Estimation of line-based target registration error

Abstract

We present a novel method for estimating target registration error (TRE) in point-to-line registration. We develop a spatial stiffness model of the registration problem and derive the stiffness matrix of the model which leads to an analytic expression for predicting the root-mean-square (RMS) TRE. Under the assumption of isotropic localization noise, we show that the stiffness matrix for line-based registration is equal to the difference of the stiffness matrices for fiducial registration and surface-based registration. The expression for TRE is validated in the context of freehand ultrasound calibration performed using a tracked line fiducial as a calibration phantom. Measurements taken during calibration of a tracked linear ultrasound probe were used in simulations to assess TRE of point-to-line registration and the results were compared to the values predicted by the analytic expression. The difference between predicted and simulated RMS TRE magnitude for targets near the centroid of the registration points was less than 5% of the simulated magnitude when using more than 6 registration points. The difference between predicted and simulated RMS TRE magnitude for targets over the entire ultrasound image was almost always less than 10% of the simulated magnitude when using more than 10 registration points. TRE magnitude was minimized near the centroid of the registration points and the isocontours of TRE were elliptic in shape.