Here is the function that calculates the folding index and intrinsic curvature 
index of the surface - 
https://github.com/freesurfer/freesurfer/blob/dev/utils/mrisurf_metricProperties.cpp#L11335

int MRIScomputeCurvatureIndices(MRIS *mris, double *pici, double *pfi)
{
  int vno;
  VERTEX *vertex;
  double k1, k2, ici, fi, area, Kmax, Kmin;

  ici = fi = 0.0;
  for (vno = 0; vno < mris->nvertices; vno++) {
    vertex = &mris->vertices[vno];
    if (vertex->ripflag) {
      continue;
    }
    if (vno == Gdiag_no) {
      DiagBreak();
    }
    k1 = (double)vertex->k1;
    k2 = (double)vertex->k2;
    area = (double)vertex->area;
    if (vertex->K > 0) {
      ici += area * (double)vertex->K;
    }
    Kmax = (double)fabs(k1);
    Kmin = (double)fabs(k2);
    fi += area * Kmax * (Kmax - Kmin);
  }

  *pfi = fi / (4.0 * M_PI);
  *pici = ici / (4.0 * M_PI);
  return (NO_ERROR);
}

From: [email protected] 
<[email protected]> On Behalf Of littlepotato
Sent: Friday, August 2, 2024 5:40 AM
To: [email protected]
Subject: [Freesurfer] Inquiry on Calculation Methods for Folding Index and 
Intrinsic Curvature Index in mris_anatomical_stats


        External Email - Use Caution

Dear FreeSurfer Support Team,
I am writing to inquire about the specific methods and formulas used by the 
mris_anatomical_stats function in Freesurfer to calculate the Folding Index and 
Intrinsic Curvature Index for each label based on annotation files.  Could you 
please provide detailed information on: the algorithms or mathematical formulas 
used to calculate the Folding Index and  Intrinsic Curvature Index for each 
label.

If there are any available documentation, publications, or example commands 
illustrating these calculations, I would greatly appreciate your sharing them.

Thank you for your assistance.

Best regards,

Amber Lin
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