Deep-Learning-with-PyTorch

Convolutions in action
199
one-half the convolution kernel’s width (in our case, 3//2 = 1) smaller on each side.
This explains why we’re missing two pixels in each dimension.
However, PyTorch gives us the possibility of padding the image by creating ghost pixels
around the border that have value zero as far as the convolution is concerned. Figure
8.3 shows padding in action.
In our case, specifying padding=1 when kernel_size=3 means i00 has an extra set
of neighbors above it and to its left, so that an output of the convolution can be computed
even in the corner of our original image. 3 The net result is that the output has
now the exact same size as the input:
# In[16]:
conv = nn.Conv2d(3, 1, kernel_size=3, padding=1)
output = conv(img.unsqueeze(0))
img.unsqueeze(0).shape, output.shape
Now with padding
# Out[16]:
(torch.Size([1, 3, 32, 32]), torch.Size([1, 1, 32, 32]))
zeros
outside
0 1 0 0 1 0
1 1 1 0 0 1 1 1 0
0 1 0 1 0 0 1 0 0
0 1 0 0 0 1 0 0
0 0 0 0 0 0 0 0
0 1 0
0 1 1 1
1 0 1 0
0 1 0 0
0 0 0 0
0
1
0
0
1
1
1
0
0 1 0
1 1 1
0 1 0
0 0
0 0
0 1 0 0 0 0 1 0
1 1 1 1 0 1 1 1
0 1 0 0 0 0 1 0
0 0 0 0 0 0 0
0 1
0 1 0
1 1 1
0 1 0
0
1
0
0
0
0
0
0
0
1
0
0 1 0
1 1 1
0 1 0
0
0
0
0
0
0
0
0
OUTPUT
2 2 2 0
2 5 2 1
2 2 2 0
0 1 0 0
0
1
0
0
0 1 0
1 1 1
0 1 0
0 0 0
0 1 0 0
1 0 1 0
0 1 1 1
0 0 1 0
0 1 0 1 0
1 1 1 1 1
0 1 0 1 0
0 0 0 0
0 1 0 0
1 1 0 1 0
0 1 1 1 1
0 0 0 1 0
0
1
1
1
0 1 0
1 1 1
0 1 0
0
1
0
0
0
0
0
0
0 1 0 0
1 1 1 0
0 1 0 0
1 1 1 0
0 1 0
0 1 0 0
1 1 1 0
0 0 1 0
0 1 1 1
0 1 0
0 1 0 0
1 1 1 0
0 1 0 1 0
0 0 1 1 1
0 1 0
Figure 8.3
Zero padding to preserve the image size in the output
3
For even-sized kernels, we would need to pad by a different number on the left and right (and top and bottom).
PyTorch doesn’t offer to do this in the convolution itself, but the function torch.nn.functional
.pad can take care of it. But it’s best to stay with odd kernel sizes; even-sized kernels are just odd.