Image Denoising by Statistical Area Thresholding

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.

Keywords

image denoising mathematical morphology area opening and closing random image threshold function Poisson approximation lattice animals 

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Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.MAP5, UMR CNRS 8145Université René DescartesParis

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