A.: Monocular template-based reconstruction of inextensible surfaces

Abstract. We present different approaches to reconstructing an inex-tensible surface from point correspondences between an input image and a template image representing a flat reference shape from a fronto-parallel point of view. We first propose a ‘point-wise ’ method, i.e. a method that only retrieves the 3D positions of the point correspondences. This method is formulated as a second-order cone program and it han-dles inaccuracies in the point measurements. It relies on the fact that the Euclidean distance between two 3D points must be shorter than their geodesic distance (which can easily be computed from the tem-plate image). We then present an approach that reconstructs a smooth 3D surface based on Free-Form Deformations. The surface is represented as a smooth map from the template image space to the 3D space. Our idea is to say that the 2D-3D map must be everywhere a local isometry. This induces conditions on the Jacobian matrix of the map which are included in a least-squares minimization problem.