Automated image segmentation is a crucial step to characterize and quantify the morphometry of blood vessels. Adaptive Optics Ophthalmoscopy (AOO) images of eye fundus allow visualizing retinal vessels with a high resolution, especially arterial bifurcations, suitable to morphometric biomarkers measurements. In this paper, we propose a fully automatic hybrid approach based on a modified U-Net convolutional neu-ral network and active contours for segmenting retinal vessel branches and bifurcations with high precision. The obtained segmentation results are within the range of intra-and inter-user variability, and meet the performance of our previous semi-automatic approach in terms of precision and reproducibility, while being obtained in a completely automatic way.