Intraoperative 2D/3D Registration via Spherical Similarity Learning and Inference-Time Differentiable Levenberg-Marquardt Optimization
This work addresses the challenge of accurate instrument and implant localization in medical imaging, representing an incremental improvement over existing similarity learning frameworks.
The paper tackled the problem of intraoperative 2D/3D registration for aligning preoperative 3D volumes with real-time 2D radiographs by proposing a method using spherical similarity learning and differentiable Levenberg-Marquardt optimization, resulting in superior accuracy on real and synthetic datasets.
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 these limitations, we explore similarity learning in non-Euclidean spherical feature spaces to better capture and fit complex manifold structure. We extract feature embeddings using a CNN-Transformer encoder, project them into spherical space, and approximate their geodesic distances with Riemannian distances in the bi-invariant SO(4) space. This enables a more expressive and geometrically consistent deep similarity metric, enhancing the ability to distinguish subtle pose differences. During inference, we replace gradient descent with fully differentiable Levenberg-Marquardt optimization to accelerate convergence. Experiments on real and synthetic datasets show superior accuracy in both patient-specific and patient-agnostic scenarios.