Single Wall Closed-form Differential Ultrasound Calibration

In freehand 3D ultrasound, images are acquired while the position of the transducer is recorded with a tracking device. Calibration is essential in this technique to find the transformation from the image coordinates to the reference coordinate system. The single wall technique is a common calibration method because a simple plane phantom is used. Despite its advantages, such as ease of phantom construction and image analysis, this method requires large number of images to converge to the solution. One reason is a lack of a closed-form solution. Also, the technique uses slightly ill-conditioned sets of equations with a high condition number due to limited range of scanning motions that produce clear images of the plane. Here, a novel closed-form formulation has been proposed for the single wall calibration technique. Also, differential measurements of the plane image are used instead of absolute plane detection to improve accuracy. The closed-form solution leads to more accurate and robust results while providing an insight into understanding error propagation and finding the optimal set of transducer poses. Results have been compared to the conventional single wall technique. A residual error of 0.14 mm is achieved for the proposed method compared to 0.91 mm in the conventional approach.