Curvature Estimation of Point Set Data Based on the Moving-Least Square Surface

Curvature estimation is a basic step in many point relative applications such as feature recognition, segmentation, shape analysis and simplification. This paper proposes a moving-least square （MLS） surface based method to evaluate curvatures for unorganized point cloud data. First a variation of the projection based MLS surface is adopted as the underlying representation of the input points. A set of equations for geometric analysis are derived from the implicit definition of the MLS surface. These equations are then used to compute curvatures of the surface. Moreover, an empirical formula for determining the appropriate Gaussian factor is presented to improve the accuracy of curvature estimation. The proposed method is tested on several sets of synthetic and real data. The results demonstrate that the MLS surface based method can faithfully and efficiently estimate curvatures and reflect subtle curvature variations. The comparisons with other curvature computation algorithms also show that the presented method performs well when handling noisy data and dense points with complex shapes.