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Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy

David P. Feldman·James P. Crutchfield
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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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David P. Feldman, James P. Crutchfield. 2002-12-04. Structural Information in Two-Dimensional Patterns: Entropy Convergence and Excess Entropy. https://doi.org/10.1103/physreve.67.051104

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