Multi-Temperature Annealing: A New Approach for the Energy-Minimization of Hierarchical Markov Random Field Models (bibtex)
by Josiane Zerubia, Zoltan Kato, Mark Berthod
Abstract:
As it is well known, optimization of the energy function of Markov Random Fields is very expensive. Hierarchical models have usually much more communication per pixel than monogrid ones. This is why classical annealing schemes are too slow, even on a parallel machine, to minimize the energy associated with such a model. However, taking benefit of the pyramidal structure of the model, we can define a new annealing scheme: the Multi-Temperature Annealing (MTA), which consists of associating higher temperatures to coarser levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalisation of the annealing theorem of Geman and Geman. We have applied the algorithm to image classification and tested it on synthetic and real images.
Reference:
Josiane Zerubia, Zoltan Kato, Mark Berthod, Multi-Temperature Annealing: A New Approach for the Energy-Minimization of Hierarchical Markov Random Field Models, In Proceedings of International Conference on Pattern Recognition, volume 1, Jerusalem, Israel, pp. 520-522, 1994, IEEE.
Bibtex Entry:
@string{icpr="Proceedings of International Conference on Pattern Recognition"}
@InProceedings{Zerubia-etal94,
  author =	 {Zerubia, Josiane and Kato, Zoltan and Berthod, Mark},
  title =	 {Multi-Temperature Annealing: A New Approach for the
                  Energy-Minimization of Hierarchical {M}arkov Random
                  Field Models},
  booktitle =	 icpr,
  pages =	 {520-522},
  year =	 1994,
  volume =	 1,
  address =	 {Jerusalem, Israel},
  month =	 oct,
  organization = {IAPR},
  publisher =	 {IEEE},
  ps =		 {../papers/icpr94.ps},
  abstract =	 {As it is well known, optimization of the energy
                  function of Markov Random Fields is very
                  expensive. Hierarchical models have usually much
                  more communication per pixel than monogrid
                  ones. This is why classical annealing schemes are
                  too slow, even on a parallel machine, to minimize
                  the energy associated with such a model. However,
                  taking benefit of the pyramidal structure of the
                  model, we can define a new annealing scheme: the
                  Multi-Temperature Annealing (MTA), which consists of
                  associating higher temperatures to coarser levels,
                  in order to be less sensitive to local minima at
                  coarser grids. The convergence to the global optimum
                  is proved by a generalisation of the annealing
                  theorem of Geman and Geman. We have applied the
                  algorithm to image classification and tested it on
                  synthetic and real images.}
}
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