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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.
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- Characterization of Semi-open Subcomplexes in Abstract Cellular Complex
G. Sai Sundara Krishnan
- Springer India
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