Anisotropic Spectral Manifold Wavelet Descriptor

Abstract

In this paper, we present a powerful spectral shape descriptor for shape analysis, named Anisotropic Spectral Manifold Wavelet Descriptor (ASMWD). We proposed a novel manifold harmonic signal processing tool termed Anisotropic Spectral Manifold Wavelet Transform (ASMWT) first. ASMWT allows to comprehensively analyse signals from multiple wavelet diffusion directions on local manifold regions of the shape with a series of low‐pass and band‐pass frequency filters in each direction. Based on the ASMWT coefficients of a very simple signal, the ASMWD is efficiently constructed as a localizable and discriminative multi‐scale point descriptor. Since the wavelets used in our descriptor are direction‐sensitive and able to robustly reconstruct the signals with a finite number of scales, it makes our descriptor compact, efficient, and unambiguous under intrinsic symmetry. The extensive experiments demonstrate that our descriptor achieves significantly better performance than the state‐of‐the‐art descriptors and can greatly improve the performance of shape matching methods including both handcrafted and learning‐based methods.