Optimization on Lie Manifolds and Projective Tracking

Template tracking based on the space transformation model can often be reduced to solve a nonlinear least squares optimization problem over a Lie manifold of parameters. The algorithm on the vector space has more limitations when it concerns the nonlinear projective warps. We show that exploiting the special structure of Lie manifolds allows one to devise a method for optimizing on Lie manifolds in a computationally efficient manner. The new method relies on the differential geometry of Lie manifolds and the underlying connections between Lie groups and their associated Lie algebras. The comparative projective tracking experiments validate the effectiveness of the template tracking based on the Lie manifolds optimization.