A Topology Preserving Non-rigid Registration Method Using a Symmetric Similarity Function-Application to 3-D Brain Images
3-D non-rigid brain image registration aims at estimating consistently long-distance and highly nonlinear deformations corresponding to anatomical variability between individuals. A consistent mapping is expected to preserve the integrity of warped structures and not to be dependent on the arbitrary choice of a reference image: the estimated transformation from A to B should be equal to the inverse transformation from B to A. This paper addresses these two issues in the context of a hierarchical parametric modeling of the mapping, based on B-spline functions. The parameters of the model are estimated by minimizing a symmetric form of the standard sum of squared differences criterion. Topology preservation is ensured by constraining the Jacobian of the transformation to remain positive on the whole continuous domain of the image as a non trivial 3-D extension of a previous work  dealing with the 2-D case. Results on synthetic and real-world data are shown to illustrate the contribution of preserving topology and using a symmetric similarity function.
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