12 research outputs found

    Acta Polytechnica Hungarica 2020

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    Comments on "On Approximating Euclidean Metrics by Weighted t-Cost Distances in Arbitrary Dimension"

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    Mukherjee (Pattern Recognition Letters, vol. 32, pp. 824-831, 2011) recently introduced a class of distance functions called weighted t-cost distances that generalize m-neighbor, octagonal, and t-cost distances. He proved that weighted t-cost distances form a family of metrics and derived an approximation for the Euclidean norm in Zn\mathbb{Z}^n. In this note we compare this approximation to two previously proposed Euclidean norm approximations and demonstrate that the empirical average errors given by Mukherjee are significantly optimistic in Rn\mathbb{R}^n. We also propose a simple normalization scheme that improves the accuracy of his approximation substantially with respect to both average and maximum relative errors.Comment: 7 pages, 1 figure, 3 tables. arXiv admin note: substantial text overlap with arXiv:1008.487

    Approximation of the Euclidean distance by Chamfer distances

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    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. 5x5 and 7x7) neighborhoods

    Acta Cybernetica : Volume 20. Number 3.

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