In interventional radiology, navigating devices under the sole guidance of fluoroscopic images inside a complex architecture of tortuous and narrow vessels like the cerebral vascular tree is a difficult task. Visualizing the device in 3D could facilitate this navigation. For curvilinear devices such as guide-wires and catheters, a 3D reconstruction may be achieved using two simultaneous fluoroscopic views, as available on a biplane acquisition system. The purpose of this paper is to present a new automatic three-dimensional curve reconstruction method that has the potential to reconstruct complex 3D curves and does not require a perfect segmentation of the endovascular device. Using epipolar geometry, our algorithm translates the point correspondence problem into a segment correspondence problem. Candidate 3D curves can be formed and evaluated independently after identifying all possible combinations of compatible 3D segments. Correspondence is then inherently solved by looking in 3D space for the most coherent curve in terms of continuity and curvature. This problem can be cast into a graph problem where the most coherent curve corresponds to the shortest path of a weighted graph. We present quantitative results of curve reconstructions performed from numerically simulated projections of tortuous 3D curves extracted from cerebral vascular trees affected with brain arteriovenous malformations as well as fluoroscopic image pairs of a guide-wire from both phantom and clinical sets. Our method was able to select the correct 3D segments in 97.5% of simulated cases thus demonstrating its ability to handle complex 3D curves and can deal with imperfect 2D segmentation.