We describe our submission to the Brain Tumor Segmentation Challenge (BraTS) at MICCAI 2012, which is based on our method for tissue-specific segmentation of high-grade brain tumors . The main idea is to cast the segmentation as a classification task, and use the discriminative power of context information. We realize this idea by equipping a classification forest (CF) with spatially non-local features to represent the data, and by providing the CF with initial probability estimates for the single tissue classes as additional input (along-side the MRI channels). The initial probabilities are patient-specific, and computed at test time based on a learned model of intensity. Through the combination of the initial probabilities and the non-local features, our approach is able to capture the context information for each data point. Our method is fully automatic, with segmentation run times in the range of 1-2 minutes per patient. We evaluate the submission by cross-validation on the real and synthetic, high- and low-grade tumor BraTS data sets.