Transitive and Symmetric Nonrigid Image Registration
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The main topic of this thesis is nonrigid image registration for medical applications. We start with an overview and classification of existing registration techniques. We develop a general nonrigid image registration algorithm. It uses spline functions to describe the deformation and uses multi-scale strategy to search for the optimal transformation. Then we present a new registration operator that is transitive and symmetric. We investigate the theoretical implication of these properties and apply this operator to the registration of sequences of MR cardiac images. In the second part of the thesis, two methods, one 2D and one 3D, for validation of nonrigid image registration algorithms are proposed and compared to a manual validation strategy. Both methods provide pairs of deformed images as well as corresponding true displacement fields with known accuracy. Nonrigid registration algorithms can be run on the pairs of images and their outputs can be compared to the true displacement fields that were generated manually by five observers. While these phantom validation studies do not provide physically correct deformations, they are certainly a useful way to test the algorithm's ability to recover various deformation patterns.