A regularity statistic for images

Measures of statistical regularity or complexity for time series are pervasive in many fields of research and applications, but relatively little effort has been made for image data. This paper presents a method for quantifying the statistical regularity in images. The proposed method formulates the entropy rate of an image in the framework of a stationary Markov chain, which is constructed from a weighted graph derived from the Kullback-Leibler divergence of the image. The model is theoretically equal to the well-known approximate entropy (ApEn) used as a regularity statistic for the complexity analysis of one-dimensional data. The mathematical formulation of the regularity statistic for images is free from estimating critical parameters that are required for ApEn.