This paper addresses the problem of obtaining complete, detailed reconstructions of textureless shiny objects. We present an algorithm which uses silhouettes of the object, as well as images obtained under changing illumination conditions. In contrast with previous photometric stereo techniques, ours is not limited to a single viewpoint but produces accurate reconstructions in full 3D. A number of images of the object are obtained from multiple viewpoints, under varying lighting conditions. Starting from the silhouettes, the algorithm recovers camera motion and constructs the object's visual hull. This is then used to recover the illumination and initialise a multi-view photometric stereo scheme to obtain a closed surface reconstruction. There are two main contributions in this paper: Firstly we describe a robust technique to estimate light directions and intensities and secondly, we introduce a novel formulation of photometric stereo which combines multiple viewpoints and hence allows closed surface reconstructions. The algorithm has been implemented as a practical model acquisition system. Here, a quantitative evaluation of the algorithm on synthetic data is presented together with complete reconstructions of challenging real objects. Finally, we show experimentally how even in the case of highly textured objects, this technique can greatly improve on correspondence-based multi-view stereo results.