Medial Spectral Coordinates for 3D Shape Analysis

In recent years there has been a resurgence of interest in our community in the shape analysis of 3D objects represented by surface meshes, their voxelized interiors, or surface point clouds. In part, this interest has been stimulated by the increased availability of RGBD cameras, and by applications of computer vision to autonomous driving, medical imaging, and robotics. In these settings, spectral coordinates have shown promise for shape representation due to their ability to incorporate both local and global shape properties in a manner that is qualitatively invariant to isometric transformations. Yet, surprisingly, such coordinates have thus far typically considered only local surface positional or derivative information. In the present article, we propose to equip spectral coordinates with medial (object width) information, so as to enrich them. The key idea is to couple surface points that share a medial ball, via the weights of the adjacency matrix. We develop a spectral feature using this idea, and the algorithms to compute it. The incorporation of object width and medial coupling has direct benefits, as illustrated by our experiments on object classification, object part segmentation, and surface point correspondence.