Existing algorithms for surface reconstruction from point sets are defeated by moderate amounts of noise and outliers, which makes them unapplicable to point clouds originating from multi-view image data. In this paper, we present a novel method which incorporates the input images in the surface reconstruction process for a better accuracy and robustness. Our approach is based on the medial axis transform of the scene, which our algorithm estimates through a global photoconsistency optimization by simulated annealing. A faithful polyhedral representation of the scene is then obtained by inversion of the medial axis transform.