Capturing 3D stretchable surfaces from single images in closed form

Trabajo presentado al CVPR 2009 celebrado en Miami del 20 al 25 de junio.We present a closed-form solution to the problem of recovering the 3D shape of a non-rigid potentially stretchable surface from 3D-to-2D correspondences. In other words, we can reconstruct a surface from a single image without a priori knowledge of its deformations in that image. State-of-the-art solutions to non-rigid 3D shape recovery rely on the fact that distances between neighboring surface points must be preserved and are therefore limited to inelastic surfaces. Here, we show that replacing the inextensibility constraints by shading ones removes this limitation while still allowing 3D reconstruction in closed-form. We demonstrate our method and compare it to an earlier one using both synthetic and real data.This work was supported by projects: 'Perception, action & cognition through learning of object-action complexes.' (4915), 'CONSOLIDER-INGENIO 2010 Multimodal interaction in pattern recognition and computer vision' (V-00069), 'Percepción y acción ante incertidumbre' (4803), 'Priors para la detección 3D en tiempo real de objetos rígidos y deformables' (4805). This work has been partially funded by the Spanish Ministry of Science and Innovation under projects 200850I055, DPI2008-06022, and Consolider Ingenio 2010 CSD2007-00018, by EU PACO-PLUS project FP6-2004-IST-4-27657, and by the Swiss National Science Foundation.Peer Reviewe