Capturing 3D stretchable surfaces from single images in closed form

We present a closed form solution to the problem of recovering the 3D shape of a nonrigid 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 nonrigid 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.