Weighted distances on the truncated hexagonal grid

Abstract

Recently chamfer distances have been developed not only on the usual integer grids, but also on some non traditional grids including grids which are not lattices. In this paper the truncated hexagonal grid is considered: its pixels are dodecagons and two shaped (oriented) triangles. Two types of 'natural' neigh-borhood relations are considered on the grid, consequently two weights are used to describe the chamfer distances. Formulae to compute the minimal weights of a connecting path, i.e., the distance of any two pixels, are provided to cases depending on the relative ratio of the weights. Some properties of these distances, including metricity are also analysed. Digital disks based on the weighted distances are also investigated. In some cases, these disks may not be convex, moreover they may contain holes. The con-ditions of holes are characterised. (c) 2021 Elsevier B.V. All rights reserved.