Projected gradient based color image decomposition

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5567 LNCS, Issue , 2009, Pages 295-306

  Duval, Vincent ^a   Aujol, Jean François ^b   Vese, Luminita ^c  

^a INSTITUT TELECOM   (France)

^b Paris Descartes University   (France)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Color image decomposition; Color texture modeling; Projected gradient algorithm

Indexed keywords

COLOR IMAGE DECOMPOSITION; COLOR IMAGES; COLOR TEXTURE MODELING; COLOR TEXTURES; DECOMPOSITION MODEL; GEOMETRIC INFORMATION; IMAGE DECOMPOSITION; NUMERICAL SCHEME; ORIGINAL IMAGES; OSCILLATING PATTERN; PROJECTED GRADIENT; PROJECTED GRADIENT ALGORITHM; TWO-COMPONENT; VECTOR VALUED;

COLOR IMAGE PROCESSING; COMPUTER VISION; TEXTURES;

COLOR;

EID: 69049110196     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-02256-2_25     Document Type: Conference Paper

References (33)

1. Rudin, L., Osher, S., Fatemi, E.: Non linear total variation based noise removal algorithms. Physica D 60, 259-268 (1992)
2. Chan, T., Shen, J.: Image processing and analysis - Variational, PDE, wavelet, and stochastic methods. SIAM Publisher, Philadelphia (2005)
3. Aubert, G., Kornprobst, P.: Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations. Applied Mathematical Sciences, vol. 147. Springer, Heidelberg (2001)
4. Meyer, Y.: Oscillating patterns in image processing and nonlinear evolution equations. In: The fifteenth Dean Jacqueline B. Lewis memorial lectures. University Lecture Series, vol. 22. American Mathematical Society, Providence, RI (2001)
5. Mumford, D., Gidas, B.: Stochastic models for generic images. Quarterly of Applied Mathematics LIV(1) (2001)
6. Vese, L., Osher, S.J.: Modeling textures with total variation minimization and oscillating patterns in image processing. Journal of Scientific Computing 19(1-3), 553-572 (2003)
7. Osher, S., Solé, A., Vese, L.: Image decomposition and restoration using total variation minimization and the H-1 norm. SIAM Journal on Multiscale Modeling and Simulation 1(3), 349-370 (2003)
8. Aujol, J.F., Aubert, G., Blanc-Féraud, L., Chambolle, A.: Image decomposition into a bounded variation component and an oscillating component. Journal of Mathematical Imaging and Vision 22(1), 71-88 (2005)
9. Aubert, G., Aujol, J.: Modeling very oscillating signals. Application to image processing. Applied Mathematics and Optimization 51(2), 163-182 (2005)
10. Aujol, J.F., Chambolle, A.: Dual norms and image decomposition models. International Journal on Computer Vision 63(1), 85-104 (2005)
11. Yin, W., Goldfarb, D., Osher, S.: A comparison of three total variation based texture extraction models. Journal of Visual Communication and Image Representation 18(3), 240-252 (2007)
12. Garnett, J., Jones, P., Le, T., Vese, L.: Modeling oscillatory components with the homogeneous spaces BMO-α and W-α,p. Pure and Applied Mathematics Quarterly (to appear)
13. Le, T., Vese, L.: Image decomposition using total variation and div (BMO). Multiscale Modeling and Simulation, SIAM Interdisciplinary Journal 4(2), 390-423 (2005)
14. Lieu, L., Vese, L.: Image restoration and decomposition via bounded total variation and negative hilbert-sobolev spaces. Applied Mathematics & Optimization 58, 167- 193 (2008)
15. Sapiro, G., Ringach, D.L.: Anisotropic diffusion of multivalued images with applications to color filtering. IEEE Transactions on Image Processing 5(11), 1582-1586 (1996)
16. Sochen, N., Kimmel, R., Malladi, R.: A general framework for low level vision. IEEE Transactions on Image Processing 7(3), 310-318 (1998)
17. Aujol, J.F., Kang, S.H.: Color image decomposition and restoration. Journal of Visual Communication and Image Representation 17(4), 916-928 (2006)
18. Bresson, X., Chan, T.: Fast minimization of the vectorial total variation norm and applications to color image processing. Inverse Problems and Imaging (IPI) (accepted) (2007)
19. Blomgren, P., Chan, T.: Color TV: Total variation methods for restoration of vector valued images. IEEE Transactions on Image Processing 7(3), 304-309 (1998)
20. Vese, L., Osher, S.: Color texture modeling and color image decomposition in a variational-PDE approach. In: Proceedings of the Eighth International Symposium on Symbolic and Numeric Algorithms for Scientific Computing (SYNASC 2006), pp. 103-110. IEEE, Los Alamitos (2006)
21. Aujol, J., Gilboa, G.: Constrained and SNR-based solutions for TV-Hilbert space image denoising. Journal of Mathematical Imaging and Vision 26(1-2), 217-237 (2006)
22. Vogel, C.: Computational Methods for Inverse Problems. Frontiers in Applied Mathematics, vol. 23. SIAM, Philadelphia (2002)
23. Chan, T., Golub, G., Mulet, P.: A nonlinear primal-dual method for total variationbased image restoration. SIAM Journal on Scientific Computing 20(6), 1964-1977 (1999)
24. Chambolle, A.: An algorithm for total variation minimization and its applications. JMIV 20, 89-97 (2004)
25. Chambolle, A.: Total variation minimization and a class of binary MRF models. In: Rangarajan, A., Vemuri, B.C., Yuille, A.L. (eds.) EMMCVPR 2005. LNCS, vol. 3757, pp. 136-152. Springer, Heidelberg (2005)
26. Darbon, J., Sigelle, M.: Image restoration with discrete constrained total variation part I: Fast and exact optimization. Journal of Mathematical Imaging and Vision 26(3), 277-291 (2006)
27. Weiss, P., Aubert, G., Blanc-Féraud, L.: Efficient schemes for total variation minimization under constraints in image processing. SIAM Journal on Scientific Computing (to appear) (2007)
28. Aujol, J.: Some algorithms for total variation based image restoration. CMLA Preprint 2008-05 (2008), http://hal.archives-ouvertes.fr/hal-00260494/en/
29. Zhu, M., Wright, S., Chan, T.: Duality-based algorithms for total variation image restoration, UCLA CAM Report 08-33 (May 2008)
30. Bermudez, A., Moreno, C.: Duality methods for solving variational inequalities. Comp. and Maths. with Appls. 7(1), 43-58 (1981)
31. Duval, V., Aujol, J.F., Vese, L.: A projected gradient algorithm for color image decomposition. Technical report, UCLA, CAM Report 08-40 (2008)
32. Ciarlet, P.G.: Introduction á l'Analyse Numérique Matricielle et á l'Optimisation. Dunod (1998)
33. Aujol, J., Gilboa, G., Chan, T., Osher, S.: Structure-texture image decomposition - modeling, algorithms, and parameter selection. International Journal of Computer Vision 67(1), 111-136 (2006)