Non-rigid 3D CT/MR Liver Registration with Discontinuous Transforms Using Total Variation Regularization

Non-rigid multi-modal image registration plays an important role in many medical applications. Many advanced methods have been developed in deformable registration. However, conventional non-rigid registration assumes a global smooth deformation field throughout the image, so difficulties arise with handling the discontinuous displacement field and lead to poor correspondences at these sliding boundaries. These discontinuities exist for organs such as liver or lungs, which have a sliding motion during respiration. In this chapter we use total variation (TV) as a term to preserve the discontinuous boundaries for liver registration on computed tomography (CT)/magnetic resonance imaging. With benefits from the parametric transformation model known as free-form deformation, we analytically acquire an explicit optimization scheme for our method and compare our method with L₂ regularization on both public and clinical data sets. The proposed method has been demonstrated to have a more credible displacement field near the discontinuous interface in both the public 4-dimensional CT data set and the clinical CT/magnetic resonance imaging data set.