RadGS-Reg+: Teacher-student radiative Gaussian reconstruction and 3D/3D registration for lumbar CT/X-ray registration

Accurate registration between preoperative CT and intraoperative X-ray is essential for image-guided lumbar spine surgery, yet remains challenging because conventional 2D/3D registration methods operate in projection space and suffer from spatial information loss, domain discrepancy, and limited robustness under noisy sparse-view imaging. In this work, we propose RadGS-Reg+, a reconstruction-first framework that reformulates lumbar CT/X-ray registration as a 3D/3D alignment problem. Instead of directly matching digitally reconstructed radiographs to intraoperative X-rays, RadGS-Reg+ first reconstructs an X-ray-conditioned registration-oriented vertebral representation from biplanar X-rays and then aligns it with the preoperative CT through 3D/3D pose regression. The framework integrates a CT-based teacher network for vertebral anatomical prior learning, a student reconstruction network trained by semi-supervised cross-modal distillation, adaptive feature fusion for biplanar view integration, counterfactual regularization for suppressing spurious responses caused by overlapping anatomy, and a discrepancy-aware fusion module for robust 3D/3D registration. Experiments on a real intraoperative lumbar dataset with five-fold cross-validation show that the proposed method achieves 90.93% SSIM and 29.27 dB PSNR in reconstruction, and 1.57 mm mTRE, 90.22% success rate, and 0.86 s runtime in registration. The code is available at: github.com/shenao1995/RadGS_Reg.