Image to cols

Can we convert convolution into matrix dot operation? ! Image to cols.

Now, we can use dot operation to calculate cnn convolution!.

From this figure, given a matrix [N,C,H,W] and filter [K,K] we can get the resolution of converted matrix:

Colum size:

$$W' = C * K * K$$

Row size:

$$H' = N * (\frac{(W - K + P)}{S}+1) *（\frac{(H - K + P)}{S}+1）$$

In this context:

N is the number of samples.
C is the number of channels.
H is the height of the input matrix.
W is the width of the input matrix.
K is the size of the filter.
P is the padding applied to the input matrix.
S is the stride of the filter.