Best simple octagonal distances in digital geometry (Q1185937)

The author shows that out of the class of neighbourhood sequences which have the same characteristic value there exists exactly one metric which has a simple functional form and incidentally satisfies the metricity conditions too. A revision of the available results on octagonal distances is given and a characterization for such simple octagonal distances is derived. The author introduces new error analyses involving these simple metrics. The error between the octagonal and the true euclidean distances is estimated in the asymptotic order by using a continuous approximation of the octagonal metric. Minimization of the absolute and the relative errors of the average of these simple distances with regard to the euclidean norm are carried out to identify the best approximate diginal distance in 2-D digital geometry. Four different simple metrics are recommended for practical use in digital approximation.