Capturing 3D Stretchable Surfaces from Single Images in Closed Form

We present a closed-form solution to the problem of re- covering 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 in- elastic 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.