Treffer: A set of novel normal-assisted surface registration algorithms and analysis for image-guided surgery

Ph.D. ; Current surgical navigation system’s success relies on one key step, which is aligning the pre-operative space with the intra-operative space. The biggest challenge that the pre-to- intra registration faces is that the intra-operative points are usually corrupted with noise and contain a lot of outliers, which will decrease the accuracy of the registration significantly. Registration error is one of the largest error in surgical navigation. It is of great value if we can provide the surgeon with accurate registration uncertainties. ; This thesis focuses on the registration problem in surgical navigation. We first provide a new type of error to evaluate the accuracy of the paired-point rigid registration. In addition, we develop two novel robust and accurate rigid point set registration methods. ; During the surgical procedure, providing the surgeon with accurate surgical instrument tracking error helps the surgeon make the right decision. Considering this, we develop a new type of error for the paired-point rigid registration. We refer to this error as total target registration error(TTRE). Target localization error in two spaces to be registered is considered in TTRE. We have derived the statistics of TTRE including the mean and covariance matrix. During surgery,we can visualize the covariance of the TTRE to help the surgeon make the right decision. ; To increase the registration’s accuracy and robustness, we formulate the generalized point set registration (GPSR) problem. The registration is formulated as a maximum likelihood (ML) problem and solved with the expectation maximization(EM)technique. The utilization of the normal vectors that can be extracted from the point sets can significantly improve the registration’s accuracy and robustness. The positional error is assumed to be isotropic, which means that the error is the same in all directions. In the expectation step, the posterior probabilities that represent the correspondences are updated given the current rigid transformation. In the ...