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Morphological Erosions and Openings: Fast Algorithms Based on Anchors

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Abstract

Several efficient algorithms for computing erosions and openings have been proposed recently. They improve on van Herk’s algorithm in terms of number of comparisons for large structuring elements. In this paper we introduce a theoretical framework of anchors that aims at a better understanding of the process involved in the computation of erosions and openings. It is shown that the knowledge of opening anchors of a signal f is sufficient to perform both the erosion and the opening of f.

Then we propose an algorithm for one-dimensional erosions and openings which exploits opening anchors. This algorithm improves on the fastest algorithms available in literature by approximately 30% in terms of computation speed, for a range of structuring element sizes and image contents.

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Authors and Affiliations

  1. Department of Electricity, Electronics and Computer Science, Montefiore B28, Sart Tilman, B-4000, Liège, Belgium

    M. Van Droogenbroeck

  2. CSIRO Mathematical & Information Sciences, Macquarie University, Locked Bag 17, Building E6B, North Ryde, NSW, 2113, Australia

    M. J. Buckley

Authors
  1. M. Van Droogenbroeck
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  2. M. J. Buckley
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Corresponding authors

Correspondence to M. Van Droogenbroeck or M. J. Buckley.

Additional information

M. van Droogenbroeck received the degree in Electrical Engineering and the Ph. D. degree from the Catholic University of Louvain (UCL) in 1990 and 1994 respectively. During his PhD he spent two years at the Center of Mathematical Morphology (CMM) of the School of Mines of Paris. In April 1994, he joined the New Development Department of Belgacom. He was appointed as the Head of the Belgian Delegation in the ISO/MPEG Committee and as a representative to the World Wide Web Consortium. Since 1998, M. Van Droogenbroeck has been a member of the Faculty of Applied Sciences at the University of Liège, where he is currently an associate professor. His interests are in image processing, multimedia and telecommunications.

M.J. Buckley received the degree of B.Sc. (Hons) from the University of Sydney in 1983 and a Ph.D from the University of New South Wales in 1995. Since 1984 he has been a research scientist at CSIRO Mathematical and Information Sciences in Sydney, Australia, where he is currently a Principal Research Scientist. M.J. Buckley has worked on a wide range of applied technology projects, including real-time crack detection in road pavement, genomics and highcontent screening for drug discovery. His interests are algorithms for image analysis and image processing, signal analysis and dynamic programming methods.

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Van Droogenbroeck, M., Buckley, M.J. Morphological Erosions and Openings: Fast Algorithms Based on Anchors. J Math Imaging Vis 22, 121–142 (2005). https://doi.org/10.1007/s10851-005-4886-2

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