Factorization for non-rigid and articulated structure using metric projections

This paper describes a new algorithm for recovering the 3D shape and motion of deformable and articulated objects purely from uncalibrated 2D image measurements using an iterative factorization approach. Most solutions to non-rigid and articulated structure from motion require metric constraints to be enforced on the motion matrix to solve for the transformation that upgrades the solution to metric space. While in the case of rigid structure the metric upgrade step is simple since the motion constraints are linear, deformability in the shape introduces non-linearities. In this paper we propose an alternating least-squares approach associated with a globally optimal projection step onto the manifold of metric constraints. An important advantage of this new algorithm is its ability to handle missing data which becomes crucial when dealing with real video sequences with self-occlusions. We show successful results of our algorithms on synthetic and real sequences of both deformable and articulated data.