Sandwich distances: new results
Jean-Marie Becker, Dinu Coltuc · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1998
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.