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

Abstract Two-dimensional sample entropy (SampEn2D) is a recently developed method in the field of information theory for evaluating the regularity or predictability of images. SampEn2D, though powerful, has two key limitations: (1) SampEn2D values are undefined for small-sized images; and (2) SampEn2D is computationally expensive for several real-world applications. To overcome these drawbacks, we introduce the two-dimensional dispersion entropy (DispEn2D) measure. To evaluate the ability of DispEn2D, in comparison with SampEn2D, we use various synthetic and real datasets. The results demonstrate that DispEn2D distinguishes different amounts of white Gaussian and salt and pepper noise. The periodic images, compared with their corresponding synthesized ones, have lower DispEn2D values. The results for Kylberg texture dataset show the ability of DispEn2D to differentiate various textures. Although the results based on DispEn2D and SampEn2D for both the synthetic and real datasets are consistent in that they lead to similar findings about the irregularity of images, DispEn2D has three main advantages over SampEn2D: (1) DispEn2D, unlike SampEn2D, does not lead to undefined values; (2) DispEn2D is noticeably quicker; and (3) The coefficient of variations and Mann–Whitney U test-based p-values for DispEn2D are considerably smaller, showing the more stability of the DispEn2D results. Overall, thanks to its successful performance and low computational time, DispEn2D opens up a new way to analyze the uncertainty of images.