Fast surface-based measurements using first eigenfunction of the Laplace-Beltrami Operator: Interest for sulcal description

In this paper we propose a fast method to compute the longitudinal extension of surfaces using the extrema of the first eigenfunction of Laplace-Beltrami Operator and the hot spots conjecture. We also propose an original definition of the surface width based on the distance to the longest geodesic. We show that the implementation of our new definition of length is consistent with the one computed from brute force and that the time complexity is considerably improved. We have tested the numerical efficiency of our approach on simple simulations and applied it to cortical surface patches from a real MRI dataset. Besides our approach enriches global descriptors of sulci shapes with a third dimension : length, depth and now width.