A Metric on Shape Space with Explicit Geodesics

@article{Michor2007AMO,
  title={A Metric on Shape Space with Explicit Geodesics},
  author={Peter W. Michor and David Mumford and Jayant Shah and Laurent Younes},
  journal={arXiv: Differential Geometry},
  year={2007}
}
This paper studies a specific metric on plane curves that has the property of being isometric to classical manifold (sphere, complex projective, Stiefel, Grassmann) modulo change of parametrization, each of these classical manifolds being associated to specific qualifications of the space of curves (closed-open, modulo rotation etc...) Using these isometries, we are able to explicitely describe the geodesics, first in the parametric case, then by modding out the paremetrization and considering… 

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