Advances in 3D imaging have recently made 3D surface scanners, capable of capturing textured surfaces at video rate, affordable and common in computer vision. This is a relatively new source of data, the potential of which has not yet been fully exploited as the problem of non-rigid registration of surfaces is difficult. While registration based on shape alone has been an active research area for some time, the problem of registering surfaces based on texture information has not been addressed in a principled way. We propose a novel, efficient and reliable, fully automatic method for performing groupwise non-rigid registration of textured surfaces, such as those obtained with 3D scanners. We demonstrate the robustness of our approach on 3D scans of human faces, including the notoriously difficult case of inter-subject registration. We show how our method can be used to build high-quality 3D models of appearance fully automatically.