Curvature-based spectral signatures for non-rigid shape retrieval

Abstract The geometric properties of descriptors derived from the diffusion geometry family have many valuable properties for shape analysis. These descriptors, also known as diffusion distances, use the eigenvalues and eigenfunctions of the Laplace–Beltrami operator to construct invariant metrics about the shape. Although they are invariant to many transformations, non-rigid deformations still modify the shape spectrum. In this paper, we propose a shape descriptor framework based on a Lagrangian formulation of dynamics on the surface of the object. We show how our framework can be applied to non-rigid shape retrieval, once it benefits from the analysis and the automatic identification of shape joints, using a curvature-based scheme to identify these regions. We also propose modifications to the Improved Wave Kernel Signature in order to keep descriptors more stable against non-rigid deformations. We compare our spectral components with the classic ones and our spectral framework with state-of-the-art non-rigid signatures on traditional benchmarks, showing that our shape spectra is more stable and discriminative and clearly outperforms other descriptors in the SHREC’10, SHREC’11 and SHREC’17 benchmarks.