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April 10, 2026Fractal and Fractional0 citationsOpen Access

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

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PHPriyanka HarjuleMDMukesh DeluRKRajesh Kumar

Key Points

  • The aim is to develop an effective method for segmenting retinal blood vessels to aid in diagnosing retinal complications.
  • Utilized a fractional Hessian matrix to model blood vessels.
  • Integrated adaptive principal curvature estimation for local shape feature extraction.
  • Implemented the framework with nonsingular and nonlocal kernels.
  • Assessed effectiveness using various publicly available datasets.
  • Achieved 96.77% accuracy and 98.82% specificity on the DRIVE database.
  • Achieved 96.91% accuracy and 98.69% specificity on the STARE database.
  • Achieved 95.90% accuracy and 98.36% specificity on the HRF database.
  • Demonstrated competitive performance compared to several deep learning methods.

Abstract

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.

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Cite This Study

Harjule et al. (2026) studied this question.

synapsesocial.com/papers/69d896166c1944d70ce07518https://doi.org/10.3390/fractalfract10040246
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