Image-based 3D modeling via Cheeger sets

We propose a novel variational formulation for generating 3D models of objects from a single view. Based on a few user scribbles in an image, the algorithm automatically extracts the object silhouette and subsequently determines a 3D volume by minimizing the weighted surface area for a fixed user-specified volume. The respective energy can be efficiently minimized by means of convex relaxation techniques, leading to visually pleasing smooth surfaces within a matter of seconds. In contrast to existing techniques for single-view reconstruction, the proposed method is based on an implicit surface representation and a transparent optimality criterion, assuring high-quality 3D models of arbitrary topology with a minimum of user input.