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Multimedia Tools and Applications

, Volume 75, Issue 13, pp 7909–7930 | Cite as

A generalized relative total variation method for image smoothing

  • Qiegen Liu
  • Biao Xiong
  • Dingcheng Yang
  • Minghui Zhang
Article

Abstract

Recently, two piecewise smooth models L0smoothing and relative total variation (RTV) have been proposed for feature/structure-preserving filtering. One is very efficient for tackling image with little texture patterns and the other has appearance performance on image with abundant uniform textural details. In this work, we present a general relative total variation (GRTV) method, which generalizes the advantages of both approaches. The efficiency of RTV depends on the defined windowed total variation (WTV) and windowed inherent variation (WIV), which focus on edge enhancing and texture suppressing respectively. The key innovations of the presented GRTV method are to extend the norm of WTV in RTV from 1 to [0, 1] and set the norm of WIV inversely proportional to the norm of WTV. These modifications substantially improve the structure extraction ability of RTV. The presented GRTV also improves the edge-boundary enhancing ability of L0smoothing and further enables it to deal with images containing complex textural details and noises. Furthermore, the L2-norm data fidelity term replaced by L1-norm is discussed. Experimental results demonstrate that the proposed method presents better performance as the state-of-the-art methods do.

Keywords

Image smoothing Structure preserving non-convex regularization Iterative Reweighed Least Square 

Notes

Acknowledgments

This work was partly supported by the National Natural Science Foundation of China under 61362001, 62162084, 61261010, 61365013, 51165033, the Science and Technology Department of Jiangxi Province of China under 20121BBE50023, 20132BAB211030, Young Scientists Training Program of Jiangxi Province under 20133ACB21007, 20142BCB23001, International Scientific Cooperation Project of Jiangxi Province under 20141BDH80001, Jiangxi Advanced Project for Post-doctoral Research Funds under 2014KY02 and Post-doctoral Research Funds under 2014 M551867.

References

  1. 1.
    Alliney S (1992) Digital filters as absolute norm regularizers. IEEE Trans Signal Process 40(6):1548–1562CrossRefMATHGoogle Scholar
  2. 2.
    Alliney S (2004) A variational approach to remove outliers and impulse noise. J Math Imaging Vis 20(12):99–120MathSciNetGoogle Scholar
  3. 3.
    Bae S, Durand F (2007) Defocus magnification. Comput Graph Forum 26(3):571–579CrossRefGoogle Scholar
  4. 4.
    Bresson X, Esedoglu S, Vandergheynst P, Thiran JP, Osher SJ (2007) Fast global minimization of the active contour/snake model. J Math Imaging Vis 28(2):151–167MathSciNetCrossRefGoogle Scholar
  5. 5.
    Buades A, Coll B, Morel J-M (2005) A non-local algorithm for image denoising. CVPR 2:60–65MATHGoogle Scholar
  6. 6.
    Buades A, Le TM, Morel J-M, Vese LA (2010) Fast cartoon + texture image filters. IEEE Trans Image Process 19(8):1978–1986MathSciNetCrossRefGoogle Scholar
  7. 7.
    Cheng X, Zeng M, Liu X (2014) Feature-preserving filtering with L0 gradient minimization. Comput Graph 38:150–157CrossRefGoogle Scholar
  8. 8.
    Dabov K, Foi A, Katkovnik V, Egiazarian KO (2007) Image denoising by sparse 3-d transform-domain collaborative filtering. IEEE Trans Image Process 16(8):2080–2095MathSciNetCrossRefGoogle Scholar
  9. 9.
    Durand F, Dorsey J (2002) Fast bilateral filtering for the display of high-dynamic-range images. ACM Trans Graph 21(3):257–266CrossRefGoogle Scholar
  10. 10.
    Farbman Z, Fattal R, Lischinski D, Szeliski R (2008) Edge-preserving decompositions for multi-scale tone and detail manipulation. ACM Trans Graph 27:3CrossRefGoogle Scholar
  11. 11.
    Fattal R, Agrawala M, Rusinkiewicz S (2007) Multiscale shape and detail enhancement from multi-light image collections. ACM Trans Graph 26:3Google Scholar
  12. 12.
    Gorodnitsky B (1997) Rao, Sparse signal reconstruction from limited data using FOCUSS: a re-weighted minimum norm algorithm. IEEE Trans Signal Process 45(3):600–616CrossRefGoogle Scholar
  13. 13.
    He K, Sun J, Tang X (2010) Guided Image Filtering. In ECCV: 1–14Google Scholar
  14. 14.
    Karacan L, Erdem E, Erdem A (2013) Structure preserving image smoothing via region covariances. ACM Trans Graph 32(6)Google Scholar
  15. 15.
    Liu Q, Wang S, Luo J, Zhu Y, Ye M (2012) An augmented Lagrangian approach to general dictionary learning for image denoising. J Vis Commun Image Represent 23(5):753–766CrossRefGoogle Scholar
  16. 16.
    Nikolova M (2002) Minimizers of cost-functions involving nonsmooth data-fidelity terms. SIAM J Numer Anal 40(3):965–994MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Perazzi F et al. (2012) Saliency filters: Contrast based filtering for salient region detection. In CVPRGoogle Scholar
  18. 18.
    Perona P, Malik J (1990) Scale-space and edge detection using anisotropic diffusion. IEEE Trans Pattern Anal Mach Intell 12:629–639CrossRefGoogle Scholar
  19. 19.
    Rao BD, Delgado KK (1999) An affine scaling methodology for best basis selection. IEEE Trans Signal Process 47(1):187–200MathSciNetCrossRefMATHGoogle Scholar
  20. 20.
    Rodrguez P, Wohlberg B (2008) An efficient algorithm for sparse representations with lp data fidelity term, in: Proceedings of 4th IEEE Andean Technical Conference (ANDESCON)Google Scholar
  21. 21.
    Rodrguez P, Wohlberg B (2009) Efficient minimization method for a generalized total variation functional. IEEE Trans Image Process 18(2):322–332MathSciNetCrossRefGoogle Scholar
  22. 22.
    Rouselle F, Knaus C, Zwicker M (2012) Adaptive rendering with non-local means filtering, ACM Trans Graph 31(6).Google Scholar
  23. 23.
    Rudin L, Osher S, Fatemi E (1992) Nonlinear total variation based noise removal algorithms. Phys D 60(1–4):259–68MathSciNetCrossRefMATHGoogle Scholar
  24. 24.
    Shen C-T, Chang F-J, Hung Y-P, Pei S-C (2010) Edge-preserving image decomposition using L1 fidelity with L0 gradient, SIGGRAPH ASIAGoogle Scholar
  25. 25.
    Tomasi C, Manduchi R (1998) Bilateral filtering for gray and color images. In ICCV. 839–846Google Scholar
  26. 26.
    Winnem¨Oller H, Olsen SC, Gooch B (2006) Real-time video abstraction. ACM Trans Graph 25(3):1221–1226CrossRefGoogle Scholar
  27. 27.
    Xu L, Lu C, Xu Y, Jia J (2011) Image smoothing via L0 gradient minimization. ACM Trans Graph 30(6);174:1–174:12. doi: 10.1145/2024156.2024208
  28. 28.
    Xu L, Yan Q, Xia Y, Jia J (2012) Structure extraction from texture via relative total variation. ACM Trans Graph 31(6)Google Scholar
  29. 29.
    Ye C, Tao D, Song M, Jacobs DW (2013) Sparse norm filtering, M Wu - arXiv preprint arXiv:1305.3971, 2013 - arxiv.org.Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Qiegen Liu
    • 1
  • Biao Xiong
    • 2
  • Dingcheng Yang
    • 1
  • Minghui Zhang
    • 1
  1. 1.Department of Electronic Information EngineeringNanchang UniversityNanchangPeople’s Republic of China
  2. 2.Faculty of Geo-Information Science and Earth Observation - ITCUniversity of TwenteEnschedeThe Netherlands

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