When you step into the world of science you are prone to believe that everything you read in a scientific journal is simply perfect. It must be, right? After peer review and citations and several years, it must be the whole truth.
Several years later, you learn, in a hard way that presented is not 100% true. There is probably a trick used in the described protocol that you need to figure out yourself because the authors "forgot" to mention everything. You will also probably find out that the concentrations should be 5-10 times lower or higher.
And approximately 5 years later, you can just look at the paper and say - no way that this worked well.
Don't get me wrong, a lot of scientific papers are valid, but there are three "classes" of results:
- Poor Conferences, low-impact journals, "promising results" - in other words, not trust them a single word. Those were made from leftovers
- Classical journals, there you will find the results that are nor wrong, but if your life depends on them - good luck...
- Real contributions, battle-hardened, tested in medicine, space, engineering and industry (not Theranos scam)
Fractals and Images
As you know, fractals are cool looking psychedelic lines, like those tree-like structures:
You can also play with fractals if you visit: https://www.cs.unm.edu/~joel/PaperFoldingFractal/paper.html it's ok, it's safe
Now it's time for some real applications.
Imagine that you have a line, of the size X.
If you double the X, the surface becomes X^2 and the volume becomes X^3.
So... What would happen if the one-dimensional fractal lengths are doubled? What would be the spatial content of that fractal? It does not need to be an integer (1 - line, 2 - surface), it can be any number between, 1.57 or 1.73. And that number can tell us some very subtle differences in texture, or in type/ shape of objects.
There is yet another useful property, and it's lacunarity. If you speak some of Roman languages, you will understand that it's some measure of the gaps between the fractals while they fill the space between. And this is what bothers me...
How to...
Recently, I'm in ImageJ mood. Matlab became a bit boring, like a too long relationship.
And there is a handy plugin called FracLac. The colour scheme includes violet and light blue and makes my eyes popping out.
The inspiration came from this article, but my intuition was buzzing.
Let's do some analysis
Freshly baked mitochondria, FracLac... Go!
Db = 1.2893 Mean Lac = 1.5468
And if I select it just a bit differently, because there is no objective rule how to do it...
Db = 1.3998 Mean Lac = 1.4008
Wonderful Method...
Soooo robust and reliable like a cat!
Is it possible to use fractal dimension as a tool for feature extraction / texture analysis? Yes...
However...
Never fully trust the publications, ask a Pro ;)