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Extending Continuous Cuts: Anisotropic Metrics and Expansion Moves

Olsson, Carl LU ; Byröd, Martin LU ; Overgaard, Niels Christian LU and Kahl, Fredrik LU (2009) IEEE International Conference on Computer Vision (ICCV), 2009 In Proceedings of 2009 IEEE 12th International Conference on Computer Vision (ICCV) p.405-412
Abstract
The concept of graph cuts is by now a standard method for all sorts of low level vision problems. Its popularity is largely due to the fact that globally or near globally optimal solutions can be computed using efficient max flow algorithms. On the other hand it has been observed that this method may suffer from metrication errors. Recent work has begun studying continuous versions of graph cuts, which give smaller metrication errors. Another advantage is that continuous cuts are straightforward to parallelize. In this paper we extend the class of functionals that can be optimized in the continuous setting to include anisotropic TV-norms. We show that there is a so called coarea formula for these functionals making it possible to minimize... (More)
The concept of graph cuts is by now a standard method for all sorts of low level vision problems. Its popularity is largely due to the fact that globally or near globally optimal solutions can be computed using efficient max flow algorithms. On the other hand it has been observed that this method may suffer from metrication errors. Recent work has begun studying continuous versions of graph cuts, which give smaller metrication errors. Another advantage is that continuous cuts are straightforward to parallelize. In this paper we extend the class of functionals that can be optimized in the continuous setting to include anisotropic TV-norms. We show that there is a so called coarea formula for these functionals making it possible to minimize them by solving a convex problem. We also show that the concept of α-expansion moves can be reformulated to fit the continuous formulation, and we derive approximation bounds in analogy with the discrete case. A continuous version of the Potts model for multi-class segmentation problems is presented, and it is shown how to obtain provably good solutions using continuous α-expansions. (Less)
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author
organization
publishing date
type
Chapter in Book/Report/Conference proceeding
publication status
published
subject
in
Proceedings of 2009 IEEE 12th International Conference on Computer Vision (ICCV)
pages
8 pages
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
conference name
IEEE International Conference on Computer Vision (ICCV), 2009
external identifiers
  • WOS:000294955300052
  • Scopus:77953225317
ISBN
978-1-4244-4419-9
DOI
10.1109/ICCV.2009.5459206
language
English
LU publication?
yes
id
e8298764-3d96-4f6e-9948-6e790405ff11 (old id 1687617)
date added to LUP
2011-06-10 21:21:29
date last changed
2016-10-13 04:48:49
@misc{e8298764-3d96-4f6e-9948-6e790405ff11,
  abstract     = {The concept of graph cuts is by now a standard method for all sorts of low level vision problems. Its popularity is largely due to the fact that globally or near globally optimal solutions can be computed using efficient max flow algorithms. On the other hand it has been observed that this method may suffer from metrication errors. Recent work has begun studying continuous versions of graph cuts, which give smaller metrication errors. Another advantage is that continuous cuts are straightforward to parallelize. In this paper we extend the class of functionals that can be optimized in the continuous setting to include anisotropic TV-norms. We show that there is a so called coarea formula for these functionals making it possible to minimize them by solving a convex problem. We also show that the concept of α-expansion moves can be reformulated to fit the continuous formulation, and we derive approximation bounds in analogy with the discrete case. A continuous version of the Potts model for multi-class segmentation problems is presented, and it is shown how to obtain provably good solutions using continuous α-expansions.},
  author       = {Olsson, Carl and Byröd, Martin and Overgaard, Niels Christian and Kahl, Fredrik},
  isbn         = {978-1-4244-4419-9},
  language     = {eng},
  pages        = {405--412},
  publisher    = {ARRAY(0x5790c50)},
  series       = {Proceedings of 2009 IEEE 12th International Conference on Computer Vision (ICCV)},
  title        = {Extending Continuous Cuts: Anisotropic Metrics and Expansion Moves},
  url          = {http://dx.doi.org/10.1109/ICCV.2009.5459206},
  year         = {2009},
}