Lifting Vectorial Variational Problems: A Natural Formulation Based on Geometric Measure Theory and Discrete Exterior Calculus

@article{Mllenhoff2019LiftingVV,
  title={Lifting Vectorial Variational Problems: A Natural Formulation Based on Geometric Measure Theory and Discrete Exterior Calculus},
  author={Thomas M{\"o}llenhoff and Daniel Cremers},
  journal={2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)},
  year={2019},
  pages={11109-11118}
}
  • Thomas Möllenhoff, Daniel Cremers
  • Published 2019
  • Computer Science, Engineering
  • 2019 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)
  • Numerous tasks in imaging and vision can be formulated as variational problems over vector-valued maps. We approach the relaxation and convexification of such vectorial variational problems via a lifting to the space of currents. To that end, we recall that functionals with polyconvex Lagrangians can be reparametrized as convex one-homogeneous functionals on the graph of the function. This leads to an equivalent shape optimization problem over oriented surfaces in the product space of domain… CONTINUE READING
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