Intrinsic Tolerance in C-Arm Imaging: How Extrinsic Re-optimization Preserves 3D Reconstruction Accuracy

\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.