Processing of textured surfaces represented as surfel sets: representation, compression and geodesic paths

A method for representation and lossy compression of textured surfaces is presented. The input surfaces are represented by surfels (surface elements), i.e., by a set of colored, oriented, and sized disks. The position and texture of each surfel are mapped onto a sphere. The mapping is optimized for preservation of geodesic distances. The components of the resulting spherical vector-valued function are decorrelated by the Karhunen-Loeve transform and represented by spherical wavelets. Successful representation and reconstruction is demonstrated. Methods for geodesic distance computation on surfaces represented by surfels are presented.