Comparing Measured and Theoretical Target Registration Error of an Optical Tracking System

The goal of this thesis is to experimentally measure the accuracy of an optical tracking system used in commercial surgical navigation systems. We measure accuracy by constructing a mechanism that allows a tracked target to move with spherical motion (i.e., there exists a single point on the mechanism—the center of the sphere—that does not change position when the tracked target is moved). We imagine that the center of the sphere is the tip of a surgical tool rigidly attached to the tracked target. The location of the tool tip cannot be measured directly by the tracking system (because it is impossible to attach a tracking marker to the tool tip) and must be calculated using the measured location and orientation of the tracking target. Any measurement error in the tracking system will cause the calculated position of the tool tip to change as the target is moved; the spread of the calculated tool tip positions is a measurement of tracking error called the target registration error (TRE). The observed TRE will be compared to an analytic model of TRE to assess the predictions of the analytic model

Analysis of point based image registration errors with applications in single molecule microscopy

We present an asymptotic treatment of errors involved in point-based image registration where control point (CP) localization is subject to heteroscedastic noise; a suitable model for image registration in fluorescence microscopy. Assuming an affine transform, CPs are used to solve a multivariate regression problem. With measurement errors existing for both sets of CPs this is an errors-in-variable problem and linear least squares is inappropriate; the correct method being generalized least squares. To allow for point dependent errors the equivalence of a generalized maximum likelihood and heteroscedastic generalized least squares model is achieved allowing previously published asymptotic results to be extended to image registration. For a particularly useful model of heteroscedastic noise where covariance matrices are scalar multiples of a known matrix (including the case where covariance matrices are multiples of the identity) we provide closed form solutions to estimators and derive their distribution. We consider the target registration error (TRE) and define a new measure called the localization registration error (LRE) believed to be useful, especially in microscopy registration experiments. Assuming Gaussianity of the CP localization errors, it is shown that the asymptotic distribution for the TRE and LRE are themselves Gaussian and the parameterized distributions are derived. Results are successfully applied to registration in single molecule microscopy to derive the key dependence of the TRE and LRE variance on the number of CPs and their associated photon counts. Simulations show asymptotic results are robust for low CP numbers and non-Gaussianity. The method presented here is shown to outperform GLS on real imaging data.</p