Bayesian Image Analysis

  • Donald Geman
  • Stuart Geman
Conference paper
Part of the NATO ASI Series book series (volume 20)


In [8] we introduced a class of image models for various tasks in digital image processing. These models are multi-level or “hierarchical” Markov Random Fields (MRFs). Here we pursue this approach to image modelling and analysis along some different lines, involving segmentation, boundary finding, and computer tomography. Similar models and associated optimization algorithms appear regularly in other work involving immense spatial systems; some examples are the studies in these proceedings on statistical mechanical systems (e.g. ferromagnets, spin-glasses and random fields), the work of Hinton and Sejnowski [14], Hopfield [15], and von der Malsburg and Bienenstock [19], in neural modeling and perceptual inference, and other work in image analysis, e.g. Besag [2], Kiiveri and Campbell [17], Cross and Jain [5], Cohen and Cooper [4], Elliott and Derin [7], Deviver [6], Grenander [11], and Marroquin [20]. The use of MRFs and related stochastic processes as models for intensity data has been prevalent in the image processing literature for some time now; we refer the reader to [8] and standard references for a detailed account of the genealogy.


Posterior Distribution Perceptual Inference Gibbs Distribution Edge Site Edge Variable 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Donald Geman
    • 1
  • Stuart Geman
    • 2
  1. 1.Department of Mathematics and StatisticsUniversity of MassachusettsAmherstUSA
  2. 2.Division of Applied MathematicsBrown UniversityProvidenceUSA

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