Graph-Based Shape Analysis for Heterogeneous Geometric Datasets: Similarity, Retrieval and Substructure Matching

Practically all existing shape analysis and processing algorithms have been developed for specific geometric representations of 3D models. However, the product development process always involves a large number of often incompatible geometric representations tailored to specific computational tasks that take place during this process. Consequently, a substantial effort has been expended to develop robust geometric data translation and conversion algorithms, but the existing methods have well known limitations. The Maximal Disjoint Ball Decomposition (MDBD) was recently defined as a unique and stable geometric construction and used to define universal shape descriptors based on the contact graph associated with MDBD. In this paper, we demonstrate that by applying graph analysis tools to MDBD in conjunction with graph convolutional neural networks and graph kernels, one can effectively develop methods to perform similarity, retrieval and substructure matching from geometric models regardless of their native geometric representation. We show that our representation-agnostic approach achieves comparable performance with state-of-the-art geometric processing methods on standard yet heterogeneous benchmark datasets while supporting all valid geometric representations.