Contextual unmixing of geospatial data based on Bayesian modeling

Image classification has a long history for estimating landcover categories by feature vectors, and various methods have been proposed from many viewpoints; statistics, machine learning and others. Multivariate normal distributions are frequently used to model feature distributions. Also, it is known that contextual classification methods based on Markov random fields (MRF) improve non-contextual classifiers successfully. If low-spatial resolution images are given, a pixel may be covered by two or more land-cover categories. Thus, we are required to estimate fractions of categories covering the pixel. This issue is called unmixing, and it is usually solved by the linear equation derived by the assumption such that the observed feature vector is composed by a convex combination of the category reflectance signatures. In the recent years, several Bayesian approaches were proposed for the unmixing problem. Markov chain Monte Carlo (MCMC) methods were applied to linear unmixing of hyperspectral images. A hierarchical Bayesian algorithm proposed by combining bilinear models with MCMC was also discussed for nonlinear unmixing to handle scattering effects. In this paper, we consider Bayesian models and variable selection is examined. Logistic regression is reviewed and hierarchic Bayesian models are provided where a Gibbs sampling procedure was used for posterior estimation.