On Shape of Plane Elastic Curves

@article{Mio2006OnSO,
  title={On Shape of Plane Elastic Curves},
  author={Washington Mio and Anuj Srivastava and Shantanu H. Joshi},
  journal={International Journal of Computer Vision},
  year={2006},
  volume={73},
  pages={307-324}
}
We study shapes of planar arcs and closed contours modeled on elastic curves obtained by bending, stretching or compressing line segments non-uniformly along their extensions. Shapes are represented as elements of a quotient space of curves obtained by identifying those that differ by shape-preserving transformations. The elastic properties of the curves are encoded in Riemannian metrics on these spaces. Geodesics in shape spaces are used to quantify shape divergence and to develop morphing… 
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