Esfandiar Nava-Yazdani, Christoph von Tycowicz, Hans-Christian Hege, and I have just uploaded an updated preprint of our work “Geodesic analysis in Kendall's shape space with epidemiological applications” (previously entitled “A shape trajectories approach to longitudinal statistical analysis”) to the arXiv. This work is part of the ECMath / MATH+ project CH-15 “Analysis of Empirical Shape Trajectories”.
Abstract. We analytically determine Jacobi fields and parallel transports and compute geodesic regression in Kendall's shape space. Using the derived expressions, we can fully leverage the geometry via Riemannian optimization and thereby reduce the computational expense by several orders of magnitude. The methodology is demonstrated by performing a longitudinal statistical analysis of epidemiological shape data. As an example application we have chosen 3D shapes of knee bones, reconstructed from image data of the Osteoarthritis Initiative (OAI). Comparing subject groups with incident and developing osteoarthritis versus normal controls, we find clear differences in the temporal development of femur shapes. This paves the way for early prediction of incident knee osteoarthritis, using geometry data alone.