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.

We present an algorithm able to register a known 3D deformable model to a set of 2D matched points extracted from a single image. Unlike previous approaches, the problem is solved simultaneously for both the rigid and non-rigid parameters of the model. The key advantage of our approach is the projection of an initial affine estimation of the motion parameters into the motion manifold corresponding to the exact parametrization of the problem. This projection is formulated as theminimization of the distance between the affine solution and the surface of the manifold. Such optimization results in a quadratically constrained quadratic minimization problem that can be efficiently solved with standard optimization tools. Synthetic and real tests demonstrate the effectiveness of the approach.