Provably convergent structure and motion estimation for perspective systems

Estimation of structure and motion in computer vision systems can be performed using a dynamic systems approach, where states and parameters in a perspective system are observed. This paper presents a new approach to the structure estimation problem, where the estimation of the 3D-positions of feature points on a moving object is reformulated as a parameter estimation problem. For each feature point, a constant parameter is estimated, from which it is possible to calculate the time-varying 3D-position. The estimation method is extended to the estimation of motion, in the form of angular velocity estimation. The combined structure and angular velocity observer is shown stable using Lyapunov theory and persistency of excitation based arguments. The estimation method is illustrated with simulation examples, demonstrating the estimation convergence.