Predicting error in point-based registration

Point-based registration is the task of transforming one set of points to try to make it “look like” another set. In this dissertation, we examine the application of point-based registration to stereotactic neurosurgery, and we investigate the way in which the placement of the “fiducial” points (those used for registration) affects the accuracy with which a surgical target may be located.; In point-based image registration, there are three types of error. Fiducial localization error (FLE) is the imprecision in locating the points used for registration. Fiducial registration error (FRE) is the distance between corresponding fiducial points after registration is performed. Target registration error (TRE) is the distance after registration between corresponding points in the image other than the fiducials. In surgical applications, TRE is the most important error, and limiting TRE is vital for successful surgical navigation.; In 1979, Sibson used perturbation theory to derive an approximate relationship between FLE and FRE in the case that the registration transform consists of a rotation and translation. We use a similar approach to give for the first time a quantitative relationship between FLE and TRE, and we show that TRE, unlike FRE, is influenced by the shape of the fiducial configuration. We prove by means of numerical simulations that our approximation is sound, and we use clinical data to demonstrate that our theoretical results give a useful predictor of TRE in practice.; We extend our derivations to the case that the registration transform is a similarity transform, i.e. it consists of rotation, translation, and an isotropic (same in all directions) scale factor. We give an expression for the relationship between FLE and TRE in this case. We apply a maximum likelihood approach to the problem of choosing the scale factor, and we demonstrate that in many cases this approach gives a scale factor that is superior to the one given by the traditional method.