Matlab图像旋转
####以坐标原点为中心旋转的原理:
点p0p_0p0绕坐标原点逆时针方向旋转θ\thetaθ角度得到点p1p_1p1.
从①②可以得到旋转变换的矩阵公式:
[x1y11]\begin{bmatrix}x_1&y_1&1\end{bmatrix}[x1y11]=[x0y01]\begin{bmatrix}x_0&y_0&1\end{bmatrix}[x0y01][cos(θ)sin(θ)0−sin(θ)cos(θ)0001]\begin{bmatrix}cos(\theta)&sin(\theta)&0\\-sin(\theta)&cos(\theta)&0\\0&0&1\end{bmatrix}⎣⎡cos(θ)−sin(θ)0sin(θ)cos(θ)0001⎦⎤
还可以得到逆运算矩阵公式:
[x0y01]\begin{bmatrix}x_0&y_0&1\end{bmatrix}[x0y01]=[x1y11]\begin{bmatrix}x_1&y_1&1\end{bmatrix}[x1y11][cos(θ)−sin(θ)0sin(θ)cos(θ)0001]\begin{bmatrix}cos(\theta)&-sin(\theta)&0\\sin(\theta)&cos(\theta)&0\\0&0&1\end{bmatrix}⎣⎡cos(θ)sin(θ)0−sin(θ)cos(θ)0