Abstract
A new class of distance functions has been defined in n-D, where the distance between neighboring points may be more than unity. A necessary and sufficient condition for such distance functions to satisfy the properties of a metric has been derived. These metrics, called t-cost distance, give the length of the shortest t-path between two points in n-D digital space. Some properties of their hyperspheres are also studied. Suitability of these distances as viable alternative to Euclidean distance in n-D has been explored using absolute and relative error criteria. It is shown that lower dimension (2-D and 3-D) distance measures presently used in digital geometry can be easily derived as special cases. Finally most of these results have been extended for the natural generalization of integral costs to real costs.
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