A Hierarchical Markov Random Field Model and Multitemperature Annealing for Parallel Image Classification

Zoltan Kato, Marc Berthod, Josiane Zerubia

Research output: Contribution to journalArticle

70 Citations (Scopus)


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 multitemperature 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 generalization of the annealing theorem of S. Geman and D. Geman (IEEE Trans. Pattern Anal. Mach. Intell. 6, 1984, 721-741).

Original languageEnglish
Pages (from-to)18-37
Number of pages20
JournalGraphical Models and Image Processing
Issue number1
Publication statusPublished - Jan 1996

ASJC Scopus subject areas

  • Modelling and Simulation
  • Computer Vision and Pattern Recognition
  • Geometry and Topology
  • Computer Graphics and Computer-Aided Design

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