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

TL;DR

This paper introduces information-theoretic measures based on entropy convergence to quantify and analyze spatial structure and correlations in two-dimensional patterns, offering a new perspective beyond traditional methods.

Contribution

It develops a novel approach using entropy convergence rates to measure global correlation and structure in multi-dimensional spatial systems.

Findings

Entropy density can be estimated via converging conditional entropies.

The convergence behavior of these entropies indicates the degree of spatial correlation.

Comparison shows advantages over mutual-information and structure-factor methods.

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.