0-Gaps on 3D Digital Curves

TL;DR

This paper investigates the properties of 0-gaps in 3D digital curves, establishing a linear relationship between the number of 0-gaps and the counts of various cells in the digital object, with implications for digital geometry applications.

Contribution

It provides a novel mathematical characterization of 0-gaps in 3D digital curves, linking them to cell counts and advancing understanding in digital geometry.

Findings

Number of 0-gaps expressed as a linear combination of cell counts.

Establishes a formal relationship between gaps and cell structure in 3D digital curves.

Contributes to combinatorial analysis in digital geometry.

Abstract

In Digital Geometry, gaps are some basic portion of a digital object that a discrete ray can cross without intersecting any voxel of the object itself. Such a notion is quite important in combinatorial image analysis and it is strictly connected with some applications in fields as CAD and Computer graphics. In this paper we prove that the number of $0$-gaps of a $3$D digital curve can be expressed as a linear combination of the number of its $i$-cells (with $i = 0, \ldots, 3$).