<title>Application of geometric hulls to digital curve characterizations</title>

Abstract

Convex hulls have been extensively studied and have been shown to have many useful applications in disciplines such as biomedical imaging, CAD/CAM and computer graphics. A convex hull of a point set, S, is the union of all line segments from p to q where p and q are elements of S. Edelsbrunner et al has extended the convex hull, which has linear constraints, to the alpha hull, which is circularly constrained. Specifically, the alpha-hull is the union of all circular arcs of radius 1/alpha joining p and q where p and q are endpoints of a circular arc. This paper extends the concept of the convex and alpha hulls to allow for extensions to curves of arbitrary complexity. Whereas current definitions assume that the curve connecting p and q is of finite length, we broaden the definitions to include infinite line segments between those points, thus forming the infinite hull. Similar extensions exist for circular and elliptical hulls as well as general curves. It is shown that the infinite hull counterparts can be applied to the characterization of a digital curve in linear time.© (1999) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.