Fast algorithm for color texture image inpainting using the non-local CTV model

Journal of Global Optimization

Volumn 62, Issue 4, 2015, Pages 853-876

  Duan, Jinming ^a   Pan, Zhenkuan ^b   Zhang, Baochang ^d   Liu, Wanquan ^c   Tai, Xue Cheng ^e  

^a UNIVERSITY OF NOTTINGHAM   (United Kingdom)

^b QINGDAO UNIVERSITY   (China)

^c CURTIN UNIVERSITY   (Australia)

^d BEIHANG UNIVERSITY   (China)

^e UNIVERSITY OF BERGEN   (Norway)

Author keywords

Color texture images inpainting; CTV model; Mumford Shad model; Non local model; The split Bregman algorithm

Indexed keywords

ALGORITHMS; COLOR; HEURISTIC ALGORITHMS; IMAGE PROCESSING; NUMERICAL MODELS; TEXTURES;

COLOR TEXTURE IMAGES; INPAINTING; MODEL AND ALGORITHMS; NONLOCAL MODELS; NUMERICAL EXPERIMENTS; NUMERICAL IMPLEMENTATION; SPLIT BREGMAN ALGORITHMS; TEXTURE IMAGE INPAINTING;

IMAGE TEXTURE;

EID: 84937972855     PISSN: 09255001     EISSN: 15732916     Source Type: Journal    
DOI: 10.1007/s10898-015-0290-7     Document Type: Article

References (46)

1. Aubert, G., Kornprobst, P.: Mathematical problems in image processing: partial differential equations and the calculus of variations, 2nd edn. Springer, Berlin, Germany (2006)
2. Bertalmío, M., Sapiro, G., Caselles, V., Ballester, C.: Image inpainting. In: Proceedings of SIGGRAPH, pp. 417–424 (2000)
3. Bertalmio, M., Bertozzi, A., Sapiro, G.: Navier-Stokes, fluid-dynamics, and image and video inpainting. In Proceedings of IEEE-CVPR, pp. 355–362 (2001)
4. Chan, T., Shen, J.: Mathematical models of local non-texture inpaintings. SIAM J. Appl. Math. 62(3), 1019–1043 (2002)
5. Bertozzi, A., Esedoglu, S., Gillette, A.: Inpainting of binary images using the cahn-hilliard equation. IEEE Trans. Image Process. 16(1), 285–291 (2007)
6. Chan, T., Shen, J.: Non-texture inpainting by curvature-driven diffusions (CDD). J. Vis. Commun. Image Represent. 12(4), 436–449 (2001)
7. Chan, T., Kang, S., Shen, J.: Euler’s elastica and curvature-based image inpainting. SIAM J. Appl. Math. 63(2), 564–592 (2002)
8. Esedoglu, S., Shen, J.: Digital inpainting based on the Mumford–Shah–Euler image model. Eur. J. Appl. Math. 13(4), 353–370 (2002)
9. Tai, X., Hahn, J., Chung, G.: A fast algorithm for Euler’s elastica model using augmented Lagrangian method. SIAM J. Appl. Math. 4(1), 313–344 (2011)
10. Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Phys. D 60(1/4), 259–268 (1992)
11. Nitzberg, M., Mumford, D., Shiota, T.: Filering, segmentation, and depth, LNCS, vol. 662. Springer, Berlin, Germany (1993)
12. Efros, A., Leung, T.: Texture synthesis by nonparametric sampling. In: Proceedings of the IEEE ICCV, pp. 1033–1038 (1999)
13. Criminisi, A., Pérez, P., Toyama, K.: Region filling and object removal by exemplar-based inpainting. IEEE Trans. Image Process. 13(9), 1200–1212 (2004)
14. Xu, Z., Jian, S.: Image inpainting by patch propagation using patch sparsity. IEEE Trans. Image Process. 19(3), 1153–1165 (2010)
15. Arias, P., Caselles, V., Facciolo, G., Sapiro, G.: A variational framework for exemplar-based image inpainting. Int. J. Comput. Vis. 93(3), 1–29 (2011)
16. Arias, P., Caselles, V., Facciolo, G.: Analysis of a variational framework for exemplar-based image inpainting. SIAM Multiscale Model. Simul. 10(2), 473–514 (2012)
17. Bertalmio, M., Vese, L., Sapiro, G., Osher, S.: Simultaneous structure and texture image inpainting. IEEE Trans. Image Process. 12(8), 882–889 (2003)
18. Cai, J., Chan, R., Shen, Z.: A framelet-based image inpainting algorithm. Appl. Comput. Harmon. Anal. 24(2), 131–149 (2008)
19. Cai, J., Chan, R., Shen, Z.: Simultaneous cartoon and texture inpainting. Inverse Probl. Imaging 4(3), 379–395 (2010)
20. Buades, A., Coll, B., Morel, J.: A review of image denoising algorithms, with a new one. SIAM Multiscale Model. Simul. 4(2), 490–530 (2005)
21. Gilboa, G., Osher, S.: Nonlocal operators with applications to image processing. SIAM Multiscale Model. Simul. 7(3), 1005–1028 (2008)
22. Peyré, G., Bougleux, S., Cohen, L.: Non-local regularization of inverse problems. LNCS 5304, 57–68 (2008)
23. Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and associated variational problems. CPAM XLII, 577–685 (1989)
24. Lou, Y., Zhang, X., Osher, S., Bertozzi, A.: Image recovery via non local operators. J. Sci. Comput. 42(2), 185–197 (2010)
25. Zhang, X., Burger, M., Bresson, X., Osher, S.: Bregmanized nonlocal regularization for deconvolution and sparse reconstruction. SIAM J. Imaging Sci. 3(3), 253–276 (2010)
26. Ma, W., Osher, S.: A TV Bregman iterative model of Retinex theory, University California, Los Angeles, UCLA CAM Report, pp. 10–13 (2010)
27. Zosso, D., Tran, G., Osher, S.: A unifying retinex model based on non-local differential operators. University California, Los Angeles, UCLA CAM Report, pp. 13–03 (2013)
28. Jung, M., Bresson, X., Chan, T.F., Vese, L.A.: Nonlocal Mumford–Shah regularizers for color image restoration. IEEE Trans. Image Process. 20(6), 1583–1598 (2011)
29. Yang, J., Yin, W., Zhang, Y., Wang, Y.: A fast algorithm for edge-preserving variational multichannel image restoration. SIAM J. Imaging Sci. 2(2), 569–592 (2009)
30. Ambrosio, L., Tortorelli, V.M.: Approximation of functionals depending on jumps by elliptic functionals via Gamma-convergence. Commun. Pure Appl. Math. 49, 999–1036 (1990)
31. Blomgren, P., Chan, T.: Color TV: total variation methods for restoration of vector-valued images. IEEE Trans. Image Process. 7(3), 304–309 (1998)
32. Yu, Y., Pan, Z., Wei, W., Jiang, J.: Edge preserving of some variational models for vectorial image denoising. J. Gr. Images 16(12), 2223–2230 (2011)
33. Duan, J., Pan, Z., Tai, X.: Some non-local TV models for restoration of color texture images. J. Gr. Images 18(7), 753–760 (2013)
34. Goldstein, T., O’Donoghue, B., Setzer, S., Baraniuk, R.: Fast alternating direction optimization methods. SIAM J. Image Sci. 7(3), 1588–1623 (2014)
35. Goldfarb, D., Ma, S., Scheinberg, K.: Fast alternating linearization methods for minimizing the sum of two convex functions. Math. Program. 141, 349–382 (2013)
36. Goldstein, T., Osher, S.: The split Bregman method for L1-regularized problems. SIAM J. Imaging Sci. 2, 323–343 (2009)
37. Kampa, K., Metha, S., Chou, C.A., Chaovalitwongse, W.A., Grabowski, T.J.: Sparse optimization in feature selection: application in neuroimaging. J. Glob. Optim. 59, 439–457 (2014)
38. Xu, R., Jiao, J., Zhang, B., Ye, Q.: Pedestrian detection in images via cascaded L1-norm minimization learning method. Pattern Recognit. 45, 2573–2583 (2012)
39. Goldstein, T., Osher, S.: The split Bregman algorithm for L1 regularized problems. SIAM J. Imaging Sci. 2(2), 323–343 (2009)
40. Duan, J., Pan, Z., Liu, W., Tai, X.: Color texture image inpainting using the non local CTV model. J. Sign. Inf. Process. 4(3B), 43–51 (2013)
41. Shah, J.: A common framework for curve evolution, segmentation and anisotropic diffusion. Proceedings of IEEE Conference Computer Vision and Pattern Recognition, pp. 136–142 (1996)
42. Duan, J., Pan, Z., He, X., Wei, W., Liu, C.: Mumford–Shah model on implicit surfaces. J. Softw. 23(suppl. 2), 53–63 (2012)
43. Bar, L., Brook, A., Sochen, N., Kiryati, N.: Deblurring of color images corrupted by impulsive noise. IEEE Trans. Image Process. 16(4), 1101–1111 (2007)
44. Bresson, X.: A short note for nonlocal TV minimization (2009), Online
45. Wang, Z., Bovik, A.C., Sheikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13(4), 600–612 (2004)
46. Jung, M., Peyre, G., Cohen, L.: Non-local segmentation and inpainting. IEEE International Conference on Image Processing, Brusslels: Belgium (2011)