In the rapidly evolving field of intravascular ultrasound (IVUS), the assessment of vessel morphology still lacks a geometrically correct three-dimensional (3-D) reconstruction. The IVUS frames are usually stacked up to form a straight vessel, neglecting curvature and the axial twisting of the catheter during the pullback. Our method combines the information about vessel cross-sections obtained from IVUS with the information about the vessel geometry derived from biplane angiography. First, the catheter path is reconstructed from its biplane projections, resulting in a spatial model. The locations of the IVUS frames are determined and their orientations relative to each other are calculated using a discrete approximation of the Frenet-Serret formulas known from differential geometry. The absolute orientation of the frame set is established, utilizing the imaging catheter itself as an artificial landmark. The IVUS images are segmented, using our previously developed algorithm. The fusion approach has been extensively validated in computer simulations, phantoms, and cadaveric pig hearts.