A Real-Time 2D-3D Registration Algorithm for Spine Surgery Navigation Using Accelerated Gradient Optimization

Two-dimensional to three-dimensional (2D–3D) medical image registration plays a critical role in image-guided spinal surgery, enabling accurate alignment between intraoperative fluoroscopy and preoperative CT volumes. However, existing methods often suffer from slow convergence or high computational demands, limiting their use in time-sensitive clinical settings. To address this challenge, we propose a semi-automatic 2D–3D registration algorithm that integrates a grid-based initialization strategy with Nesterov-accelerated gradient (NAG) optimization. The method first coarsely aligns anatomical landmarks via vertebral segmentation on a grid, then refines the transformation parameters by maximizing a novel similarity metric—Normalized Cross-Correlation–Gradient Difference–Projection Distance Error (NGE)—using momentum-enhanced gradient descent. Evaluated on clinical spine datasets, our approach achieves a root mean square (RMS) registration error of 0.82 ± 0.15 mm with an average processing time of 15.2 seconds per case, outperforming conventional gradient descent (28.7 s) and Gauss–Newton (22.4 s) methods in both speed and accuracy. These results demonstrate the algorithm’s potential for real-time surgical navigation, where rapid and sub-millimeter precision is essential.