Open AccessOn 1-gaps in 3D digital objects
Author(s) -
Angelo Maimone,
Giorgio Nordo
Publication year - 2011
Publication title -
filomat
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 34
eISSN - 2406-0933
pISSN - 0354-5180
DOI - 10.2298/fil1103085m
Subject(s) - intersection (aeronautics) , object (grammar) , digital geometry , mathematics , dimension (graph theory) , voxel , position (finance) , set (abstract data type) , discrete geometry , computer vision , geometry , artificial intelligence , computer graphics (images) , digital image , computer science , combinatorics , image (mathematics) , image processing , geography , cartography , finance , economics , programming language
In Digital Geometry, a gap is a location of a digital object through which a discrete ray can penetrate with no intersection. More specifically, for a 3D digital object we distinguish between 0- and 1-gaps depending on the relative position of such a ray. Although in some applications it is important to know how many gaps has a set of voxels, it is quite complicated to find an efficient algorithm to directly count them. In this paper, we provide a formula that states the number of 1-gaps of a generic 3D object using the notion of free cell of dimension 1 and 2.