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

TL;DR

Gradient entropy (GradEn) extends slope entropy to two dimensions, effectively capturing image features for classification with low computational cost, outperforming existing 2D entropy methods in diverse datasets.

Contribution

This paper introduces GradEn, a novel 2D entropy method that incorporates both symbolic patterns and amplitude information for improved image analysis.

Findings

GradEn effectively distinguishes various image characteristics.

GradEn outperforms other 2D entropy methods in classification accuracy.

GradEn maintains low computational cost for image analysis.

Abstract

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.