Hi Graham -
First off, your observation that the FI seems correlated with area is completely correct. I'm not sure if you have the FS source code? Anyway, looking at the relevant code in 'mrisurf.c', the
MRIScomputeCurvatureIndices(...)
function pretty much computes the folding index (fi) as
fi += area * Kmax * (Kmax - Kmin) ;
and then, once having summed over the surface, simply divides by
*pfi = fi / (4.0*M_PI) ;
In essence, this is Van Essen's Folding index -- although I personally do have some issues with it. First of all, Van Essen normalizes his measure with 1/4/pi, indicating that the 1/4pi is the "integral for a cylinder the length of which equals its diameter). I seem to think this integral should be (1/2pi)^2, i.e. 1/4/pi^2. Either way, this is merely a fixed constant and doesn't change the behaviour.
And irrespective of the 1/4pi or not, the measure is a strict function of "size", or more accurately, the radius of curvature. Since the curvatures run as the inverse of radius, the curvature values in small sulci/gyri can dominate the 'Folding Index', even if they are 'folded' exactly the same as larger sulci/gyri. In fact, there is nothing really related to 'folding' per se in the measure, so it is arguably something of a misnomer - but I fear I am digressing.
I know Bruce originally wrote the FI into FS, but based on this quick re-analysis, I'm kind of thinking that we should normalize the fi (and ici for that matter) with the area overwhich each measure measure is computed...
*pfi = fi / (4.0*M_PI) / areaCounted;
This makes potentially more sense and removes the area dependency. What do you think, Bruce? -=R