Abstract
In this article, we describe a novel unsupervised spectral image segmentation algorithm. This algorithm extends the classical Gaussian Mixture Model-based unsupervised classification technique by incorporating a spatial flavor into the model: the spectra are modelized by a mixture of K classes, each with a Gaussian distribution, whose mixing proportions depend on the position. Using a piecewise constant structure for those mixing proportions, we are able to construct a penalized maximum likelihood procedure that estimates the optimal partition as well as all the other parameters, including the number of classes. We provide a theoretical guarantee for this estimation, even when the generating model is not within the tested set, and describe an efficient implementation. Finally, we conduct some numerical experiments of unsupervised segmentation from a real dataset.
Highlights
Unsupervised Segmentation of Spectral Images with a Spatialized Gaussian Mixture Model and Model Selection — In this article, we describe a novel unsupervised spectral image segmentation algorithm
This algorithm extends the classical Gaussian Mixture Model-based unsupervised classification technique by incorporating a spatial flavor into the model: the spectra are modelized by a mixture of K classes, each with a Gaussian distribution, whose mixing proportions depend on the position
Located at the SOLEIL Synchrotron (Saint-Aubin, France), IPANEMA is a platform that is unique in the world, dedicated to the study of ancient material
Summary
Located at the SOLEIL Synchrotron (Saint-Aubin, France), IPANEMA is a platform that is unique in the world, dedicated to the study of ancient material. Amongst them the most classical are based on the hierarichal Markov field; see, for instance, the work of Farag et al [9], in which spatial regularization is imposed on the clustering labels Another direction is that of Tarabalka et al [10] in which the regions are initially segmented using a spatial method and combined according to spectral criteria. More sophisticated spatial models have been proposed, e.g. using a random Markov field to impose spatial constraints on the mixture proportions [15], even presenting efficient optimization algorithms for univariate or color RGB images [16].Whilst avoiding the model selection problem, these latter methods only consider the semi-unsupervised case since the proposed algorithms rely on the user to provide the number of classes, K, and typically to set the spatial regularization parameter(s).
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