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

摘要

As the motion of the heart is a 3D phenomenon, its evaluation fromnsequences of 2D images causes a great loss of information on the motionnitself. Our aim is therefore to process real 3D echocardiographic imagesnand to carry out an automatic way of evaluating the movements of thencardiac structures. To estimate the optical flow, a mathematical modelnbased on the continuum theory is used; echocardiographic images cannindeed be considered a function of a conserved quantity (the acousticnimpedance). Since we need to calculate the velocity vector for everynpoint in the image and every image is built with more than 2 millionnvoxels (128×128×128), we implement a multigrid relaxationnmethod to accelerate the computation of an approximate solutionnotherwise too slow with a simple iterative solver. The experiments onnsimulated velocity fields have demonstrated an effective speed-up in thenevaluation of motion, and the calculation on real echo images has givenna realistic estimation of the 3D dynamics of the heart