Versatile entropic measure of grey level inhomogeneity

TL;DR

This paper introduces a versatile entropic measure to analyze grey level inhomogeneity across scales, revealing hidden periodicities, dependencies, and temporal stability in patterns like solar granulation.

Contribution

It proposes a new entropic measure for GLI analysis that detects scale-dependent inhomogeneity, periodicity, and pattern evolution, including phenomena like mesogranulation.

Findings

Detects grey level periodicity through measure minima

Reveals multiple intersecting curves indicating complex dependencies

Finds temporal stability and initial dominance of specific peaks in granulation patterns

Abstract

The entropic measure for analysis of grey level inhomogeneity (GLI) is proposed as a function of length scale. It allows us to quantify the statistical dissimilarity of the actual macrostate and the maximizing entropy of the reference one. The maximums (minimums) of the measure indicate those scales at which higher (lower) average grey level inhomogeneity appears compared to neighbour scales. Even a deeply hidden statistical grey level periodicity can be detected by the equally distant minimums of the measure. The striking effect of multiple intersecting curves (MIC) of the measure has been revealed for pairs of simulated patterns, which differ in shades of grey or symmetry properties, only. This indicates for a non-trivial dependence of the GLI on length scale. In turn for evolving photosphere granulation patterns, the stability in time of the first peak position has been found. Interestingly, at initial steps of the evolution clearly dominates the third peak. This indicates for a temporary grouping of granules at length scale that may belong to mesogranulation phenomenon. This behaviour has similarities with that reported by Consolini, Berrilli et al. (2003, 2005) for binarized granulation images of a different data set.