Sandwich distances

Jean-Marie Becker; Dinu Coltuc; Michel Jourlin

doi:10.1117/12.279652

20 October 1997 Sandwich distances

Jean-Marie Becker, Dinu Coltuc, Michel Jourlin

Proceedings Volume 3168, Vision Geometry VI; (1997) https://doi.org/10.1117/12.279652
Event: Optical Science, Engineering and Instrumentation '97, 1997, San Diego, CA, United States

Abstract

Many authors, e.g., Rosenfeld and Pfaltz, Borgefors..., have proposed efficient and/or accurate approximations of euclidian distance on a 2D or 3D grid with methods which are connected, more or less directly, to norm derived distances, e.g., with L_p norms. This paper enlarges the scope in a continuous and m-dimensional framework. It presents a new broad class of distances, called 'sandwich' or 'periodic' distances. They are obtained by compounding in a periodic manner a certain number of norm-derived distances. The main result of this paper is the proof of a sufficient condition under which the triangular inequality is fulfilled, i.e., that the unit balls of the compounded distances belong to an ascending chain. Moreover, the theory includes weighted distances, giving this tool a high degree of flexibility.

Citation Download Citation

Jean-Marie Becker, Dinu Coltuc, and Michel Jourlin "Sandwich distances", Proc. SPIE 3168, Vision Geometry VI, (20 October 1997); https://doi.org/10.1117/12.279652

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