X-ray angiography is widely used in cardiac interventions to visualize coronary vessels, assess integrity, detect stenoses, and guide treatment. In this paper, we propose a framework for reconstructing 3D vessel trees from biplanar X-ray images which are extracted from two X-ray videos captured at different C-arm angles. The proposed framework consists of three main components: image segmentation, motion phase matching, and 3D reconstruction. We developed an automatic video segmentation method for X-ray angiography to enable semantic segmentation, support both image segmentation, and motion phase matching. The goal of the motion phase matching is to identify a pair of X-ray images that correspond to a similar respiratory and cardiac motion phase; thereby reducing errors in 3D reconstruction. This is achieved by tracking a stationary object such as an injection balloon, a catheter, or a lead, within the X-ray video. The semantic segmentation approach assigns different labels to different object classes thereby enabling accurate differentiation between blood vessels, balloons, and catheters. Once a suitable image pair is selected, key anatomical landmarks (vessel branching points and endpoints) are matched between the two views using a heuristic method that minimizes reconstruction errors. This is followed by a novel geometric reconstruction algorithm to generate the 3D vessel tree. The algorithm computes the 3D vessel centrelines by determining the intersection of two 3D surfaces. Compared to traditional methods based on epipolar constraints, the proposed approach simplifies the reconstruction workflow and improves overall accuracy. We trained and validated our segmentation method on 62 X-ray angiography video sequences. On the test set, our method achieved a segmentation accuracy of 0.703. The 3D reconstruction framework was validated by measuring the reconstruction error of key anatomical landmarks, achieving a reprojection errors of 0.62 mm ± 0.38mm.