by Bülow, T and Klette, R
Abstract:
We consider simple digital curves in a 3D orthogonal grid as special polyhedrally bounded sets. These digital curves model digitized curves or arcs in three-dimensional Euclidean space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. So far, no algorithm was known for the calculation of such a shortest polygonal curve. This paper provides an iterative algorithmic solution for approximating the minimum-length polygon of a given simple digital space-curve. The theoretical foundations of this algorithm are presented as well as experimental results.
Reference:
Digital curves in 3D space and a linear-time length estimation algorithm (Bülow, T and Klette, R), In IEEE Transactions on Pattern Analysis and Machine Intelligence, volume 24, 2002.
Bibtex Entry:
@article{blow2002digitalalgorithm,
author = "Bülow, T and Klette, R",
journal = "IEEE Transactions on Pattern Analysis and Machine Intelligence",
month = "Jul",
pages = "962--970",
title = "Digital curves in 3D space and a linear-time length estimation algorithm",
volume = "24",
year = "2002",
abstract = "We consider simple digital curves in a 3D orthogonal grid as special polyhedrally bounded sets. These digital curves model digitized curves or arcs in three-dimensional Euclidean space. The length of such a simple digital curve is defined to be the length of the minimum-length polygonal curve fully contained and complete in the tube of this digital curve. So far, no algorithm was known for the calculation of such a shortest polygonal curve. This paper provides an iterative algorithmic solution for approximating the minimum-length polygon of a given simple digital space-curve. The theoretical foundations of this algorithm are presented as well as experimental results.",
doi = "10.1109/TPAMI.2002.1017622",
issn = "0162-8828",
issue = "7",
keyword = "Cellular complexes",
keyword = "Curve length",
keyword = "Digital geometry",
keyword = "Space curves",
language = "eng",
}