Questionable results from FracLac fractal dimension analysis

So I’m trying to calculate fractal dimension for different vessel networks, here is an example:
729 WT_c1 V2 Binary RLQ Periphery.tif (61.2 KB)

I am using the plugin FracLac, and a basic box counting method leads to this kind of graph:

In the lower end of epsilon (or the box size), the count reaches a plateau which is expected. However, I thought that FracLac should be automatically stopping the analysis once it reaches plateaus like these at the higher and lower ends to the box sizes, since they can skew the results.

I am concerned that FracLac is not giving me reliable results. What should I do?

Thanks,
MichelN

Note: Using FIJI 1.53j

I think this might be a methodological issue, rather than unreliable results from the program.
First, you could use log-sized boxes so the log-log plot is not driven by the too-many points on the right hand side of the plot.
Second, you could/should discard the part of the plot where the same repeated values appear (as it obviously it is not capturing the relation that is expected, or it just not fractal at those scales).
Since most natural objects might show scaling over a limited range of scales, think carefully what is that range and report that according to the real-size ranges of the the object. That stepped function that appears at epsilon of 3.5 is showing that the box increments are not detecting any scaling when you change epsilon. That is why I suggested log increments.

But in any event, with natural objects, this is always a probabilistic ‘estimation’ of D and as such it depends on other things that you are not controlling, like the initial position of the boxes. If you move the set around a tiny bit it might change the number of filled boxes. To avoid that effect, some people use many random positions of the grids and average the number of filled boxes.
Hope it helps.

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This definitely helps, thank you very much! I’ve run into other difficulties, but I will leave those for another time.

Cheers,
MichelN