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6 - Basics of random fields

from Part II - Stochastic models

Published online by Cambridge University Press:  05 November 2014

Aly A. Farag
Aly A. Farag
Affiliation:
University of Louisville, Kentucky
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Summary

Introduction

This chapter describes the basics of random fields with focus on models that have been useful for image synthesis, filtering, segmentation, and registration. There is a vast literature on the subject. Besag [6.1], Geman and Geman [6.2], Derin and Elliott [6.3], and Dubes and Jain [6.4] are among the accessible literature in this area. Various books and monograms exist as well. Rue and Held [6.5], and Adler and Taylor [6.6] deal with some basics of random fields, and Blake et al. [6.7] contains examples of applied work on the random field in image analysis and computer vision. From an algorithmic point of view, Dubes and Jain [6.4] is excellent introductory reading.

In simple terms, a random field is a random process in which the index set is multidimensional. As random variables are the building blocks of random processes, they are also the basic ingredients of random fields. To introduce the subject of random fields, we provide examples of random experiments that produce outputs in one or more dimensions.

Type
Chapter
Information
Biomedical Image Analysis
Statistical and Variational Methods
 , pp. 131 - 162
Publisher: Cambridge University Press
Print publication year: 2014

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References

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Derin, H. and Elliott, H., Modeling and segmentation of noisy and textured images using Gibbs random fields. IEEE Trans. Pattern Anal. Machine Intel. 9(1) (1987) 39–55.CrossRefGoogle ScholarPubMed
Dubes, R. C. and Jain, A. K., Random field models in image analysis. J. Appl. Stat. 16 (1989) 131–164.CrossRefGoogle Scholar
Rue, H. and Held, L., Gaussian Markov Random Fields: Theory and Applications. Boca Raton, FL: Chapman and Hall/CRC (2005).CrossRefGoogle Scholar
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  • Basics of random fields
  • Aly A. Farag, University of Louisville, Kentucky
  • Book: Biomedical Image Analysis
  • Online publication: 05 November 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139022675.010
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  • Basics of random fields
  • Aly A. Farag, University of Louisville, Kentucky
  • Book: Biomedical Image Analysis
  • Online publication: 05 November 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139022675.010
Available formats
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Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Basics of random fields
  • Aly A. Farag, University of Louisville, Kentucky
  • Book: Biomedical Image Analysis
  • Online publication: 05 November 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139022675.010
Available formats
×