Multilevel Thresholding for Image Partitioning Using Median Grayscale-Based 2D Entropy in 3X3 Neighborhoods

A novel automatic segmentation approach is developed through two-dimensional entropy-based histogram construction. Traditional methodologies, such as the Abutaleb technique, primarily focus on analyzing the central gray value and arithmetic mean within local neighborhoods. However, these conventional approaches demonstrate limitations in comprehensively capturing the spatial variations and contextual relationships among adjacent pixels. To address this constraint, we propose an enhanced 2D histogram formulation that integrates the central pixel's intensity with the median value derived from a <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$3 \times 3$</tex> pixel's neighborhood. This median-based characterization effectively preserves edge information while reducing noise sensitivity compared to conventional mean-based approaches. Comprehensive multilevel segmentation experiments conducted on standard test images from the MATLAB Image Processing Toolbox demonstrate the superior performance of our method in terms of boundary preservation and region consistency. Quantitative evaluations reveal significant improvements in structural similarity metrics compared to existing histogram construction techniques.