Locally Adaptive Total p-Variation Regularization for Non-Rigid Image Registration With Sliding Motion.

Due to the complicated thoracic movements which contain both sliding motion occurring at lung surfaces and smooth motion within individual organs, respiratory estimation is still an intrinsically challenging task. In this paper, we propose a novel regularization term called locally adaptive total p-variation (LaTpV) and embed it into a parametric registration framework to accurately recover lung motion. LaTpV originates from a modified Lp-norm constraint (1 < p < 2), where a prior distribution of p modeled by the Dirac-shaped function is constructed to specifically assign different values to voxels. LaTpV adaptively balances the smoothness and discontinuity of the displacement field to encourage an expected sliding interface. Additionally, we also analytically deduce the gradient of the cost function with respect to transformation parameters. To validate the performance of LaTpV, we not only test it on two mono-modal databases including synthetic images and pulmonary computed tomography (CT) images, but also on a more difficult thoracic CT and positron emission tomography (PET) dataset for the first time. For all experiments, both the quantitative and qualitative results indicate that LaTpV significantly surpasses some existing regularizers such as bending energy and parametric total variation. The proposed LaTpV based registration scheme might be more superior for sliding motion correction and more potential for clinical applications such as the diagnosis of pleural mesothelioma and the adjustment of radiotherapy plans.