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 might be a major risk factor for the development of knee osteoarthritis, we develop confidence tubes for curves following a perturbation model on SO(3) using the Gaussian kinematic formula which are equivariant under gait similarities and have precise coverage even for small sample sizes. Applying them to gait curves from eight volunteers undergoing kneeling tasks and adjusting for different walking speeds and marker replacement at different visits, allows us to identify at which phases of the gait cycle the gait pattern changed due to kneeling.