# Dimensionality of convolutional layers & convolution operations

I am trying to understand the dimensionality of the outputs of convolution operations. Suppose a convolutional layer with the following characteristics:

• Input map $\textbf{x} \in R^{H\times W\times D}$
• A bank of $F$ filters, each of dimension $\textbf{f} \in R^{H'\times W'\times D}$
• A stride of $<s_x,s_y>$ for the corresponding x and y dimensions of the input map
• Either valid or same padding (explain for both if possible)

What should be the expected dimensionality of the output map expressed in terms of $H, W, D, F, H', W', s_x, s_y$?

• Maybe a little more self research next time? – DuttaA Sep 15 '18 at 18:50

where, $$p_{x}$$ and $$p_{y}$$ are padding values. (equal on both sides). You can have different padding on left and right side. (similarly top and bottom). If same padding, equation will have $$2*p_{x}$$ or $$2*p_{y}$$, else you can just add values of both padding and replace in the equations. (For example $$p_{xLeft} + p_{xRight}$$)