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3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve

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Abstract

3D non-rigid shape similarity is a meaningful and challenging task in deformable shape analysis. In this paper, we present a 3D non-rigid shape similarity measure framework based on Laplace-Beltrami operator which achieves the state-of-the-art performance in shape analysis tasks. The presented framework is used to measure 3D non-rigid shape similarity by calculating the Fréchet distance between the shape spectral distances distribution curves extracting geometry and topology information of shapes. Here, the wave diffusion distance within shape spectral distances is selected because it can describe the shape with high accuracy and does not depend on the time parameter. In addition, our framework is more flexible and computationally efficient: it can be generalized to any distance distribution curves and different distances between the shape distances distribution curves. Experiment results show that the proposed framework can measure 3D non-rigid shape similarity accurately and robustly on benchmarks and have good performance in 3D non-rigid shape retrieval.

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Acknowledgements

The authors would like to thank the anonymous reviewers for their constructive comments. This research was partially supported by the National Key Cooperation between the BRICS of China(No.2017YFE0100500), National Key R&D Program of China (No. 2017YFB1002604) and Beijing Natural Science Foundation of China (No.4172033).

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Authors and Affiliations

  1. School of Artificial Intelligence, Beijing Normal University, Beijing, China

    Dan Zhang, Zhongke Wu, Xingce Wang, Chenlei Lv & Mingquan Zhou

  2. Engineering Research Center of Virtual Reality and Applications, Ministry of Education, Beijing Key Laboratory of Digital Preservation and Virtual Reality for Cultural Heritage, Beijing Normal University, Beijing, 100875, China

    Dan Zhang, Zhongke Wu, Xingce Wang, Chenlei Lv & Mingquan Zhou

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  1. Dan Zhang
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  2. Zhongke Wu
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Correspondence to Xingce Wang.

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Zhang, D., Wu, Z., Wang, X. et al. 3D non-rigid shape similarity measure based on Fréchet distance between spectral distance distribution curve. Multimed Tools Appl 80, 615–640 (2021). https://doi.org/10.1007/s11042-020-09420-5

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