# What is the dimensionality of the output map, given the dimensionality of the input map, number of filters, stride and padding?

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 set of $$F$$ filters, each of dimension $$\textbf{f} \in R^{H'\times W'\times D}$$
• A stride of $$$$ for the corresponding $$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 $$H, W, D, F, H', W', s_x, s_y$$? 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 $$p_{xLeft} + p_{xRight}$$)