Measurement and analysis of error in rigid-body point-based registration systems

Abstract

Registration is the process of determining the geometrical transformation that aligns points in one space to corresponding points in another space. Many image-guidance surgical systems rely on rigid-body, point-based registration of fiducial markers attached to the patient. Marker locations in image space and physical space are used to provide the transformation that maps a point from one space to the other. Error in localizing the marker locations results in fiducial registration error (FRE), which is the error in aligning the fiducial markers after registration, and target registration error (TRE), which is the error in aligning targets (points not used in the registration). This dissertation focuses on measuring, analyzing, and predicting these errors. The distribution of TRE and its magnitude at any target has been well analyzed before. In this dissertation we derive for the first time the first-order approximation of the distribution of FRE of any individual fiducial marker. The results are shown to agree closely with ground truth using simulations. Using this new knowledge on FRE statistics, a method is proposed to identify a fiducial marker that is possibly compromised in a fiducial system. Then new methods are introduced for the validation of fiducial systems and targeting systems. These validation methods analyze the components of the measured TRE and use them to estimate the error of using a certain device at intended target regions. The major advantage of these methods is that they can be conducted outside the operating room yet still provide good estimates of the error expected inside the operating room. It is hoped that the results in this dissertation can be used to increase our understanding of error in fiducial-based image registration, and, as a result, improve the effectiveness of image guidance in surgical procedures.