Robust Crease Detection and Curvature Estimation of Piecewise Smooth Surfaces from Triangle Mesh Approximations Using Normal Voting

David L. Page, Andreas F. Koschan, Yiyong Sun, Joon Ki Paik, Mongi A. Abidi

Abstract: In this paper, we describe a robust method for the estimation of curvature on a triangle mesh, where this mesh is a discrete approximation of a piecewise smooth surface. The proposed method avoids the computationally expensive process of surface fitting and instead employs normal voting to achieve robust results. This method detects crease discontinuities on the surface to improve estimates near those creases. Using a voting scheme, the algorithm estimates both principal curvatures and principal directions for smooth patches. The entire process requires one user parameter-the voting neighborhood size, which is a function of sampling density, feature size, and measurement noise. We present results for both synthetic and real data and compare these results to an existing algorithm developed by Taubin (1995).