The edge of darkness is upon us!

I assume that now we know how to find edges in a given image u. It's simple, just take the derivative!

Today, I want to find the smooth regions. Well, it's kind of silly, as now that we have edges, the rest of the image is kind of edgeless. Right... but I would like to assign a number from 0 to 1 to it ... where 1 indicates a flat region and zero indicates an edge, in other words I want to make the edges appear dark.

There are many ways to do it. One of the ways to do it is to look at the function $$g(x, y):=\frac{1}{\sqrt{1+|K*\nabla u(x, y)|}}.$$ Where, K is your favourite smoothing kernel. (I will leave it to you to code this as an exercise. It is a four liner.)

Staring at this function is a refreshing activity, something that I love to do in my spare time.

Boo in the edge of darkness

Lenna in the edge of darkness

Barbara in the edge of darkness