A Mathematical Framework for Retinal Vessel Segmentation: Fractional Hessian-Based Curvature Analysis

This study proposes an improved retinal blood vessel segmentation method to enhance the diagnosis of microvascular retinal complications. The proposed method extracts local shape features from retinal images utilizing a fractional Hessian matrix, which models blood vessels as surface structures characterized by ridges and valleys resulting from variations in curvature. The methodology integrates adaptive principal curvature estimation with a new framework leveraging the fractional Hessian matrix with nonsingular and nonlocal kernels. The effectiveness of the suggested method is assessed using publicly accessible datasets, including DRIVE, HRF, STARE, and some real images obtained from a local hospital. The proposed segmentation achieves 96.77% accuracy and 98.82% specificity on the DRIVE database, 96.91% accuracy and 98.69% specificity on STARE, and 95.90% accuracy and 98.36% specificity on the HRF database. Optimal parameters for the fractional order and Gaussian standard deviation were empirically determined by maximizing segmentation accuracy. Our findings show that the proposed approach achieves competitive performance compared to the listed methods, including several deep learning approaches, while maintaining significant computational efficiency. The output of the suggested method can be further utilized with deep learning techniques, which will be applied in the clinical context of diabetic retinopathy and glaucoma to identify abnormalities likely related to disease progression and different stages.