Hybrid Entropy

I think I have Hybrid Entropy working - and it was a lot quicker to implement than I had anticipated. Maybe I was comparing it to Non-Probabilistic Entropy (formally referred to as De Luca) and the time in which it took me to implement that, however I had to complete far more ground work for that, which Hybrid sort of piggybacks off of.

Let's get up some screenshots:

You'll notice there's now an elapsed time line - I added this to keep an eye on performance.

The mean per each iteration

The adjusted input images.

Working?

I think so, however I am reluctant to write this off as a success just yet as the mathematics behind it was one of the trickier ones.

Sander's original hybrid entropy ¹, took just two items, Symbol 0 and Symbol 1, whereas we have 3 - low, medium & high grey-level values. This meant Neil and I had to sit down and work through how we could modify the existing solution to fit our own needs, and this caused a lot of confusion.

So until I can show Neil and see that he's happy with the outputs, I'm not quite calling this one a success.

So how does it compare?

This is interesting, as we can see on Iteration 3 it finds a local optima, however continues to find a more optimal solution on Iteration 5.

Interesting to note how much slower Non-Probabilistic Entropy is compared to the other two - this may be indicating to more optimisation needed.

Shannon Entropy cannot really be compared to it's Fuzzy Entropy counter-parts, so we will just focus on comparing them. As expected, Hybrid (being both probabilistic and possibilistic) retains the lowest entropy, however it is interesting that Non-Probabilistic has the biggest decline (maybe because it started so much higher?).

For now I'm counting this as working however this is subject to change once I speak to Neil - I'm sure there will be an update in an upcoming Weekly Post!