Check Your Understanding: Convolution
A two-dimensional, 3x3 convolutional filter is applied to a two-dimensional 4x4 input feature map (no padding added):
What is the shape of the output feature map?
2x2
As the 3x3 filter slides over the 4x4 feature map, there are 4 unique locations in which
it can be placed, which results in a 2x2 output feature map:
3x3
While the filter itself is 3x3, the output feature map is smaller because there are fewer
than 9 (3 times 3) possible locations where the filter can be placed on the 4x4 input
feature map.
4x4
To generate an output feature map with the same dimensions as the input feature map
with no padding, the convolutional filter would have to be 1x1 in shape. A filter
larger than 1x1 will produce an output feature map that is smaller than the input
feature map. Because our filter is 3x3, the output feature map must be smaller
than 4x4.