Geometric moment-based spectral descriptors for robust non-rigid 3D shape analysis.

Abstract

Numerous 3D shape descriptors have been proposed in recent years, among which spectral descriptors have gained significant prominence. However, widely used spectral signatures, such as the Heat Kernel Signature (HKS), Scale-Invariant HKS (SIHKS), and Wave Kernel Signature (WKS), suffer from parameter dependence, where heuristic and sub-optimal scale selection limits their robustness and generalizability. To address this limitation, this paper introduces a novel class of descriptors termed Geometric Moments of Spectral Shape Descriptors (GMSDs). By integrating temporal and spatial domains, GMSDs leverage invariant moment theory to calculate six moment terms, creating a theoretical framework that significantly enhances performance in non-rigid 3D shape analysis. GMSDs not only inherit the desirable properties of standard spectral signatures, such as isometric invariance and robustness to noise and topological changes, but also effectively mitigate parameter sensitivity. Extensive experiments on the TOSCA, SCAPE, SHREC 2011, and SHREC 2015 benchmarks demonstrate that GMSDs achieve superior performance in both shape correspondence and retrieval tasks compared to state-of-the-art methods.