Spatially aggregating spectral descriptors for nonrigid 3D shape retrieval: a comparative survey

This paper presents a comprehensive review and analysis of recent spectral shape descriptors for nonrigid 3D shape retrieval. More specifically, we compare the latest spectral descriptors based on the Laplace–Beltrami (LB) operator, including ShapeDNA, heat kernel signature, scale invariant heat kernel signature, heat mean signature, wave kernel signature, and global point signature. We also include the eigenvalue descriptor (EVD), which is a geodesic distance-based shape signature. The global descriptors ShapeDNA and EVD are compared via the chi-squared distance, while all local descriptors are compared using the codebook model. Moreover, we investigate the ambiguity modeling of codebook for the densely distributed low-level shape descriptors. Inspired by the ability of spatial cues to improve discrimination between shapes, we also propose to adopt the isocontours of the second eigenfunction of the LB operator to perform surface partition, which can significantly ameliorate the retrieval performance of the time-scaled local descriptors. In addition, we introduce an intrinsic spatial pyramid matching approach in a bid to further enhance the retrieval accuracy. Extensive experiments are carried out on two 3D shape benchmarks to assess the performance of the spectral descriptors. Our proposed approach is shown to provide the best performance.