User:Panjasan/Matrix-Table

The general expression of a convolution is

$g_{x,y}=\omega *f_{x,y}=\sum _{i=-a}^{a}{\sum _{j=-b}^{b}{\omega _{i,j}f_{x-i,y-j}}},$

where $g(x,y)$ is the filtered image, $f(x,y)$ is the original image, $\omega$ is the filter kernel. Every element of the filter kernel is considered by $-a\leq i\leq a$ and $-b\leq j\leq b$ .

Depending on the element values, a kernel can cause a wide range of effects:

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Operation	Kernel ω	Image result g(x,y)
Identity	${\begin{bmatrix}\ \ 0&\ \ 0&\ \ 0\\\ \ 0&\ \ 1&\ \ 0\\\ \ 0&\ \ 0&\ \ 0\end{bmatrix}}$
Ridge or edge detection	${\begin{bmatrix}0&-1&0\\-1&\ \ 4&-1\\0&-1&0\end{bmatrix}}$
Ridge or edge detection	${\begin{bmatrix}-1&-1&-1\\-1&\ \ 8&-1\\-1&-1&-1\end{bmatrix}}$
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)	${\frac {-1}{256}}{\begin{bmatrix}1&4&6&4&1\\4&16&24&16&4\\6&24&-476&24&6\\4&16&24&16&4\\1&4&6&4&1\end{bmatrix}}$

User:Panjasan/Matrix-Table

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