如何理解仿射变换

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简单来说,“仿射变换”=“线性变换”+“平移”,Y=WX+B (X,Y,B为n维向量,W为n*n维矩阵)

概念:

Y=WX+B (X,Y,B为n维向量,W为n*n维矩阵)

直观理解:

变换前是直线的,变换后依然是直线

一条直线上各个位置之间的距离比例保持不变

例子:

一维:y=kx+b

二维:旋转,缩放,推移,移动,镜面反射等;new_x = ax+by , new_y = cx+dy

性质:

x和y完全等价,是一个无损的变换。且不存在变形,扭曲等。可以认为x和y是完全等价的两个量。

应用:

雷达回波dbz和彩云雷达强度0-15之间的变换