Application of geometric hulls to digital curve characterizations

Robert R. Goldberg; Jonathan Robinson

doi:10.1117/12.360280

27 August 1999 Application of geometric hulls to digital curve characterizations

Robert R. Goldberg, Jonathan Robinson

Proceedings Volume 3836, Machine Vision Systems for Inspection and Metrology VIII; (1999) https://doi.org/10.1117/12.360280
Event: Photonics East '99, 1999, Boston, MA, United States

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.

Citation Download Citation

Robert R. Goldberg and Jonathan Robinson "Application of geometric hulls to digital curve characterizations", Proc. SPIE 3836, Machine Vision Systems for Inspection and Metrology VIII, (27 August 1999); https://doi.org/10.1117/12.360280

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