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Segmentation methods based on pixel classification are powerful but often slow. We introduce two general algorithms, based on sparse classification, for optimizing the computation while still obtaining accurate segmentations. The computational costs of the algorithms are derived, and they are demonstrated on real 3-D magnetic resonance imaging and 2-D radiograph data. We show that each algorithm is optimal for specific tasks, and that both algorithms allow a speedup of one or more orders of magnitude on typical segmentation tasks.