Isotropic Total Variation Regularization of Displacements in Parametric Image Registration

Abstract

Abstract-Spatial regularization is essential in image registration, which is an ill-posed problem. Regularization can help to avoid both physically implausible displacement fields and local minima during optimization. Tikhonov regularization (squared 2-norm) is unable to correctly represent non-smooth displacement fields, that can, for example, occur at sliding interfaces in the thorax and abdomen in image time-series during respiration. In this paper, isotropic Total Variation (TV) regularization is used to enable accurate registration near such interfaces. We further develop the TV-regularization for parametric displacement fields and provide an efficient numerical solution scheme using the Alternating Directions Method of Multipliers (ADMM). The proposed method was successfully applied to four clinical databases which capture breathing motion, including CT lung and MR liver images. It provided accurate registration results for the whole volume. A key strength of our proposed method is that it does not depend on organ masks that are conventionally required by many algorithms to avoid errors at sliding interfaces. Furthermore, our method is robust to parameter selection, allowing the use of the same parameters for all tested databases. The average target registration error (TRE) of our method is superior (10% to 40%) to other techniques in the literature. It provides precise motion quantification and sliding detection with sub-pixel accuracy on the publicly available breathing motion databases (mean TREs of 0.95 mm for DIR 4D CT, 0.96 mm for DIR COPDgene, 0.91 mm for POPI databases).

Statistical Motion Mask and Sliding Registration

“…However, results with this spacing and w go = [0.8, 0.85, 0.9] are very close together and below 1.34mm. Compared with other methods, our resulting average landmark registration error is lower than those reported for instance by Papiez et al [10] (1.95mm), Wu et al [14] (1.47mm), Delmon et al [5] (1.66mm), and Berendsen et al [1] (1.36mm); but slightly larger the one reported by Hua et al [7] (1.17mm) or Vishnevskiy et al [13] (0.95mm). A comprehensive list of landmark errors achieved by various algorithms is published on the DIR-Lab website [11].…”

“…Several registration methods for handling sliding motion have been proposed in the literature [1,5,7,10,13,14]. Most of these methods require a segmentation of the sliding regions either in the target image or in both target and source image.…”

“…individual slices, projections) which can be very challenging or impossible to accurately segment. Some methods do not require a prior segmentation in either image, but use a regularisation term that permits sliding motion [13]. While such methods are appealing, there is a possibility they may not correctly represent the sliding motion in areas of homogeneous intensities, for instance where the liver meets the chest wall.…”

Non-rigid point cloud registration based lung motion estimation using tangent-plane distance

“…The lung surface is usually segmented from 4DCT images, and during the segmentation procedure, the corresponding information is lost. Besides, many researchers indicate that the lung motion estimation suffers from the sliding motion [1,2,11]. A possible solution is to reduce the constraint of the motion along the tangent direction.…”

“…The breathing motion is arisen from the contraction of the diaphragmatic muscle area, and there exists severe sliding motion in the lateral areas of the lung. Many researchers indicate that the lung motion estimation suffers from the sliding motion [1,2,11], and a possible reason is that the sliding motion would plague the registration by the existence of local minima. Accurate respiratory motion estimation is important in radiation therapy of lung cancer.…”