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 (128/spl times/128/spl times/128), 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.

[1]  C. Lamberti,et al.  Evaluation of differential optical flow techniques on synthesized echo images , 1996, IEEE Transactions on Biomedical Engineering.

[2]  J. Meunier,et al.  Echographic image mean gray level changes with tissue dynamics: a system-based model study , 1995, IEEE Transactions on Biomedical Engineering.

[3]  J. Seward,et al.  Diagnostic Performance of Two‐Dimensional Versus Three‐Dimensional Transesophageal Echocardiography Images of Selected Pathologies Evaluated by Receiver Operating Characteristic Analysis , 1994, Echocardiography.

[4]  Motion evaluation from synthesized 3-D Echocardiograms , 1994 .

[5]  W. Hackbusch.  Multi-Grid Methods , 1994 .

[6]  Jean Meunier,et al.  Ultrasonic texture motion analysis: theory and simulation , 1993, Medical Imaging.

[7]  J. Seward,et al.  Three- and four-dimensional cardiovascular ultrasound imaging: a new era for echocardiography. , 1993, Mayo Clinic proceedings.

[8]  R. Leahy,et al.  Computation of 3-D velocity fields from 3-D cine CT images of a human heart. , 1991, IEEE transactions on medical imaging.

[9]  P. Simard,et al.  Restoration of the velocity field of the heart from two-dimensional echocardiograms. , 1989, IEEE transactions on medical imaging.

[10]  J. Michael Fitzpatrick,et al.  The existence of geometrical density-image transformations corresponding to object motion , 1988, Comput. Vis. Graph. Image Process..

[11]  Wilfried Enkelmann,et al.  Investigations of multigrid algorithms for the estimation of optical flow fields in image sequences , 1988, Comput. Vis. Graph. Image Process..

[12]  Vladimir Aleksandrovich Shutilov,et al.  Fundamental Physics of Ultrasound , 1988 .

[13]  D. Bai.  Multigrid Methods for Integral and Differential Equations (D. J. Paddon and H. Holstein, eds.) , 1987 .

[14]  G. Mailloux,et al.  Computer Analysis of Heart Motion from Two-Dimensional Echocardiograms , 1987, IEEE Transactions on Biomedical Engineering.

[15]  D. J. Paddon,et al.  Multigrid Methods for Integral and Differential Equations. , 1987 .

[16]  Gilbert Strang,et al.  Introduction to applied mathematics , 1988 .

[17]  Demetri Terzopoulos,et al.  Image Analysis Using Multigrid Relaxation Methods , 1986, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[18]  Tomaso Poggio,et al.  Computational vision and regularization theory , 1985, Nature.

[19]  F. Glazer.  Multilevel Relaxation in Low-Level Computer Vision , 1984 .

[20]  I. Cohen.  Echocardiography (3rd Ed.). , 1982 .

[21]  Berthold K. P. Horn,et al.  Determining Optical Flow , 1981, Other Conferences.

[22]  D. Brandt,et al.  Multi-level adaptive solutions to boundary-value problems math comptr , 1977 .

[23]  D. D. Streeter,et al.  Engineering Mechanics for Successive States in Canine Left Ventricular Myocardium: II. Fiber Angle and Sarcomere Length , 1973, Circulation research.

[24]  J. Ross,et al.  Fiber Orientation in the Canine Left Ventricle during Diastole and Systole , 1969, Circulation research.