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PET-CT is now accepted as the best imaging technique for non-invasive staging of lung cancers, and a computer-based abnormality detection is potentially useful to assist the reading physicians in diagnosis. In this paper, we present a new fully-automatic approach to detect abnormalities in the thorax based on global context inference. A max-margin learning-based method is designed to infer the global contexts, which together with local features are then classified to produce the detection results adaptively. The proposed method is evaluated on clinical PET-CT images from NSCLC studies, and high detection precision and recall are demonstrated.