Adaptive Graph Diffusion Regularisation for Discontinuity Preserving Image Registration

Registration of thoracic images is central when studying for example physiological changes of the lung. Due to sliding organ motion and intensity changes based on respiration the registration of thoracic images is challenging. We present a novel regularisation method based on adaptive anisotropic graph diffusion. Without the need of a mask it preserves discontinuities of the transformation at sliding organ boundaries and enforces smoothness in areas with similar motion. The graph diffusion regularisation provides a direct way to achieve anisotropic diffusion at sliding organ boundaries by reducing the weight of corresponding edges in the graph which cross the sliding interfaces. Since the graph diffusion is defined by the edge weights of the graph, we develop an adaptive edge weight function to detect sliding boundaries. We implement the adaptive graph diffusion regularisation method in the Demons registration framework. The presented method is tested on synthetic 2D images and on the public 4D-CT DIR-Lab data set, where we are able to correctly detect the sliding organ boundaries.