Objective: The sliding motion of the liver during respiration violates the homogeneous motion smoothness assumption in conventional non-rigid image registration and commonly results in compromised registration accuracy. This paper presents a novel approach, registration with 3D active contour motion segmentation (RAMS), to improve registration accuracy with discontinuityaware motion regularization. Methods: A Markov random field-based discrete optimization with dense displacement sampling and self-similarity context metric is used for registration, while a graph cuts-based 3D active contour approach is applied to segment the sliding interface. In the first registration pass, a maskfree L1 regularization on an image-derived minimum spanning tree is performed to allow motion discontinuity. Based on the motion field estimates, a coarse segmentation finds the motion boundaries. Next, based on MR signal intensity, a fine segmentation aligns the motion boundaries with anatomical boundaries. In the second registration pass, smoothness constraints across the

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