Geodesics on Shape Spaces with Bounded Variation and Sobolev Metrics

@article{Nardi2016GeodesicsOS,
  title={Geodesics on Shape Spaces with Bounded Variation and Sobolev Metrics},
  author={Giacomo Nardi and Gabriel Peyr{\'e} and François-Xavier Vialard},
  journal={SIAM J. Imaging Sci.},
  year={2016},
  volume={9},
  pages={238-274}
}
This paper studies the space of $BV^2$ planar curves endowed with the $BV^2$ Finsler metric over its tangent space of displacement vector fields. Such a space is of interest for applications in image processing and computer vision because it enables piecewise regular curves that undergo piecewise regular deformations, such as articulations. The main contribution of this paper is the proof of the existence of the shortest path between any two $BV^2$-curves for this Finsler metric. Such a result… 

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