Probabilities and Statistics on Riemannian Manifolds : A Geometric approach

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Matrix-valued kernels for shape deformation analysis (2013, background): “The knowledge of such geometry (and in particular, of curvature) is fundamental as it allows one to infer, for example, about the uniqueness of geodesics between shapes, the existence of conjugate points, and the wellposedness of the problem of computing the intrinsic (or Karcher’s) mean [54] of a d”
Intrinsic Statistics on Riemannian Manifolds: Basic Tools for Geometric Measurements (2006, background): “In our case, the measure is induced by the Riemannian metric but the problem is only lifted: which Riemannian metric do we have to choose ? For transformation groups and homogeneous manifolds, we showed in [1] that an invariant metric is a good geometric choice, even if such a metric does not always”
A Riemannian Framework for Tensor Computing (2005, methodology): “As described in [Pennec, 2004], we may generalize most of the usual statistical methods by using the exponential chart at the mean point.”