Intraoperative 2D/3D Registration via Spherical Similarity Learning and Differentiable Levenberg-Marquardt Optimization

Intraoperative 2D/3D registration aligns preoperative 3D volumes with real-time 2D radiographs, enabling accurate localization of instruments and implants. A recent fully differentiable similarity learning framework approximates geodesic distances on SE(3), expanding the capture range of registration and mitigating the effects of substantial disturbances, but existing Euclidean approximations distort manifold structure and slow convergence. To address the above limitations, we explore similarity learning on non-Euclidean spherical feature spaces to improve the ability to capture and fit complex manifold features. We extract feature embeddings using a CNN-Transformer encoder, project them into spherical space, and approximate their geodesic distances with Riemannian geodesic distances in the bi-invariant SO(4) space. This enables the learning of a more expressive and geometrically consistent deep similarity metric, enhancing the network's ability to distinguish subtle pose differences. Fully differentiable Levenberg-Marquardt optimization is adopted to replace the existing gradient descent method to accelerate the convergence of the search during inference phase. Experiments on real and synthetic datasets show superior accuracy in both patient-specific and patient-agnostic scenarios.