Riemannian Center of Mass and so called karcher mean

By Hermann Karcher. 2014

61 citations recorded by the source corpus.

The Riemannian center of mass was constructed in (GrKa) (1973). In (GKR1, GKR2, Gr, Ka, BuKa) (1974-1981) it was successfully applied with more refined estimates. Probably in 1990 someone renamed it without justification into karcher mean and references to the older papers were omitted by those using the new name. As a consequence newcomers started to reprove results from the above papers. - Here I explain the older history. The Euclidean center of mass is an affinenotion. I will use discrete mass points rather than mass distributions, for simpler wording. Let pi 2 R n be points of weight mi with P mi = 1 (for convenience). The center is defined, without reference to a metric, as:

Subfields: Applied Mathematics, Geometry and Topology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/43722a35e7f3fed558e3d92ab2144f54a53ee2f4

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In Applied Mathematics

In Geometry and Topology

In Statistical and Nonlinear Physics

Citations in the corpus

Trunk-Branch Ensemble Convolutional Neural Networks for Video-Based Face Recognition (2016, background): “where μ̂c is the Karcher mean (Riemannian geometric mean) [54] that also lies on the unit hypersphere.”
Barycentric subspace analysis on manifolds (2016, methodology): “This is now generally called Karcher mean, although there is a dispute on the naming (Karcher, 2014).”
Computational Optimal Transport (2018, background): “This process is often referred to as “Fréchet” or “Karcher” mean (see Karcher [2014] for an historical account).”