Nonlinear Multiscale Analysis of 3D Echocardiographic Sequences

Introduces a new model for multiscale analysis of space-time echocardiographic sequences. The proposed nonlinear partial differential equation, representing the multiscale analysis, filters the sequence while keeping the space-time coherent structures. It combines the ideas of regularized Perona-Malik anisotropic diffusion and the Galilean invariant movie multiscale analysis of Alvarez et al. (Arch. Rat. Mech. Anal., vol. 123, p. 200-57, 1993). A numerical method for solving the proposed partial differential equation is suggested and its stability is shown. Computational results on synthesized and real sequences are provided. A qualitative and quantitative evaluation of the accuracy of the method is presented.

[1]  Joachim Weickert,et al.  A Review of Nonlinear Diffusion Filtering , 1997, Scale-Space.

[2]  G. Marx,et al.  Dynamic Three‐Dimensional Echocardiography: , 1994 .

[3]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[4]  Jitendra Malik,et al.  Scale-Space and Edge Detection Using Anisotropic Diffusion , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Luis Alvarez,et al.  Formalization and computational aspects of image analysis , 1994, Acta Numerica.

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

[7]  Max A. Viergever,et al.  Efficient and reliable schemes for nonlinear diffusion filtering , 1998, IEEE Trans. Image Process..

[8]  K. Mikula,et al.  A coarsening finite element strategy in image selective smoothing , 1997 .

[9]  Karol Mikula,et al.  Slowed Anisotropic Diffusion , 1997, Scale-Space.

[10]  Gene H. Golub,et al.  Matrix Computations, Third Edition , 1996 .

[11]  C. Lamberti,et al.  Application of continuum theory and multi-grid methods to motion evaluation from 3D echocardiography , 1997, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[12]  J. Kacur,et al.  Solution of nonlinear diffusion appearing in image smoothing and edge detection , 1995 .

[13]  P. Lions.  AXIOMATIC DERIVATION OF IMAGE PROCESSING MODELS , 1994 .

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

[15]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[16]  Vicent Caselles,et al.  What is the Best Causal Scale Space for Three-Dimensional Images? , 1996, SIAM J. Appl. Math..

[17]  J. Sethian,et al.  Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations , 1988 .

[18]  P. Lions,et al.  User’s guide to viscosity solutions of second order partial differential equations , 1992, math/9207212.

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

[20]  J. Sethian.  Numerical algorithms for propagating interfaces: Hamilton-Jacobi equations and conservation laws , 1990 .

[21]  William E. Lorensen,et al.  Marching cubes: a high resolution 3D surface construction algorithm , 1996 .

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

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

[24]  P. Lions,et al.  Axioms and fundamental equations of image processing , 1993 .

[25]  Bart M. ter Haar Romeny,et al.  Geometry-Driven Diffusion in Computer Vision , 1994, Computational Imaging and Vision.

[26]  L Weinert,et al.  Determination of Right Atrial and Right Ventricular Size by Two-Dimensional Echocardiography , 1979, Circulation.

[27]  P. Lions,et al.  Image selective smoothing and edge detection by nonlinear diffusion. II , 1992 .

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

[29]  Alessandro Sarti,et al.  Numerical solution of parabolic equations related to level set formulation of mean curvature flow , 1998 .

[30]  J. Sethian.  Level set methods : evolving interfaces in geometry, fluid mechanics, computer vision, and materials science , 1996 .

[31]  F. Guichard.  Axiomatisation des analyses multi-échelles d'images et de films , 1994 .

[32]  Tony Lindeberg,et al.  Scale-Space Theory in Computer Vision , 1993, Lecture Notes in Computer Science.