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Gibbs Random Fields, Cooccurrences, and Texture Modeling
January 1994 (vol. 16 no. 1)
pp. 24-37

Gibbs random field (GRF) models and features from cooccurrence matrices are typically considered as separate but useful tools for texture discrimination. The authors show an explicit relationship between cooccurrences and a large class of GRF's. This result comes from a new framework based on a set-theoretic concept called the "aura set" and on measures of this set, "aura measures." This framework is also shown to be useful for relating different texture analysis tools. The authors show how the aura set can be constructed with morphological dilation, how its measure yields cooccurrences, and how it can be applied to characterizing the behavior of the Gibbs model for texture. In particular, they show how the aura measure generalizes, to any number of gray levels and neighborhood order, some properties previously known for just the binary, nearest-neighbor GRF. Finally, the authors illustrate how these properties can guide one's intuition about the types of GRF patterns which are most likely to form.

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Index Terms:
image texture; mathematical morphology; set theory; Markov processes; statistics; Gibbs random fields; cooccurrences; texture modeling; texture discrimination; set-theoretic concept; aura set; aura measures; texture analysis tools; morphological dilation; gray levels; neighborhood order
I.M. Elfadel, R.W. Picard, "Gibbs Random Fields, Cooccurrences, and Texture Modeling," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 16, no. 1, pp. 24-37, Jan. 1994, doi:10.1109/34.273719
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