Normal Vector Voting: Crease Detection and Curvature Estimation on Large, Noisy Meshes

This paper describes a robust method for crease detection and curvature estimation on large, noisy triangle meshes. We assume that these meshes are approximations of piecewise-smooth surfaces derived from range or medical imaging systems and thus may exhibit measurement or even registration noise. The proposed algorithm, which we call normal vector voting, uses an ensemble of triangles in the geodesic neighborhood of a vertex-instead of its simple umbrella neighborhood-to estimate the orientation and curvature of the original surface at that point. With the orientation information, we designate a vertex as either lying on a smooth surface, following a crease discontinuity, or having no preferred orientation. For vertices on a smooth surface, the curvature estimation yields both principal curvatures and principal directions while for vertices on a discontinuity we estimate only the curvature along the crease. The last case for no preferred orientation occurs when three or more surfaces meet to form a corner or when surface noise is too large and sampling density is insufficient to determine orientation accurately. To demonstrate the capabilities of the method, we present results for both synthetic and real data and compare these results to the G. Taubin (1995, in Proceedings of the Fifth International Conference on Computer Vision, pp. 902-907) algorithm. Additionally, we show practical results for several large mesh data sets that are the motivation for this algorithm.