Estimating Principal Curvatures and Principal Directions from Discrete Surfaces Using Discrete Curve Model

摘要

Accurate estimation of the principal curvatures and principal directions from discrete surfaces is an important problem in many applications. In this paper, a novel method is proposed for estimating the principal curvatures and principal directions from discrete surfaces. In the proposed method, the local discrete surface is modeled by a set of discrete curves. This discrete curve model has much more degrees of freedom, and therefore can better represent the local surface geometry. Based on the geometric properties of the discrete curves, which are calculated by using the definitions of the discrete derivatives, we can estimate the principal curvatures and principal directions from discrete surfaces according to the Euler formula. The proposed method is independent of any analytic curve or surface, and estimates the principal curvatures and principal directions directly from discrete data points, which makes it suitable for different geometric shapes of discrete surfaces. Furthermore, because of the discrete derivatives, the proposed method shows more robustness to noise. The experimental results demonstrate that the proposed method has good performance, and is robust to noise and suitable for different surface shapes.