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A fast convex hull algorithm inspired by human visual perception

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Abstract

This paper proposes a convex hull algorithm for high dimensional point set, which is faster than the well-known Quickhull algorithm in many cases. The main idea of the proposed algorithm is to exclude inner points by early detection of global topological properties. The algorithm firstly computes an initial convex hull of \(2*d + 2^{d}\) extreme points. Then, it discards all the inner points which are inside the inscribed ball of the initial convex hull. The other inner points are processed recursively according to the relationships of points and facets. Maximum inscribed circle affine transformations are also designed to accelerate the computation of the convex hull. Experimental results show that the proposed algorithm achieves a significant saving of computation time in comparison with the Quickhull algorithm in 3, 4 and 5 dimensional space. The space efficiency of the proposed algorithm is also demonstrated by experimental results.

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Acknowledgments

This work was financially supported by Project No.106112016CDJXY180002, 0903005203327, 02160011044104 supported by the Fundamental Research Funds for the Central Universities. This work was also supported by the Research Grants of MYRG2015-00049-FST, MYRG2015-00050-FST, RDG009/FST-TYY/2012; 008-2014-AMJ from Macau.

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Authors and Affiliations

  1. College of Computer Science, Chongqing University, Chongqing, 400030, People’s Republic of China

    Runzong Liu

  2. Faculty of Science and Technology, University of Macau, Macau, China

    Yuan Yan Tang

  3. South China University of Technology, Guangdong Sheng, China

    Patrick P. K. Chan

Authors
  1. Runzong Liu
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  2. Yuan Yan Tang
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  3. Patrick P. K. Chan
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Correspondence to Runzong Liu.

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Liu, R., Tang, Y.Y. & Chan, P.P.K. A fast convex hull algorithm inspired by human visual perception. Multimed Tools Appl 77, 31221–31237 (2018). https://doi.org/10.1007/s11042-018-6185-0

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  • DOI: https://doi.org/10.1007/s11042-018-6185-0

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