Projective Tracking Based on Second-Order Optimization on Lie Manifolds

Template tracking based on the space transformation model can usually 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. Exploiting the special structure of Lie manifolds allows one to devise a method for optimizing on Lie manifolds in a computationally efficient manner. The mapping between a Lie group and its Lie algebra can make us to utilize the specific properties of the target tracking to propose a second-order minimization tracking method. This approach needs not calculating the Hessian matrix and reduces the computation complexity. The comparative experiments with the algorithm based on the vector space and the Gauss-Newton algorithm based on the Lie algebra parameterization validate the feasibility and high effectiveness of our method.