.CTA angiography brings potentially useful information forguidance in an interventional procedure. It comes with the challenge ofregistering this 3D modality to the projection of the coronary arterieswhich are deforming with the cardiac motion. A tree-spline i.e. a treewith a spline attached to each edge and shared control points betweenthese points describes a 3D coronary tree and is able to represent itsdeformation along the time. We combine this description with a registra-tion algorithm operating between the tree-spline and the angiographicprojection of the coronary tree. It starts by the estimation of a rigidtransformation for the iso cardiac phase time followed by a non-rigiddeformation of the tree driven by the pairings formed between the pro-jection of the edges of the tree-spline and the observed x-ray projectionof the coronary arteries. The pairings are built taking into account thetree topology consistency. Anatomical constraints of length preservationis enforced when deforming the arteries. The proposed approach hasbeen evaluated with clinical data issued from ten different clinical caseswhich enabling to form twenty three different experimental conditions.Encouraging results have been obt