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Comparing Curves in Homogeneous Spaces. (arXiv:1712.04586v1 [math.DG])
来源于:arXiv
Of concern is the study of the space of curves in homogeneous spaces.
Motivated by applications in shape analysis we identify two curves if they only
differ by their parametrization and/or a rigid motion. For curves in Euclidean
space the Square-Root-Velocity-Function (SRVF) allows to define and efficiently
compute a distance on this infinite dimensional quotient space. In this article
we present a generalization of the SRVF to curves in homogeneous spaces. We
prove that, under mild conditions on the curves, there always exist optimal
reparametrizations realizing the quotient distance and demonstrate the
efficiency of our framework in selected numerical examples. 查看全文>>