A versatile entropic measure of grey level inhomogeneity

An entropic measure for the 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 (MICs) of the measure has been revealed for pairs of simulated patterns, which differ in shades of grey or symmetry properties only. In turn, for evolving photosphere granulation patterns, the stability in time of the first peak position has been found. Interestingly, the third peak is dominant at initial steps of the evolution. This indicates a temporary grouping of granules at a length scale that may belong to the mesogranulation phenomenon. This behaviour has similarities with that reported by Consolini, Berrilli et al. [G. Consolini, F. Berrilli, A. Florio, E. Pietropaolo, L.A. Smaldone, Astron. Astrophys. 402 (2003) 1115; F. Berrilli, D. Del Moro, S. Russo, G. Consolini, Th. Straus, Astrophys. J. 632 (2005) 677] for binarized granulation images of a different data set.