ConferenceProceedings
brunet2010accv
Monocular Template-based Reconstruction of Smooth and Inextensible Surfaces
2010
Brunet
Florent
Hartley
Richard
Bartoli
Adrien
Navab
Nassir
Malgouyres
Rémy
Kimmel
Ron
Klette
Reinhard
Sugimoto
Akihiro
52-66
6494
Proceedings of the Tenth Asian Conference on Computer Vision (ACCV 2010)
Lecture Notes in Computer Science
We present different approaches to reconstructing an inextensible 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 handles 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 template 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.