Purpose: Telemedicine networks are being established in several countries for mass screening of retinal pathologies, like diabetic retinopathy or age-related macular degeneration. Images are acquired by trained technicians, using different fundus cameras models. The quality of the resulting images could be insufficient for interpretation by ophthalmologists or automated systems. With the use of hand- held retinographs, this problem will only worsen. An efficient method is presented to estimate the quality of eye fundus images using a relatively simple convolutional neural network. One of the objectives of the method is to give feed-back to the user during acquisition, so that an image can be re-acquired if the quality is too low for image interpretation. The method is based on the estimation of the visibility of the fovea and surrounding vessels. Methods: 6098 images have been extracted from the e-ophtha database, provided by the OPHDIAT telemedecine network. When the fovea and surrounding vessels were considered visible, the center of the fovea was marked on those images. Pre-processing includes image subsamplingof the green channel to 128x128, as our tests have shown that this resolution is good enough for the task. The method uses a purely convolutional neural network, simple enough in order to speed-up prediction and reduce energy consumption. The network learns to predict a 20 pixel diameter disk centered on the fovea, when visible, or nothing, when not visible. A post-processing step based on mathematical morphology gives the final segmentation result. If a single connected component is predicted by the network, its centroid is considered as the center of the fovea. Results: The accuracy of the method is 96.4%, and it correctly identifies ungradable images in 98,7% cases. The precision of the fovea position, when detected, is measured on our database, as well as on the Aria database. The mean test errors are respectively equal to 0.95 and 1.4 pixels, and the maximal errors equal to 4.85 and 6 pixels. Conclusion: The presented method paves the way towards the deployment of embedded quality estimation of eye fundus color images and decreases the number of ungradable images. This work was funded by the French ”Fonds Unique Interministériel” through the Retinoptic project and supported by the Medicen and Systematic competitive clusters.