Riemannian Means as Solutions of Variational Problems
2006 ◽
Vol 9
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pp. 86-103
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Keyword(s):
Data Set
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We formulate a variational problem on a Riemannian manifoldMwhose solutions are piecewise smooth geodesies that best fit a given data set of time labelled points inM. By a limiting process, these solutions converge to a single point inM. which we prove to be the Riemannian mean of the given points for some particular Riemannian manifolds such as Euclidean spaces, connected and compact Lie groups, and spheres.