Abstract
A subclass of general octagonal distances defined by neighbourhood sequences [2] have been characterized here which have a strikingly simple closed functional form. These are called simple distances. Minimization of the average absolute (normalized) and average relative errors of these simple distances with regard to the euclidean norm have been carried out to identify the best approximate digital distances in 2-D digital geometry. The direct errors have also been analyzed and the effect of finite domain sizes on the approximation has been highlighted. It is shown that the neighbourhood sequences {2}, {1, 2}, {1, 1, 2}, and {1, 1, 2, 1, 2} have special significance in distance measurement in digital geometry.
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