Peter Savadjiev1, Yogesh Rathi1, Martha E. Shenton1, Sylvain Bouix1, Carl-Fredrik Westin2
1Psychiatry Neuroimaging Laboratory, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States; 2Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States
We introduce a novel method for computing multi-scale fibre tract shape and geometry based on the differential geometry of curve sets. By measuring the variation of a curve's tangent vector at a given point in all directions orthogonal to the curve, we obtain a ``2D dispersion orientation distribution function (ODF)'' at that point. That is, we compute a function on the unit circle which describes the extent to which the fibres disperse, or fan, along each direction on the circle. Our formulation is then easily incorporated into a continuous scale-space framework.