3D shape descriptor design based on HKS and persistent homology with stability analysis

Abstract

In recent years, with the rapid development of the computer aided design and computer graphics, a large number of 3D models have emerged, making it a challenge to quickly find models of interest. As a concise and informative representation of 3D models, shape descriptors are a key factor in achieving effective retrieval. In this paper, we propose a novel global descriptor for 3D models that incorporates both geometric and topological information. We refer to this descriptor as the persistent heat kernel signature descriptor (PHKS). Constructed by concatenating our isometry-invariant geometric descriptor with topological descriptor, PHKS possesses high recognition ability, while remaining insensitive to noise and can be efficiently calculated. Retrieval experiments of 3D models on the benchmark datasets show considerable performance gains of the proposed method compared to other descriptors based on HKS and advanced topological descriptors.