Confidence Tubes for Curves on SO(3) and Identification of Subject-Specific Gait Change after Kneeling

Abstract: In order to identify changes of gait patterns, e.g. due to prolonged occupational kneeling, which is believed to be major risk factor, among others, for the development of knee osteoarthritis, we develop confidence tubes for curves following a Gaussian perturbation model on SO(3). These are based on an application of the Gaussian kinematic formula to a process of Hotelling statistics and we approximate them by a computible version, for which we show convergence. Simulations endorse our method, which in application to gait curves from eight volunteers undergoing kneeling tasks, identifies phases of the gait cycle that have changed due to kneeling tasks. We find that after kneeling, deviation from normal gait is stronger, in particular for older aged male volunteers. Notably our method adjusts for different walking speeds and marker replacement at different visits.