Monocular Reconstruction of Conformal Surfaces through Optimization

In this paper we study monocular reconstruction of extensible surfaces undergoing conformal deformation. Given a 3D template, its image and a set of point correspondences from a specific image of the deformed surface, the goal is to determine the 3D positions of the points as well as the stretching factor at each point. To perform such reconstruction, we define an optimization procedure that makes use of the re-projection error, so-called upper-bound model, constraints associated with conformal deformation, and those resulting from the assumption that the motion amplitude of boundary points is restricted. These points lie on the surface border which varies by the camera viewpoint. The upper-bound model is used in a variational form where the bound on the Euclidean distance of point pairs decreases in a sequence of optimizations, from which the best reconstruction is selected. Our experimental study revealed that this approach achieves accurate results.