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.
Abstract (translated)
术中2D/3D配准将术前的三维体积与实时二维影像对齐，使得手术器械和植入物的位置能够被精确地定位。最近提出的一种完全可微相似性学习框架，在SE(3)上近似测地距离，从而扩大了注册范围并减轻了重大干扰的影响；然而，现有的欧几里得近似方法会扭曲流形结构，并减缓收敛速度。为了解决这些问题，我们探索在非欧几里得球面特征空间中进行相似性学习，以更好地捕捉和拟合复杂的流形结构。我们使用CNN-Transformer编码器提取特征嵌入，将其投影到球面上，并通过SO(4)双不变量空间中的黎曼距离来近似它们的测地距离。这使得深度相似度度量更具表现力且几何一致性更强，从而增强了区分细微姿态差异的能力。在推理过程中，我们用完全可微的Levenberg-Marquardt优化方法替代梯度下降法，以加快收敛速度。实验证明，在真实和合成数据集上进行测试时，无论是患者特定的情况还是无差别情况，该方法均表现出更高的准确性。
URL
https://arxiv.org/abs/2509.06890
