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The Number of Gaps in Binary Pictures

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Advances in Visual Computing (ISVC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 3804))

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Abstract

This paper identifies the total number of gaps of object pixels in a binary picture, which solves an open problem in 2D digital geometry (or combinatorial topology of binary pictures). We obtain a formula for the total number of gaps as a function of the number of object pixels (grid squares), vertices (corners of grid squares), holes, connected components, and 2 × 2 squares of pixels. It can be used to test a binary picture (or just one region: e.g., a digital curve) for gap-freeness.

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Author information

Authors and Affiliations

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

    Valentin E. Brimkov

  2. Dipartimento di Matematica, Università di Messina, 98166, Messina, Italy

    Angelo Maimone & Giorgio Nordo

  3. Department of Computer Science, SUNY Fredonia, Fredonia, NY, 14063, USA

    Reneta P. Barneva

  4. CITR Tamaki, University of Auckland, Building 731, Auckland, New Zealand

    Reinhard Klette

Authors
  1. Valentin E. Brimkov
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  2. Angelo Maimone
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  3. Giorgio Nordo
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  4. Reneta P. Barneva
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  5. Reinhard Klette
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Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, Reno, USA

    George Bebis

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

    Richard Boyle

  3. Desert Research Institute, Reno, NV, USA

    Darko Koracin

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

    Bahram Parvin

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© 2005 Springer-Verlag Berlin Heidelberg

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Brimkov, V.E., Maimone, A., Nordo, G., Barneva, R.P., Klette, R. (2005). The Number of Gaps in Binary Pictures. In: Bebis, G., Boyle, R., Koracin, D., Parvin, B. (eds) Advances in Visual Computing. ISVC 2005. Lecture Notes in Computer Science, vol 3804. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11595755_5

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  • DOI: https://doi.org/10.1007/11595755_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30750-1

  • Online ISBN: 978-3-540-32284-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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