sh2amp will indeed be the key to this. Other than that, to pitch in to this particular one:
I think I’m getting what you’re after or might be thinking about; but just something to take into account: it might look like an FOD (with only one peak, or in any case) has pretty narrow lobes due to how it’s rendered with the radius scaling type of visualisation we’re used to looking at (the “3D” FODs we all look at in the viewer), but that’s sometimes a bit deceiving. The angle to which you can still sample a positive amplitude is pretty wide actually. Also, beyond that, the amplitude will not hit a “constant” zero for the rest of the angular domain. Instead, you’ll get a Gibbs effect: it’ll briefly dip below zero and start to then Gibbs-style over and undershoot around zero (at best). This matters for what you’re trying to measure / extract here:
sh2amp only gives you discrete samples for a predefined set of orientations, so it’s hard to get from that the exact extent to which the “lobe stretches”.
What I’d recommend to get something like this more robustly, is to basically apply a small amplitude threshold, just like we do to segment fixels or perform tractography: essentially within those commands/algorithms, the threshold is the thing that says “here’s where the lobe ends, the rest might just be noise or something else undesirable”. So at a high level, to get the thing you’re after, you could do something along the lines of:
- Get the peaks (and thus their orientation) itself via
- Sample the FOD via
sh2amp for a relatively dense set of orientations.
- Then threshold the output of this to the small amplitude I mentioned. Use a similar value you’d use for fixel segmentation or tractography, e.g. 0.06 or something similar.
- After this thresholding, find the orientation among those that survived the threshold (i.e. the set of orientations “part of” the lobe) which has the largest angle with the peak you got earlier from
- This is the angle you’re after (up to a limited precision, which relates directly to the density of the FOD sampling you used for
If you can assume up front that the FODs for which you do this only have one large main peak (and the next peak in line is basically very small, or just noise or Gibbs effect related; and thus falls below the applied threshold in the above process), this should be very robust.