A multiscale phase field method for joint segmentation-rigid registration - Application to motion estimation of human knee joint

Image based registration of rigid objects has been frequently addressed in the literature to obtain an object's motion parameters. In this paper, a new approach of joint segmentation-rigid registration, within the variational framework of the phase field approximation of the Mumford-Shah's functional, is proposed. The defined functional consists of two Mumford-Shah equations, extracting the discontinuity set of the reference and target images due to a rigid spatial transformation. Multiscale minimization of the proposed functional after finite element discretization provided a sub-pixel, robust algorithm for edge extraction as well as edge based rigid registration. The implementation considerations of the proposed method, including memory usage, convergence rate and effects of parameters selection, was discussed and its efficacy was examined in a comprehensive set of synthetic, phantom and clinical experiments. It was found that the proposed joint segmentation-rigid registration method provides improved results, in comparison with the currently available methods which are often based on maximizing images similarities, especially when the reference and target images are of different qualities. A high registration accuracy was obtained when estimating the knee joint kinematics through MR images taken at different joint configurations. It was concluded that the proposed method can be effectively used in applications where 3D image registration of rigid objects is concerned, e.g. for estimation of the motion parameters of human joints.