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Illumination problems in digital images. A statistical point of view

Author

Listed:
  • Geffray, S.
  • Klutchnikoff, N.
  • Vimond, M.

Abstract

This paper focuses on the statistical treatment of illumination artefacts on digital images in the presence of an additional random noise. We assume that this artefact consists of “smooth” variations of the intensity of the signal of interest R. Such an assumption is classically modelled using a function L which acts in a multiplicative way on R. Our goal is to estimate R from observations of a random variable Y which obeys the regression model Y=RL+ε. Our main contribution lies in the derivation of a new estimator of R which is shown to be consistent under suitable identifiability and regularity conditions. The accuracy of this new estimation procedure is studied from a theoretical point of view through the rate of convergence of the uniform risk. Applications to real Scanning Electron Microscopy images are presented, as well as a qualitative study of the performances of our method with respect to other image processing techniques.

Suggested Citation

  • Geffray, S. & Klutchnikoff, N. & Vimond, M., 2016. "Illumination problems in digital images. A statistical point of view," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 191-213.
    • Handle: RePEc:eee:jmvana:v:150:y:2016:i:c:p:191-213
    DOI: 10.1016/j.jmva.2016.05.001
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    References listed on IDEAS

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    1. F. Comte & Y. Rozenholc, 2004. "A new algorithm for fixed design regression and denoising," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(3), pages 449-473, September.
    2. J. Polzehl & V. G. Spokoiny, 2000. "Adaptive weights smoothing with applications to image restoration," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 335-354.
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