Daniel Voigt Godoy - Deep Learning with PyTorch Step-by-Step A Beginner’s Guide-leanpub

If we assume the filter is a square matrix of size f, we can simplify the expression
above to:
Equation 5.2 - Shape after a convolution (square filter)
Makes sense, right? The filter has its dimensions reduced from (f, f) to (1, 1), so the
operation reduces the original size by (f-1).
"But I’d like to keep the image size, is it possible?"
Sure it is! Padding comes to our rescue in this case. We’ll get to that in a couple of
sections.
Convolving in PyTorch
Now that we know how a convolution works, let’s try it out using PyTorch. First, we
need to convert our image and filter to tensors:
image = torch.as_tensor(single).float()
kernel_identity = torch.as_tensor(identity).float()
Since kernel and filter are used interchangeably, especially when it comes to
arguments of different methods, I am calling the variable kernel_identity, even
though it is exactly the same identity filter we have used so far.
Just like the activation functions we saw in Chapter 4, convolutions come in two
flavors: functional and module. There is a fundamental difference between the
two, though: The functional convolution takes the kernel / filter as an argument
while the module has (learnable) weights to represent the kernel / filter.
Let’s use the functional convolution, F.conv2d(), to apply the identity filter to our
input image (notice we’re using stride=1 since we moved the region around one
pixel at a time):
convolved = F.conv2d(image, kernel_identity, stride=1)
convolved
352 | Chapter 5: Convolutions