Nice post. Some questions/comments:
Spatial content of an object is not a uniquely defined. It depends on how you measure spatial content. For example, a one dimensional fractal still has dimension one in terms of topological dimension, but its box counting dimension might be greater than one.
What is Db? (Box counting dimension maybe?)
On a quick glance it seems that the article gives bounds Db and Mean lac to derive properties. So it it is not really a constant but more a very rough guess. If I understand it correctly they say that they use the whole mitochondria for the computation.
It was box-counting... I wanted to try Higuchi, but I didn't have Matlab on that computer: https://revistas.eia.edu.co/index.php/Reveiaenglish/article/download/1206/1128
Db,
Page 12, https://imagej.nih.gov/ij/plugins/fraclac/fraclac-manual.pdf
This approach is very new, and I'm not 100% sure what should I look at...
The first idea was to do some texture analysis, because under the stress / normal conditions, MTH should change their shape from "rod-like" to "cirlce-like".
But it was very bad and not reliable...
Then I've found this MiNa Plug-in, but in reality (poor contrast, overlapped MTH, noise) and it was subjective.
After I've found this tool for Z-stacks but it's also a complete mess with real-life images.
My next attempt was, ok, back to "textures", now with some fractals. In the paper, they obtained an incredibly linear dependence between the "network of MTH" and level of stress. But in reality - it was again subjective.
At the end, I've found that some people used machine learning to distinguish the proportion of 4 different shapes of MTH.
Probably that would be the only solution, to make particles out of them, manually select them into the categories (I have no clear idea how many of them) and after a harsh training - to try...
I'm constantly seeing such hardly reproducible, subjective analyses that are beautifully packed into some statistics so every biologist can say - woooow!!! It's so perect!
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