Precise segmentation of retinal blood vessels (RBVs) is pivotal in ophthalmology research, aiding in detecting diverse retinal abnormalities. This study proposes a contrast-limited adaptive histogram equalisation (CLAHE) technique to improve retinal image quality and visibility of microvascular structures. We aimed to determine the complexity of blood vessels using fractal dimensions (FD) and compare different metrics for their effectiveness. We employed the UNet architecture to separate blood vessels, and our results on the DRIVE retinal fundus image standard dataset showed an impressive accuracy rate of 97.24%, surpassing traditional filtering methods. Box counting, information, capacity, correlation, and probability dimensions are used in the FD analysis to help us understand the complex and irregular structures of retinal blood vessels. These metrics are valuable for detecting and monitoring retinal diseases in clinical settings. Our comparison with other techniques reveals promising results, particularly in the capacity and information dimensions, with statistical significance (P < 0.05). The potential of fractal dimensions as a screening tool for diabetic retinopathy underscores their importance in epidemiological studies.