Have a personal or library account? Click to login
A digital 3D Jordan-Brouwer separation theorem Cover

References

  1. V. E. Brimkov, R. Klette, Border and surface tracing - theoretical foundations, IEEE Trans. Patt. Anal. Machine. Intell., 30 (2008), 577–590.
  2. M. Greenberg, Lectures on Algebraic Topology, Benjamin, New York, 1967.
  3. B. Gru¨nbaum, G. C. Shepard, Tilings & Patterns, Dover Publ., New York, 2020.
  4. E. D. Khalimsky, R. Kopperman, P. R. Meyer, Computer graphics and connected topologies on finite ordered sets, Topology Appl, 36 (1990), 1–17.
  5. T. Y. Kong, W. Roscoe, Continuous analogs of axiomatized digital surfaces, Comput. Vision Graphics Image Process., 29 (1985), 60–86.
  6. T. Y. Kong, A. Rosenfeld, Digital topology: Introduction and survey, Comput. Vision Graphics Image Process., 48 (1989), 357–393.
  7. R. Kopperman, P.R. Meyer, R. Wilson, RA Jordan surface theorem for three-dimensional digital spaces, Discrete Comput. Geom., 6 (1991), 155–161.
  8. E. Melin, Digital surfaces and boundaries in Khalimsky spaces, J. Math. Imaging and Vision, 28 (2007), 169–177.
  9. D. G. Morgenthaler, A. Rosenfeld, Surfaces in three dimensional digital images, Information and Control 28 (1981), 227–247.
  10. M. Reed, A. Rosenfeld, Recognition of surfaces in three dimensional digital images, Information and Control 53 (1982), 108–120.
  11. A. Rosenfeld, Picture Languages, Academic Press, New York, 1979.
  12. J. Šlapal, Graphs with a path partition for structuring digital spaces, Information Sciences, 233 (2013), 305–312.
  13. J. Šlapal, A ternary relation for structuring the digital plane, in: AMCSE 2016, ITM Web of Conferences 9 (2017), 01012, pp. 1-5.
  14. J. Šlapal, Relation-induced connectedness in the digital plane, Aequat. Math. 92 (2018), 75–90.
  15. J. Šlapal, A 3D digital Jordan-Brouwer separation theorem, Comput. Appl. Math., 39 (2020), 211, pp. 1–10.
DOI: https://doi.org/10.2478/auom-2024-0034 | Journal eISSN: 1844-0835 | Journal ISSN: 1224-1784
Language: English
Page range: 161 - 172
Submitted on: May 3, 2023
Accepted on: Oct 21, 2023
Published on: Oct 17, 2024
Published by: Ovidius University of Constanta
In partnership with: Paradigm Publishing Services
Publication frequency: 3 issues per year

© 2024 Josef Šlapal, published by Ovidius University of Constanta
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.