We propose an exact method for efficiently and robustly computing the visual hull of an object from image contours. Unlike most existing approaches, ours computes an exact description of the visual hull polyhedron associated to polygonal image contours. Furthermore, the proposed approach is fast and allows real-time recovery of both manifold and watertight visual hull polyhedra. The process involves three main steps. First, a coarse geometrical approximation of the visual hull is computed by retrieving its viewing edges, an unconnected subset of the wanted mesh. Then, local orientation and connectivity rules are used to walk along the relevant viewing cone intersection boundaries, so as to iteratively generate the missing surface points and connections. A final connection walkthrough allows us to identify the planar contours for each face of the polyhedron. Implementation details and results with synthetic and real data are presented.