Bayesian Hyperspectral Image Segmentation With Discriminative Class Learning

Abstract

This paper introduces a new supervised technique to segment hyperspectral images: the Bayesian segmentation based on discriminative classification and on multilevel logistic (MLL) spatial prior. The approach is Bayesian and exploits both spectral and spatial information. Given a spectral vector, the posterior class probability distribution is modeled using multinomial logistic regression (MLR) which, being a discriminative model, allows to learn directly the boundaries between the decision regions and, thus, to successfully deal with high-dimensionality data. To control the machine complexity and, thus, its generalization capacity, the prior on the multinomial logistic vector is assumed to follow a componentwise independent Laplacian density. The vector of weights is computed via the fast sparse multinomial logistic regression (FSMLR), a variation of the sparse multinomial logistic regression (SMLR), conceived to deal with large data sets beyond the reach of the SMLR. To avoid the high computational complexity involved in estimating the Laplacian regularization parameter, we have also considered the Jeffreys prior, as it does not depend on any hyperparameter. The prior probability distribution on the class-label image is an MLL Markov–Gibbs distribution, which promotes segmentation results with equal neighboring class labels. The <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$\alpha$</tex></formula> -expansion optimization algorithm, a powerful graph-cut-based integer optimization tool, is used to compute the maximum a posteriori segmentation. The effectiveness of the proposed methodology is illustrated by comparing its performance with the state-of-the-art methods on synthetic and real hyperspectral image data sets. The reported results give clear evidence of the relevance of using both spatial and spectral information in hyperspectral image segmentation.