Assignment P1
Student: Jan Hendrik Dithmar, 2031259, jadi5003@stud.uni-saarland.de

Filename convention: the different numbers which are attached to the filename
indicate the inputs which you would make to the programme in order.
Example: fabric-<sigma>-<iterations>.pgm
         office-n40-<sigma>-<iterations>.pgm

Problem 1
(b)
Since the minimum increases and the maximum decreases, the new greyvalues still
lie between the old minimum and old maximum which means that the
maximum-minimum-principle is satisfied.
The mean always stays the same which is a property of linear diffusion filtering.
Since the minimum and the maximum change and the mean does not, the variance also
changes. The minimum and the maximum get closer together, so the variance has
to decrease which it does.
For time steps larger than 0.25, the algorithm gets unstable. After 10 iterations
for example you cannot see any structure. See here fabric-0.5-5.pgm and
fabric-0.5-10.pgm.

(d)
Linear diffusion is actually not suitable for image denoising because this
technique also removes structures of the image and not only noise. You can see
this by having a look at the difference images where you can see some structures
of the office.
Linear diffusion: office-n40-0.15-30.pgm
Difference image: office-n40-0.15-30-diff.pgm