Freehand ultrasound calibration using the Unscented Kalman Filter

Three-dimensional freehand ultrasound has found several clinical applications, such as image-guided surgery and radiotherapy, since the last decade. A key step of all the freehand ultrasound imaging systems is calibration. Calibration is the procedure to estimate a two to three-dimensional transformation matrix which precisely maps two-dimensional ultrasound images to the physical coordinate. This paper presents a novel freehand ultrasound calibration algorithm which is based on a sequential least squares method, known as the Unscented Kalman Filter (UKF) algorithm. This method has significant advantages over the prior approaches, where the block least squares techniques have been employed to perform the ultrasound probe calibration. One of the advantages is that. it computes the calibration parameters as well as their variances sequentially by processing the sample points, collected from ultrasound images of a designed phantom, one by one. Variance evaluation can be used to generate a confidence measure for the estimated calibration matrix. It also enables us to stop the calibration procedure once the desired confidence measure is met or informs us to collect more sample points to improve the calibration accuracy. The proposed calibration method is evaluated by using a custom designed N-wire phantom. The simulation results confirm that the proposed calibration algorithm converges to the same solution as the block least squares algorithms, while having the above mentioned practical advantages.