User:KCote/sandbox

Digital Image Processing

In digital image processing the affine transformations scale, rotate, translate, mirror and sheer images as the following examples show:

Transformation Name	Affine Matrix	Example
Identity	${\begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}}$
Edge detection	${\begin{bmatrix}\ \ 1&0&-1\\\ \ 0&0&\ \ 0\\-1&0&\ \ 1\end{bmatrix}}$
	${\begin{bmatrix}0&\ \ 1&0\\1&-4&1\\0&\ \ 1&0\end{bmatrix}}$
	${\begin{bmatrix}-1&-1&-1\\-1&\ \ 8&-1\\-1&-1&-1\end{bmatrix}}$
Sharpen	${\begin{bmatrix}\ \ 0&-1&\ \ 0\\-1&\ \ 5&-1\\\ \ 0&-1&\ \ 0\end{bmatrix}}$
Box blur (normalized)	${\frac {1}{9}}{\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}}$
Gaussian blur 3 × 3 (approximation)	${\frac {1}{16}}{\begin{bmatrix}1&2&1\\2&4&2\\1&2&1\end{bmatrix}}$
Gaussian blur 5 × 5 (approximation)	${\frac {1}{256}}{\begin{bmatrix}1&4&6&4&1\\4&16&24&16&4\\6&24&36&24&6\\4&16&24&16&4\\1&4&6&4&1\end{bmatrix}}$
Unsharp masking 5 × 5 Based on Gaussian blur with amount as 1 and threshold as 0 (with no image mask)	${\frac {-1}{256}}{\begin{bmatrix}1&4&\ \ 6&4&1\\4&16&\ \ 24&16&4\\6&24&-476&24&6\\4&16&\ \ 24&16&4\\1&4&\ \ 6&4&1\end{bmatrix}}$

The above are just a few examples of effects achievable by convolving kernels and images.

Origin

The origin is the position of the kernel which is above (conceptually) the current output pixel. This could be outside of the actual kernel, though usually it corresponds to one of the kernel elements. For a symmetric kernel, the origin is usually the center element.