Image decomposition using adaptive second-order total generalized variation
- 651 Downloads
This paper proposes a new model for image decomposition which separates an image into a cartoon, consisting only of geometric objects, and an oscillatory component, consisting of textures or noise. The proposed model is given in a variational formulation with adaptive second-order total generalized variation (TGV). The adaptive behavior preserves the key features such as object boundaries and textures while avoiding staircasing effect. To speed up the computation, the split Bregman method is used to solve the proposed model. Experimental results and comparisons demonstrate the proposed model is more effective for image decomposition than the methods of the state-of-the-art image decomposition models.
KeywordsImage decomposition Cartoon Texture TGV Split Bregman Staircasing effect
This work is supported by the National Science Foundation of China (No. 60872138, 61105011, 61271294). Meanwhile, the authors also thank Editor-in-Chief Prof. Murat Kunt and anonymous reviewers for their constructive comments that greatly improve this paper.
- 1.Meyer, Y.: Oscillating patterns in image processing and nonlinear evolution equations. University Lecture Series, American Mathematical Society, Boston (2001)Google Scholar
- 2.Rudin, L., Osher, S., Fatemi, E.: Nonlinear total variation based noise removal algorithms. Physica. D 60, 259–268 (1992)Google Scholar
- 3.Vese, L., Osher, S.: Modeling textures with total variation minimization and oscillating patterns in image processing. J. Math. Imaging Vis. 20, 7–18 (2004)Google Scholar
- 5.Jiang, L., Yin, H., Feng, X.: Adaptive variational models for image decomposition combining staircase reduction and texture extraction. J. Syst. Eng. Electron. 20(2), 254–259 (2009)Google Scholar
- 10.Jiang, L., Feng, X., Yin, H.: Image decomposition using optimally sparse representations and a variational approach. Signal, Image and Video Processing 22(4), 1287–1292 (2007)Google Scholar
- 13.Bredies, K., Valkonen, T.: Inverse problems with second-order total generalized variation constraints. In: Proceedings of SampTA 2011–9th International Conference on Sampling Theory and Applications, Singapore, pp. 1–4 (2011)Google Scholar
- 14.Bredies, K., Dong, Y., Hintermüller M.: Spatially dependent regularization parameter selection in total generalized variation models for image restoration. International Journal of Computer Mathematics, pp. 1–15 (2012), online, doi: 10.1080/00207160.2012.700400
- 16.Dong, F., Liu, Z., Kong, D., Liu, K.: An improved LOT model for image restoration. J. Math. Imaging Vis. 34(1), 89–97 (2009)Google Scholar
- 19.Goldstein, T., Bresson, X., Osher, S.: Geometric applications of the split Bregman method: Segmentation and surface reconstruction. J. Sci. Comput. 45(1–3), 272–293 (2010) Google Scholar
- 20.Afonso, M., Bioucas-Dias, J., Figueiredo, M.: An augmented lagrangian approach to the constrained optimization formulation of imaging inverse problems. IEEE Trans. Image Process. 20(3), 681–695 (2011)Google Scholar