Abstract
In this paper the absolute and relative errors between Euclidean and m-neighbor distance have been studied for n-D digital geometry. Over the n-D space the absolute error has been shown to be unbounded. However, the relative error is shown to be bounded from above by n m . An efficient algorithm for determining the maxima of the relative error is presented. The existence of a still simpler and more efficient algorithm is conjectured. The use of the estimate of maximum relative error as a measure of the quality of approximation of Euclidean distance by an m-neighbor distance is discussed. The nature of the error function is shown graphically.
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