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2 October 1998 Sandwich distances: new results
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Abstract
On the discrete grid, the alternate use of V4-V8 neighborhoods is known to approximate the Euclidean distance. This problem was analyzed in the continuous setting and, more generally, it was shown that, if a certain inclusion holds for the unit balls of k distances, their alternate use yields a true distance, called sandwich distance. This paper elaborates on this topic. The initial scope is enlarged by defining new families of distances, called mixed distances. They are compositions of linear combinations of distances and of sandwich distances. Two examples of iterations of mixed distances are investigated. Their unit balls are polygons with 2k sides; their convergence towards the Euclidean disk is analyzed.
© (1998) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Jean-Marie Becker and Dinu Coltuc "Sandwich distances: new results", Proc. SPIE 3454, Vision Geometry VII, (2 October 1998); https://doi.org/10.1117/12.323260
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