An Adaptive Window Approach for Image Smoothing and Structures Preserving

  • Charles Kervrann
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3023)


A novel adaptive smoothing approach is proposed for image smoothing and discontinuities preservation. The method is based on a locally piecewise constant modeling of the image with an adaptive choice of a window around each pixel. The adaptive smoothing technique associates with each pixel the weighted sum of data points within the window. We describe a statistical method for choosing the optimal window size, in a manner that varies at each pixel, with an adaptive choice of weights for every pair of pixels in the window. We further investigate how the I-divergence could be used to stop the algorithm. It is worth noting the proposed technique is data-driven and fully adaptive. Simulation results show that our algorithm yields promising smoothing results on a variety of real images.


Mean Square Error Noise Variance Image Decomposition Image Smoothing Adaptive Choice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Barash, D.: A fundamental relationship between bilateral filtering, adaptive smoothing and the nonlinear diffusion equation. IEEE Trans. Patt. Anal. Mach. Intell. 24(6), 844–847 (2002)CrossRefGoogle Scholar
  2. 2.
    Hamza, A.B., Krim, H.: A variational approach to maximum a posteriori estimation for image denoising. In: Figueiredo, M., Zerubia, J., Jain, A.K. (eds.) EMMCVPR 2001. LNCS, vol. 2134, pp. 19–34. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  3. 3.
    Blake, A., Zisserman, A.: Visual Reconstruction. MIT Press, Cambridge (1987)Google Scholar
  4. 4.
    Black, M.J., Sapiro, G.: Edges as outliers: Anisotropic smoothing using local image statistics. In: Nielsen, M., Johansen, P., Fogh Olsen, O., Weickert, J. (eds.) Scale-Space 1999. LNCS, vol. 1682, pp. 259–270. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  5. 5.
    Catte, F., Lions, P.-L., Morel, J.-M., Coll, T.: Image selective smoothing and edgedetection by nonlinear diffusion. SIAM J. Numerical Analysis 29(1), 182–193 (1992)zbMATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    Chan, T., Osher, S., Shen, J.: The digital TV filter and nonlinear denoising. IEEE. Trans. Image Process. 10(2), 231–241 (2001)zbMATHCrossRefGoogle Scholar
  7. 7.
    Chu, C.K., Glad, K., Godtliebsen, F., Marron, J.S.: Edge-preserving smoothers for image processing. J. Am. Stat. Ass. 93(442), 526–555 (1998)zbMATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Comaniciu, D., Meer, P.: Mean-shift: a robust approach toward feature space analysis. IEEE Trans. Patt. Anal. Mach. Intel. 24(5), 603–619 (2002)CrossRefGoogle Scholar
  9. 9.
    Csiszár, I.: Why least squares and maximum entropy? An axiomatic approach to inference for linear inverse problems. Ann. Statist. 19, 2032–2066 (1991)zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Gasser, T., Sroka, L., Jennen Steinmetz, C.: Residual variance and residual pattern in nonlinear regression. Biometrika 73, 625–633 (1986)zbMATHCrossRefMathSciNetGoogle Scholar
  11. 11.
    Gilboa, G., Sochen, N., Zeevi, Y.Y.: Texture preserving variational denoising using an adaptive fidelity term. In: Proc. VLSM 2003, Nice, France (2003)Google Scholar
  12. 12.
    Godtliebsen, F., Spjotvoll, E., Marron, J.S.: A nonlinear Gaussian filter applied to images with discontinuities. J. Nonparametric Statistics 8, 21–43 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Juditsky, A.: Wavelet estimators: adapting to unknown smoothness. Math. Methods of Statistics 1, 1–20 (1997)MathSciNetGoogle Scholar
  14. 14.
    Lepski, O.: Asymptotically minimax adaptive estimation 1: uppers bounds. SIAM J. Theory of Prob. and Appl. 36(4), 654–659 (1991)Google Scholar
  15. 15.
    Maurizot, M., Bouthemy, P., Delyon, B., Juditski, A., Odobez, J.-M.: Determination of singular points in 2D deformable flow fields. In: IEEE Int. Conf. Image Processing, Washington, DC (1995)Google Scholar
  16. 16.
    Meyer, Y.: Oscillating patterns in image processing and nonlinear evolution equations. University Lecture Series, vol. 22. AMS, Providence (2002)Google Scholar
  17. 17.
    Mrazek, P.: Selection of optimal stopping time for nonlinear diffusion filtering. Int. J. Comp. Vis. 52(2/3), 189–203 (2003)CrossRefGoogle Scholar
  18. 18.
    Mumford, D., Shah, J.: Optimal approximations by piecewise smooth functions and variational problems. Comm. Pure and Appl. Math. 42(5), 577–685 (1989)zbMATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    Osher, S., Solé, A., Vese, L.: Image decomposition and restoration using total variation minimization and the H− 1 norm. Multiscale Model. Simul. 1(3), 349–370 (2003)zbMATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Patt. Anal. Mach. Intell. 12(7), 629–639 (1990)CrossRefGoogle Scholar
  21. 21.
    Rudin, L., Osher, S., Fatemi, E.: Nonlinear Total Variation based noise removal algorithms. Physica D 60, 259–268 (1992)zbMATHCrossRefGoogle Scholar
  22. 22.
    Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proc. Int. Conf. Comp. Vis. (ICCV 1998), Bombay, India, pp. 839–846 (1998)Google Scholar
  23. 23.
    van de Weijer, J., van den Boomgaard, R.: Local mode filtering. In: Proc. Comp. Vis. Patt. Recogn (CVPR 2001), Kauai, Hawaii, USA, vol. II, pp. 428–433 (2001)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2004

Authors and Affiliations

  • Charles Kervrann
    • 1
  1. 1.IRISA – INRIA Rennes / INRA – Mathématiques et Informatique AppliquéesRennes CedexFrance

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