Intrinsic Tolerance in C-Arm Imaging: How Extrinsic Re-optimization Preserves 3D Reconstruction Accuracy
Authors: Lin Li, Benjamin Aubert, Paul Kemper, Aric Plumley
Organizations: AIX, Alphatec Spine, 1950 Camino Vida Roble, Carlsbad, CA 92008, USA · EOS, EOS Imaging Inc., 7275 Rue Saint-Urbain Suite 400, Montreal, QC H2R 2Y5, Canada
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. \noindentMethods: 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. \noindentResults: 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. \noindentConclusion: 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.
Figures & tables
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.
In 3D reconstruction, camera calibration is an essential element for achieving high fidelity and accuracy of the reconstructed geometry. While existing approaches rely upon 2D planar calibration, this work proposes a framework tailored for 3D reconstruction that is based on predicting scene rays, which adds flexibility to the reconstruction pipeline and enables the use of recent advances in camera models. Novel metrics, reconstruction and intersection error, derived from predicted scene rays are employed in combination with a bootstrapping procedure that statistically evaluates different calibration objects and calibration pipelines for both intrinsic and extrinsic camera parameters. The results show that the generalized distortion model more faithfully captures physical camera effects and yields an improvement in calibration accuracy. Reprojection error is shown to be a potentially misleading indicator of 3D accuracy, and the proposed ray-based metrics provide a more holistic assessment. An icosahedron calibration target is designed to enrich calibration information for 3D reconstruction together with a ring-feature-based detector. The icosahedral target yields approximately 40% lower mean intersection and more stable calibration across bootstrap trials on synthetic data, while real-data performance demands very tight fabrication tolerances.
Dennis Ruppel, Hasan Kutlu, Kai A. Neumann +4
Fraunhofer Institute for Computer Graphics Research, Darmstadt · Computer Vision, Imaging and Data Analysis Group, Technical University of Applied Sciences Würzburg-Schweinfurt · Mathematical and Applied Visual Computing, Technical University Darmstadt
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.
Lin Li, Chaochao Zhou, Benjamin Aubert +2
Department of Mathematics, Tulane University · Department of Computer Science, University of Illinois Urbana-Champaign · EOS, EOS Imaging Inc. +2
Accurate camera intrinsic calibration is fundamental to robot perception, and the accuracy depends on the quality of the collected images. However, existing target-based calibration methods often require the practitioner to manually filter out high-quality images and to specify an appropriate radial distortion order. This paper presents a fully automatic intrinsic calibration pipeline that determines both from the collected data. We adopt an iterative rejection scheme that estimates parameters on a candidate image set and removes views whose mean residual exceeds a multiple of the median. Crucially, this process runs independently under each candidate distortion order, so that the retained image set is consistent with the residual scale of that order. Further, the distortion order is selected on held-out images, with the intrinsics and distortion fixed and only the board pose re-estimated, ensuring that an added coefficient is supported by independent observations. Finally, we integrate both steps into an interactive calibration tool that supports full-pipeline data inspection and parameter estimation. Experiments on our own camera data and five public real-world datasets show that image filtering reduces the held-out reprojection error by 25%, the order selection further by 5%, achieving the lowest held-out mean among four compared configurations without manual image selection. We will release the code and data to facilitate future research.
Xiangcheng Hu
Department of Electronic and Computer Engineering, The Hong Kong University of Science and Technology, Hong Kong SAR, China