An improved tortuosity measurement method combining curvature-based, breadth-first search and Euclidean distance for retinal image analysis

Retinal vascular tortuosity is a clinically relevant biomarker linked to systemic and ocular diseases; however, its quantitative assessment particularly the distinction between arteries and veins remains underexplored in both healthy and pathological conditions. This study investigates tortuosity behavior using three publicly available retinal fundus image datasets: Digital Retinal Images for Vessel Extraction (DRIVE), High-Resolution Fundus (HRF), and Labelled Eye fundus Segmentation-Artery Vein (LES-AV). A standardized analytical pipeline combining curvature-based metrics, breadth-first search (BFS) and Euclidean distance was applied following vessel segmentation, artery-vein separation, skeletonization, and optic disc-based tracing. BFS algorithm was utilized for vessel path tracing, chosen for its robustness and suitability in navigating complex vascular structures with high reproducibility. Five comparative analyses were performed: artery <i>vs</i>. vein tortuosity; healthy <i>vs</i>. diseased eyes (glaucoma and diabetic retinopathy); and cross-dataset comparisons under both healthy and pathological conditions. Across all datasets, veins consistently exhibited higher tortuosity than arteries in healthy eyes, confirmed by large effect sizes (Cohen's d), despite weak correlation between the two vessel types. Diabetic retinopathy cases showed an amplified artery-vein separation, suggesting disease-induced vascular changes. Glaucomatous eyes exhibited mixed patterns, with HRF artery-vein differences maintained and LES-AV showing diminished separation, partly due to non-normal data distribution. A key finding highlights the significant influence of imaging characteristics especially field of view (FOV) on tortuosity measurement. Datasets with a wider field of view, such as DRIVE and HRF (45° FOV, optical disc (OD) positioned nasally), captured more peripheral, tortuous vessels and reported higher tortuosity values. In contrast, the LES-AV dataset with a narrower 30° FOV and centered optic disc, resulted in lower tortuosity measurements and weaker artery-vein differentiation. These anatomical and technical differences emphasize the need to handle FOV and orientation settings when designing or comparing tortuosity-based diagnostic studies. In conclusion, retinal vascular tortuosity appears to be a vessel-specific feature which is robust and capable of capturing both pathological and variations in dataset. The findings support its integration into automated diagnostic frameworks and highlight the importance of standardizing imaging parameters particularly FOV and anatomical orientation in future retinal biomarker research.