Multi-scale object representation using surface patches

We introduce an approach to the representation of curved or polyhedral 3-D objects and apply this representation to pose estimation. The representation is based on surface patches with uniform curvature properties extracted at multiple scales. These patches are computed using multiple alternative decompositions of the surface based on the signs of the mean and Gaussian curvatures. Initial coarse decompositions are subsequently re ned using a curvature compatibilityscheme to rectify the e ect of noise and quantization errors. The extraction of simple uniform curvature features is limited by the fact that the optimal scale of processing for a single object is very di cult to determine. As a solution we propose the segmentation of range data into patches at multiple scales. A hierarchical ranking of these patches is then used to describe individual objects based on geometric information. These geometric descriptors are ranked according to several criteria expressing their estimated stability and utility. The applicability of the resulting multi-scale description is demonstrated by estimating the pose of a 3-D object. Pose estimation is cast as an optimal matching problem. The geometric pose transformation is computed by matching two representations, which amounts to nding the three-patch correspondence that produces the best global consistency. Examples of the multi-scale representation applied to both real and simulated range data are presented. E ective pose estimation is demonstrated and the algorithm's behaviour in the presence of noise is validated