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This paper deals with topology preservation in three-dimensional (3-D) deformable image registration. This work is a nontrivial extension of , which addresses the case of two-dimensional (2-D) topology preserving mappings. In both cases, the deformation map is modeled as a hierarchical displacement field, decomposed on a multiresolution B-spline basis. Topology preservation is enforced by controlling the Jacobian of the transformation. Finding the optimal displacement parameters amounts todoi:10.1109/tip.2005.846026 pmid:15887550 fatcat:qsu2n5fpyvaktij4j65ykyc5ji