https://c3cris.github.io/c3ann/

c3ann is a proof of concept of a Digit Recognition by Convolutional Artificial Neural Network.

$${g(x,y)=\omega *f(x,y)=\sum _{dx=-a}^{a}{\sum _{dy=-b}^{b}{\omega (dx,dy)f(x-dx,y-dy)}}}$$

$${\frac {1}{9}}{\begin{bmatrix}\ \ 1&\ \ 1&\ \ 1\\ \ 1&\ \ 1&\ \ 1\\ \ 1&\ \ 1&\ \ 1\end{bmatrix}}$$

$$\sum = (x_1 \times w_1 ) +(x_2 \times w_2 ) + \cdots + (x_n \times w_n )$$

$$\textrm{Sigmoid} = \frac{1}{1+e^{-x}}$$

$$\textrm{Sigmoid}' = \frac{e^{-x}}{\left ( 1+e^{-x} \right )^{2}}$$