H∞ filtering and physical modeling for robust kinematics estimation

A robust H_∞ algorithm for object kinematics estimation from image sequences is presented. The framework relies on both the physical modeling of the object structure and behavior, and the minimization of the worst-case error filtering criterion. By employing the finite element method, the system dynamics of the object is constructed as a set of physically meaningful partial differential equations, which are then converted into continuous- and discrete-time state space representations. In contrast to the popular Kalman filtering strategy which produces the minimum-mean-square-error estimates, the mini-max H_∞ filter is adopted which assumes no prior statistics knowledge on the external disturbances. A series of experiments are performed using synthetic data of various noise types and levels to assess the accuracy and robustness of the H_∞ filtering framework, and to make comparisons to the Kalman filtering results. Practical applications to magnetic resonance image sequences of the heart are also presented.