3 research outputs found
Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy
The Cramer-Rao lower bound for the estimation of the affine transformation
parameters in a multivariate heteroscedastic errors-in-variables model is
derived. The model is suitable for feature-based image registration in which
both sets of control points are localized with errors whose covariance matrices
vary from point to point. With focus given to the registration of fluorescence
microscopy images, the Cramer-Rao lower bound for the estimation of a feature's
position (e.g. of a single molecule) in a registered image is also derived. In
the particular case where all covariance matrices for the localization errors
are scalar multiples of a common positive definite matrix (e.g. the identity
matrix), as can be assumed in fluorescence microscopy, then simplified
expressions for the Cramer-Rao lower bound are given. Under certain simplifying
assumptions these expressions are shown to match asymptotic distributions for a
previously presented set of estimators. Theoretical results are verified with
simulations and experimental data
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