A Note on Dimension and Gaps in Digital Geometry

Abstract

The notion of gap is quite important in combinatorial image analysis and it
finds several useful applications in fields as CAD and computer graphics. On the
other hand, dimension is a fundamental concept in General Topology and it was
recently extended to digital objects. In this paper, we show that the dimension
of a 2D digital object equipped with an adjacency relation A ( 2 f0; 1g) can
be determinated by the number of its gaps besides some other parameters like the
number of its pixel, vertices and edges.