Total Variation Filtered Demons for Improved Registration of Sliding Organs

We present a new approach to regularize the displacement field of the accelerated Demons registration algorithm. The accelerated Demons algorithm uses Gaussian smoothing to penalize oscillatory motion in the displacement fields during registration. This regularization approach is often applied and ensures a smooth deformation field. However, when registering images with discontinuities in their motion field such as from organs sliding along the chest wall, the assumption of a smooth deformation field is invalid. In this work, we propose using total variation based smoothing that is known to better retain the discontinuities in the deformation field. The proposed approach is a first step towards automatically recovering breathing induced organ motion with good accuracy. 1. Introduction Nonrigid image registration methods, Maintz and Viergever [1], play an important role in today’s modern medical diagnostics and Image-Guided Therapy (IGT) systems. They can be broadly split into two main categories, namely, the feature and intensity based approaches. Feature based methods extract corresponding image points as a part of the preprocessing, whereas the intensity based methods make direct use of the image voxels intensities. One of the well-known intensity based methods is optical flow by Horn and Schunk [2]. Because of the ill-posedness of image registration, additional information in a form of regularization rules is necessary. They usually come in form of heuristical rules with underlying physical reasoning. Recent developments in medical imaging, such as 4DMRI developed by Von Siebenthal et al. [3], allow capturing 4-dimensional (3D+time) breathing organ motion. Today’s registration methods, however, generally are not suitable for registering these data sets, as the heuristical regularization rules produce invalid motion fields across sliding organ boundaries by enforcing smooth deformations fields. A need for properly handling discontinuities is thus a prerequisite when registering these data sets. Lots of research has been devoted to discontinuity preserving registration in the last couple of years. For example, some studies preserve motion discontinuities by using joint registration/segmentation. Kiriyanthan et al. [4] utilize robust regularization energy formulations. In Ruan et al. [5], authors propose a regularization energy that encodes a discriminative treatment of different type of motion discontinuities, by using Helmholtz-Hodge decomposition. In another approach, Heinrich et al. [6] present a framework using variational formulation of the