Semi-implicit finite volume scheme for image processing in 3D cylindrical geometry

Journal of Computational and Applied Mathematics

Volumn 161, Issue 1, 2003, Pages 119-132

  Mikula, Karol ^a   Sgallari, Fiorella ^b  

^a SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

^b UNIVERSITY OF BOLOGNA   (Italy)

Author keywords

Cylindrical geometry; Echocardiography; Finite volume method; Image processing; Nonlinear diffusion; Partial differential equations; Semi implicit scheme

Indexed keywords

GEOMETRY; IMAGE ANALYSIS; MEDICAL IMAGING; NONLINEAR EQUATIONS;

ECHOCARDIOGRAPHIC IMAGES;

ECHOCARDIOGRAPHY;

IMAGE PROCESSING; MEDICAL APPLICATION;

EID: 0242710860     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-0427(03)00549-1     Document Type: Article

References (23)

1. Alvarez L. Guichard F. Lions P.L. Morel J.-M. Axioms and fundamental equations of image processing Arch. Rational Mech. Anal. 123 1993 200-257
2. Cardinal H.N. Gill J.D. Fenster A. Analysis of geometrical distortion and statistical variance in length, area and volume in a linearly scanned 3D ultrasound image IEEE Trans. Med. Imaging 19 2000 632-651
3. Catté F. Lions P.L. Morel J.-M. Coll T. Image selective smoothing and edge detection by nonlinear diffusion SIAM J. Numer. Anal. 29 1992 182-193
4. Cottet G.H. Germain L. Image processing through reaction combined with non-linear diffusion Math. Comp. 61 1993 659-673
5. ESAOTE Biomedica, Firenze - private communications, 2000.
6. R. Eymard, T. Gallouet, R. Herbin, The finite volume method, in: Ph. Ciarlet, J.L. Lions (Eds.), Handbook of Numerical Analysis, Vol. 7, Elsevier, Amsterdam, 2000.
7. Fenster A. Downey D.B. 3-D ultrasound imaging: a review IEEE Eng. Med. Biol. Mag. 15 1996 41-51
8. Handlovičová A. Mikula K. Sgallari F. Variational numerical methods for solving nonlinear diffusion equations arising in image processing J. Visual Comm. Image Represent. 13 2002 217-237
9. Kačur J. Mikula K. Solution of nonlinear diffusion appearing in image smoothing and edge detection Appl. Numer. Math. 17 1995 47-59
10. Kichenassamy S. The Perona-Malik paradox SIAM J. Appl. Math. 57 1997 1328-1342
11. Koenderink J.J. The structure of images Biol. Cybernet. 50 1984 363-370
12. Kufner A. John O. Fuč́k S. Function Spaces 1977 Academia Prague
13. Mikula K. Ramarosy N. Semi-implicit finite volume scheme for solving nonlinear diffusion equations in image processing Numer. Math. 89 2001 561-590
14. Montagnat J. Sermesant M. Delingette H. Malandain G. Ayache N. Anisotropic filtering for model-based segmentation of 4D cylindrical echocardiographic images Pattern Recognition Lett. 24 2003 815-828
15. Nitzberg M. Shiota T. Nonlinear image filtering with edge and corner enhancement IEEE Trans. Pattern Anal. Mach. Intell. 14 1992 826-833
16. Patankar S.V. Numerical Heat Transfer and Fluid Flow 1980 Hemisphere Washington
17. Perona P. Malik J. Scale space and edge detection using anisotropic diffusion IEEE Trans. Pattern Anal. Mach. Intell. 12 1990 629-639
18. Saad Y. Iterative Methods for Sparse Linear Systems 1996 PWS Boston
19. Sarti A. Mikula K. Sgallari F. Nonlinear multiscale analysis of three-dimensional echocardiographic sequences IEEE Trans. Med. Imaging 18 1999 453-466
20. Weickert J. Anisotropic Diffusion in Computer Vision 1998 Teubner Stuttgart
21. Weickert J. Anisotropic diffusion filters for image processing based quality control Fasano A. Primicerio M. Proceedings of Seventh European Conference on Mathematics in Industry 1994 355-362 Teubner Stuttgart
22. Whitaker R.T. Pizer S.M. A multiscale approach to nonuniform diffusion CVGIP: Image Understand. 57 1993 99-110
23. A.P. Witkin, Scale-space filtering, Proceedings of the Eighth International Conference on Artificial Intelligence, Vol. 2, 1983, pp. 1019-1022.