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.

熵算法已广泛应用于时间序列分析。算法给出的熵值量化了数据结构的不规则性。对于更高的不规则数据结构，熵更高。置换熵 (PE) 和幅度感知置换熵 (AAPE) 都曾用于分析时间序列。与其他指标相比，这两个指标具有计算速度快且简单的优势。然而，已经提出了较少的熵度量来处理图像。二维熵算法可用于研究纹理和分析图像的不规则结构。在此，我们建议将 AAPE 扩展用于二维分析（AAPE${}_{2D}$）。据我们所知，AAPE${}_{2D}$从未有人提议分析图像的纹理。为了比较的目的，我们还研究了二维排列熵（PE${}_{2D}$) 来分析纹理分析中幅度考虑的影响。在本研究中，我们比较了 AAPE${}_{2D}$PE法${}_{2D}$在不规则判别、参数敏感性和人工纹理区分方面。两个AAPE${}_{2D}$和体育${}_{2D}$似乎是有趣的基于熵的图像纹理分析方法。当应用于健康受试者和肺炎患者的胸部 X 射线生物医学数据集时，两种方法都显示出在统计学上区分两组$磷<0.01$. 最后，使用 SVM 模型和多尺度熵值作为特征，AAPE${}_{2D}$平均达到 75.7% 的准确率，略好于 PE 的结果${}_{2D}$. 总的来说，这两种熵算法都是有希望的，并且得出了相似的结论。这项工作是朝着开发其他基于熵的纹理度量迈出的新一步。