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Computational Visual Media 2023, 9(3): 461-477 https://doi.org/10.1007/s41095-022-0290-8
Research Article | Open Access | Issue | Published: 21 March 2023

An anisotropic Chebyshev descriptor and its optimization for deformable shape correspondence

Show Author's Information Shengjun Liu1,  Hongyan Liu1,  Wang Chen1,  Dong-Ming Yan2,  Ling Hu3,  Xinru Liu1,  Qinsong Li4( )
School of Mathematics and Statistics, Central South University, Changsha 410000, China
State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China, and School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 101408, China
School of Mathematics and Statistics, Hunan First Normal University, Changsha 410000, China
Big Data Institute, Central South University, Changsha 410000, China
Keywords:
deep learning, shape matching, shape descriptor, anisotropic descriptor, spectral descriptor, spectral convolution
Cite this article:
Liu S, Liu H, Chen W, et al. An anisotropic Chebyshev descriptor and its optimization for deformable shape correspondence. Computational Visual Media, 2023, 9(3): 461-477. https://doi.org/10.1007/s41095-022-0290-8
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Abstract Full text About this article

Shape descriptors have recently gained popularity in shape matching, statistical shape mode-ling, etc. Their discriminative ability and efficiency play a decisive role in these tasks. In this paper, we first propose a novel handcrafted anisotropic spectral descriptor using Chebyshev polynomials, called the anisotropic Chebyshev descriptor (ACD); it can effec-tively capture shape features in multiple directions. The ACD inherits many good characteristics of spectral descriptors, such as being intrinsic, robust to changes in surface discretization, etc. Furthermore, due to the orthogonality of Chebyshev polynomials, the ACD is compact and can disambiguate intrinsic symmetry since several directions are considered. To improve the ACD’s discrimination ability, we construct a Chebyshev spectral manifold convolutional neural network (CSMCNN) that optimizes the ACD and produces a learned ACD. Our experimental results show that the ACD outperforms existing state-of-the-art handcrafted descriptors. The combination of the ACD and the CSMCNN is better than other state-of-the-art learned descriptors in terms of discrimination, efficiency, and robustness to changes in shape resolution and discretization.


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About this article

An anisotropic Chebyshev descriptor and its optimization for deformable shape correspondence

Show Author's information Shengjun Liu1, Hongyan Liu1, Wang Chen1, Dong-Ming Yan2, Ling Hu3, Xinru Liu1, Qinsong Li4( )
School of Mathematics and Statistics, Central South University, Changsha 410000, China
State Key Laboratory of Multimodal Artificial Intelligence Systems, Institute of Automation, Chinese Academy of Sciences, Beijing 100190, China, and School of Artificial Intelligence, University of Chinese Academy of Sciences, Beijing 101408, China
School of Mathematics and Statistics, Hunan First Normal University, Changsha 410000, China
Big Data Institute, Central South University, Changsha 410000, China

Abstract

Shape descriptors have recently gained popularity in shape matching, statistical shape mode-ling, etc. Their discriminative ability and efficiency play a decisive role in these tasks. In this paper, we first propose a novel handcrafted anisotropic spectral descriptor using Chebyshev polynomials, called the anisotropic Chebyshev descriptor (ACD); it can effec-tively capture shape features in multiple directions. The ACD inherits many good characteristics of spectral descriptors, such as being intrinsic, robust to changes in surface discretization, etc. Furthermore, due to the orthogonality of Chebyshev polynomials, the ACD is compact and can disambiguate intrinsic symmetry since several directions are considered. To improve the ACD’s discrimination ability, we construct a Chebyshev spectral manifold convolutional neural network (CSMCNN) that optimizes the ACD and produces a learned ACD. Our experimental results show that the ACD outperforms existing state-of-the-art handcrafted descriptors. The combination of the ACD and the CSMCNN is better than other state-of-the-art learned descriptors in terms of discrimination, efficiency, and robustness to changes in shape resolution and discretization.

Keywords: deep learning, shape matching, shape descriptor, anisotropic descriptor, spectral descriptor, spectral convolution

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Publication history
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Publication history

Received: 17 February 2022
Accepted: 28 April 2022
Published: 21 March 2023
Issue date: September 2023

Copyright

© The Author(s) 2023.

Acknowledgements

We acknowledge the anonymous reviewers for their valuable comments. This work was supported by the National Natural Science Foundation of China (Nos. 62172447, 61876191), Hunan Provincial Natural Science Foundation of China (No. 2021JJ30172), and the Open Project Program of the National Laboratory of Pattern Recognition (NLPR) (No. 202200025).

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