Abstract
Image decomposition refers to the splitting of an image into two or more components. In this paper, a clean image is separated into two parts: one is the cartoon component, consisting only of geometric structure, and the other is the oscillatory component, consisting of texture. Three parts for noisy image are considered: cartoon, texture, and noise. To better decompose an image, we propose two new variational models. In our models, two adaptive regularization terms are introduced. The two regularization terms are determined by an adaptive function which can discriminate the cartoon and texture of an image automatically. Experimental results illustrate the effectiveness of the proposed models for image decomposition.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Rudin L, Osher S, Fatemi E. Nonlinear total variation based noise removal algorithms. Physica D, 1992, 60: 259–268
Meyer Y. Oscillating patterns in image processing and nonlinear evolution equations. Boston: University Lecture Series, American Mathematical Society Providence, RI, 2001
Vese L, Osher S. Modeling textures with total variation minimization and oscillating patterns in image processing. J Math Imaging Vis, 2004, 20: 7–18
Osher S, Sole A, Vese L. Image decomposition and restoration using total variation minimization and the H −1 Norm. Multiscale Model Simul, 2003, 1: 349–370
Aujol J F, Aubert G, Blanc-Feraud L, et al. Image decomposition into a bounded variation component and an oscillating component. J Math Imaging Vis, 2005, 22: 71–88
Aujol J F, Chambolle A. Dual norms and image decomposition models. Int J Comput Vision, 2005, 63: 85–104
Lu C W, Song G X. Image decomposition using adaptive regularization and div(BMO). J Syst Eng Electron, 2011, 22: 358–364
Jiang L L, Yin H Q, Feng X C. Adaptive variational models for image decomposition combining staircasing reduction and texture extraction. J Syst Eng Electron, 2009, 20: 254–259
Chan T F, Esedoglu S, Parky F. Image decomposition combining staircasing reduction and texture extraction. J Vis Commun Image R, 2007, 18: 464–486
Starck J L, Elad M, Donoho D L. Image decomposition via the combination of sparse representations and a variational approach. IEEE Trans Image Process, 2005, 14: 1570–1582
Li Y F, Feng X C. Coupled dictionary learning method for image decomposition. Sci China Inf Sci, 2011, doi: 10.1007/s11432-011-4365-x
Buades A, Le T M, Morel J M, et al. Fast cartoon+ texture image filters. IEEE Trans Image Process, 2010, 19: 1978–1986
Tikhonov A N, Arsenin V Y. Solutions of Ill-Posed Problems. Washington DC: Winston & Sons Incorporation, 1977
Chambolle A. An algorithm for total variation minimization and applications. J Math Imaging Vis, 2004, 20: 89–97
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Xu, J., Feng, X., Hao, Y. et al. Adaptive variational models for image decomposition. Sci. China Inf. Sci. 57, 1–8 (2014). https://doi.org/10.1007/s11432-012-4716-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11432-012-4716-2