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The 3D/2D registration for 3D pre-operative images (computed tomography, CT) and 2D intra-operative images (X-ray) plays an important role in image-guided spine surgeries. Conventional iterative-based approaches suffer from time-consuming processes. Existing learning-based approaches require high computational costs and face poor performance on large misalignment because of projection-induced losses or ill-posed reconstruction. In this paper, we propose a Progressive 3D/2D rigid Registration network with the guidance of Single-view Cycle Synthesis, named PRSCS-Net. Specifically, we first introduce the differentiable backward/forward projection operator into the single-view cycle synthesis network, which reconstructs corresponding 3D geometry features from two 2D intra-operative view images (one from the input, and the other from the synthesis). In this way, the problem of limited views during reconstruction can be solved. Subsequently, we employ a self-reconstruction path to extract latent representation from pre-operative 3D CT images. The following pose estimation process will be performed in the 3D geometry feature space, which can solve the dimensional gap, greatly reduce the computational complexity, and ensure that the features extracted from pre-operative and intra-operative images are as relevant as possible to pose estimation. Furthermore, to enhance the ability of our model for handling large misalignment, we develop a progressive registration path, including two sub-registration networks, aiming to estimate the pose parameters via two-step warping volume features. Finally, our proposed method has been evaluated on a public dataset CTSpine1k and an in-house dataset C-ArmLSpine for 3D/2D registration. Results demonstrate that PRSCS-Net achieves state-of-the-art registration performance in terms of registration accuracy, robustness, and generalizability compared with existing methods. Thus, PRSCS-Net has potential for clinical spinal disease surgical planning and surgical navigation systems. • We provide a high-accuracy, robust, memory-efficient, and real-time 3D/2D registration algorithm, named PRSCS-Net. Expensive experiments on a public and an in-house datasets exhibit superior registration performance, which demonstrates its potential in spine surgery navigation. • To reduce the memory costs and extract the essential geometry features, we utilize a differentiable backward projector(DBP) and a feature refinement module (FRM) to establish 3D/2D correspondence between the 3D pre-operative CT and the 2D intra-operative X-ray. • To avoid higher radiation exposure, we propose a single view cycle synthesis path (SVCSP) to extract the 3D geometry features from a single intra-operative view with another synthesis orthogonal view. • To hand large misalignment, we design a progressive registration path (PRP) to sequentially warp two 3D intra-operative geometry features extracted in SVCSP. [ABSTRACT FROM AUTHOR]