In this paper a method to remove the divergence from a vector field is presented. When applied to a displacement field, this will remove all local compression and expansion. The method can be used as a post-processing step for (unconstrained) registered images, when volume changes in the deformation field are undesired. The method involves solving Poisson's equation for a large system. Algorithms to solve such systems include Fourier analysis and Cyclic Reduction. These solvers are vastly applied in the field of fluid dynamics, to compensate for numerical errors in calculated velocity fields. The application to medical image registration as described in this paper, has to our knowledge not been done before. To show the effect of the method, it is applied to the registration of both synthetic data and dynamic MR series of the liver. The results show that the divergence in the displacement field can be reduced by a factor of 10 - 1000 and that the accuracy of the registration increases.,
Progress in Biomedical Optics and Imaging - Proceedings of SPIE
Medical Imaging 2008: Image Processing

Hameeteman, R., Veenland, J., & Niessen, W. (2008). Volume preserving image registration via a post-processing stage. In Progress in Biomedical Optics and Imaging - Proceedings of SPIE (Vol. 6914). doi:10.1117/12.770646