A Hankel Determinant—Driven Framework for Medical Image Enhancement Using Bi-Univalent Functions

This study introduces a new approach to image enhancement by integrating ideas from geometric function theory with modern computer vision techniques. A specific subclass \(B(\hbar)\) of bi-univalent functions is constructed, and its associated Hankel determinants are employed to design convolution-based enhancement filters. These determinants are incorporated as adaptive weights within the filtering process to improve image quality. The effectiveness of the proposed framework is assessed using widely accepted performance measures, including PSNR, SSIM, MSE, standard deviation, and Pearson correlation coefficient. Experimental results on various medical imaging datasets demonstrate clear improvements compared to existing methods. The proposed method is evaluated on different medical images obtained from publicly available Kaggle and Radiopaedia datasets. Quantitative comparison of the proposed method against two histogram-based enhancement methods, QDHE and CLAHE, demonstrates substantial improvements across all quality metrics, achieving superior image enhancement with better preservation of fine structural details. An ablation study confirms that Hankel weights contribute approximately 4.5 dB and directional fusion contributes 2.8 dB to the average PSNR. The findings demonstrate a quantifiable connection between the theory of Hankel determinants and practical image processing applications.