In this paper, we present an object-centric, fixeddimensional 3D shape representation for robust matching of partially observed object shapes, which is an important component for object categorization from 3D data. A main problem when working with RGB-D data from stereo, Kinect, or laser sensors is that the 3D information is typically quite noisy. For that reason, we accumulate shape information over time and register it in a common reference frame. Matching the resulting shapes requires a strategy for dealing with partial observations. We therefore investigate several distance functions and kernels that implement different such strategies and compare their matching performance in quantitative experiments. We show that the resulting representation achieves good results for a large variety of vision tasks, such as multi-class classification, person orientation estimation, and articulated body pose estimation, where robust 3D shape matching is essential.