Structure and Motion Estimation in Rigid Body Perspective Dynamic Systems

Abstract: Abstract This thesis concerns different aspects of recursive estimation of structure and motion in dynamic rigid body perspective systems, where the three-dimensional position of observed object feature points are expressed as states in a system of deterministic or stochastic differential equations describing the object motion, combined with a set of output equations in the form of two-dimensional perspective measurements obtained using a single camera. Firstly, a number of novel hybrid matching constraints are derived for the recovery of motion parameters in a rigid body perspective system where the measurements can be considered as arriving at closely spaced time instants. It is illustrated how the hybrid constraints can be combined with an existing state estimation algorithm, in order to obtain a complete algorithm for estimation of both structure and motion. Secondly, a novel parametrization is introduced for the dynamic perspective system. The parametrization allows for application of well established results from observer theory, in order to construct a provably convergent observer for three-dimensional point positions, assuming knowledge of the motion parameters. The parametrization is further utilized to construct an adaptive observer for the estimation of both position and angular velocity. Thirdly, given perspective observations of multiple feature points on the same rigid object, and assuming knowledge of the motion parameters, we investigate the use of a connected filter for improved structure estimation, uti- lizing information common to the observed points. Finally, we investigate the possibilities to construct a nonlinear filter for structure estimation in dynamic perspective systems using linear design methods.

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