Uncertainty propagation and analysis of image-guided surgery

A successful image-guided surgical intervention requires accurate measurement of coordinate systems. Uncertainty is introduced every time a pose is measured by the optical tracking system. When we transform a measured pose into a different coordinate system, the covariance (which encodes the uncertainty of the pose) must be propagated to this new coordinate system. In this paper, we describe a method for propagating covariances estimated from registration, tracking, and instrument calibration into the tip of the surgical tool. This is clinically important, since it is at the tool tip that the clinician cares about uncertainty. We demonstrate that the propagation method, which is computed in real time as the tool moves through space, reliably computes the propagated covariance by comparing our estimate to true covariances from Monte Carlo simulations.