Approximations of the Euclidean distance by chamfer distances

Details Approximations of the Euclidean distance by chamfer distances Approximations of the Euclidean distance by chamfer distances

2012-01-04

arxiv.org/abs/1201.0876v1

Computer Science

Information Theory

Preprint submitted to Acta Cybernetica, 20 pages

Scientific paper

Chamfer distances play an important role in the theory of distance transforms. Though the determination of the exact Euclidean distance transform is also a well investigated area, the classical chamfering method based upon "small" neighborhoods still outperforms it e.g. in terms of computation time. In this paper we determine the best possible maximum relative error of chamfer distances under various boundary conditions. In each case some best approximating sequences are explicitly given. Further, because of possible practical interest, we give all best approximating sequences in case of small (i.e. 5 by 5 and 7 by 7) neighborhoods.

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