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A heuristic convexity measure for 3D meshes

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Abstract

In this paper we propose a heuristic convexity measure for 3D meshes. Built upon a state-of-the-art convexity measure that employs a time-consuming genetic algorithm for optimization, our new measure projects only once a given 3D mesh onto the orthogonal 2D planes along its principal directions for an initial estimation of mesh convexity, followed by a correction calculation based on mesh slicing. Our measure experimentally shows several advantages over the state-of-the-art one: first, it accelerates the overall computation by approximately an order of magnitude; second, it properly handles those bony meshes usually overestimated by the state-of-the-art measure; third, it improves the accuracy of the state-of-the-art measure in 3D mesh retrieval.

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Acknowledgements

The authors would like to thank Dr. Lian for his supports and patience in answering our questions. The authors would also like to thank the reviewers for their precious time and constructive comments. This work has been supported by the National Natural Science Foundation of China (61202291).

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Authors and Affiliations

  1. The School of Computer Science and Software Engineering, East China Normal University, Shanghai, 200062, China

    Rui Li, Lei Liu, Yun Sheng & Guixu Zhang

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  1. Rui Li
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  2. Lei Liu
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  3. Yun Sheng
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  4. Guixu Zhang
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Correspondence to Yun Sheng.

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Li, R., Liu, L., Sheng, Y. et al. A heuristic convexity measure for 3D meshes. Vis Comput 33, 903–912 (2017). https://doi.org/10.1007/s00371-017-1385-6

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  • DOI: https://doi.org/10.1007/s00371-017-1385-6

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