Topology preservation for image-registration-related deformation fields (Q500891)

The authors design a theoretically well-motivated and computationally efficient method taking as input the deformation field that does not comply with the topology preservation criteria, and giving as output a corrected version of this deformation, as faithful as possible to the original one. They propose to decompose the reconstruction problem into independent problems of smaller dimensions, yielding a natural parallelization of the computations and reducing the computational time. Theoretical results are established such as the existence and uniqueness of the solution of the involved minimization problem, the characterization of the solution, the convergence of the method when the number of data increases to infinity as well as the discretization of the problem. Finally, some numerical examples are given to show the effectiveness of the proposed method.