Three-dimensional reconstructions of tortuous vessels such as coronary arteries can be obtained by data fusion between biplane angiography and IVUS frames of a pullback sequence. The 3D course of the tortuous vessel is first determined from the angiograms and then combined with the 2D representations regarding the 3D course (e.g., segmented IVUS frames of a pullback sequence) using a data fusion apparatus and method: The determination of the 3D pullback path is represented by the external energy of the tortuous vessel and the internal energy of a line object such as a catheter.