Sparse surface modeling with curved patches

Traditional segmentation algorithms for range images create partitions of connected and non-overlapping-but potentially irregularly shaped-regions corresponding to world surfaces. This paper presents an alternative paradigm based on regularly shaped curved patches (paraboloids) that model local contact regions potentially compatible with e.g. a robot´s toe, heel, or fingertip. These patches randomly sample the environment surface but are not required to strictly partition it. They are fit to neighborhoods of the range data and then validated for fit quality and fidelity to the actual data-extrapolations (like hole-filling) which are not directly supported by data are avoided. Two different neighborhood formation methods based on k-d tree and triangle mesh data structures are compared, and results are presented for 10 datasets taken in natural rocky terrain.