Estimation of physiologically plausible deformations is critical for several medical applications. For example, lung cancer diagnosis and treatment requires accurate image registration which preserves sliding motion in the pleural cavity, and the rigidity of chest bones. This paper addresses these challenges by introducing a novel approach for regularisation of non-linear transformations derived from a bilateral filter. For this purpose, the classic Gaussian kernel is replaced by a new kernel that smoothes the estimated deformation field with respect to the spatial position, intensity and deformation dissimilarity. The proposed regularisation is a spatially adaptive filter that is able to preserve discontinuity between the lungs and the pleura and reduces any rigid structures deformations in volumes. Moreover, the presented framework is fully automatic and no prior knowledge of the underlying anatomy is required. The performance of our novel regularisation technique is demonstrated on phantom data for a proof of concept as well as 3D inhale and exhale pairs of clinical CT lung volumes. The results of the quantitative evaluation exhibit a significant improvement when compared to the corresponding state-of-the-art method using classic Gaussian smoothing.