Structural Information in Two-Dimensional Patterns:
Entropy Convergence and Excess Entropy
D.P. Feldman and J.P. Crutchfield, Structural Information in
Two-Dimensional Patterns: Entropy Convergence and Excess Entropy.
Physical Review E. 67:051104. 2003.
Abstract
We develop information-theoretic measures of spatial structure and
pattern in more than one dimension. As is well known, the entropy
density of a two-dimensional configuration can be efficiently and
accurately estimated via a converging sequence of conditional
entropies. We show that the manner in which these conditional
entropies converge to their asymptotic value serves as a measure of
global correlation and structure for spatial systems in any
dimension. We compare and contrast entropy-convergence with
mutual-information and structure-factor techniques for quantifying and
detecting spatial structure.
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