Hi, Clément-

That sounds a reasonable thing to do: ReHo should provide a measure of homogeneity of time series across ROIs.

Re. "Since I increase the number of regions and so the number of subdivisions in each atlas I may expect a relatively linear increase of the mean ReHo for each atlas?"
Well, I'm not sure about that. I don't really know what to expect, to be honest. I don't know what to expect as ROIs get larger. I guess you will just have to calculate and find out.

In my view, how you equate ROIs across the different ICA splits seems harder-- inherently, at each level you will have a different number of ROIs, so how will you track the splits? (And indeed, people always talk about ICA being "data driven" and better than seedbased correlation for providing non seed-location-driven maps, but the number of ICs selected *heavily* affects the output maps and divisions of networks...)

Re. "Does this will really identify an atlas that could be 'ideal' for a correlation matrix analysis?"
Well, I don't know about being able to define and *ideal* correlation matrix-- my guess is that smaller ROIs have a better chance of being homogeneous: consider, an ROI of one voxel has a pretty homogeneous time series! So, there are probably other considerations than just homogeneity that one might want to account for. However, as a general way to proceed, looking at homogeneity seems useful; how that is balanced with size of ROIs, for example, is a separate (and harder?) question.

NB: based on this recent thread:
[afni.nimh.nih.gov]
... I have updated the output format of the ROI-based ReHo calcs to a (hopefully) nicer format. So, you might want to update your AFNI version before embarking on these calcs:

@update.afni.binaries -d

--pt