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Most methods for structure-function analysis in medical images usually are based on voxel-wise statistical tests performed on registered Magnetic Resonance (MR) images across subjects. A major drawback of such methods is the inability to accurately locate regions that manifest nonlinear associations with clinical variables. In this paper we propose Bayesian Morphological Analysis (BMA) methods, based on a Bayesian-network representation, for the analysis of MR brain images. First, we describe how Bayesian networks can represent probabilistic associations among voxels and clinical (functional) variables. Second, we present a model-selection framework, which generates a Bayesian network that captures structure-function relationships from MR brain images and functional variables. We demonstrate our methods in the context of determining associations between regional brain atrophy (as demonstrated on MR images of the brain), and functional deficits. We employ two data sets for this evaluation: the first contains MR images of 11 subjects, where associations between regional atrophy and a functional deficit are almost linear; the second data set contains MR images of the ventricles of 84 subjects, where the structure-function association is nonlinear. Our methods successfully identify voxel-wise morphological changes that are associated with functional deficits in both data sets, whereas standard statistical analysis (i. e., t-test and paired t-test) finds only some of these changes in the linear-association case, and fails in the nonlinear-association case.