AFSMWD: A Descriptor Flexibly Encoding Multiscale and Oriented Shape Features

Ling Hu, Haibo Wang, Xuguang Yang, Haojun Xu and Yongzhong Liao ()
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Ling Hu: School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China
Haibo Wang: Institute of Engineering Modeling and Scientific Computing, Central South University, Changsha 410083, China
Xuguang Yang: School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China
Haojun Xu: Institute of Engineering Modeling and Scientific Computing, Central South University, Changsha 410083, China
Yongzhong Liao: School of Mechanical and Electrical Engineering, Changsha Institute of Technology, Changsha 410004, China

Mathematics, 2024, vol. 12, issue 18, 1-15

Abstract: Shape descriptors are extensively used in shape analysis tasks such as shape correspondence, segmentation and retrieval, just to name a few. Their performances significantly determine the efficiency and effectiveness of subsequent applications. For this problem, we propose a novel powerful descriptor called Anisotropic Fractional Spectral Manifold Wavelet Descriptor (AFSMWD), built upon an extended manifold signal processing tool named Anisotropic Fractional Spectral Manifold Wavelet (AFSMW), which is also presented for the first time in this paper. The novelty of AFSMW is integrating the fractional theory into the common anisotropic spectral manifold wavelet. Compared to the existing wavelets, it provides one more new parameter, namely, the fractional order, to balance or enhance the transform coefficients among different shape vertices, enabling more flexible local shape analysis and more hidden shape structural information explored. Due to the advantages of this added parameter and the capability of analyzing shape features from multiple scales and orientations, the AFSMW allows us to construct the powerful descriptor AFSMWD just using the AFSMW transform coefficients of a very simple function. The proposed descriptor appears to be especially localizable, discriminative, and robust to noises. Extensive experiments have demonstrated that our descriptor has outperformed the state-of-the-art descriptors, nearly achieving 22% improvements to the most related work ASMWD and 69% to the recent popular work WEDS on the FAUST dataset. Its superiorities are also announced in some challenging occasions such as shapes with large deformation or topological partiality.

Keywords: shape descriptor; spectral manifold wavelet; fractional order (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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