  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.
