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?(? ? {0,1g} can be determinated by the number of its gaps besides some other parameters like the number of its pixel, vertices and edges.

0-Gaps on 3D Digital Curves

“…More recently, in [16] and [17] two formulas which express, respectively the number of 1-gaps of a generic 3D object of dimension α = 1, 2 and the number of (n − 2)-gaps of a generic digital n-object, by means of a few simple intrinsic parameters of the object itself were found. Furtermore, in [18] the relationship existing between the dimension of a 2D digital object equipped with an adjacency relation A α (α ∈ {0, 1}) and the number of its gaps was investigated.…”