Gibbs random fields, cooccurrences, and texture modeling

Gibbs random field (GRF) models and features from cooccurrence matrices are typically considered as separate but useful tools for texture discrimination. In this paper we 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: We 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, we 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, we illustrate how these properties can guide one's intuition about the types of GRF patterns which are most likely to form.