Application of continuum theory and multi-grid methods to motion evaluation from 3D echocardiography

As the motion of the heart is a 3D phenomenon, its evaluation from sequences of 2D images causes a great loss of information on the motion itself. Our aim is therefore to process real 3D echocardiographic images and to carry out an automatic way of evaluating the movements of the cardiac structures. To estimate the optical flow, a mathematical model based on the continuum theory is used; echocardiographic images can indeed be considered a function of a conserved quantity (the acoustic impedance). Since we need to calculate the velocity vector for every point in the image and every image is built with more than 2 million voxels (128x128x128), we implement a multigrid relaxation method to accelerate the computation of an approximate solution otherwise too slow with a simple iterative solver. The experiments on simulated velocity fields have demonstrated an effective speed-up in the evaluation of motion, and the calculation on real echo images has given a realistic estimation of the 3D dynamics of the heart.