To establish a 3D/2D registration method for preoperative CT and intra-operative X-ray images in imageguided spine surgery. We propose a 3D/2D registration algorithm based on 3D image reconstruction. The algorithm performs 3D image reconstruction of 2D orthogonal view X-ray images, thus converting the problem into 3D/3D registration. By constructing an end-to-end framework that combines the two tasks of reconstruction and registration, the geodesic distance is measured in the 3D manifold space to complete the registration. We conducted experiments on the public dataset CTSpine1k. The tests on two test sets with different initial registration errors showed that for data with small initial errors, the proposed algorithm achieved a rotation estimation error of 0.115±0.095° and a translation estimation error of 0.144±0.124 mm; for data with larger initial errors, a rotation estimation error of 0.792±0.659° and a translation estimation error of 0.867±0.701 mm were achieved. The proposed method can achieve robust and accurate 3D/2D registration at a speed that meets real-time requirements to improve the performance of spine surgery navigation.