Topology preserving deformable image matching using constrained hierarchical parametric models

In this paper, we address the issue of topology preservation in deformable image matching. A novel constrained hierarchical parametric approach is presented, that ensures that the mapping is globally one-to-one and thus preserves topology in the deformed image. The transformation between the source and target images is parameterized at different scales, using a decomposition of the deformation vector field over a sequence of nested (multiresolution) subspaces. The Jacobian of the mapping is controlled over the continuous domain of the transformation, ensuring actual topology preservation on the whole image support. The resulting fast nonlinear constrained optimization algorithm enables to track large nonlinear deformations while preserving the topology. Experimental results are presented both on simulated data and on real medical images.