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.

中文翻译：

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各向异性谱流形小波描述符

在本文中，我们提出了一种用于形状分析的功能强大的光谱形状描述符，称为各向异性光谱歧管小波描述符（ASMWD）。我们首先提出了一种新颖的歧管谐波信号处理工具，称为各向异性谱流形小波变换（ASMWT）。ASMWT允许在形状的局部流形区域上的多个小波扩散方向上综合分析信号，并在每个方向上使用一系列低通和带通频率滤波器。基于一个非常简单的信号的ASMWT系数，ASMWD被有效地构造为可本地化和区分性的多尺度点描述符。由于描述符中使用的小波具有方向敏感性，并且能够以有限数量的标度稳健地重构信号，因此使描述符变得紧凑，高效，在内在对称性下毫不含糊。广泛的实验表明，我们的描述符比最先进的描述符具有明显更好的性能，并且可以大大改善形状匹配方法（包括手工方法和基于学习的方法）的性能。