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We present a novel approach to simultaneously reconstruct the 3D structure of a non-rigid coronary tree and estimate point correspondences between an input X-ray image and a reference 3D shape. At the core of our approach lies an optimization scheme that iteratively fits a generative 3D model of increasing complexity and guides the matching process. As a result, and in contrast to existing approaches that assume rigidity or quasi-rigidity of the structure, our method is able to retrieve large non-linear deformations even when the input data is corrupted by the presence of noise and partial occlusions. We extensively evaluate our approach under synthetic and real data and demonstrate a remarkable improvement compared to state-of-the-art.