In this paper, we propose a method based on morphological and topological analysis for the segmentation of vessels in eye fundus images. This is a very important problem, in particular for the quantitative assessment of microvascular damage due to arterial hypertension, diabetes and aging, such as branch retinal vein occlu-sions. This paper addresses the segmentation step required for such studies. A pre-processing step includes a morphological filtering to enhance the vessels. Attribute images are then built from a combination of a top-hat transform (i.e., a non linear operation) with linear filters at two different scales, leading to complementary information. Linear structure extraction is then performed using path-opening filters. The final segmentation relies on a fusion step and automatic thresholding. From this segmentation, a graph representation is then extracted, suitable for further quantitative analysis. The method has been evaluated on a large database of images, and good results have been obtained, in particular in terms of accuracy (average of 94.33% over the whole database, with a standard deviation of 0.61) and specificity (average of 97.88% over the whole database, with a standard deviation of 0.57). These results compare favorably to the ones obtained by other methods on the same database. The proposed approach can therefore be further exploited for temporal analysis of retinal diseases.