Approximating the Euclidean distance using non-periodic neighbourhood sequences Original Research Article

In this paper, we discuss some possibilities of approximating the Euclidean distance in Z2 by the help of digital metrics induced by neighbourhood sequences. Contrary to the earlier approaches, we use general (non-periodic) neighbourhood sequences which allows us to derive more precise results. We determine these metrics which can be regarded as the best approximations to the Euclidean distance in some sense. We compare our results with earlier studies of Das (J. Approx. Theory 68 (1992) 155) and Mukherjee et al. (Pattern Recognition Lett. 21 (2000) 573).