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Three-dimensional salient point detection based on the Laplace–Beltrami eigenfunctions

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Abstract

Three-dimensional (3D) salient point detection is a fundamental problem in computer graphics and computer vision. We propose a new method using the Laplace–Beltrami eigenfunctions for detecting the salient points of 3D models. We compute the extrema of the low-frequency Laplace–Beltrami eigenfunctions and remove the redundancy of the extrema. Merging the extrema of the eigenfunctions, we keep the extrema appearing simultaneously on no less than a certain number of eigenfunctions as the candidate salient points. Clustering these extrema, we consider the representatives of the clusters as the final salient points. Our experimental results demonstrate that the proposed method is effective for 3D salient point detection. Besides that, some experiments are also conducted to verify that the proposed method is insensitive to small boundary noise.

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Acknowledgements

We thank Martin Reuter for making available his “ShapeDNA-tria” software and Gabriel Peyré for his toolboxes—“Toolbox Fast Marching” and “Toolbox Graph”.

Funding

This research was supported by Natural Science Foundation of Shandong province (No. ZR2019BF026, ZR2019MF013, ZR2017BF031), Project of Jinan Scientific Research Leader’s Laboratory (No. 2018GXRC023) and Doctoral Program of University of Jinan (No. 160100313).

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Authors and Affiliations

  1. Shandong Provincial Key Laboratory of Network based Intelligent Computing, University of Jinan, Jinan, 250022, China

    Dongmei Niu, Han Guo & Xiuyang Zhao

  2. School of Computer Science and Technology, Shandong University, 1500 Shunhua Road, Jinan, 250101, China

    Caiming Zhang

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  1. Dongmei Niu
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  2. Han Guo
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Correspondence to Xiuyang Zhao.

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Niu, D., Guo, H., Zhao, X. et al. Three-dimensional salient point detection based on the Laplace–Beltrami eigenfunctions. Vis Comput 36, 767–784 (2020). https://doi.org/10.1007/s00371-019-01658-x

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