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


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.


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



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.


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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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