Coplanarity Constrained Ultrasound Probe Calibration Based on N-Wire Phantom

Objective N-wire phantom-based ultrasound probe calibration has been used widely in many freehand tracked ultrasound imaging systems. The calibration matrix is obtained by registering the coplanar point cloud in ultrasound space and non-coplanar point cloud in tracking sensor space based on the least squares method. This method is sensitive to outliers and loses the coplanar information of the fiducial points. In this article, we describe a coplanarity-constrained calibration algorithm focusing on these issues. Methods We verified that the out-of-plane error along the oblique wire in the N-wire phantom followed a normal distribution and used it to remove the experimental outliers and fit the plane with the Levenberg–Marquardt algorithm. Then, we projected the points to the plane along the oblique wire. Coplanarity-constrained point cloud registration was used to calculate the transformation matrix. Results Compared with the other two commonly used methods, our method had the best calibration precision and achieved 25% and 36% improvement of the mean calibration accuracy than the closed-form solution and in-plane error method respectively at depth 16. Experiments at different depths revealed that our algorithm had better performance in our setup. Conclusion Our proposed coplanarity-constrained calibration algorithm achieved significant improvement in both precision and accuracy compared with existing algorithms with the same N-wire phantom. It is expected that calibration accuracy will improve when the algorithm is applied to all other N-wire phantom-based calibration procedures. N-wire phantom-based ultrasound probe calibration has been used widely in many freehand tracked ultrasound imaging systems. The calibration matrix is obtained by registering the coplanar point cloud in ultrasound space and non-coplanar point cloud in tracking sensor space based on the least squares method. This method is sensitive to outliers and loses the coplanar information of the fiducial points. In this article, we describe a coplanarity-constrained calibration algorithm focusing on these issues. We verified that the out-of-plane error along the oblique wire in the N-wire phantom followed a normal distribution and used it to remove the experimental outliers and fit the plane with the Levenberg–Marquardt algorithm. Then, we projected the points to the plane along the oblique wire. Coplanarity-constrained point cloud registration was used to calculate the transformation matrix. Compared with the other two commonly used methods, our method had the best calibration precision and achieved 25% and 36% improvement of the mean calibration accuracy than the closed-form solution and in-plane error method respectively at depth 16. Experiments at different depths revealed that our algorithm had better performance in our setup. Our proposed coplanarity-constrained calibration algorithm achieved significant improvement in both precision and accuracy compared with existing algorithms with the same N-wire phantom. It is expected that calibration accuracy will improve when the algorithm is applied to all other N-wire phantom-based calibration procedures.