Information theory and Shannon entropy are essential for quantifying irregularity in complex systems or signals. Recently, two-dimensional entropy methods, such as two-dimensional sample entropy, distribution entropy, and permutation entropy, have been proposed for analyzing 2D texture or image data. This paper introduces Gradient entropy (GradEn), an extension of slope entropy to 2D, which considers both symbolic patterns and amplitude information, enabling better feature extraction from image data. We evaluate GradEn with simulated data, including 2D colored noise, 2D mixed processes, and the logistic map. Results show the ability of GradEn to distinguish images with various characteristics while maintaining low computational cost. Real-world datasets, consist of texture, fault gear, and railway corrugation signals, demonstrate the superior performance of GradEn in classification tasks compared to other 2D entropy methods. In conclusion, GradEn is an effective tool for image characterization, offering a novel approach for image processing and recognition.

翻译：信息论与香农熵对于量化复杂系统或信号的不规则性至关重要。近年来，诸如二维样本熵、分布熵和排列熵等二维熵方法被提出，用于分析二维纹理或图像数据。本文介绍了梯度熵（GradEn），它是斜率熵向二维的扩展，同时考虑了符号模式和幅度信息，从而能够从图像数据中更好地提取特征。我们使用模拟数据（包括二维有色噪声、二维混合过程和逻辑映射）对GradEn进行了评估。结果表明，GradEn能够在保持较低计算成本的同时，有效区分具有不同特征的图像。在真实世界数据集（包括纹理、故障齿轮和铁路波磨信号）上的实验表明，与其他二维熵方法相比，GradEn在分类任务中具有更优越的性能。总之，GradEn是一种有效的图像表征工具，为图像处理与识别提供了一种新方法。