Differentials-based segmentation and parameterization for point-sampled surfaces

Efficient parameterization of point-sampled surfaces is afundamental problem in the field of digital geometry processing. Inorder to parameterize a given point-sampled surface for minimaldistance distortion, a differentials-based segmentation andparameterization approach is proposed in this paper. Our approachpartitions the point-sampled geometry based on two criteria:variation of Euclidean distance between sample points, and angulardifference between surface differential directions. According to theanalysis of normal curvatures for some specified directions, a newprojection approach is adopted to estimate the local surfacedifferentials. Then a k-means clustering (k-MC) algorithm isused for partitioning the model into a set of charts based on theestimated local surface attributes. Finally, each chart isparameterized with a statistical method --- multidimensional scaling(MDS) approach, and the parameterization results of all charts forman atlas for compact storage.