx+y\end{array}\right]=\left[\begin{array}{cc}1& 0\\ m& 1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]$$

Reference

• https://en.wikipedia.org/wiki/Shear_mapping