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Sliding effects often occur along tissue/organ boundaries. For instance, it is widely observed that the lung and diaphragm slide against the rib cage and the atria during breathing. Conventional homogeneous smooth registration methods fail to address this issue. Some recent studies preserve motion discontinuities by either using joint registration/segmentation or utilizing robust regularization energy on the motion field. However, allowing all types of discontinuities is not strict enough for physical deformations. In particular, flows that generate local vacuums or mass collisions should be discouraged by the energy functional. In this study, we propose a regularization energy that encodes a discriminative treatment of different types of motion discontinuities. The key idea is motivated by the Helmholtz-Hodge decomposition, and regards the underlying motion flow as a superposition of a solenoidal component, an irrotational component and a harmonic part. The proposed method applies a homogeneous penalty on the divergence, discouraging local volume change caused by the irrotational component, thus avoiding local vacuum or collision; it regularizes the curl field with a robust functional so that the resulting solenoidal component vanishes almost everywhere except on a singular set where the large shear values are preserved. This singularity set corresponds to sliding interfaces. Preliminary tests with both simulated and clinical data showed promising results.