The classification of retinal vessels into arteries and veins in eye fundus images is a relevant task for the automatic assessment of vascular changes. This paper presents a new approach to solve this problem by means of a Fully-Connected Convolutional Neural Network that is specifically adapted for artery/vein classification. For this, a loss function that focuses only on pixels belonging to the retinal vessel tree is built. The relevance of providing the model with different chromatic components of the source images is also analyzed. The performance of the proposed method is evaluated on the RITE dataset of retinal images, achieving promising results, with an accuracy of 96% on large caliber vessels, and an overall accuracy of 84% .