A new diffusion-based variational model for image denoising and segmentation

Journal of Mathematical Imaging and Vision

Volumn 26, Issue 1-2, 2006, Pages 115-125

  Li, Fang ^a,b   Shen, Chaomin ^a   Pi, Ling ^c  

^a EAST CHINA NORMAL UNIVERSITY   (China)

^b South West University ^*  (China)

^c SHANGHAI JIAO TONG UNIVERSITY   (China)

Author keywords

Bounded variation function; Ginzburg Landau model; Heat flow; Image denoising; Segmentation

Indexed keywords

ALGORITHMS; AUTOMATION; COLOR IMAGE PROCESSING; CONTOUR MEASUREMENT; EDGE DETECTION; MATHEMATICAL MODELS;

BOUNDED VARIATION FUNCTION; GINZBURG LANDAU MODEL; HEAT FLOW; IMAGE DENOISING;

IMAGE SEGMENTATION;

EID: 33751526511     PISSN: 09249907     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10851-006-8303-2     Document Type: Article

References (20)

1. G. Aubert, J.F. Aujol, and L.B. Feraud, "Detecting codimention-two objects in an image with Ginzburg-Landau models, " to appear in Int. J. Comput. Vis.
2. G. Aubert and L. Vese, "A variational method in image recovery, " SIAM J. Numer. Anal., Vol. 34, No. 5, pp. 577-584, 1997.
3. C.A.Z. Barcelos and Y. Chen, "Heat flows and related minimization problem in image restoration, " Comput. Mat. App., Vol. 39, pp. 81-97, 2000.
4. F. Bethuel, H. Brezis, and F. Helein, "Singular limit for the minimization of Ginzburg-Landau functionals, " CRAS I-MATH, Vol. 314, pp. 891-895, 1992.
5. P.V. Blomgren and T.F. Chan, "Color TV: Total variation methods for restoration of vector valued images, " IEEE Trans. Image Process., Vol. 7, pp. 304-309, 1998.
6. V. Caselles, R. Kimmel, and G. Sapiro, "Geodesic active contours, " Int. J. Comput. Vis., Vol. 22, No. 1, pp. 61-79, 1997.
7. T.F. Chan, S.H. Kang, and J. Shen, "Total variation denoising and enhancement of color images based on the CB and HSV color models, " J. Vis. Commun. Image Rep., Vol. 12, pp. 422-435, 2001.
8. T.F. Chan, S. Osher, and J. Shen, "The digital TV filter and non-linear denoising, " IEEE Trans. Image Process., Vol. 10, No. 2, pp. 231-241, 2001.
9. T.F. Chan and J. Shen, "Variational restoration of non-flat image features: Models and algorithms, " SIAM J. App. Math., Vol. 61, pp.1338-1361, 2000.
10. T.F. Chan and L.A. Vese, "Active contour without edges, " IEEE Trans. Image Process., Vol. 22, pp. 61-79, 1997.
11. X.Y. Chen, S. Jimbo, and Y. Morita, "Stablization of vortices in the Ginzburg-Landau equation with variable diffusion coefficients, " SIAM J. Math. Anal., 1998.
12. Y. Chen and T. Wunderli, "Adaptive total variation for image restoration in BV space, " J. Math. Anal. Appl., Vol. 272, pp. 117-137, 2002.
13. M. Kass, A. Witkin, and D. Terzopoulos, "Snakes: Active contour models, " Int. J. Comput. Vis., Vol. 1, pp. 321-331, 1988.
14. F.H. Lin and X.P. Yang, Geometric Measure Theory-An Introduction, Advanced Mathematics. International Press: Boston, 2001.
15. - 1 norm, " SIAM J. Multiscale Model. Simu., Vol. 1:3, pp. 349-370, 2003.
16. L. Rudin, S. Osher, and E. Fatemi, "Nonlinear total variation based noise removal algorithms, " Physica D., Vol. 60, pp. 259-268, 1992.
17. B. Tang, G. Sapiro, and V. Caselles, "Diffusion of general data on non-flat manifolds via Harmonic maps theory: The direction diffusion case, "Int. J. Comput. Vis., Vol. 36, pp. 149-161, 2000.
18. B. Tang, G. Sapiro, and V. Caselles, "Color image enhancement via chromaticity diffusion, " IEEE Trans. Image Process., Vol. 10, pp. 701-707, 2001.
19. P.E. Trahanias, D. Karako, and A.N. Venetsanopoulos, "Directional processing of color images: Theory and experimental results, " IEEE Trans. Image Process., Vol. 5, No. 6, pp. 868-880, 1996.
20. L. Vese and S. Osher, "Modeling textures with total variation minimization and oscillating patterns in image processing, " J. Sci. Comput., Vol. 19, No. 1-3, pp. 553-572, 2003.