On the Notion of Dimension in Digital Spaces

摘要

Dimension is a fundamental concept in topology. Mylopoulos and Pavlidis [17] provided a definition for discrete spaces. In the present paper we propose an alternative one for the case of planar digital objects. It makes up certain shortcomings of the definition from [17] and implies dimensionality properties analogous to those familiar from classical topology. We also establish relations between dimension of digital objects and their Euler characteristic.