F2D-RetinaNet: a feature-to-decision dual-path network with fractional operators for retinal disease detection and gradingDownload PDF Download PDF ArticleOpen accessPublished: 17 October 2026Mukesh Delu1,Priyanka Harjule1,Rajesh Kumar2,3,Kushal Gajjar4 &…Pilani Nkomozepi3 Scientific Reports (2026) Cite this articleView saved research We’re sharing this article early to provide faster access to peer-reviewed, accepted research. It is citable and carries a permanent DOI. This version is subject to further edits and will be replaced automatically by the final Version of Record. All legal disclaimers apply.AbstractVisible pathological abnormalities and vascular integrity help diagnose retinal diseases. This paper introduces a unified feature-to-decision framework that first extracts vasculature and enhances lesions. First, this study proposes the fractional anisotropic diffusion–based hybrid enhancement (FADHE) method that selectively amplifies lesion contrast and vessel visibility in the green channel using long-memory fractional diffusion dynamics. Second, this study introduces a fractional Hessian-based attention U-Net (FHAU-Net), a multi-scale vessel segmentation model that leverages fractional Hessian responses across eight fractional orders and attention-guided skip connections to capture fine vessel structures. Finally, this work designs a dual-branch disease grading model, F2D-RetinaNet, which jointly processes the enhanced image and vessel map to learn lesion-related and vascular feature representations for the recognition and grading of retinal diseases. The FHAU-Net model achieved a Dice coefficient of 0.8987, a sensitivity of 0.9084, an accuracy of 0.9804, and a specificity of 0.9876 across the unified test set, which contains variations in resolution, acquisition site, camera type, and imaging conditions. The F2D-RetinaNet is evaluated for Diabetic retinopathy (DR) detection, DR grading, and multiclass retinal disease classification tasks. Extensive testing and comparisons to the baseline procedures support the reliability of the proposed methodology on the datasets evaluated here.AcknowledgementsThe authors thank the public retinal image dataset providers, which greatly aided the experimental validation of this study. The authors also express their gratitude to SMS Hospital Jaipur for providing real-world clinical retinal images for external testing.Author informationAuthors and AffiliationsDepartment of Mathematics, Malaviya National Institute of Technology Jaipur, Jaipur, 302017, IndiaMukesh Delu & Priyanka HarjuleDepartment of Electrical Engineering, Malaviya National Institute of Technology Jaipur, Jaipur, 302017, IndiaRajesh KumarDepartment of Human Anatomy and Physiology, Faculty of Health Sciences, University of Johannesburg, Johannesburg, 2006, South AfricaRajesh Kumar & Pilani NkomozepiDepartment of Electronics and Communication Engineering, Malaviya National Institute of Technology Jaipur, Jaipur, 302017, IndiaKushal GajjarAuthorsMukesh DeluView author publicationsSearch author on:PubMed Google ScholarPriyanka HarjuleView author publicationsSearch author on:PubMed Google ScholarRajesh KumarView author publicationsSearch author on:PubMed Google ScholarKushal GajjarView author publicationsSearch author on:PubMed Google ScholarPilani NkomozepiView author publicationsSearch author on:PubMed Google ScholarCorresponding authorsCorrespondence to Priyanka Harjule or Pilani Nkomozepi.Ethics declarationsCompeting interestsThe authors declare no competing interests.Ethical approvalInstitutional ethics committee approval was obtained to use retrospective clinical fundus images from SMS Hospital. The collaborating ophthalmologist provided these images fully anonymized and de-identified, and granted authorized permission for their use and publication. No direct human or animal experiments were conducted by the authors.Additional informationPublisher's noteSpringer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.A pseudocode of the proposed frameworkA pseudocode of the proposed frameworkThis appendix summarises, in algorithmic form, the two image-processing stages that constitute the front end of the proposed framework. Algorithm 1 corresponds to the FADHE enhancement described in Section 2.1, and Algorithm 2 corresponds to the fractional Hessian vesselness map described in Section 2.2.1. Equation numbers referenced inside the algorithms are those of the main text, and all parameter values are as listed in Table 2.A.1 FADHE enhancementAlgorithm 1Full size imageFractional anisotropic diffusion-based hybrid enhancement (FADHE).A.2 Fractional Hessian vesselness mapAlgorithm 2Full size imageFractional hessian vesselness map.Rights and permissionsOpen Access This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it. 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