User:KCote/sandbox

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Filter type	Kernel or mask	Example
Original Image	${\begin{bmatrix}0&0&0\\0&1&0\\0&0&0\end{bmatrix}}$
lowpass	${\frac {1}{9}}\times {\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}$
Scale	${\begin{bmatrix}c_{x}=2&0&0\\0&c_{y}=1&0\\0&0&1\end{bmatrix}}$	File:Affine Transformation Scale Checkerboard.jpg
Rotate	${\begin{bmatrix}\cos(\theta )&\sin(\theta )&0\\-\sin(\theta )&\cos(\theta )&0\\0&0&1\end{bmatrix}}$	File:Affine Transformation Rotated Checkerboard.jpg
Shear	${\begin{bmatrix}1&c_{x}=0.5&0\\c_{y}=0&1&0\\0&0&1\end{bmatrix}}$	File:Affine Transformation Shear Checkerboard.jpg

References

Berger, Marcel (1987), Geometry I, Berlin: Springer, ISBN 3-540-11658-3