Journal of Mathematical Imaging and Vision

, Volume 60, Issue 1, pp 50–69 | Cite as

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

  • Romain Abraham
  • Maïtine BergouniouxEmail author
  • Pierre Debs


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.


Image processing Galton–Watson Grain filters Cracks 

Mathematics Subject Classification

60J80 68U10 94A12 



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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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.Laboratoire MAPMO, CNRS, UMR 7349, Fédération Denis Poisson, FR 2964Université d’OrléansOrléans Cedex 2France

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