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Chamfer metrics in mathematical morphology

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Abstract

This paper presents an integration of chamfer metrics into mathematical morphology. Because chamfer metrics can approximate the Euclidean metric accurately, morphological operations based on chamfer metrics give a good approximation to morphological operations that use Euclidean discs as structuring elements. First, a formal definition of chamfer metrics is presented and some properties are discussed. Then, a number of morphological operations based on chamfer metrics are defined. These include the medial axis, the medial line, size and antisize distributions, and the opening transform. A theoretical analysis of some properties of these operators is provided. This analysis concentrates on the relation between distance transformations and reconstructions and the morphological operators just mentioned. This leads to a number of efficient algorithms for the computation of the morphological operators. All algorithms (except for the opening transform) require a fixed number of image scans and are based on local operations only. An algorithm for the opening transform that is 50–100 times as fast as the brute-force algorithm is presented.

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Authors and Affiliations

  1. TNO Human Factors Research Institute, Kampweg 5, 3769 DE, Soesterberg, The Netherlands

    P. F. M. Nacken

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  1. P. F. M. Nacken
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This research was supported by the Foundation for Computer Science in the Netherlands (SION), with financial support from the Netherlands Organization for Scientific Research (NWO). This research was part of a project in which the TNO Human Factors Research Institute, CWI, and the University of Amsterdam cooperated.

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Nacken, P.F.M. Chamfer metrics in mathematical morphology. J Math Imaging Vis 4, 233–253 (1994). https://doi.org/10.1007/BF01254101

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