Relative volume constraints for single view 3D reconstruction

We introduce the concept of relative volume constraints in order to account for insufficient information in the reconstruction of 3D objects from a single image. The key idea is to formulate a variational reconstruction approach with shape priors in form of relative depth profiles or volume ratios relating object parts. Such shape priors can easily be derived either from a user sketch or from the object's shading profile in the image. They can handle textured or shadowed object regions by propagating information. We propose a convex relaxation of the constrained optimization problem which can be solved optimally in a few seconds on graphics hardware. In contrast to existing single view reconstruction algorithms, the proposed algorithm provides substantially more flexibility to recover shape details such as self-occlusions, dents and holes, which are not visible in the object silhouette.