A Closed-Form Differential Formulation for Ultrasound Spatial Calibration: Multi-wedge Phantom

Calibration is essential in freehand 3-D ultrasound to find the spatial transformation from the image coordinates to the sensor coordinate system. Calibration accuracy has significant impact on image-guided interventions. We introduce a new mathematical framework that uses differential measurements to achieve high calibration accuracy. Accurate measurements of axial differences in ultrasound images of a multi-wedge phantom are used to calculate the calibration matrix with a closed-form solution. The multi-wedge phantom has been designed based on the proposed differential framework and can be mass-produced inexpensively using a 3-D printer. The proposed method enables easy, fast and highly accurate ultrasound calibration, which is essential for most current ultrasound-guided applications and also widens the range of new applications. The precision of the method using only a single image of the phantom is comparable to that of the standard N-wire method using 50 images. The method can also directly take advantage of the fine sampling rate of radiofrequency ultrasound data to achieve very high calibration accuracy. With 100 radiofrequency ultrasound images, the method achieves a point reconstruction error of 0.09 ± 0.39 mm.