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In this paper, we address the problem of multimodal registration of coronary vessels by developing a 3D parametrical model of vessel trees from computer tomography data and registering it to angiography images during intervention. Thus, the interventionist takes profit from 3D data otherwise only available before the intervention. This facilitates orientation in ambiguous radiographs, interactive visualization of all vessel structures to estimate their mutual position and navigation within the vessel system and ultimately reduces the radiation the patient and the physicians are exposed to. The model is build by exploring the branching vessel tree starting from a single position and successively expanding through the vessels guided by a local deformable surface. The result is a tree of cylindrical segments each adapted to the vessel walls that is registered to angiography images in a fast and robust way. Validation on 8 patients confirms the robustness of our method.