Complexity-Entropy Causality Plane as a Complexity Measure for Two-Dimensional Patterns
Open Access
- 14 August 2012
- journal article
- research article
- Published by Public Library of Science (PLoS) in PLOS ONE
- Vol. 7 (8), e40689
- https://doi.org/10.1371/journal.pone.0040689
Abstract
Complexity measures are essential to understand complex systems and there are numerous definitions to analyze one-dimensional data. However, extensions of these approaches to two or higher-dimensional data, such as images, are much less common. Here, we reduce this gap by applying the ideas of the permutation entropy combined with a relative entropic index. We build up a numerical procedure that can be easily implemented to evaluate the complexity of two or higher-dimensional patterns. We work out this method in different scenarios where numerical experiments and empirical data were taken into account. Specifically, we have applied the method to fractal landscapes generated numerically where we compare our measures with the Hurst exponent; liquid crystal textures where nematic-isotropic-nematic phase transitions were properly identified; 12 characteristic textures of liquid crystals where the different values show that the method can distinguish different phases; and Ising surfaces where our method identified the critical temperature and also proved to be stable.Keywords
This publication has 26 references indexed in Scilit:
- Complexity measures and information planes of x-ray astrophysical sourcesJournal of Statistical Mechanics: Theory and Experiment, 2011
- Measuring ecological complexityEcological Indicators, 2010
- Estimating coupling direction between neuronal populations with permutation conditional mutual informationNeuroImage, 2010
- A unified index to measure ecological diversity and species rarityEcography, 2008
- Extracting features of Gaussian self-similar stochastic processes via the Bandt-Pompe approachPhysical Review E, 2007
- Distinguishing Noise from ChaosPhysical Review Letters, 2007
- Dynamics of rough surfaces generated by two-dimensional lattice spin modelsPhysical Review E, 2007
- Structural information in two-dimensional patterns: Entropy convergence and excess entropyPhysical Review E, 2003
- Permutation Entropy: A Natural Complexity Measure for Time SeriesPhysical Review Letters, 2002
- Multimodality image registration by maximization of mutual informationIEEE Transactions on Medical Imaging, 1997