Abstract
Shape descriptors have recently gained popularity in shape matching, statistical shape modeling, 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 effectively 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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Our source code is available at https://github.com/Wang-Chen9/Anisotropic-Chebyshev-Descriptor.
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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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Conceptualization: Shengjun Liu, Ling Hu. Methodology: Qinsong Li. Formal analysis and investigation: Hongyan Liu, Wang Chen, Qinsong Li. Writing—original draft preparation: Hongyan Liu, Wang Chen. Writing—review and editing: Shengjun Liu, Hongyan Liu, Wang Chen, Dong-Ming Yan, Ling Hu, Xinru Liu, Qinsong Li. Funding acquisition: Shengjun Liu, Ling Hu. Supervision: Shengjun Liu, Xinru Liu. All authors read and approved the final manuscript.
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Shengjun Liu is a full professor in the School of Mathematics and Statistics at Central South University, China. His research interests include geometric modeling, reverse engineering, computer graphics, and computer-aided geometric design. Liu has his D.Eng. degree in computer science and technology from Zhejiang University.
Hongyan Liu is a master student in the School of Mathematics and Statistics, Central South University, China, supervised by Prof. Shengjun Liu. Her research interests include geometric processing and 3D vision.
Wang Chen is a master student in the School of Mathematics and Statistics, Central South University, China, supervised by Prof. Xinru Liu. His research interests include geometric processing and 3D vision.
Dong-Ming Yan is a professor at the State Key Laboratory of Multimodal Artificial Intelligence Systems (MAIS) and the National Laboratory of Pattern Recognition of the Institute of Automation, Chinese Academy of Sciences (CAS). He received his Ph.D. degree from Hong Kong University in 2010 and his master and bachelor degrees from Tsinghua University in 2005 and 2002, respectively. His research interests include computer graphics, computer vision, pattern recognition, and AR/VR.
Ling Hu is a lecturer in the School of Mathematics and Statistics at Hunan First Normal University, China. She received her Ph.D. degree from the Central South University, China, in 2019. Her research interests include geometric modeling and 3D vision.
Xinru Liu is an associate professor in the School of Mathematics and Statistics at Central South University, China. He received his Ph.D. degree in applied mathematics and now is working on computer-aided geometric design, numerical optimization, and data mining.
Qinsong Li is a lecturer in Big Data Institute at Central South University, China. He received his Ph.D. degree from Central South University in 2022, supervised by Prof. Shengjun Liu. His research interests include geometric processing and 3D vision.
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Liu, S., Liu, H., Chen, W. et al. An anisotropic Chebyshev descriptor and its optimization for deformable shape correspondence. Comp. Visual Media 9, 461–477 (2023). https://doi.org/10.1007/s41095-022-0290-8
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DOI: https://doi.org/10.1007/s41095-022-0290-8