Gradient entropy (GradEn): The two dimensional version of slope entropy for image analysis

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.