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Image Denoising by Statistical Area Thresholding

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Abstract

Area openings and closings are morphological filters which efficiently suppress impulse noise from an image, by removing small connected components of level sets. The problem of an objective choice of threshold for the area remains open. Here, a mathematical model for random images will be considered. Under this model, a Poisson approximation for the probability of appearance of any local pattern can be computed. In particular, the probability of observing a component with size larger than k in pure impulse noise has an explicit form. This permits the definition of a statistical test on the significance of connected components, thus providing an explicit formula for the area threshold of the denoising filter, as a function of the impulse noise probability parameter. Finally, using threshold decomposition, a denoising algorithm for grey level images is proposed.

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Authors and Affiliations

  1. MAP5, UMR CNRS 8145, Université René Descartes, Paris

    D. Coupier, A. Desolneux & B. Ycart

Authors
  1. D. Coupier
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  2. A. Desolneux
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  3. B. Ycart
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Corresponding author

Correspondence to A. Desolneux.

Additional information

David Coupier is 25 years old, he is PhD student at the MAP5. He has studied mathematics at the University of Orsay—Paris XI. He is working on zero-one laws and Poisson approximations for random images. Web page: http://www.math-info.univ-paris5.fr/~coupier/

Agnés Desolneux is 30 years old, she is CNRS researcher at the MAP5. She defended her PhD thesis in applied mathematics in 2000 under the direction of Jean-Michel Morel at the ENS Cachan. She is working on statistical methods in image analysis. Web page: http://www.math-info.univ-paris5.fr/~desolneux/

Bernard Ycart is 45 years old, he is Professor of mathematics at the University Paris 5 and director of the MAP5 (FRE CNRS 2428). He is specialist of applied probabilities (Markov processes, stochastic algorithms). Web page: http://www.math-info.univ-paris5.fr/~ycart/

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Coupier, D., Desolneux, A. & Ycart, B. Image Denoising by Statistical Area Thresholding. J Math Imaging Vis 22, 183–197 (2005). https://doi.org/10.1007/s10851-005-4889-z

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  • DOI: https://doi.org/10.1007/s10851-005-4889-z

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