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Relative Convex Hull Determination from Convex Hulls in the Plane

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Combinatorial Image Analysis (IWCIA 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9448))

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Abstract

A new algorithm for the determination of the relative convex hull in the plane of a simple polygon A with respect to another simple polygon B which contains A, is proposed. The relative convex hull is also known as geodesic convex hull, and the problem of its determination in the plane is equivalent to find the shortest curve among all Jordan curves lying in the difference set of B and A and encircling A. Algorithms solving this problem known from Computational Geometry are based on the triangulation or similar decomposition of that difference set. The algorithm presented here does not use such decomposition, but it supposes that A and B are given as ordered sequences of vertices. The algorithm is based on convex hull calculations of A and B and of smaller polygons and polylines, it produces the output list of vertices of the relative convex hull from the sequence of vertices of the convex hull of A.

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Acknowledgement

The first author gratefully acknowledges support for this research from SEP and CONACYT Mexico, grant No. CB-2011-01-166223. The authors would like to thank very much to the reviewers for their careful study of the work, and for their constructive criticism and helpful comments which were important to improve the presentation of the paper.

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Authors and Affiliations

  1. Department of Automatic Control, Centro de Investigación y de Estudios Avanzados (CINVESTAV-IPN), Av. I.P.N. 2508, Col. San Pedro Zacatenco, 07000, Mexico, D.F., Mexico

    Petra Wiederhold & Hugo Reyes

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  1. Petra Wiederhold
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  2. Hugo Reyes
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Correspondence to Petra Wiederhold .

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Editors and Affiliations

  1. SUNY Fredonia, Fredonia, New York, USA

    Reneta P. Barneva

  2. Advanced Computing and Microelectronics, Indian Statistical Institute, Kolkata, Germany

    Bhargab B. Bhattacharya

  3. SUNY Buffalo State, Buffalo, New York, USA

    Valentin E. Brimkov

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Wiederhold, P., Reyes, H. (2015). Relative Convex Hull Determination from Convex Hulls in the Plane. In: Barneva, R., Bhattacharya, B., Brimkov, V. (eds) Combinatorial Image Analysis. IWCIA 2015. Lecture Notes in Computer Science(), vol 9448. Springer, Cham. https://doi.org/10.1007/978-3-319-26145-4_4

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  • DOI: https://doi.org/10.1007/978-3-319-26145-4_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26144-7

  • Online ISBN: 978-3-319-26145-4

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