In Probabilistic Deformable Registration (PDR) each voxel of an image is assigned a distribution over the potential displacement vectors. Thus the PDR has the potential to convey information on our confidence in the resulting spatial transformation. To form an uncertainty map describing the registration result, one straight forward approach is to calculate Shannon’s entropy of the obtained probabilities at every voxel. However, this simple approach ignores the spatial information associated with those probabilities. A solution to the problem is defining an uncertainty measure that incorporates the spatial information of displacement vectors.Moreover, a challenging but important problem in image registration is evaluating the performance of a registration algorithm. The direct quantitative approach is to compare the deformation field solution with the “ground truth” (GT) transformation (at all or some landmark voxels). However, in clinical data, the GT is typically unknown. To deal with the absence of GT, some methods opted to estimate registration accuracy, for example, by using uncertainty measures as a surrogate for quantitative registration error. Other methods collected training data with GT warps (and hence known error) and trained machine learning algorithms to infer registration error or to improve the registration results for novel data.In this thesis, we first examine and revise existing uncertainty definitions. Then, we propose a new spatially-based uncertainty measure that calculates the expected error of all labels with respect to the maximum a posteriori label, ExpErMAP. Subsequently, we compare it with existing definitions (on both real and synthetic data) to the expected idealized behaviour, correlation with noise and error, ability to detect pathology, and computational complexity.Secondly, we use ExpErMAP, which is shown to be superior to other methods according to the above criteria, to evaluate and improve registration results in a learning framework. Our method implements an iterative learning-based probabilistic image registration framework that consists of a training and a testing stage. The iterative improvement of the registration can be seen as a form of self learning (SL) as it does not rely on outside input between iterations.
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Thesis advisor: Hamarneh, Ghassan
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