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Magnification in Digital Topology

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Combinatorial Image Analysis (IWCIA 2004)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3322))

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Abstract

When the author was working with Prof. Azriel Rosenfeld on joint research, we proposed a very strong deformation technique in digital topology called “magnification”. In this paper, the methods are explained in detail and some applications are given.

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References

  1. Aizawa, K., Nakamura, A.: Grammars on the hexagonal array. Inter. J. of Pattern Recognition and Artificial Intteligence 3, 469–477 (1989)

    Article  Google Scholar 

  2. Klette, R., Rosenfeld, A.: Digital Geometry. Morgan Kaufmann, San Francisco (2004)

    MATH  Google Scholar 

  3. Kong, T.Y.: Topology-preserving deletion of 1’s from 2-, 3-, 4-dimensional binary images. LNCS, vol. 1347, pp. 3–18 (1997)

    Google Scholar 

  4. Kong, T.Y., Roscoe, A.W.: Simple points in 4-dimensional (and higher-dimensional) binary images (manuscript) April 2 (2004)

    Google Scholar 

  5. Latecki, L., Eckhard, U., Rosenfeld, A.: Well-compsed sets. Comput. Vision Image Understanding 61, 70–83 (1995)

    Article  Google Scholar 

  6. Latecki, L.: Multicolor well-composed pictures. Pattern Recgnition Letters 16, 425–431 (1995)

    Article  Google Scholar 

  7. Latecki, L.: 3D well-composed pictures. Graphical Models and Image Processing 59, 164–172 (1997)

    Article  Google Scholar 

  8. Nakamura, A., Rosenfeld, A.: Digital konts. Pattern Recognition 33, 1541–1553 (2000)

    Article  Google Scholar 

  9. Nakamura, A., Rosenfeld, A.: Topology-preserving deformations of fuzzy digital pictures. In: Kerre, E.E., Nachtegael, M. (eds.) Fuzzy Techniques in Image Processing, pp. 394–404. Physica, Heidelberg (2000)

    Google Scholar 

  10. Nakamura, A.: Picture languages. In: Davis, L.S. (ed.) Foundations of Image Understanding, pp. 127–155. Kluwer Academic Publishers, Boston (2001)

    Google Scholar 

  11. Nakamura, A.: Magnification method of 4D digital pictures (draft paper).

    Google Scholar 

  12. Rosenfeld, A.: Connectivity in digital pictures. J. of ACM 17, 146–160 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  13. Rosenfeld, A.: Arcs and curves in digital pictures. J of ACM 20, 81–87 (1973)

    Article  MATH  MathSciNet  Google Scholar 

  14. Rosenfeld, A.: Adjacency in digital pictures. Information and Control 26, 24–33 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  15. Rosenfeld, A.: A characterization of parallel thinning algorithms. Information and Control 29, 286–291 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  16. Rosenfeld, A.: A converse to the Jordan curve theorem for digital curves. Information and Control 29, 292–293 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  17. Rosenfeld, A.: Picture Languages. Academic Press, New York (1979)

    MATH  Google Scholar 

  18. Rosenfeld, A.: Fuzzy digital topology. Information and Control 40, 76–87 (1979)

    Article  MATH  MathSciNet  Google Scholar 

  19. Rosenfeld, A., Nakamura, A.: Local deformation of digital curves. Pattern Recognition Letters 18, 613–620 (1997)

    Article  Google Scholar 

  20. Rosenfeld, A., Kong, T.Y., Nakamura, A.: Topology-preserving deformations of two-valued digital pictures. Graphical Models and Image Processing 60, 24–34 (1998)

    Article  Google Scholar 

  21. Rosenfeld, A., Saha, P.K., Nakamura, A.: Interchangeable pairs of pixels in two-valued digital images. Pattern Recognition 34, 1853–1865 (2001)

    Article  MATH  Google Scholar 

  22. Rosenfeld, A., Nakamura, A.: Two simply connected sets that have the same area are IP-equivalent. Pattern Recognition 35, 537–541 (2002)

    Article  MATH  Google Scholar 

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© 2004 Springer-Verlag Berlin Heidelberg

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Nakamura, A. (2004). Magnification in Digital Topology. In: Klette, R., Žunić, J. (eds) Combinatorial Image Analysis. IWCIA 2004. Lecture Notes in Computer Science, vol 3322. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30503-3_20

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  • DOI: https://doi.org/10.1007/978-3-540-30503-3_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23942-0

  • Online ISBN: 978-3-540-30503-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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