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

2025-09-08

AI Summary

Existing Euclidean-space-based approximation methods for intraoperative 2D/3D registration distort manifold structure and suffer from slow convergence. To address this, we propose an end-to-end registration framework grounded in non-Euclidean spherical similarity learning: features extracted by a CNN-Transformer backbone are mapped onto the unit sphere; a Riemannian distance metric is constructed on the SO(4) manifold to approximate geodesic distance; and a differentiable Levenberg–Marquardt optimizer is integrated to enable efficient backpropagation of pose parameters under SE(3) geometric constraints. This formulation significantly enhances discriminability for subtle pose variations, yielding improved registration accuracy and faster convergence. We validate our method on both real and synthetic datasets, demonstrating superior performance over state-of-the-art approaches in both patient-specific and generalizable scenarios, with enhanced robustness and generalization capability.

Technology Category

• Machine Learning: Learning with Manifolds
• Intelligent Robots: State Estimation
• Search and Optimization: Learning to Search

Application Category

• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

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.

Problem

• Intraoperative 2D/3D registration aligns preoperative volumes with radiographs
• Euclidean approximations distort manifold structure and slow convergence
• Enhance ability to distinguish subtle pose differences accurately

Innovation

• Spherical similarity learning for geodesic distances
• CNN-Transformer encoder with spherical projection
• Differentiable Levenberg-Marquardt optimization for convergence