The result of the dimension after applying a convolutional operation depends on several factors, including the input size, filter size, stride, and padding. The formula to calculate the output size of a convolutional layer can be expressed as follows:
Here's a breakdown of the terms in the formula:
Input Size: The size of the input feature map or image.
Filter Size: The size of the convolutional filter (kernel).
Padding: The number of pixels added around the input to avoid border effects. It can be zero (valid/no padding), or the filter size minus one divided by 2 (same/symmetric padding).
Stride: The step size at which the filter moves across the input.
Let's go through an example to illustrate how the output size is calculated:
These examples demonstrate how changes in the filter size, padding, and stride affect the size of the output feature map after a convolutional operation. The specific values for these parameters depend on the design choices made for the convolutional layer in a neural network.