An unsupervised and non-parametric Bayesian Image segmentation

Abstract

We propose here an unsupervised Bayesian image segmentation based on a non-parametric Expectation-Maximisation (EM) algorithm. The non-parametric aspect comes from the use of the orthogonal probability density function (pdf) estimation, which is reduced to the estimation of the first Fourier coefficients (FC's) of the pdf with respect to a given orthogonal basis. So, the mixture identification step based on the maximisation of the likelihood can be realised without hypothesis on the distribution of the conditional pdf. This means that we do not need some assumption for the gray level image pixels distribution. The generalisation to the multivariate case can be obtained by considering the multidimensional orthogonal function basis. In this paper, we intend to give some simulation results for the determination of the smoothing parameter. This algorithm is applied to a contextual image segmentation. Such method conjugated with Bootstrap Sampling allows as the exploration of a large neighbourhood context.

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