Added handling of case K1 = 0 and/or K2 = 0 in metrics.structural_similarity

[Ouss98]

The cases K1 = 0 and/or K2 = 0 gave NaNs in S if D had zeros.
Fixed by introducing appropriate factors S1 and S2, which
we set to 1 when zeros appear in the denominator.
This fixes the case when gradient is False.

Description

Checklist

• Docstrings for all functions
• Gallery example in ./doc/examples (new features only)
• Benchmark in ./benchmarks, if your changes aren't covered by an
  existing benchmark
• Unit tests
• Clean style in the spirit of PEP8

For reviewers

• Check that the PR title is short, concise, and will make sense 1 year
  later.
• Check that new functions are imported in corresponding __init__.py.
• Check that new features, API changes, and deprecations are mentioned in
  doc/release/release_dev.rst.

[pep8speaks]

Hello @Ouss98! Thanks for updating this PR. We checked the lines you've touched for PEP 8 issues, and found:

• In the file skimage/metrics/_structural_similarity.py:

Line 230:1: W293 blank line contains whitespace
Line 233:1: W293 blank line contains whitespace
Line 237:1: W293 blank line contains whitespace
Line 239:1: W293 blank line contains whitespace

Comment last updated at 2021-08-30 09:52:26 UTC

[Ouss98]

Please, let me know if there is anything I need to change or explain.

[rfezzani]

Sorry @Ouss98 for my late answer, and thank you for your contribution.
I am wondering if it is not simpler to forbid the cases K1=0 and K2=0: I see in the reference paper [1] that K1 and K2 are just some regularization parameters made to avoid 0 division!!

[grlee77]

I am wondering if it is not simpler to forbid the cases K1=0 and K2=0

I was thinking the same thing. We already have a check that they are not negative, so it seems simple to just extend this to forbid zero values and add a test case for that.

[Ouss98]

Thank you for your replies.
Sure, forbidding the case K1 or K2 = 0 can be a solution. However, in the reference paper C1 and C2 (thus K1 and K2) are only introduced to avoid instability of the algorithm.
In the method which I propose, the instability issue is avoided without taking into account arbitrary parameters.