Filter: identify edges in images

An edge in an image is a place where brightness changes rapidly — from dark to light.

Here is how you identify them: compare each pixel with its neighbour. Is the difference large? Then there is an edge. Is the difference zero? Then the surface is uniform.

A filter performs this comparison automatically across the entire image. The filter [−1, 1] means: “take the value on the right minus the value on the left”.

Calculate by hand. A row of pixels (0 = black, 9 = white):

0  0  0  9  9  9

The filter [−1, 1] slides across and calculates right minus left:

0−0=0   0−0=0   9−0=9   9−9=0   9−9=0

Result: 0 0 9 0 0. Only one spot has a high value — exactly where the edge is.

Try it yourself with the row 0 9 0 9 0 9 (stripes). What do you get? 9 −9 9 −9 9 — everything is an edge. And with 5 5 5 5 5 (uniform grey)? Only zeros — no edge anywhere.

This is exactly what the first layer in a CNN does, except in two dimensions and with weights that the network has learned itself.