Median Grayscale-Driven Multilevel Thresholding for Adaptive 2D Entropy in Diagonally Adjacent within A 3×3 Neighbors

The implementation of 2d entropy demonstrates significant potential for adaptive image segmentation through the generation of discriminative 2D histograms. Classic​ approaches predominantly rely on central pixel intensity and spatial averages within fixed neighborhoods, yet these methods inherently neglect directional texture dynamics. Specifically, conventional metrics based on horizontal or vertical grayscale variations fail to capture holistic inter-pixel relationships due to their oversimplified linear sampling schemes. To address this limitation, we propose a ​​median-guided entropy framework​​ that integrates both central grayscale values and the statistical median of diagonally adjacent pixels within 3×3 windows. This dual-feature strategy enhances the representation of local grayscale distributions while maintaining computational efficiency. Extensive validation across all images of the MATLAB Image Toolbox dataset confirms the method's superiority in preserving edge details and reducing histogram overlap compared to conventional entropy-based segmentation systems. The proposed approach achieves an improvement in segmentation consistency metrics while preserving computational complexity comparable to traditional applications.