Energy based multiple model fitting for non-rigid structure from motion

In this paper we reformulate the 3D reconstruction of deformable surfaces from monocular video sequences as a labeling problem. We solve simultaneously for the assignment of feature points to multiple local deformation models and the fitting of models to points to minimize a geometric cost, subject to a spatial constraint that neighboring points should also belong to the same model. Piecewise reconstruction methods rely on features shared between models to enforce global consistency on the 3D surface. To account for this overlap between regions, we consider a super-set of the classic labeling problem in which a set of labels, instead of a single one, is assigned to each variable. We propose a mathematical formulation of this new model and show how it can be efficiently optimized with a variant of α-expansion. We demonstrate how this framework can be applied to Non-Rigid Structure from Motion and leads to simpler explanations of the same data. Compared to existing methods run on the same data, our approach has up to half the reconstruction error, and is more robust to over-fitting and outliers.