提出二维梯度熵，同时捕捉图像纹理的形状与强度信息。
Gradient entropy (GradEn): The two dimensional version of slope entropy for image analysis
- 将一维斜率熵扩展到二维，融合符号模式与幅值信息
- 在多种模拟和真实数据上优于其他二维熵方法
- 适合纹理分析、故障检测等图像识别任务
信息论与香农熵对量化复杂系统或信号的不规则性至关重要。近年来，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。本文引入梯度熵（GradEn），作为斜率熵向二维的扩展，同时考虑符号模式与幅值信息，从而提升图像特征提取能力。我们在模拟数据（包括二维彩色噪声、二维混合过程和逻辑映射）上评估了GradEn，结果表明其能有效区分具有不同特性的图像，且计算成本低。真实世界数据集包含纹理、故障齿轮和铁路波纹信号，结果显示GradEn在分类任务中优于其他二维熵方法。结论：GradEn是一种有效的图像表征工具，为图像处理与识别提供了新思路。
原文摘要 · Abstract (English)
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.
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