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The aim of this paper is to introduce a novel semisupervised scheme for abnormality detection and segmentation in medical images. Semisupervised learning does not require pathology modeling and, thus, allows high degree of automation. In abnormality detection, a vector is characterized as anomalous if it does not comply with the probability distribution obtained from normal data. The estimation of the probability density function, however, is usually not feasible due to large data dimensionality. In order to overcome this challenge, we treat every image as a network of locally coherent image partitions (overlapping blocks). We formulate and maximize a strictly concave likelihood function estimating abnormality for each partition and fuse the local estimates into a globally optimal estimate that satisfies the consistency constraints, based on a distributed estimation algorithm. The likelihood function consists of a model and a data term and is formulated as a quadratic programming problem. The method is applied for automatically segmenting brain pathologies, such as simulated brain infarction and dysplasia, as well as real lesions in diabetes patients. The assessment of the method using receiver operating characteristic analysis demonstrates improvement in image segmentation over two-group analysis performed with Statistical Parametric Mapping (SPM).