The analysis of fundus images may reflect systemic and cerebral vascular status through a non-invasive, rapid, and cost-effective method. Accurate characterization of the retinal vessels is critical for this status assessment. Medical professionals can perform diagnosis on measurements extracted from the retinal vessels, which are identified through segmentation. Supervised-Learning is used to perform this segmentation task and has been shown to produce higher-quality results compared to traditional methods. However, the Supervised-Learning-based binary method leads to segmentations with multiple Connected Components (CC). Amongst these components, some are disconnected retinal vessels (mentioned as branches), others are artifacts. Artifacts are disconnected miss-classified components resulting from the Supervised-Learning segmentation and that should be removed. Conversely, branches should be kept and further re-connected as they are anatomically supposed to be connected. In this study, we propose a Connected-Components-based post-processing procedure to remove artifacts while preserving the most possible amount of branches. Our methodology involves a relative threshold to cluster the CC based on their areas. We also introduce a useful evaluation metric for the segmentations in the case of measurements extractions on retinal vessels. Over 615 predicted segmentations from six datasets, we improved the dice by a substantial 0.062 leading from 0.782 to 0.844. In conclusion, our method has the potential to significantly enhance the usability and reliability of retinal vessels segmentations, making it a valuable tool for medical professionals in the assessment of systemic and cerebral vascular status. Our work also provides useful insights for future research in this area, especially to address the re-connection of the remaining branches.< Réduire