3D displacement field reconstruction on an irregular domain from planar tagged cardiac MR images

An important application of deformable motion estimation theory is the estimation of heart motion from tagged magnetic resonance image sequences. In tagged MR images, the heart appears with a spatially encoded pattern that moves with the tissue. The position of the tag pattern in each frame of the image sequence can be used to obtain sparse measurements of the heart´s 3D displacement field. In this paper, we propose a method for estimating a dense displacement field from sparse displacement measurements that is based on a multidimensional stochastic model for the smoothness and divergence of the displacement field and uses the Fisher estimation framework. The main feature of this method is that the displacement field model and the resulting estimate equation are defined only on the irregular domain of the myocardium. Simulation results are presented that demonstrate the accuracy of our method and show the effect of the tag pattern on the estimation error