DOI QR코드

DOI QR Code

IDENTIFICATION METHOD FOR DIGITAL SPACES

Han, Sang-Eon

  • Received : 2011.01.18
  • Accepted : 2011.03.03
  • Published : 2011.03.25

Abstract

The aim of the paper is to develop an identification method for digital spaces and to study its digital homotopic properties related to a strong k-deformation retract.

Keywords

digital k-graph;simple closed k-curve;digital k-fundamental group;strong k-deformation retract;identification method;adjunction space

References

  1. G. Bertrand, Simple points, topological numbers and geodesic neighborhoods in cubic grids, Pattern Recognition Letters, 15 (1994), 1003-1011. https://doi.org/10.1016/0167-8655(94)90032-9
  2. L. Boxer, Digitally continuous functions Pattern Recognition Letters 15 (1994), 833-839. https://doi.org/10.1016/0167-8655(94)90012-4
  3. L. Boxer, A classical construction for the digital fundamental group, Jour. of Mathematical Imaging and Vision, 10 (1999), 51-62. https://doi.org/10.1023/A:1008370600456
  4. S.E. Han, Computer topology and its applications, Honam Math. Jour. 25(1)(2003) 153-162.
  5. S.E. Han, Non-product property of the digital fundamental group, Information Sciences 171 (2005), 73-91. https://doi.org/10.1016/j.ins.2004.03.018
  6. S.E. Han, On the simplicial complex stemmed from a digital graph, Honam Mathematical Journal 27 (1) (2005) 115-129.
  7. S.E. Han, Connected sum of digital closed surfaces, Information Sciences 176(3)(2006), 332-348. https://doi.org/10.1016/j.ins.2004.11.003
  8. S.E. Han, Discrete Homotopy of a Closed k-Surface, LNCS 4040, Springer-Verlag Berlin, pp. 214-225, 2006.
  9. S.E. Han, Strong k-deformation retract and its applications, Journal of the Korean Mathematical Society 44(6)(2007) 1479-1503. https://doi.org/10.4134/JKMS.2007.44.6.1479
  10. S.E. Han, Comparison among digital fundamental groups and its applications, Information Sciences 178 (2008) 2091-2104. https://doi.org/10.1016/j.ins.2007.11.030
  11. S.E. Han, Equivalent ($k_0,\;k_1$)-covering and generalized digital lifting, Information Sciences 178(2)(2008) 550-561. https://doi.org/10.1016/j.ins.2007.02.004
  12. S.E. Han, The k-homotopic thinning and a torus-like digital image in $Z^n$, Journal of Mathematical Imaging and Vision 31 (1) (2008) 1-16. https://doi.org/10.1007/s10851-007-0061-2
  13. E. Khalimsky, Motion, deformation, and homotopy in finite spaces, Proceedings IEEE International Conferences on Systems, Man, and Cybernetics, (1987), 227-234.
  14. T.Y. Kong, A. Rosenfeld, Digital topology - A brief introduction and bibliography) Topological Algorithms for the Digital Image Processing, Elsevier Science, Amsterdam, 1996.
  15. A. Rosenfeld, Digital topology, Am. Math. Mon. 86 (1979) 76-87.
  16. E.H. Spanier, Algebraic Topology, McGraw-Hill Inc., New York, 1966.