Estimation of random trajectories on manifolds: application to object tracking

The parameters to be estimated in dynamical image analysis are usually restricted to a subset of the Euclidean space. This constraint is often neglected in the design of image analysis algorithms although it allows one to achieve significant improvements. This paper describes an algorithm for the estimation of parameter evolution on manifolds exploiting three sources of information: the manifold geometry, the motion model and the sensor model. Examples are provided to show that the proposed algorithm outperforms classic estimation methods in these problems.