Statistical Model of Total Target Registration Error in Image-Guided Surgery

In a paired-point rigid registration, target registration error (TRE) is deemed to be the most important quality metric. TRE usually cannot be directly measured, and thus many TRE estimation algorithms have been proposed. However, target localization errors (TLEs) in two spaces are not considered in the definition of TRE. In this paper, we propose a new type of evaluation metric that is referred to as total TRE (TTRE) at a given target point with TLE incorporated. Statistics including mean, root mean square (rms), and covariance matrix of TTRE are derived without making any assumption of the TLE magnitude. TTRE and fiducial registration error (FRE) are proved to be uncorrelated when an ideal weighting scheme is adopted in solving the registration problem. The proposed error model is validated through extensive experiments. In the first experiment with random fiducials and targets, in 90% of the test cases, there shows no difference between the predicted and simulated TTRE statistics when six fiducials are used. In the second experiment of deep-brain stimulation surgery, the mean value of CC(TTRE,FRE) being 8.9246 x 10(-4) +/- 0.0389 was observed, which indicates that TTRE and FRE are uncorrelated. In the third experiment of surgical tool-tip tracking, the mean and standard deviation of percentage differences between predicted and simulated TTRE rms values are 2.22% +/- 0.77% for the planar tool and 2.62% +/- 0.59% for the textral tool. In summary, our proposed algorithm can well model the TTRE metric. Note to Practitioners-This paper was motivated by considering the existence of target localization error in two spaces to be registered in a rigid point-based registration. Given fiducial localization error (FLE) and TLE probability distributions, the proposed TTRE model gives the covariance matrix and root mean square of TTRE at a given target point. The possible applications of the proposed TTRE model in an image-guided surgery (IGS) include: 1) estimation of surgical tool-tip tracking error distribution when pivot calibration uncertainty is considered; 2) accuracy evaluation of an image-to-patient registration; 3) updating of a preoperative surgical plan on a computed tomography/MRI image to consider the registration error at a given target point; and 4) estimation of real-time tool-tip error in touching a desired true surgical target, such as a tumor during surgery. To use the proposed error estimation algorithm, FLE and TLE in two spaces to be registered have to be known or estimated in advance to a registration process. The proposed error model is validated through extensive simulations.