A unified approach to surface-based registration for image-guided surgery

Image-guided surgery often requires establishing the relationship between the coordinate frame of the patient and the coordinate frame of a preoperative model of the patient. This relationship is often established by finding a registration transformation that maps points measured on the patient to the preoperative model. In this dissertation I study the estimation of the expected registration accuracy and methods for selecting registration points. The contributions made in this dissertation include a method for analyzing registration error, an analytic expression for shape-based target registration error (TRE), two algorithms for sequentially selecting registration points, a particle-filter registration algorithm, and a unified filter-selection algorithm.; The registration problem is modelled after a passive elastic mechanism. Such mechanisms have been extensively studied and are characterized by a 6 x 6 spatial-stiffness matrix. Coordinate-frame invariant quantities called the principal rotational stiffnesses and the principal translational stiffnesses can be computed from the stiffness matrix; these quantities are related to the amount of energy an agent must expend to produce specific types of displacements of the mechanism. The principal stiffnesses are used to produce equations that predict the expected TRE for rigid fiducial registration and rigid shape-based registration.; The spatial-stiffness concept is also used to propose two algorithms for sequentially selecting registration points. The TREseq algorithm selects the next registration point that minimizes the expected TRE, and the Qseq algorithm selects the next registration point that maximizes a quality measure based on the principal stiffnesses. These algorithms are compared to an algorithm proposed by Simon [71].; The point selection algorithms are limited to preoperative use because they require exact location and surface-normal information. I propose that this limitation can be overcome by estimating the uncertainties in the registration parameters and accounting for these uncertainties in the selection process. The registration parameters and uncertainties are estimated sequentially using a particle filter. The uncertainties are propagated through the Qseq point selection process to produce a distribution of quality measures on each model point. The unified filter-selection registration algorithm has increasingly better TRE behavior as registration points with higher mean quality measure are used.