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On Connectedness of Discretized Objects

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Advances in Visual Computing (ISVC 2013)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 8033))

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Abstract

A major problem in computer graphics, image processing, numerical analysis and other applied areas is constructing a relevant object discretization. In a recent work [1] we investigated an approach for constructing a connected discretization of a set A ⊆ ℝn by taking the integer points within an offset of A of a certain radius, and determined the minimal value of the offset radius which guarantees connectedness of the discretization, provided that A is path-connected. In the present paper we prove that the same results hold when A is connected but not necessarily path-connected. We also demonstrate similar facts about Hausdorff discretization, thus generalizing a theorem from [18]. The proofs combine approaches and techniques from [1] and [18].

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Author information

Authors and Affiliations

  1. Mathematics Department, SUNY Buffalo State College, Buffalo, NY, 14222, USA

    Valentin E. Brimkov

Authors
  1. Valentin E. Brimkov
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Editor information

Editors and Affiliations

  1. University of Nevada, Reno, NV, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Arizona State University, Tempe, AZ, USA

    Baoxin Li

  6. Mitsubishi Electric Research Laboratories, Cambridge, MA, USA

    Fatih Porikli

  7. University of California, Riverside, CA, USA

    Victor Zordan

  8. AT&T Research Labs, Florham Park, NJ, USA

    James Klosowski

  9. ZIRST, Saint-Ismier Cedex, France

    Sabine Coquillart

  10. Qualcomm Research, San Diego, CA, USA

    Xun Luo

  11. Oxford e-Research Centre, University of Oxford, Oxford, UK

    Min Chen

  12. IBM, Hawthorne, NY, USA

    David Gotz

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Brimkov, V.E. (2013). On Connectedness of Discretized Objects. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2013. Lecture Notes in Computer Science, vol 8033. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41914-0_25

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  • DOI: https://doi.org/10.1007/978-3-642-41914-0_25

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-41913-3

  • Online ISBN: 978-3-642-41914-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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