Accuracy estimation in freehand ultrasound probe calibration

Three-dimensional, freehand ultrasound is an imaging technique that has seen increasing applications in computer assisted surgery. A key element of this technique is image calibration, in order to estimate a three-dimensional homogeneous transformation that maps the position of individual pixels from the ultrasound image coordinate to the ultrasound probe coordinate frames. The transformation is typically calculated through imaging a calibration phantom of known geometry, and solving for the transformation parameters (either in closed-form or iteratively) The calibration error achieved through this process is usually assumed to be constant for all the pixels in the image. In this paper, we propose a novel method to estimate the calibration accuracy for individual pixels within an ultrasound image by employing the Unscented Kalman Filter (UKF). Based on the variances of calibration parameters extracted by UKF, a mean square residual error is estimated for each individual pixel in the ultrasound image. We demonstrate that the calibration error could in fact significantly vary for different pixels in the image. This observation could potentially impact the image registration process in computer assisted surgery applications. The method has been validated through simulations and experiments.