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Alignment of angiographic 3D scans to 2D projections is an important issue for 3D depth perception and navigation during interventions. Currently, in a setting where only one 2D projection is available, methods employing a rigid transformation model present the state of the art for this problem. In this work, we introduce a method capable of deformably registering 3D vessel structures to a respective single projection of the scene. Our approach addresses the inherent ill-posedness of the problem by incorporating a priori knowledge about the vessel structures into the formulation. We minimize the distance between the 2D points and corresponding projected 3D points together with regularization terms encoding the properties of length preservation of vessel structures and smoothness of deformation. We demonstrate the performance and accuracy of the proposed method by quantitative tests on synthetic examples as well as real angiographic scenes.