Ridges and umbilics of a sampled smooth surface: a complete picture gearing toward topological coherence

Abstract: Consider a smooth surface, and at each point which is not an umbilic, respectively paint in blue (red) anything related to the maximum (minimum) principal curvature. Given such a surface, a blue (red) ridge is a curve on the surface such that at each of its points, the principal blue (red) curvature has an extremum,along its blue (red) curvature line. Ridges are curves of extremal curva- ture and therefore encode important informations used in segmentation, registration, matching and surface analysis. Surprisingly, no method developed so far to report ridges from a mesh approximating a smooth