Second-Order Shape Optimization for Geometric Inverse Problems in Vision

@article{Balzer2014SecondOrderSO,
  title={Second-Order Shape Optimization for Geometric Inverse Problems in Vision},
  author={Jonathan Balzer and Stefano Soatto},
  journal={2014 IEEE Conference on Computer Vision and Pattern Recognition},
  year={2014},
  pages={3850-3857}
}
  • J. Balzer, Stefano Soatto
  • Published 11 November 2013
  • Mathematics, Computer Science
  • 2014 IEEE Conference on Computer Vision and Pattern Recognition
We develop a method for optimization in shape spaces, i.e., sets of surfaces modulo re-parametrization. Unlike previously proposed gradient flows, we achieve superlinear convergence rates through an approximation of the shape Hessian, which is generally hard to compute and suffers from a series of degeneracies. Our analysis highlights the role of mean curvature motion in comparison with first-order schemes: instead of surface area, our approach penalizes deformation, either by its Dirichlet… 
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