Differentials-Based Segmentation and Parameterization for Point-Sampled Surfaces

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 differentialslbased 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.