Topological Structure in Digital Image Processing : A Survey

Authors

  • Nibedita Roy  Department of Computer Science and Technology, Bodoland University, Kokrajhar, Assam, India
  • Ajit Das  Department of Computer Science and Technology, Bodoland University, Kokrajhar, Assam, India

Keywords:

digital image processing, topology, digital topology etc

Abstract

Image processing is a technique with the help of this we can perform some operations on image. Digital image processing is the use of computer algorithms to perform image processing on digital images. Digital topology deals with properties and features of two-dimensional (2D) or three-dimensional (3D) digital images that correspond to topological properties (e.g., connectedness) or topological features (e.g., boundaries) of objects. This article is an overview of recent research of generalized topological property in the field of digital image processing. In this study we present the general framework on topology and digital image processing.

References

  1. P Alexandroff and H.Hopf, Topologiei, SPPRINGER(1935)
  2. E.D.Khalimsky, on topologies of generalized segments, Soviet Math.10,1508-1511(1969)
  3. Azril Rosenfeld, Connectivity in digital pictures, Assoc. Compt. Mach. 17, pp.146-160(1970)
  4. Azril Rosenfeld, Arcs and Curves in digital pictures, Assoc. Compt. March 20, pp.81-87(1973).
  5. Azril Rosenfeld, Adjacency in digital pictures, Information and Control 26, pp.24-33.(1974).
  6. Azriel Rosenfeld, Digital topology, The American Mathematical Monthly, Vol. 86, No. 8, pp.177-184(1979).
  7. R.Rosenfeld, Picture languages, Academic Press, New York (1979).
  8. V.A.Kovalevsky, Discrete topology and contour analysis, pattern recogit. Lett.2, no.5,281-288 (1984)
  9. A.W.Roscoe, T.Y.Kong, A theory of binary digital pictures, Computer Vision, Graphics and Image Processing 32(2), pp.221243(1985).
  10. Azril Rosenfeld, Continuous function on digital picture, Pattern Recognition letter, V_4, pp.177-184(1986).
  11. A.Rosenfeld, T.Y.kong, Digital topology: Introduction and Survey, Computer Vision, Graphics and Image Processing 48, 357-393 (1989).
  12. V.A.Kovalevsky, finite topology as applied to image analysis, computer vision, Graphics and Image Processing 46, 141-161(1989).
  13. R.Kopperman, E.D.Khalimsky and P.R.Meyer, Boundaries in digital planes, Journal of Applied Mathematics and Stochastic Analysis: Volume 3, Number 1 (1990).
  14. E. Khalimsky, R. Kopperman, P.R. Meyer, “Computer Graphics and Connected Topologies on Finite Ordered Sets”, Topology and its Applications, 36, pp. 1–17,(1990).
  15. P.R.Meyer, T.Y.Kong, R.Kopperman, A topological approach to digital topology, American Mathematical monthly 38, pp.901-917 (1991).
  16. Alberto Mrquez, Eladio Domnguez, Angel Francs, A framework for digital topology,(1992).
  17. E.H.Kronheimer, The topology of digital images, Topology and its Applications, 46:279303 (1992).
  18. A.W.Roscoe, T.Y.Kong and A.Rosenfeld, Concepts of digital topology, topology and its application 45, 219-262 (1992).
  19. Longin Latecki, Topologycal connectedness and 8-connectedness in digital pictures, CVGIP:Image understanding, 57:261262(1993).
  20. T.Y.Kong, On topology preservation in 2-d and 3-d thinning, International Journal of Pattern Recognition and Artificial Intelligence, 9:813844(1995).
  21. M.B.Smyth, Semi-metrics, closure spaces and digital topology, Theoret. Comput. Sci. 151,257276(1995).
  22. Walter Kropatsch, Pavel Ptak, Helmut Kofler, Digital topologies revisited: An approach based on the topological point-neighbourhood, Austrian National Fonds zuir Forderung der wissenschaftlichen Forschung (1997).
  23. Gilles Bertrand and Michel Couprie, A Model for digital topology (1999).
  24. G.J.F.Banon, New insight on digital topology, Mathematical Morphology and its Applications to Image and Signal processing Computational Imaging and vision Volume 18, pp.139-148 (2000).
  25. A.R.Frances, A.Quintero, R.Ayala, E.Domnguez, Homotopy in digital space, Discrete Geometry for Computer Imagery Vol.1953 of lecture notes in Computer Science, Springer, PP.314(2000).
  26. Eladio Domynguez and Angel R.Frances, An axiomatic approach to digital topology, Springer-Verlag Berlin Heidelberg: Digital and Image Geometry, LNCS 2243, pp.316,(2001).
  27. J Slapal, Closure operations for digital topology, Theor. Comp. Sci. 305,457471 (2003).
  28. U.Eckhardt and L.Latecki, Topologies for the digital spaces Z^2and Z^3, Computer Vision Image Understanding, 90, pp.295-312 (2003).
  29. J.Slapal, A digital analogue of the Jordan curve theorem, Discr. Appl. Math. !39, 231251. (2004).
  30. Melin.E., Continuous extension in topological digital spaces, U.U.D.M. Report2, Uppsala University(2004).
  31. Melin.E., Digital straight lines in the Khalimsky plane, Math. Scand. 96, 4962(2005).
  32. Jerry L.Prince Ying Bai, Xiao Han, Digital topology on adaptive octree grids,(November 2007).
  33. Zhige Jia Qinggquan, Li Guobin Zhu, Xiaoli liu, A multi-level image description model scheme based on digital topology, Stilla U al(Eds) PIA07. International Archives of Photogrammetry, Remote Sensing Information Sciences, 36 (2007).
  34. Melin.E., digital surfaces and boundaries in Khalimsky spaces, Spaces. Journal of Mathematical Imaging and Vision, 28, 169-177(2007).
  35. Longin Latecki, Ulrich Eckhardt, Digital topology, (February 26, 2008).
  36. J Slapal, A quotient-universal digital topology, Theor. Comp. Sci., 405: 164175, (2008).
  37. J.Slapal, Convenient closure operators on Z^2, Lect. Notes in Comp. Sci., 5852:425436, (2009).
  38. Y.X.Zhang Sen Liang, Digital topology optimization design and manufacturing based on the level set method, Modern Applied Science, Vol.5, No.5;(2011).
  39. Vladimir Kovalevsky, Axiomatic digital topology,  J Math Imaging, 26: 41-58.
  40. Michel Couprie Christian, Ronse Loic Mazo, Nicolas Passat, Digital imaging: a unified topological framework, Journal of Mathematical Imaging and Vision 44(1): 19-37 (September 2012).
  41. Jeang Min Kang and Sang-Eon Han, Compression of Khalimsky topological spaces, Faculty of  Sciences and Mathematics, University of Nis. Serbia, Filomat 26:611011114 (2012).
  42. J Slapal, topological structuring of the digital plane, Discrete Mathematics and Theoretical Computer Science, Vol. 15:2, 165-175 (2013).
  43. Loic Mazo, A framework for digital label images, (Mar 20, 2014).

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Published

2017-12-31

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Section

Research Articles

How to Cite

[1]
Nibedita Roy, Ajit Das, " Topological Structure in Digital Image Processing : A Survey, IInternational Journal of Scientific Research in Computer Science, Engineering and Information Technology(IJSRCSEIT), ISSN : 2456-3307, Volume 2, Issue 6, pp.481-485, November-December-2017.