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We introduce a novel stereo algorithm for computing a disparity map from a stereo image pair by minimizing a global cost function. The approach consists of two steps. First a "traditional" correlation-based similarity measurement is performed, then a relaxation takes place to eliminate possible ambiguities. The relaxation is formulated as a cost-optimizing approach, taking into account both the stereoscopic continuity constraint and considerations of the pixel similarity. The special formulation guarantees the existence of a unique minimum of the cost function which can be easily and rapidly found by standard numerical procedures. Results on real and synthetic images demonstrate the operative potential of the approach.