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A novel algorithm is proposed for performing unsupervised tissue classification in medical images by combining conventional clustering techniques with edge-adaptive segmentation techniques. Based on the fuzzy C-means algorithm, the algorithm computes a smooth segmentation while simultaneously estimating an edge field. Unlike most tissue classification algorithms that incorporate a smoothness constraint, the edge field estimation prevents the algorithm from smoothing across tissue boundaries, thereby producing robust yet accurate results. The algorithm is formulated as the minimization of an objective function that includes penalty terms to ensure that both the segmentation and edge field are relatively smooth. To compute the edge field, a difference equation with spatially varying coefficients is solved using an efficient multigrid algorithm. Some preliminary results applying the method to synthetic and magnetic resonance images are presented.