In this paper we propose a new strategy for the recovery of complex anatomical deformations that exhibit local discontinuities, such as the shearing found at the lung-ribcage interface, using multi-grid octree B-splines. B- spline based image registration is widely used in the recovery of respiration induced deformations between CT images. However, the continuity imposed upon the computed deformation field by the parametrizing cubic B- spline basis function results in an inability to correctly capture discontinuities such as the sliding motion at organ boundaries. The proposed technique eﬃciently captures deformation within and at organ boundaries without the need for prior knowledge, such as segmentation, by selectively increasing deformation freedom within image regions exhibiting poor local registration. Experimental results show that the proposed method achieves more physically plausible deformations than traditional global B-spline methods.