Discontinuity preserving regularization for modeling sliding in medical image registration

Sliding effects often occur along tissue/organ boundaries. However, most conventional registration techniques either use smooth parametric bases or apply homogeneous smoothness regularization, and fail to address the sliding issue. In this study, we propose a class of discontinuity-preserving regularizers that fit naturally into optimization-based registration. The proposed regularization encourages smooth deformations in most regions, but preserves large discontinuities supported by the data. Variational techniques are used to derive the descending flows. We discuss general conditions on such discontinuity-preserving regularizers, and their properties based on an anisotropic filtering interpretation. Preliminary tests with 2D CT data show promising results.