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Digital Products, Wedges, and Covering Spaces

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Abstract

The paper [9] introduces the important tool of the digital covering space for studying the digital fundamental group. From a classical construction of algebraic topology [16,17,19], we show the existence of digital universal covering spaces and their significance for the study of the digital fundamental group.

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References

  1. D. Angluin, “Local and global properties in networks of processors,” Proceedings ACM STOC, Vol. 12, pp. 82–93, 1980.

  2. C. Berge, Graphs and Hypergraphs, 2nd. ed. North-Holland, Amsterdam, 1976.

    MATH  Google Scholar 

  3. L. Boxer, “Digitally continuous functions,” Pattern Recognition Letters, Vol. 15, pp. 833–839, 1994.

    Article  MATH  Google Scholar 

  4. L. Boxer, “A classical construction for the digital fundamental group,” Journal of Mathematical Imaging and Vision, Vol. 10, pp. 51–62, 1999.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. Boxer, “Properties of digital homotopy,” Journal of Mathematical Imaging and Vision, Vol. 22, pp. 19–26, 2005.

    Article  MathSciNet  Google Scholar 

  6. L. Boxer, “Homotopy properties of sphere-like digital images,” Journal of Mathematical Imaging and Vision, Vol. 24, pp. 167–175, 2006.

    Article  MathSciNet  Google Scholar 

  7. F. Harary, Graph Theory, Addison-Wesley Publishing: Reading, MA, 1969.

    Google Scholar 

  8. S.E. Han, “Digital coverings and their applications,” Journal of Applied Mathematics and Computing, Vol. 18, pp. 487–495, 2005.

    Google Scholar 

  9. S.E. Han, “Non-product property of the digital fundamental group,” Information Sciences, Vol. 171, pp. 73–91, 2005.

    Article  MathSciNet  Google Scholar 

  10. G.T. Herman, “Oriented surfaces in digital spaces,” CVGIP: Graphical Models and Image Processing, Vol. 55, pp. 381–396, 1993.

    Article  Google Scholar 

  11. E. Khalimsky, “Motion, deformation, and homotopy in finite spaces,” in Proceedings IEEE Intl. Conf. on Systems, Man, and Cybernetics, pp. 227–234, 1987.

  12. T.Y. Kong, “A digital fundamental group,” Computers and Graphics, Vol. 13, pp. 159–166, 1989.

    Article  Google Scholar 

  13. T.Y. Kong, A.W. Roscoe, and A. Rosenfeld, “Concepts of digital topology,” Topology and its Applications, Vol. 46, pp. 219–262, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  14. J. Kratochvil, A. Proskurowski, and J.A. Telle, “Covering regular graphs,” Journal of Combinatorial Theory, Series B, Vol. 71, pp. 1–16, 1997.

    Article  MATH  MathSciNet  Google Scholar 

  15. R. Malgouyres, “Homotopy in 2-dimensional digital images,” Theoretical Computer Science, Vol. 230, pp. 221–233, 2000.

    Article  MATH  MathSciNet  Google Scholar 

  16. W.S. Massey, Algebraic Topology: An Introduction, Harcourt, Brace, and World: New York, 1967.

    Google Scholar 

  17. J.R. Munkres, Topology: A First Course, Prentice-Hall: Englewood Cliffs, NJ, 1975.

    Google Scholar 

  18. A. Rosenfeld, “‘Continuous‘ functions on digital pictures,” Pattern Recognition Letters, Vol. 4, pp. 177–184, 1986.

    Article  MATH  Google Scholar 

  19. E.H. Spanier, Algebraic Topology, McGraw-Hill: New York, 1966.

    Google Scholar 

  20. Q.F. Stout, “Topological matching,” in Proc. 15th Annual Symp. on Theory of Computing, 1983, pp. 24–31.

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Correspondence to Laurence Boxer.

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Laurence Boxer is Professor and past Chair of Computer and Information Sciences at Niagara University, and Research Professor of Computer Science and Engineering at the State University of New York at Buffalo. He received a Bachelor’s in Mathematics from the University of Michigan at Ann Arbor; Master’s and PhD in Mathematics from the University of Illinois at Urbana-Champaign; and Master’s in Computer Science from the State University of New York at Buffalo. Dr. Boxer’s research interests are in the fields of algorithms and digital topology. He is co-author of Algorithms Sequential and Parallel: A Unified Approach, an innovative textbook whose second edition is published by Charles River Media.

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Boxer, L. Digital Products, Wedges, and Covering Spaces. J Math Imaging Vis 25, 159–171 (2006). https://doi.org/10.1007/s10851-006-9698-5

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  • DOI: https://doi.org/10.1007/s10851-006-9698-5

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