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Automatic Choice of the Threshold of a Grain Filter via Galton–Watson Trees: Application to Granite Cracks Detection

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Abstract

The goal of this paper is the presentation of a post-processing method allowing to remove impulse noise in binary images, while preserving thin structures. We use a grain filter. We propose a method to automatically determine the required threshold using Galton–Watson processes. We present numerical results and a complete analysis on a synthetic image. We end the numerical section considering a specific application to granite samples crack detection: Here we deal with X-tomography images that have been binarized via preprocessing techniques and we want to remove residual impulse noise while keeping cracks and micro-cracks structure.

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Notes

  1. We thank Olivier Rozenbaum, ISTO, Université d’Orléans, CNRS, BRGM.

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Acknowledgements

We would like to thank all the anonymous referees for their fruitful comments that helped to improve this paper a lot.

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Authors and Affiliations

  1. Laboratoire MAPMO, CNRS, UMR 7349, Fédération Denis Poisson, FR 2964, Université d’Orléans, B.P. 6759, 45067, Orléans Cedex 2, France

    Romain Abraham, Maïtine Bergounioux & Pierre Debs

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  1. Romain Abraham
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  2. Maïtine Bergounioux
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  3. Pierre Debs
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Correspondence to Maïtine Bergounioux.

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Abraham, R., Bergounioux, M. & Debs, P. Automatic Choice of the Threshold of a Grain Filter via Galton–Watson Trees: Application to Granite Cracks Detection. J Math Imaging Vis 60, 50–69 (2018). https://doi.org/10.1007/s10851-017-0743-3

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