Pattern theory is a mathematical framework for representing and analyzing regular structures. In Grenander's (1993) formulation, primitive generators are combined subject to bond and compatibility rules to form configurations, while group actions describe permitted changes. probability measures on the resulting configuration spaces model variation and support statistical inference. The framework has been applied to images, shapes, language, and other structured data.
Pattern Theory
See also
Group Action, Model, Pattern Recognition, Probability MeasureExplore with Wolfram|Alpha
References
Grenander, U. General Pattern Theory: A Mathematical Study of Regular Structures. Oxford, England: Clarendon Press, 1993. https://doi.org/10.1093/oso/9780198536710.001.0001.Cite this as:
Weisstein, Eric W. "Pattern Theory." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PatternTheory.html