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We present a unified approach to Expectation-Maximization (EM) and Level Set image segmentation that combines the advantages of the two algorithms via a geometric prior that encourages local classification similarity. Compared to level sets, our method increases the information returned by providing probabilistic soft decisions, is easily extensible to multiple regions, and does not require solving Partial Differential Equations (PDEs). Relative to the basic mixture model EM, the unified algorithm improves robustness to noise while smoothing class transitions. We illustrate the versatility and advantages of the algorithm on two real-life problems: segmentation of induced pluripotent stem cell (iPSC) colonies in phase contrast microscopic images and information recovery from brain magnetic resonance images (MRI).