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This paper describes a novel approach for reconstructing a closed continuous surface of an object from multiple calibrated color images and silhouettes. Any accurate reconstruction must satisfy (1) photo-consistency and (2) silhouette consistency constraints. Most existing techniques treat these cues identically in optimization frameworks where silhouette constraints are traded off against photo-consistency and smoothness priors. Our approach strictly enforces silhouette constraints, while optimizing photo-consistency and smoothness in a global graph-cut framework. We transform the reconstruction problem into computing max-flow/min-cut in a geometric graph, where any cut corresponds to a surface satisfying exact silhouette constraints (its silhouettes should exactly coincide with those of the visual hull); a minimum cut is the most photo-consistent surface amongst them. Our graph-cut formulation is based on the rim mesh, (the combinatorial arrangement of rims or contour generators from many views) which can be computed directly from the silhouettes. Unlike other methods, our approach enforces silhouette constraints without introducing a bias near the visual hull boundary and also recovers the rim curves. Results are presented for synthetic and real datasets.