A well-balanced flow equation for noise removal and edge detection

IEEE Transactions on Image Processing

Volumn 12, Issue 7, 2003, Pages 751-763

  Barcelos, Celia Aparecida Zorzo ^a,b   Boaventura, Maurílio ^c   Silva Jr , Evanivaldo Castro ^c  

^a FEDERAL UNIVERSITY OF UBERLÂNDIA   (Brazil)

^b FEDERAL UNIVERSITY OF GOIÁS   (Brazil)

^c SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

Author keywords

Diffusion equation; Edge detection; Image processing; Noise removal

Indexed keywords

DIFFERENTIAL EQUATIONS; DIFFUSION; MATHEMATICAL MODELS; NOISE ABATEMENT;

NOISE REMOVAL;

EDGE DETECTION;

EID: 0042665416     PISSN: 10577149     EISSN: None     Source Type: Journal    
DOI: 10.1109/TIP.2003.814242     Document Type: Article

References (20)

1. L. Alvarez and J. Esclarim, "Image quantization using reaction-diffusion equations," SIAM J. Appl. Math., vol. 1, no. 57, pp. 153-175, 1997.
2. L. Alvarez, P. L. Lions, and J. M. Morel, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal., vol. 29, no. 3, pp. 845-866, 1992.
3. C. A. Z. Barcelos, Edge-Preserving Regularization in Image Restoration, 2002.
4. C. A. Z. Barcelos and Y. Chen, "Heat flows and related minimization problem in image restoration," Comput. Math. Applicat., no. 39, pp. 81-97, 2000.
5. F. Catté, T. Coll, P. L. Lions, and J. M. Morel, "Image selective smoothing and edge detection by nonlinear diffusion," SIAM J. Numer. Anal., vol. 29, pp. 182-193, 1992.
6. A. Chambolle and P. L. Lions, "Image recovery via total variation minimization and related problems," Numer. Math., vol. 76, pp. 167-188, 1997.
7. Y. Chen, C. A. Z. Barcelos, and B. A. Mair, "Smoothing and edge detection by time-varying coupled nonlinear diffusion equations," Comput. Vis. Image Understand., vol. 82, no. 2, pp. 85-100, 2001.
8. Y. Chen, B. C. Vemuri, and L. Wang, "Image denoising and segmentation via nonlinear diffusion," Comput. Math. Applicat., vol. 39, no. 5/6, pp. 131-149, 2000.
9. M. G. Crandall, H. Ishii, and P. L. Lions, "User's guide to viscosity solutions of second order partial differential equations," Bull. Amer. Math. Soc., vol. 27, no. 1, pp. 1-67, 1992.
10. J. J. Koenderink, "The struture of images," Biol. Cybern., vol. 50, pp. 363-370, 1984.
11. J. Malik and P. Perona, "Scale-space and edge detection using anisotropic diffusion," IEEE Trans. Pattern Anal Machine Intell., vol. 12, no. 7, pp. 629-639, 1990.
12. D. Marr and E. Hildreth, "Theory of edge detection," in Proc. R. Soc. Lond. B, vol. 207, 1980, pp. 187-217.
13. J. M. Morel and S. Solimini, Variational Methods in Image Segmentation. Boston, MA: Birkhäuser, 1995.
14. K. N. Nordström, "Biased anisotropic diffusion: a unified regularization and diffusion approach to edge detection," Image Vis. Comput., no. 8, pp. 318-327, 1990.
15. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms," Phys. D, vol. 60, pp. 259-268, 1992.
16. J. A. Sethian, Level Set Methods. Cambridge, U.K.: Cambridge Univ. Press, 1996.
17. R. Teixeira, "Introdução aos Espaços de Escala," in 23° Colóquio Brasileiro de Matemática. Rio de Janeiro: IMPA, 2001.
18. A. P. Witkin, "Scale-space filtering," in Proc. IJCAI, Karlsruhe, 1983, pp. 1019-1021.
19. G. Whitten, "Scale space tracking and deformable sheet models for computational vision," IEEE Trans. Pattern Anal. Machine Intell., vol. 15, pp. 697-706, 1993.
20. Y. L. You and M. Kaveh, "Fouth-order partial differential equations for noise removal," IEEE Trans. Image Processing, vol. 9, pp. 1723-1730, Oct. 2000.