Abstract
The concept of abstract cellular complexes was introduced by Kovalevsky (Computer Vision, Graphics and Image Processing, 46:141–161, 1989) and established that the topology of cellular complex is the only possible topology of finite sets to describe the structure of images. Further, the topological notions of connectedness and continuity in abstract cellular complexes were introduced while using the notions of an open subcomplex, closed subcomplex, and boundary of a subcomplex, etc. In this paper, the notion of semi-open subcomplex in abstract cellular complex is introduced and some of its basic properties are studied by defining the notions of semi-closure, semi-frontier, and semi-interior. Further, a homogeneously n-dimensional complex is characterized while using the notion of semi-open subcomplexes. Introduced is also the concept of a quasi-solid in subcomplex. Finally, a new algorithm for tracing the semi-frontier of an image is presented.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
P.Alexandroff and H.Hopf, Topologie I, Springer, 1935.
Azriel Rosenfled, Digital topology, The American Mathematical Monthly, 8, pp 621–630, 1979.
Azriel Rosenfled, and A.C. Kak, Digital picture processing, Academic Press, 1976.
V.Kovalevsky, “Finite topology as applied to image analysis”, Computer Vision, Graphics and Image processing, 46, pp 141–161, 1989.
V.Kovalevsky, Digital geometry based on the topology of abstract cellular complexes, in proceedings of the Third International Colloquium “discrete Geometry for computer Imagery”, University of Strasbourg, pp 259–284, 1993.
V.Kovalevsky, “Algorithms and data structures for computer topology”, in G.Bertrand et al.(Eds), LNCS 2243, Springer, pp 37–58, 2001.
V.Kovalevsky, Algorithms in digital geometry based on cellular topology In R.Klette. and J.Zunic(Eds.), LNCS 3322, Springer, pp 366–393, 2004.
V.Kovalevsky, Axiomatic Digital Topology, Springer Math image vis 26, pp 41–58, 2006.
V.Kovalevsky, Geometry of Locally Finite spaces, Publishing House Dr.Baerbel Kovalevski, Berlin, 2008.
N.Levine, Semi-open sets and semi-continuity in topological spaces, American Mathematical Monthly, 70, pp 36–41, 1963.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer India
About this paper
Cite this paper
Vijaya, N., Krishnan, G.S.S. (2014). Characterization of Semi-open Subcomplexes in Abstract Cellular Complex. In: Krishnan, G., Anitha, R., Lekshmi, R., Kumar, M., Bonato, A., Graña, M. (eds) Computational Intelligence, Cyber Security and Computational Models. Advances in Intelligent Systems and Computing, vol 246. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1680-3_30
Download citation
DOI: https://doi.org/10.1007/978-81-322-1680-3_30
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-1679-7
Online ISBN: 978-81-322-1680-3
eBook Packages: EngineeringEngineering (R0)