C臂成像的内在容忍度：如何通过外在重新优化保持3D重建精度
Intrinsic Tolerance in C-Arm Imaging: How Extrinsic Re-optimization Preserves 3D Reconstruction Accuracy
AI总结：
研究通过重新优化外在参数补偿内在校准误差，证明在存在一定内在校准误差时，能保持3D重建精度，为简化C臂系统设置提供了可行路径。
摘要：
目的：C臂荧光摄影的3D重建依赖于准确的内在校准，这在临床实践中往往具有挑战性。本研究通过重新优化外在参数来补偿内在校准误差，以确保高精度的重建准确性。方法：我们使用五种商业C臂系统进行了仿真和实际实验。内在参数在受控增量下进行扰动。焦距增加了100到700像素（约20毫米到140毫米），主点增加了20到200像素。对于每种扰动，我们（1）从已知的仿真实体几何体中重建3D点，（2）使用标准优化重新估计外在姿态，（3）测量重建和重投影误差相对于真实值。结果：即使焦距误差高达500像素（约100毫米，假设名义焦距约为1000毫米），平均3D重建误差仍低于0.2毫米。较大的焦距偏差（700像素）使误差增加到仅约0.3毫米。主点位移高达200像素在重新优化外在参数后引入了可忽略的重建误差，重投影误差增加低于0.5像素。结论：适度的内在校准误差可以通过外在重新优化有效缓解，保持亚毫米级的3D重建准确性。这种内在容忍度表明，可以通过放松校准精度要求来简化C臂系统设置，从而减少临床工作流程负担，而不影响性能。
英文摘要：
\textbf{Purpose:} C-arm fluoroscopy's 3D reconstruction relies on accurate intrinsic calibration, which is often challenging in clinical practice. This study ensures high-precision reconstruction accuracy by re-optimizing the extrinsic parameters to compensate for intrinsic calibration errors. \noindent\textbf{Methods:} We conducted both simulation and real-world experiments using five commercial C-arm systems. Intrinsic parameters were perturbed in controlled increments. Focal length was increased by 100 to 700 pixels ($\approx$20 mm to 140 mm) and principal point by 20 to 200 pixels. For each perturbation, we (1) reconstructed 3D points from known phantom geometries, (2) re-estimated extrinsic poses using standard optimization, and (3) measured reconstruction and reprojection errors relative to ground truth. \noindent\textbf{Results:} Even with focal length errors up to 500 pixels ($\approx$100 mm, assuming a nominal focal length of $\sim$1000 mm), mean 3D reconstruction error remained under 0.2 mm. Larger focal length deviations (700 pixels) elevated error to only $\approx$0.3 mm. Principal point shifts up to 200 pixels introduced negligible reconstruction error once extrinsic parameters were re-optimized, with reprojection error increases below 0.5 pixels. \noindent\textbf{Conclusion:} Moderate errors in intrinsic calibration can be effectively mitigated by extrinsic re-optimization, preserving submillimeter 3D reconstruction accuracy. This intrinsic tolerance suggests a practical pathway to relax calibration precision requirements, thereby simplifying C-arm system setup and reducing clinical workflow burden without compromising performance.
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