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In this paper we consider the problem of classifying materials in a scene based on hyperspectral measurements and a known spectral library of intrinsic material reflectances. In addition to sensor noise, estimation of material reflectances is complicated by atmospheric distortion and local shadowing effects in the scene. This paper proposes a robust Bayesian classifier based on belief propagation and the introduction of two sources of additional prior structure: 1) structured variation of atmospheric distortion, and 2) a spatial Markov structure for materials and shadows in the scene. An example demonstrates substantial reduction in pixel misclassification rate using the proposed method.