DFG HU 1575/4
Statistics of Riemannian metrics and biomedical gait analysis
This research program is inspired by the "geodesic hypothesis" of Prof. Dr. Le und Prof. Dr. Kume (Univ. Nottingham und Univ. Kent, 2000) stating that "nature tends to move along geodesics". The validity of this hypothesis allows employing novel non-Euclidean statistical methodology developed among others by the Göttingen research group "Statistics in Non-Euclidean Spaces". In collaboration with the School of Rehabilitation Science (McMaster Univ., Canada) this research aims at new motion models for the knee joint that are superior to contemporary models due to increased robustness under marker misplacement. The data encountered are highly non-linear and a suitable Riemannian structure is not obvious. This mathematical part of this research aims at developing a statistical theory for the estimation of Riemannian metrics. The applied part aims to contribute fundamentally to improve diagnostic methods (e.g. early diagnostics of knee osteoarthritis and cruciate ligament insufficiencies as well as classification of early cerebral palsies in children) and facilitate the choice of critical therapeutic interventions.