Concepts of Digital Topology

Afsaneh REZAIE
1.602 1.073

Abstract


Abstract. In image processing and computer graphics an object in the plane or 3-space is often approximated digitaly by a set of pixels or voxels. Digital topology studies properties of pixels or voxels that correspond to topological properties of the original object. In this paper, we discuss about digital space and digital picture from Rosenfeld's aspect of view and introduce regular and strongly normal digital picture space. Using these introductions, we impose restrictions on adjacency relation between points to establish some important theorem in digital space like as the Jordan Curve Theorem. Also, one can explore digital fundamental group in regular digital picture space but in this paper we do not deal with it. At the end, we express that the Jordan Curve Theorem in the strongly normal digital picture space is verified.


Keywords


digital picture space, picture space, black point, white point, adjacency relation, regular digital picture space

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References


L. Boxer, A classical construction for the digital fundamental group, Journal of Mathematical Imaging and Vision 10 (1999) 51-62.

T. Y. Kong, A digital fundamental group, Comput. Graphics 13 (1989) 159-166.

T. Y. Kong, A. W. Rosco and A. Rosenfeld, Concepts of Digital Topology, Topology and its Applications 46 (1992).

T. Y. Kong and A. W. Rosco, A theory of binary digital picture, Compute Vision Graphics Image Process 32 (1989) 221-243.

T. Y. Kong. Rosenfeld, Digital Topology: Comput. Introduction and Survey Computer Vision. Graphics, and Image Processing 48 (1989) 357-393.

T. Y. Kong and A. Rosenfeld, Topological Algorithms for Digital Image Processing, 1996

Elsevier Science B. V. V. A. Kovalevsky, Discrete topology and contour definition, Pattern Recognition Letters 2 (1984) 281-288.

V. A. Kovalevsky, Introduction to Digital Topology, Why is Topology Important for Image Analysis (2010).

J. R. Munkres, Topology. A First Course, Prenncite-Hall.Inc.New Jersey, 1967.