In order to estimate a registration model of eye fundus images made of an affinity and two radial distortions, we introduce an estimation criterion based on an error between the vessels. In , we estimated this model by minimising the error between characteristics points. In this paper, the detected vessels are selected using the circle and ellipse equations of the overlap area boundaries deduced from our model. Our method successfully registers 96 % of the 271 pairs in a Public Health dataset acquired mostly with different cameras. This is better than our previous method  and better than three other state-of-the-art methods. On a publicly available dataset, ours still better register the images than the reference method.