Differentials-Based Segmentation and Parameterization for Point-Sampled Surfaces

Abstract

Efficient parameterization of point-sampled surfaces is a fundamental problem in the field of digital geometry processing. In order to parameterize a given point-sampled surface for minimal distance distortion, a differentials-based segmentation and parameterization approach is proposed in this paper. Our approach partitions the point-sampled geometry based on two criteria: variation of Euclidean distance between sample points, and angular difference between surface differential directions. According to the analysis of normal curvatures for some specified directions, a new projection approach is adopted to estimate the local surface differentials. Then a k-means clustering (k-MC) algorithm is used for partitioning the model into a set of charts based on the estimated local surface attributes. Finally, each chart is parameterized with a statistical method -- multidimensional scaling (MDS) approach, and the parameterization results of all charts form an atlas for compact storage.