Modeling Head and Hand Orientation during Motion using Quaternions

Some body parts, such as the head and the hand, change their orientation during motion. Orientation can be conveniently and elegantly represented using quaternions. The method has several advantages over Euler angles in that the problem of gimbal lock is avoided and that the orientation is represented by a single mathematical object rather than a collection of angles that can be redefined in various arbitrary ways. The use of quaternions has been popular in animation applications for some time, especially for interpolating motions. We will introduce some new applications involving statistical methods for quaternions that will allow us to present meaningful averages of repeated motions involving orientations and make regression predictions of orientation. For example, we can model how the glancing behavior of the head changes according to the target of the reach and other factors.

We will give a brief introduction to the mathematics of quaternions and how they can be used to represent orientations. We will compare it to other methods of representation. Due to the quite different mathematics involved, existing statistical methods cannot be directly applied and even simple concepts such as the average, need to be defined. We will introduce a method to analyze orientation over time via functional regression analysis with the help of quaternion splines.

We will demonstrate the utility of these methods for analyzing orientation data. We will show an application to the prediction of head and hand orientation during motion.