A Note on Dimension and Gaps in Digital Geometry

Angelo Maimone, Giorgio Nordo

The notion of \emph{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 $A_\alpha(\alpha\in\{0,1\})$ can be determinated by the number of its gaps besides some other parameters like the number of its pixel, vertices and edges.