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The vascular tree of the retina is likely the most representative and stable feature for eye fundus images in registration. Based on the reconstructed vascular tree, we propose an elastic matching algorithm to register pairs of fundus images. The identified vessels are thinned and approximated using short line segments of equal length that results a set of elements. The set of elements corresponding to one vascular tree are elastically deformed to optimally match the set of elements of another vascular tree, with the guide of an energy function to finally establish pixel relationship between both vascular trees. The mapped positions of pixels in the transformed retinal image are computed to be the sum of their original locations and corresponding displacement vectors. For the purpose of performance comparison, a weak affine model based fast chamfer matching technique is proposed and implemented. Experiment results validated the effectiveness of the elastic matching algorithm and its advantage over the weak affine model for registration of retinal fundus images.