Dynamic visual motion estimation from subspace constraints

The problem of estimating rigid motion from projections may be characterized using a nonlinear dynamical system, composed of the rigid motion constraint and the perspective map. The time derivative of the output of such a system, which is called the “motion field” and approximated by the “optical flow”, is bilinear in the motion parameters, and may be used to specify a subspace constraint on either the direction of translation or the inverse depth of the observed points. Estimating motion may then be formulated as an optimization task constrained on such a subspace. We pose the optimization problem in a system theoretic framework as the the identification of a nonlinear implicit dynamical system with parameters on a differentiable manifold, and use techniques which pertain to nonlinear estimation and identification theory to perform the optimization task in a principled manner. The application of a general method presented in by Soatto et al. (see 33rd. IEEE conf. on Decision and Control, 1994) results in a recursive and pseudo-optimal solution of the visual motion estimation problem, which has robustness properties far superior to other existing techniques we have implemented. Experiments on real and synthetic image sequences show very promising results in terms of robustness, accuracy and computational efficiency