Tracker-Free Robotic Ultrasound Calibration with a Spherical-Marker Phantom and Threshold-Free Center Localization
Authors: Kyoungmo Koo, Guangshen Ma, Xueding Wang, Mark Draelos
Organizations: Department of Robotics, University of Michigan, 2505 Hayward St, Ann Arbor, MI 48109, USA · Department of Biomedical Engineering, University of Michigan, 1150 Medical Center Dr, Ann Arbor, MI 48109, USA · Department of Ophthalmology and Visual Sciences, University of Michigan Medical School, 1000 Wall St, Ann Arbor, MI 48105, USA
Robotic ultrasound (US) calibration is essential for accurately relating US images to the robot coordinate system, but accurate and automated calibration remains challenging because existing methods often require complex phantoms or external 3D trackers. In this work, we develop a tracker-free robotic US calibration framework using a spherical-marker phantom and a highly automated perception pipeline for sphere-center localization. The proposed threshold-free image-processing method localizes the spherical feature based on each US image's intensity distribution, eliminating hand-tuned intensity thresholds and improving robustness across imaging settings without per-system retuning. Multi-pose observations of the spherical fiducial are then used to estimate the US-to-EE transformation without external tracking or prior localization of the sphere center in the robot base frame. We validate the proposed framework on a robotic US platform through repeated sphere scans and further assess the calibrated system using geometrically distinct phantoms with known CAD models. Across 12 cross-validation folds, single-marker calibration achieved sphere-center accuracy and precision of 1.75±0.51 mm and 0.85±0.11 mm, respectively, compared with 1.72±0.51 mm and 0.84±0.12 mm for three-marker calibration. Across the three reconstruction sets, the single-marker calibration yielded pooled post-registration point-to-surface MAE±SD values of 0.41±0.35 mm for the cone and 0.50±0.41 mm for the triangular prism, closely matching the three-marker results of 0.40±0.35 mm and 0.48±0.40 mm, respectively.
Figures & tables
Fig. 1: Robotic ultrasound system scanning the sphere phantom in a water tank. The US probe is rigidly attached to the robot end-effector through a custom 3D-printed platform. The robot-base, end-effector, and US-image frames are related by the forward-kinematics transform Teeb (known) and the US-to-EE calibration Tusee (to be estimated).
Fig. 2: Scan trajectory about a single sphere. The leftmost panel shows the US probe-holder CAD model and coordinate frame, with x and y in the EE plane and z along the axial direction. The probe is rotated by ±10∘ about each axis and translated in-plane by ±3 mm, yielding 45 poses from nine orientations and five translations. Red lines indicate the line of sight to the sphere center.
Fig. 3: Calibration procedure. (a) Cone-tip positions are localized by touch measurements. (b) The phantom model is registered to the robot base frame, providing reference sphere center positions. (c) Each sphere is scanned from multiple probe orientations using US probe. (d) Estimated sphere center locations by US scan. Convergence and known inter-sphere geometry are used.
Fig. 4: Threshold-free sphere localization algorithm: (a) adaptive brightness, (b) stacking the elevational sweep into a 3D volume, (c) count-based sphere fitting within the search ROI, with the dashed box showing the ROI and the red surface showing the fitted proximal hemisphere, and (d) peak-normalized radial-band refinement. The interior band extends from the center to the first rising crossing of 0.25, while the shell band is bounded by the rising and falling crossings of 0.75. The arrows mark iterative refinement of the shell/interior bands and the calibration Tusee transform.
Fig. 5: Representative B-mode cross-sections acquired at three robot poses: (a) an XYZ Euler-angle offset of (−10∘,+10∘,+10∘) with an in-plane offset of (+3,+3) mm, (b) the same orientation at the centered in-plane position, and (c) an XYZ Euler-angle offset of (+10∘,+10∘,+10∘) at the centered position. All rotations and translations are defined relative to the nominal probe pose. The red contours denote the sphere boundaries predicted by the automatic localization method.
Metric
Statistic
A
B
C
Overall
Tool prec.
MAE ± SD
0.60±0.04
0.53±0.11
0.70±0.13
0.61±0.12
RMSE
0.60
0.53
0.70
0.62
Sphere prec.
MAE ± SD
0.71±0.02
0.89±0.02
0.96±0.02
0.85±0.11
RMSE
0.71
0.89
0.96
0.86
Sphere acc.
MAE ± SD
1.16±0.12
2.26±0.14
1.82±0.30
1.75±0.51
RMSE
1.16
2.27
1.84
1.81
TABLE I: Single-marker calibration errors (mm).
Metric
Statistic
A
B
C
Overall
Sphere prec.
MAE ± SD
0.70±0.07
0.88±0.02
0.95±0.07
0.84±0.12
RMSE
0.70
0.88
0.95
0.85
Sphere acc.
MAE ± SD
1.13±0.20
2.24±0.15
1.80±0.26
1.72±0.51
RMSE
1.14
2.25
1.81
1.79
TABLE II: Three-marker calibration errors (mm).
Fig. 6: (a) Cone phantom scanned from a tilted direction. (b) US image of the scanned cone phantom and fitted red lines to the bright boundaries. (c) Triangular prism phantom scanned from tilted direction. (d) Corresponding US image and fitted red lines to the bright boundaries.
Single-marker (Sphere 1)
Three-marker (Spheres 1–3)
Phantom
Set
MAE ± SD
RMSE
Max
MAE ± SD
RMSE
Max
Cone
A
0.36±0.30
0.46
1.99
0.34±0.29
0.45
1.99
Cone
B
0.45±0.39
0.60
3.04
0.44±0.39
0.59
2.75
Cone
C
0.43±0.35
0.56
2.34
0.41±0.34
0.53
2.42
Cone
Overall
0.41±0.35
0.54
3.04
0.40±0.35
0.53
2.75
Triangular prism
A
0.45±0.34
0.57
1.59
0.44±0.33
0.55
1.50
TABLE III: Single- and Three-Marker Point-to-Surface Errors After ICP Registration (mm)
Fig. 7: Point-to-surface error heatmaps after ICP registration, shown as orthographic top-down views. The top row (a–f) shows the cone phantom, and the bottom row (g–l) shows the triangular-prism phantom. Within each row, the first three panels show the Sphere 1 single-marker calibration results for Sets A–C, while the last three show the Spheres 1–3 three-marker calibration results for Sets A–C.
Freehand 3-D ultrasound (US) imaging has attracted increasing attention owing to its intuitive volumetric visualization, ease of use, and low cost. However, accurate 3-D reconstruction critically depends on stable probe pose estimation, yet existing trackerless methods remain susceptible to accumulated pose errors, particularly over long scanning trajectories. To address this limitation, we propose a global-to-local pose estimation framework that exploits external camera observations for globally stable localization and B-mode US images for anatomy-aware local refinement. Specifically, the framework comprises a dual-camera branch that performs contextual feature aggregation across camera views and temporal observations to estimate a globally consistent probe trajectory, and a B-mode branch that performs anatomical feature aggregation from sequential US images to capture tissue-dependent local motion cues. A cross-modal fusion module subsequently integrates the contextual camera features and anatomical US features to predict pose residuals and refine the camera-derived estimates in the transformation space. Furthermore, a multi-scale pose loss constrains relative motion over multiple temporal horizons to suppress accumulated drift during extended scans. The proposed framework is validated on phantom and in vivo datasets. On two in-house datasets (FUSION-J and FUSION-L) collected using different machines, the proposed US + Dual-Cam model reduces average trajectory drift to 1.67 mm and 1.29 mm, representing improvement of 16.50% and 27.12%, respectively, over a strong dual-camera baseline, while substantially outperforming US-only pose estimation (>13 mm drift). In in vivo forearm arteries reconstruction, it achieves Hausdorff distances of 1.58 mm, demonstrating the effectiveness of the proposed method on real clinical scenarios.
Yameng Zhang, Zhongyu Chen, Dianye Huang +3
Department of Mechanical Engineering, The University of Hong Kong, Hong Kong SAR, China · Department of Mechanical and Automation Engineering, The Chinese University of Hong Kong, Hong Kong SAR, China
Ultrasound (US) provides real-time, radiation-free imaging, but the image quality depends strongly on how the probe is oriented against the patient body. Robotic US can reduce operator workload and improve acquisition consistency; however, most existing systems focus on normal positioning, where the probe is maintained perpendicular to the local surface. This constraint is inadequate for examinations like echocardiography, where obtaining a diagnostic view requires a non-normal probe angle. Consequently, a clinically useful robotic system must sense the local surface in real-time and preserve the desired probe orientation. Here, we propose an omni-directional probe-orientation control framework that integrates RGB-D perception, local-surface modeling, and task-space orientation control. The surface model fuses multi-view point clouds and provides a quadratic estimate of the local surface. A desired imaging direction is then encoded relative to the normal, enabling the probe to track arbitrary angles. The framework was evaluated through flat-surface tracking, phantom target-angle recovery, and in-vivo tracking of an expert selected view. Results show that the mean angular tracking error was 1.06 +- 0.66 deg. The system recovered a non-normal tilt angle of up to 44.39 +- 2.59 deg relative to the surface normal, and acquired the desired heart chamber view in the phantom and in-vivo experiments.
Xihan Ma, Haichong Zhang
Department of Robotics Engineering, Worcester Polytechnic Institute, 100 Institute Road, Worcester, MA 01609 USA
This work presents an RGB-D imaging-based approach to marker-free hand-eye calibration using a novel implementation of the iterative closest point (ICP) algorithm with a robust point-to-plane (PTP) objective formulated on a Lie algebra. Its applicability is demonstrated through comprehensive experiments using three well known serial manipulators and two RGB-D cameras. With only three randomly chosen robot configurations, our approach achieves approximately 90% successful calibrations, demonstrating 2-3x higher convergence rates to the global optimum compared to both marker-based and marker-free baselines. We also report 2 orders of magnitude faster convergence time (0.8 +/- 0.4 s) for 9 robot configurations over other marker-free methods. Our method exhibits significantly improved accuracy (5 mm in task space) over classical approaches (7 mm in task space) whilst being marker-free. The benchmarking dataset and code are open sourced under Apache 2.0 License, and a ROS 2 integration with robot abstraction is provided to facilitate deployment.
Martin Huber, Huanyu Tian, Christopher E. Mower +4
School of Biomedical Engineering & Imaging Sciences, King’s College London, London, UK · Noah’s Ark Lab, Huawei, London, UK · independent contributor