Extending Continuous Cuts: Anisotropic Metrics and Expansion Moves
Author
Summary, in English
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.
Department/s
- Mathematics (Faculty of Engineering)
- Mathematical Imaging Group
Publishing year
2009
Language
English
Pages
405-412
Publication/Series
Proceedings of 2009 IEEE 12th International Conference on Computer Vision (ICCV)
Document type
Conference paper
Publisher
IEEE - Institute of Electrical and Electronics Engineers Inc.
Topic
- Computer Vision and Robotics (Autonomous Systems)
- Mathematics
Conference name
IEEE International Conference on Computer Vision (ICCV), 2009
Conference date
2009-09-27 - 2009-10-04
Conference place
Kyoto, Japan
Status
Published
Research group
- Mathematical Imaging Group
ISBN/ISSN/Other
- ISBN: 978-1-4244-4419-9