Fast estimation of mean curvature on the surface of a 3D discrete object

Abstract

Discrete surfaces composed of surfels (a surfel is a facet of a voxel) have interesting features. They represent the border of a discrete object and possess the Jordan property. These surfaces, although discrete by nature, represent most of the time real world continuous surfaces for which local geometrical characteristics are useful for registration, segmentation, recognition and measure. We propose a technique designed to estimate the mean curvature field of such a surface. Our approach depends on a scale parameter and has a low computational complexity. It is evaluated on synthetic surfaces, and an application is presented the extraction of sulci on a brain surface.