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At present, 3-D reconstructions of coronary vessels are generated from intravascular ultrasound (IVUS) by stacking up ECG-gated segmented IVUS frames of a pullback sequence. This simplified approach always results in straight vessel reconstructions and, therefore, gives an incorrect representation of tortuous coronary arteries. A more realistic reconstruction of tortuous vessels may be obtained by data fusion with biplane angiography. The 3-D course of the vessel is first derived from the angiograms and then combined with the segmented IVUS images. In this paper, we focus on two problems associated with the data fusion method: The definition of the pullback path and the estimation of the IVUS catheter twist during pullback. A robust algorithm for calculation of tortuosity-induced catheter twist is reported that is based on sequential triangulation of the 3-D pullback path. The method is analyzed with computer simulations and validated in helical vessel phantoms. A largely automated data fusion approach is proposed and applied to tortuous coronary arteries in cadaveric pig hearts.