Skip to main content
SpringerLink
Log in

Robust Estimation Approach for NL-Means Filter

  • Conference paper
Advances in Visual Computing (ISVC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 5359))

Included in the following conference series:

Abstract

Edge preserved smoothing techniques have gained importance for the purpose of image denoising. A good edge preserving filter is given by NL-means filter than any other linear model based approaches. Since the weight function in NL-means filter is closely related to the error norm and influence function in robust estimation framework, this paper explores a refined approach of NL-means filter by using robust estimation function rather than the usual exponential function for its weight calculation. Here the filter output at each pixel is the weighted average of pixels in the surrounding neighborhoods using the chosen robust M-estimator function. Validations using various test images have been analyzed and the results were compared with the other known recent methods. There is a reason to believe that this refined algorithm has some interesting and notable points.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Lindenbaum, M., Fischer, M., Bruckstein, A.M.: On Gabor Contribution To Image-Enhancement. Pattern Recognition 27, 1–8 (1994)

    Article  Google Scholar 

  2. Rudin, L., Osher, S.: Nonlinear total variation based noise removal algorithms. Physica D: Nonlinear Phenomena 60(1-4), 259–268 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  3. Aurich, V., Weule, J.: Non-linear gaussian filters performing edge preserving diffusion. In: Proceedings of the DAGM Symposium, pp. 538–545. Springer, Heidelberg (1995)

    Google Scholar 

  4. Smith, S.M., Brady, J.M.: SUSAN - a new approach to low level image processing. International Journal of Computer Vision 23, 45–78 (1997)

    Article  Google Scholar 

  5. Tomasi, C., Manduchi, R.: Bilateral filtering for gray and color images. In: Proceedings of the IEEE international Conference on Computer Vision, pp. 839–846 (1998)

    Google Scholar 

  6. Efros, A., Leung, T.: Texture synthesis by non parametric sampling. In: Proceedings of the Seventh International Conference on Computer Vision, Kerkyra, Greece, vol. 2, pp. 1033–1038 (September 1999)

    Google Scholar 

  7. Barash, D.: A Fundamental Relationship between Bilateral Filtering, Adaptive Smoothing. IEEE Transactions on Pattern Analysis and Machine Intelligence 24(6), 844–847 (2002)

    Article  Google Scholar 

  8. Buades, A., Coll, B., Morel, J.M.: A Non-Local Algorithm for Image Denoising. In: Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2005), vol. 2, pp. 60–65 (2005)

    Google Scholar 

  9. Mahmoudi, M., Sapiro, G.: Fast Image and video denoising via nonlocal means of similar neighbourhoods. IEEE signal processing letters 12(12) (2005)

    Google Scholar 

  10. Coupe, P., Yger, P., Barillot, C.: Fast Non Local Means Denoising for 3D MR Images. In: Larsen, R., Nielsen, M., Sporring, J. (eds.) MICCAI 2006. LNCS, vol. 4191, pp. 33–40. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Orchard, J., Ebrahimi, M., Wong, A.: Efficient Non-Local-Means Denoising using the SVD. In: Proceedings of The IEEE International Conference on Image Processing ICIP 2008, San Diego, California, USA, October 12-15 (to appear, 2008)

    Google Scholar 

  12. Geman, S., Reynolds, G.: Constrained restoration and the recovery of discontinuities. IEEE Transactions on Pattern Analysis and Machine Intelligence 14, 367–383 (1992)

    Article  Google Scholar 

  13. Green, P.J.: Bayesian reconstructions from emission tomography data using a modified EM algorithm. IEEE Transactions on Medical Imaging 9, 84–93 (1990)

    Article  Google Scholar 

  14. Schultz, R.R., Stevenson, R.L.: Stochastic modeling and estimation of multispectral image data. IEEE Transactions on Image Processing 4, 1109–1119 (1995)

    Article  Google Scholar 

  15. Bouman, C., Sauer, K.: A generalized Gaussian image model for edge-preserving MAP estimation. IEEE Transactions on Image Processing 2, 296–310 (1993)

    Article  Google Scholar 

  16. Lange, K.: Convergence of EM image reconstruction algorithms with Gibbs smoothing. IEEE Transactions on Medical Imaging 9, 439–446 (1990)

    Article  Google Scholar 

  17. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., Stahel, W.A.: Robust Statistics: The Approach Based on Influence Functions. Wiley, New York (1986)

    MATH  Google Scholar 

  18. Meer, P., Mintz, D., Rosenfeld, A., Kim, D.Y.: Robust regression methods for computer vision: A review. International Journal of Computer Vision 6(1), 59–70 (1991)

    Article  Google Scholar 

  19. Besl, P.J., Birch, J.B., Watson, L.T.: Robust window operators. In: Second International Conference on Computer Vision, December 5-8, 1988, pp. 591–600 (1988)

    Google Scholar 

  20. Leclerc, Y.G.: Constructing simple stable descriptions for image partitioning. International Journal of Computer Vision 3, 73–102 (1989)

    Article  Google Scholar 

  21. Black, J., Sapiro, G., Marimont, D.H., Heeger, D.: Robust Anisotropic Diffusion. IEEE Transactions on Image Processing 7(3), 421–432 (1998)

    Article  Google Scholar 

  22. Geman, S., McClure, D.: Statistical methods for tomographic image reconstruction. Bulletin of the International Statistical Institute L(II), 4–5 (1987)

    Google Scholar 

  23. Perona, P., Malik, J.: Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence 12(7), 629–639 (1990)

    Article  Google Scholar 

  24. Hebert, T., Leahy, R.: A generalized EM algorithm for 3-D Bayesian reconstruction from Poisson data using Gibbs priors. IEEE Transactions on Medical Imaging 8, 194–202 (1990)

    Article  Google Scholar 

  25. Coupe, P., Yger, P., Prima, S., Hellier, P., Kervrann, C., Barillot, C.: An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images. IEEE Transactions on Medical Imaging 27(4) (April 2008)

    Google Scholar 

  26. Ghazel, M., Freeman, G.H., Vrscay, E.R.: Fractal image denoising. IEEE Transactions on Image Processing 12(12), 1560–1578 (2003)

    Article  Google Scholar 

  27. Pizurica, A., Philips, W.: Estimating probability of presence of a signal of interest in multiresolution single and multiband image denoising. IEEE Transactions on Image Processing 3(15), 654–665 (2006)

    Article  Google Scholar 

  28. Polzehl, J., Spokoiny, V.: Adaptive weights smoothing with application to image restoration. Journal Of The Royal Statistical Society Series B 62(2), 335–354 (2000)

    Article  MathSciNet  Google Scholar 

  29. Portilla, J., Strela, V., Wainwright, M., Simoncelli, E.: Image denoising using scale mixtures of Gaussians in the wavelet domain. IEEE Transactions on Image Processing 12(11), 1338–1351 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  30. Roth, S., Black, M.J.: Fields of experts: A framework for learning image priors with applications. In: proceedings of Computer Vision Pattern Recognition Conference, San Diego, CA (2005)

    Google Scholar 

  31. Orchard, J., Ebrahimi, M., Wong, A.: A Faster Non-local-Means Image Denoising using the FFT. IEEE Transactions on Image Processing (submitted, 2007)

    Google Scholar 

  32. Awate, S., Whitaker, R.: Higher-order image statistics for unsupervised, information-theoretic, adaptive image filtering. In: Proceedings of Computer Vision and Pattern Recognition, pp. 44–51 (2005)

    Google Scholar 

  33. Gilboa, G., Osher, S.: Nonlocal linear image regularization and supervised segmentation. SIAM Journal on Multiscale Modeling and Simulation 6(2), 595–630 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  34. Gilboa, G., Darbon, J., Osher, S., Chan, T.: Nonlocal convex functionals for image regularization, Tech. Rep. CAM-06-57 Dept. Math., Univ. California, Los Angeles (2006)

    Google Scholar 

  35. Brox, T., Kleinschmidt, O., Cremers, D.: Efficient Nonlocal Means for Denoising of Textural Patterns. IEEE Transactions on Image Processing 17(7) (July 2008)

    Google Scholar 

  36. Elad, M., Aharon, M.: Image denoising via sparse and redundant representations over learned dictionaries. IEEE Transactions on Image Processing 54, 3736–3745 (2006)

    Article  MathSciNet  Google Scholar 

  37. Dabov, K., Foi, A., Katkovnik, V., Egiazarian, K.: Image denoising by sparse 3d transform-domain collaborative filtering. IEEE Transactions on Image Processing 16, 2080–2095 (2007)

    Article  MathSciNet  Google Scholar 

  38. Mairal, J., Sapiro, G., Elad, M.: Learning Multiscale sparse representations for image and video restoration. Muliscale Model. Simul. SIAM Journal 7(1), 214–241 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  39. Kervrann, C., Boulanger, J.: Optimal Spatial Adaptation for Patch-Based Image Denoising. IEEE Transactions on Image Processing 15(10) (October 2006)

    Google Scholar 

  40. Kervrann, C., Boulanger, J., Coupe, P.: Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal. In: Sgallari, F., Murli, A., Paragios, N. (eds.) SSVM 2007. LNCS, vol. 4485, pp. 520–532. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  41. Kervrann, C.: An adaptive window approach for image smoothing and structures preserving. In: Proc. Eur. Conf. Computer Vision Prague, Czech Republic (2004)

    Google Scholar 

  42. Mairal, J., Elad, M., Sapiro, G.: Sparse representation for color image restoration. IEEE Transactions on Image Processing 17, 53–69 (2008)

    Google Scholar 

  43. Protter, M., Elad, M.: Image sequence denoising via sparse and redundant representations. In: IEEE Transactions on Image Processing (to appear, 2008)

    Google Scholar 

  44. Takeda, H., Farsiu, S., Milanfar, P.: Kernel regression for image processing and reconstruction. IEEE Transactions on Image Processing 16(2), 349–366 (2007)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. National Institute of Technology Calicut, India

    J. Dinesh Peter, V. K. Govindan & Abraham T. Mathew

Authors
  1. J. Dinesh Peter
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. K. Govindan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Abraham T. Mathew
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science and Engineering, University of Nevada, Reno, USA

    George Bebis

  2. NASA Ames Research Center, Moffett Field, CA, USA

    Richard Boyle

  3. Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    Bahram Parvin

  4. Desert Research Institute, Reno, NV, USA

    Darko Koracin

  5. Digital Image Research Center, Kingston University, London, UK

    Paolo Remagnino

  6. Mitsubishi Electric Research Laboratories, P.O. Box 02139, Cambridge, MA, USA

    Fatih Porikli

  7. Computer and Information Science and Engineering, University of Florida, P.O. Box, FL 32611-6120, Gainsville, USA

    Jörg Peters

  8. IBM T.J. Watson Research Center, 19 Skyline Drive, NY 10532, Hawthorne, USA

    James Klosowski

  9. 128 Memorial Mall, Stewart B001, IN 47907, West Lafayette, USA

    Laura Arns

  10. Denver Museum of Nature and Space, 2001 Colorade Blvd. Denver,, CO 80205, USA

    Yu Ka Chun

  11. Departmen of Computer Science,, NC State University, Campus Box 8206, NC 27695-8206, Raleigh, USA

    Theresa-Marie Rhyne

  12. Los Alamos National Labs, P.O. Box 1663, NM 87545, Los Alamos, USA

    Laura Monroe

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Peter, J.D., Govindan, V.K., Mathew, A.T. (2008). Robust Estimation Approach for NL-Means Filter. In: Bebis, G., et al. Advances in Visual Computing. ISVC 2008. Lecture Notes in Computer Science, vol 5359. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-89646-3_56

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-89646-3_56

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-89645-6

  • Online ISBN: 978-3-540-89646-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation