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

Lin Li, Benjamin Aubert, Paul Kemper, Aric Plumley

Abstract

\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.

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

Abstract

\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 (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 (100 mm, assuming a nominal focal length of 1000 mm), mean 3D reconstruction error remained under 0.2 mm. Larger focal length deviations (700 pixels) elevated error to only 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.
Paper Structure (20 sections, 5 figures)

This paper contains 20 sections, 5 figures.

Table of Contents

  1. INTRODUCTION
  2. METHODS
  3. Simulation Environment Setup
  4. Intrinsic Perturbation Modeling
  5. Evaluation Procedure
  6. Test Volume and Point Sampling
  7. Metrics
  8. Real C-arm Data
  9. Baseline Calibration
  10. Perturbation of Intrinsic Parameters
  11. Image Acquisition
  12. Extrinsic Re-estimation and Reconstruction
  13. Evaluation and Visual Inspection
  14. RESULTS
  15. Simulated Data
  16. ...and 5 more sections

Figures (5)

  • Figure 1: Visualization of 3D test points and their corresponding 2D projections in AP and LAT views. Left: A total of 74 3D test points selected from an initial set of 500 uniformly distributed samples within the overlapping field of view of the AP and LAT imaging planes. These points are located within the region where both views provide valid projection coverage, ensuring reliable 3D reconstruction. Top right: The 2D projections of the selected 3D points onto the AP image plane, simulating how the C-arm captures these spatial locations in the anterior-posterior view. Bottom right: The corresponding 2D projections of the same 3D points onto the LAT image plane, representing the lateral perspective projection.
  • Figure 2: 3D environment constructed from real C-arm data for extrinsic parameter re-estimation: AP and LAT images of the phantom with back-projected reconstructed BBs (left), and a 3D view of the scene with projection lines visualized (right).
  • Figure 3: Mean and standard deviation of the 3D reconstruction error versus focal length perturbation for piercing point offsets of 20 px (top left), 50 px (top right), 100 px (bottom left), and 200 px (bottom right). Errors remain below 0.5 mm even with ±700 px focal length shifts.
  • Figure 4: Mean and standard deviation of the reprojection error as a function of focal length perturbation, shown for piercing point offsets of 20 px (top left), 50 px (top right), 100 px (bottom left), and 200 px (bottom right). In all cases, the reprojection error remains below 5 pixels for both AP and LAT views, even with focal length shifts up to ±700 px.
  • Figure 5: Mean and standard deviation of the 3D reconstruction error as a function of focal length perturbation, shown for piercing point offsets of 20 px (top left), 50 px (top right), 100 px (bottom left), and 200 px (bottom right). Across all settings, errors remain below 0.2 mm even with focal length shifts up to ±500 px.