Newton-type algorithms for time-varying pose estimation

In this paper we consider the task of pose estimation for a rigid configuration of N moving points in R³, based on camera image point data. Since the Euclidean motion parameters are uniquely determined, up to a scalar factor, by the associated essential matrices, we focus on the estimation task for essential matrices. After a reformulation as a constrained optimization problem for a time-varying family of cost functions, a Newton-type path following method is applied to asymptotically track the minima of the cost functions. A discretization of a damped Newton method in a 12-dimensional parameter space is proposed that tracks the time-varying essential matrices up to first order.