(en) "We propose a Riemannian quasi-Newton method to compute a geodesic invariant to scaling, translation, rotation and reparameterization and show that it is more efficient than the current state-of-the-art coordinate-descent/path-straightening approach."
You, Y., Huang, W., Gallivan, K. A., & Absil, P.-A. (2015). A Riemannian approach for computing geodesics in elastic shape analysis. 2015 IEEE Global Conference on Signal and Information Processing, p. 727-731. https://doi.org/10.1109/GlobalSIP.2015.7418292