Testing of anisotropic diffusion

From: Olzhas Zhumabek (anonymous.from.applecity_at_[hidden])
Date: 2020-06-05 14:04:44

Hi,

Since having precomputed images is a bit of problem both delivery wise and
license wise, I've got a few ideas on how to test it.

The algorithm has the following properties:
1. It preserves the heat inside the system (e.g. after a lot of iterations,
all pixels will approach mean of the image)
2. If all pixels are at the mean value, nothing changes (minus numerical
inaccuracies)
3. Lower kappa values have more respect for edges than higher kappa values

Based on those, we could implement the following tests:

Sanity checks. One for all zeroes staying zeroes, and the second having
uniformly initialized image pertaining the values after cast to integral
values to discard the accumulated inaccuracy.

Mean value test. Initialize an image with random values, compute mean
pixel, run the algorithm for a lot of iterations (10'000) with kappa ~ 30.
It will require a small image (32x32 should work).

Higher kappa vs lower kappa test. This is a relative test, e.g. it will not
check for exact values. Instead, it will run the algorithm twice with
difference kappas on a special image (a rectangle filled with decreasing
values towards the center). A higher kappa value will make a mess, but
lower one should preserve the contours of the rectangle.

I will re-read the paper and run some preliminary tests to check if my
assumptions are correct, and get back with the results. Those tests are a
small project on its own, so I will try to get as many in as possible until
night from Monday to Tuesday, and move on to other algorithms.

Best regards,
Olzhas