Without a deformation model, monocular 3D shape recovery of deformable surfaces is severely under-constrained. Even when the image information is rich enough, prior knowledge of the feasible deformations is required to overcome the ambiguities. This is further accentuated when such information is poor, which is a key issue that has not yet been addressed. In this paper, we propose an approach to learning shape priors to solve this problem. By contrast with typical statistical learning methods that build models for specific object shapes, we learn local deformation models, and combine them to reconstruct surfaces of arbitrary global shapes. Not only does this improve the generality of our deformation models, but it also facilitates learning since the space of local deformations is much smaller than that of global ones. While using a texture-based approach, we show that our models are effective to reconstruct from single videos poorly-textured surfaces of arbitrary shape, made of materials as different as cardboard, that deforms smoothly, and much lighter tissue paper whose deformations may be far more complex.