Symmetrization of the non-rigid registration problem using inversion-invariant energies: Application to multiple sclerosis

Without any prior knowledge, the non-rigid registration of two images is a symmetric problem, i.e. we expect to find inverse results if we exchange these images. This symmetry is nonetheless broken in most of intensity-based algorithms. In this paper, we explain the reasons why most non-rigid registration algorithms are asymmetric. We show that the asymmetry of quadratic regularization energies causes an oversmoothing of expending regions relatively to shrinking regions, hampering in particular registration-based detection of evolving processes, We therefore propose to use an inversion-invariant energy to symmetrize the registration problem. To minimize this energy, two methods are used, depending on whether we compute the inverse transformation or not. Finally, we illustrate the interest of the theory using both synthetic and real data, in particular to improve the detection and segmentation of evolving lesions in MR images of patients suffering from multiple sclerosis.