Concepts of Digital Topology

Afsaneh REZAIE
1.602 1.073


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.


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

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