Visibility estimation is arguably the most difficult problem in dense 3D reconstruction from multiple arbitrary views. In this paper, we propose a simple new approach to estimating visibility based on position and orientation of local surface patches. Using our concept of oriented visibility, we present a new algorithm for multiview reconstruction based on exact global optimization of surface photoconsistency using graph cuts on a CW-complex. In contrast to many previous methods for 3D reconstruction from arbitrary views, our method does not depend on initialization and is robust to photometrically difficult situations.