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Part-in-whole matching of rigid 3D shapes using geodesic disk spectrum

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Abstract

Part-in-whole matching of rigid 3D shapes has attracted great interest in shape analysis and has various applications in computational archaeology. Rigid part-in-whole matching algorithms are mainly based on methods minimizing geometric distances and methods using local shape descriptors, which are challenging when the partial shapes are relatively small and smooth. This paper proposes a part-in-whole matching algorithm of rigid 3D shapes using geodesic disk spectrum (GDS), which achieves accurate matching results for partial shapes with arbitrary boundaries or smooth appearances. The largest enclosing geodesic disk of the partial shape and geodesic disks on the complete shape are extracted in the matching process. GDS is used as the matching descriptor, which is the distribution of shape index for enclosing points of the disk. The problem of matching partial surfaces with arbitrarily irregular boundaries to the complete shape is transformed into the matching of geodesic disks with the same radius using the proposed algorithm. GDS is discriminative, which can handle the situation when partial surfaces have few distinctive features. The proposed algorithm has been tested on various partial surfaces and obtained accurate matching results. A higher precision is achieved by comparing with existing part-in-whole matching algorithms, which proves the efficiency of the proposed algorithm.

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Acknowledgements

This research was carried out at Beijing Normal University, with the financial support of National Natural Science Foundation of China (61672103, 61572078, 61402042, and 61731015).

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Authors and Affiliations

  1. College of Information Science and Technology, Beijing Normal University, No.19, XinJieKouWai ST., HaiDian District, Beijing, 100875, People’s Republic of China

    Guoguang Du, Congli Yin, Mingquan Zhou, Zhongke Wu & Fuqing Duan

  2. Key Laboratory of Digital Protection and Virtual Reality for Cultural Heritage, Beijing, People’s Republic of China

    Guoguang Du, Congli Yin, Mingquan Zhou, Zhongke Wu & Fuqing Duan

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  1. Guoguang Du
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  2. Congli Yin
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  3. Mingquan Zhou
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  4. Zhongke Wu
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  5. Fuqing Duan
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Correspondence to Mingquan Zhou.

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Du, G., Yin, C., Zhou, M. et al. Part-in-whole matching of rigid 3D shapes using geodesic disk spectrum. Multimed Tools Appl 77, 18881–18901 (2018). https://doi.org/10.1007/s11042-017-5315-4

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  • DOI: https://doi.org/10.1007/s11042-017-5315-4

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