Hierarchical implicit surface joint limits for human body tracking

To increase the reliability of existing human motion tracking algorithms, we propose a method for imposing limits on the underlying hierarchical joint structures in a way that is true to life. Unlike most existing approaches, we explicitly represent dependencies between the various degrees of freedom and derive these limits from actual experimental data. To this end, we use quaternions to represent individual 3 DOF joint rotations and Euler angles for 2 DOF rotations, which we have experimentally sampled using an optical motion capture system. Each set of valid positions is bounded by an implicit surface and we handle hierarchical dependencies by representing the space of valid configurations for a child joint as a function of the position of its parent joint. This representation provides us with a metric in the space of rotations that readily lets us determine whether a posture is valid or not. As a result, it becomes easy to incorporate these sophisticated constraints into a motion tracking algorithm, using standard constrained optimization techniques. We demonstrate this by showing that doing so dramatically improves performance of an existing system when attempting to track complex and ambiguous upper body motions from low quality stereo data.