Approximation of the euclidean distance by Chamfer distances

Authors:
András Hajdu;Lajos Hajdu;Robert Tijdeman
Affiliations:
Faculty of Informatics, University of Debrecen, Debrecen, Hungary;University of Debrecen, Debrecen, Hungary;Mathematical Institute, Leiden University, RA Leiden, The Netherlands
Venue:
Acta Cybernetica
Year:
2012

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Abstract

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 × 5 and 7 × 7) neighborhoods.