Texture analysis using two-dimensional permutation entropy and amplitude-aware permutation entropy

Highlights

• Comparison of PE2D with the novel AAPE2D entropy algorithm.

• Texture analysis of synthetic and biomedical images.

• Both methods statistically differentiate healthy and pneumonia subjects.

• AAPE2D features achieve 75.5% accuracy, which is slightly better than PE2D.

Abstract

Entropy algorithms have been applied extensively for time series analysis. The entropy value given by the algorithm quantifies the irregularity of the data structure. For higher irregular data structures, the entropy is higher. Both permutation entropy (PE) and amplitude-aware permutation entropy (AAPE) have been previously used to analyze time series. These two metrics have the advantage, over others, of being computationally fast and simple. However, fewer entropy measures have been proposed to process images. Two-dimensional entropy algorithms can be used to study texture and analyze the irregular structure of images. Herein, we propose the extension of AAPE for two-dimensional analysis (AAPE${}_{2D}$). To the best of our knowledge, AAPE${}_{2D}$ has never been proposed to analyze texture of images. For comparison purposes, we also study the two-dimensional permutation entropy (PE${}_{2D}$) to analyze the effect of the amplitude consideration in texture analysis. In this study, we compare AAPE${}_{2D}$ method with PE${}_{2D}$ in terms of irregularity discrimination, parameters sensitivity, and artificial texture differentiation. Both AAPE${}_{2D}$ and PE${}_{2D}$ appear to be interesting entropy-based approaches for image texture analysis. When applied to a biomedical dataset of chest X-rays with healthy subjects and pneumonia patients, both methods showed to statistically differentiate both groups for $P<0.01$. Finally, using a SVM model and multiscale entropy values as features, AAPE${}_{2D}$ achieves an average of 75.7% accuracy which is slightly better than the results of PE${}_{2D}$. Overall, both entropy algorithms are promising and achieve similar conclusions. This work is a new step towards the development of other entropy-based texture measures.