Elsevier

Pattern Recognition Letters

Volume 15, Issue 9, September 1994, Pages 943-947
Pattern Recognition Letters

Strong and weak convex hulls in non-Euclidean metric: theory and application

https://doi.org/10.1016/0167-8655(94)90157-0Get rights and content

Abstract

The notion of convexity is usually defined in the plane supplied with the Euclidean metric. This paper examines what remains if we equip the plane with a distance induced by a norm which is not necessarily the Euclidean one. The basic properties of the geodesic arcs according to these non-Euclidean metrics are stated. In some cases there exists more than one geodesic arc between two points. The two associated notions of convexity, both strong and weak, are the presented. The relationships between the notion of weak convex hull and the limit of closings of increasing size are stated. Finally an application in binary image pattern recognition is described.

References (7)

  • J.-P. Aubin

    Viability Theory. Systems and Control: Foundations and Applications

    (1991)
  • G. Matheron

    Random Sets and Integral Geometry

    (1975)
  • J. Mattioli

    Métrique non euclidienne et enveloppe convexe faible

    Rapport Interne L.C.R., ASRF-91-7

    (1991)
There are more references available in the full text version of this article.

Cited by (6)

View full text