Two-dimensional dispersion entropy: An information-theoretic method for irregularity analysis of images

Two-dimensional sample entropy (SampEn(2D)) is a recently developed method in the field of information theory for evaluating the regularity or predictability of images. SampEn(2D), though powerful, has two key limitations: (1) SampEn(2D) values are undefined for small-sized images; and (2) SampEn(2D) is computationally expensive for several real-world applications. To overcome these drawbacks, we introduce the two-dimensional dispersion entropy (DispEn(2D)) measure. To evaluate the ability of DispEn(2D) , in comparison with SampEn(2D), we use various synthetic and real datasets. The results demonstrate that DispEn(2D) distinguishes different amounts of white Gaussian and salt and pepper noise. The periodic images, compared with their corresponding synthesized ones, have lower DispEn(2D) values. The results for Kylberg texture dataset show the ability of DispEn(2D) to differentiate various textures. Although the results based on DispEn(2D) and SampEn(2D) for both the synthetic and real datasets are consistent in that they lead to similar findings about the irregularity of images, DispEn(2D) has three main advantages over SampEn(2D): (1) DispEn(2D), unlike SampEn(2D), does not lead to undefined values; (2) DispEn(2D) is noticeably quicker; and (3) The coefficient of variations and Mann-Whitney U test-based p-values for DispEn(2D) are considerably smaller, showing the more stability of the DispEn(2D) results. Overall, thanks to its successful performance and low computational time, DispEn(2D) opens up a new way to analyze the uncertainty of images.