@string{cvgipgmip="Computer Vision, Graphics and Image Processing: Graphical Models and Image Processing"}
@Article{Kato-etal96,
  author =	 {Kato, Zoltan and Berthod, Mark and Zerubia, Josiane},
  title =	 {A Hierarchical {M}arkov Random Field Model and
                  Multi-Temperature Annealing for Parallel Image
                  Classification},
  journal =	 cvgipgmip,
  year =	 1996,
  volume =	 58,
  number =	 1,
  pages =	 {18--37},
  month =	 jan,
  ps =		 {papers/cvgip.ps},
  pdf =		 {papers/cvgip.pdf},
  abstract =	 {In this paper, we are interested in massively
                  parallel multiscale relaxation algorithms applied to
                  image classification. It is well known that
                  multigrid methods can improve significantly the
                  convergence rate and the quality of the final
                  results of iterative relaxation techniques. First,
                  we present a classical multiscale model which
                  consists of a label pyramid and a whole observation
                  field. The potential functions of coarser grids are
                  derived by simple computations. The optimization
                  problem is first solved at the higher scale by a
                  parallel relaxation algorithm, then the next lower
                  scale is initialized by a projection of the
                  result. Second, we propose a hierarchical Markov
                  Random Field model based on this classical model. We
                  introduce new interactions between neighbor levels
                  in the pyramid. It can also be seen as a way to
                  incorporate cliques with far apart sites for a
                  reasonable price. This model results in a relaxation
                  algorithm with a new annealing scheme: The
                  Multi-Temperature Annealing (MTA) scheme, which
                  consists of associating higher temperatures to
                  higher 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.}
}