Title: Illumination problems in digital images: A statistical point of view
Authors: Segolen Geffray - Universite de Strasbourg (France) [presenting]
Nicolas Klutchnikoff - Universite Rennes 2 (France)
Myriam Vimond - ENSAI (France)
Abstract: Interest is focused on a multi-dimensional signal $R$ observed on a grid in the presence of both an illumination artifact and an additional additive bounded variance centered noise $\varepsilon$. The illumination artifact consists of colour or grey level intensity variations which are seen on the sampled image but which are not present in $R$. Such an assumption is classically modelled using a function $L$ which acts multiplicatively on $R$. Our goal is to estimate $R$ from observations of a random variable $Y$ which obeys the regression model $Y=RL+\varepsilon$. We identify and propose a solution to an identifiability issue. We construct a consistent multi-step estimation procedure. We first make use of any consistent denoising method to estimate from the noisy data the gradient of the logarithm of the regression function. We assume that the artefact $L$ consists of ``smooth'' variations. Then we project the denoised auxiliary estimate on a finite basis of ``smooth'' functions. We deduce the final estimator of $R$ so that the proposed identifiability constraint is satisfied. An additional Monte Carlo computation is used to approximate a relevant integral. We derive an upper bound for the sup-norm risk of our estimator. Applications to different images are presented.