Skip to main content
Log in

Pixon Based Image Denoising Scheme by Preserving Exact Edge Locations

  • Original Contribution
  • Published:
Journal of The Institution of Engineers (India): Series B Aims and scope Submit manuscript

Abstract

Denoising of an image is an essential step in many image processing applications. In any image de-noising algorithm, it is a major concern to keep interesting structures of the image like abrupt changes in image intensity values (edges). In this paper an efficient algorithm for image de-noising is proposed that obtains integrated and consecutive original image from noisy image using diffusion equations in pixon domain. The process mainly consists of two steps. In first step, the pixons for noisy image are obtained by using K-means clustering process and next step includes applying diffusion equations on the pixonal model of the image to obtain new intensity values for the restored image. The process has been applied on a variety of standard images and the objective fidelity has been compared with existing algorithms. The experimental results show that the proposed algorithm has a better performance by preserving edge details compared in terms of Figure of Merit and improved Peak-to-Signal–Noise-Ratio value. The proposed method brings out a denoising technique which preserves edge details.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  1. R.C. Gonzalez, R.E. Woods, Digital Image Processing (Prentice Hall, Englewood Cliffs NJ, 2008)

    Google Scholar 

  2. G. Aubert, P. Kornprobst, Mathematical Problems in Image Processing Partial Differential Equations and the Calculus of Variations, 2nd edn. (Springer, Berlin, 2006)

    MATH  Google Scholar 

  3. F. Catte, P.L. Lions, J.M. Morel, T. Coll, Image selective smoothing and edge detection by nonlinear diffusion. SIAM J. Numer. Anal. 29(1), 182–193 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  4. S.G. Chang, B. Yu, M. Vetterli, Adaptive wavelet thresholding for image denoising and compression. IEEE Trans. Image Process. 9(9), 1532–1545 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  5. M. Jansen, Noise Reduction by Wavelet Thresholding (Springer, New York, 2001)

    Book  MATH  Google Scholar 

  6. A. Handloviová, K. Mikula, F. Sgallari, Variational numerical methods for solving nonlinear diffusion equations arising in image processing. J. Vis. Commun. Image Represent. 13, 217–237 (2002)

    Article  Google Scholar 

  7. H. Hassanpour, H. Yousefian, A. Zehtabian, in Pixon-based image segmentation. ed. by P.-G. Ho, Image Segmentation. (InTech, Rijeka, 2011), pp. 496–516. ISBN:978-953-307-228-9

  8. A.F. Koschan, M.A. Abidi, A comparison of median filter techniques for noise removal in color images. In Proceedings of 7th German Workshop on Color Image Processing, Erlangen, Germany, (2001), pp. 69–79

  9. Z. Krivá, K. Mikula, An adaptive finite volume scheme for solving nonlinear diffusion equations in image processing. J. Vis. Commun. Image Represent. 13, 22–35 (2002)

    Article  Google Scholar 

  10. Q. Lu, T. Jiang, Pixon-based image denoising with Markov random fields. Pattern Recognit. 34, 2029–2039 (2001)

    Article  MATH  Google Scholar 

  11. D. Mittal, V. Kumar, S.C. Saxena, N. Khandelwal, N. Kalra, Enhancement of the ultrasound images by modified anisotropic diffusion method. Med. Biol. Eng. Comput. 48(12), 1281–1291 (2010)

    Article  Google Scholar 

  12. P. Perona, J. Malik, Scale-space and edge detection using anisotropic diffusion. In IEEE Computer Society Workshop on Computer Vision, (1987), pp. 16–27

  13. P. Perona, J. Malik, Scale-space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 127, 629–639 (1990)

    Article  Google Scholar 

  14. R.K. Piña, R.C. Pueter, Bayesian image reconstruction: the pixon and optimal image modeling. Astron. Soc. Pac. 105(688), 630–637 (1993)

    Article  Google Scholar 

  15. R.C. Puetter, Pixon-based multiresolution image reconstruction and the quantification of picture information content. Int. J. Imaging Syst. Technol. 6, 314–331 (1995)

    Article  Google Scholar 

  16. H.G. Senel, R.A. Peteres, B. Dawant, Topological median filters. IEEE Trans. Image Process. 11, 89–104 (2002)

    Article  MathSciNet  Google Scholar 

  17. S.K. Weeratunga, C. Kamath, PDE-based nonlinear diffusion techniques for denoising scientific/industrial images: an empirical study. In Proceedings of Image Processing: Algorithms and Systems (SPIE Electronic Imaging, San Jose), pp. 279–290 (2002)

  18. E. Nadernejad, S. Sharifzadeh, S. Forchhammer, Using anisotropic diffusion equations in pixon domain for image de-noising. SIViP 7(6), 1113–1124 (2013)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Manasani Pompapathi.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Srikrishna, A., Reddy, B.E. & Pompapathi, M. Pixon Based Image Denoising Scheme by Preserving Exact Edge Locations. J. Inst. Eng. India Ser. B 97, 395–403 (2016). https://doi.org/10.1007/s40031-014-0178-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40031-014-0178-9

Keywords

Navigation