the convolution operation is the foundation of computer vision. it's what allows a neural network to "see" edges, textures, and patterns.
the sliding window
at its core, a convolution is just a sliding window (a kernel) moving across an input grid. at each step, we perform an element-wise multiplication and sum the results.
if we have an input size N x N and a kernel of size K x K, the output size O for a "valid" convolution (no padding) is:
O = N - K + 1
on the homepage, i've visualized this with an 8x8 input and a 3x3 kernel.
8 - 3 + 1 = 6
this results in a 6x6 output matrix.
why it matters
by changing the values inside the 3x3 kernel, we can perform different operations:
- sharpening: accentuates the difference between pixels.
- blurring: averages neighboring pixels.
- edge detection: finds rapid changes in intensity (gradient).
the visualizer on the homepage uses a randomized input and a simplified visual representation of this data flow.