Digital Curves in 3D Space and a Linear-Time Length Estimation Algorithm

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, including a presentation of its foundations and of experimental results. 1 Institute of Computer Science, Christian Albrechts University, Preusserstrasse 1-9, 24105 Kiel, Germany 2 The University of Auckland, Computer Science Department, CITR, Tamaki Campus (Building 731), Glen Innes, Auckland, New Zealand 

• Type: Journal
• Year: 2002
• Where: PAMI
• Authors: Thomas Bülow, Reinhard Klette
• Keywords: Digital Curve, PAMI 2002, Polygonal Curve, Simple Digital Curve