Projection-Domain Sensitivity Analysis of Vertebral DRRs Under Intrinsic Calibration Perturbation

Accurate geometric calibration is essential for fluoroscopy-guided spinal imaging, digitally reconstructed radiograph (DRR) generation, and 2D--3D vertebral registration. Although calibration quality is typically evaluated using reconstruction-based metrics such as reprojection error, its influence on projection-domain consistency remains poorly understood. This study presents a synthetic framework for evaluating how intrinsic calibration perturbations affect vertebral fluoroscopic projections and downstream registration performance. CT-derived vertebral models and controlled cone-beam imaging geometry were used to generate DRRs with both ground-truth and perturbed intrinsic calibration parameters while maintaining identical anatomy and acquisition pose. Projection-domain changes were quantified using anatomical landmark displacement, contour distance, silhouette overlap, image similarity, and landmark-based 2D--3D registration accuracy in anterior--posterior (AP) and lateral (LAT) views. Results show that even small intrinsic calibration perturbations produce measurable changes in vertebral projection geometry, contour morphology, landmark localization, and DRR appearance. Sensitivity is strongly view dependent, with LAT projections exhibiting substantially greater deformation and anatomical displacement than AP projections. These projection inconsistencies also degrade downstream 2D--3D registration, particularly rotational alignment accuracy. The findings demonstrate that projection-domain consistency complements conventional reconstruction-based calibration metrics and provides a practical framework for assessing calibration robustness. This approach may improve the reliability of DRR generation and fluoroscopy-guided vertebral registration in image-guided spinal applications.

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.