Skip to main content
SpringerLink
Log in

An efficient fuzzy inference system based approximated anisotropic diffusion for image de-noising

  • Published:
Cluster Computing Aims and scope Submit manuscript

Abstract

Fuzzy system is proven to be one of the well-effective approximation tool in soft computing techniques. The image de-noising in modern multimedia system is strongly demanded issue which has been focussed in this work and an optimal solution with the help of fuzzy inference technique has been provided. An improved and approximated anisotropic diffusion scheme has been proposed by using fuzzy based diffusion coefficient functions. The anisotropic diffusion has been redefined by formulating the diffusion coefficients in terms of degrees of noisiness of each pixel which tends to sufficiently smooth the impulse noisy pixels along with preservation of edge pixels. The proposed fuzzy rule based diffusion coefficient is applied in basic Perona–Malik diffusion as well as selective advanced diffusion scheme and tested on various standard images at different noise densities. The proposed diffusion scheme based on fuzzy rule shows the effective results on images having impulsive noise densities upto \(50\%\).

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

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
Fig. 15
Fig. 16
Fig. 17
Fig. 18

Similar content being viewed by others

References

  1. Al Shatnawi, A.M., Al Saqqar, F., Souri, A.: Arabic handwritten word recognition based on stationary wavelet transform technique using machine learning. ACM Trans. Asian Low-Resource Lang. Inf. Process. 21(43), 1–21 (2022)

    Google Scholar 

  2. Khan, N.U., Arya, K.V., Pattanaik, M.: An efficient image noise removal and enhancement method. In: 2010 IEEE international conference on systems, man and cybernetics, Istanbul, Turkey, pp. 3735–3740. October 10–13 (2010)

  3. Witkin, A.P.: “Scale-space filtering”. In: Eighth international joint conference on artificial intelligence organization, pp. 1019–1022 (1983)

  4. Annavarapu, A., Borra, S.: Development of magnetic resonance image de-noising methodologies: a comprehensive overview of the state-of-the-art. Smart Health 18, 100–138 (2020)

    Article  Google Scholar 

  5. Chinnaswami, M., Subbaram, S.: Performance evaluation of filters for de-noising the intravascular ultrasound (IVUS) images. Int. J. Inf. Technol. 13, 229–238 (2021)

    Google Scholar 

  6. Thakur, N., Khan, N.U., Sharma, S.: A review on performance analysis of PDE based anisotropic diffusion approaches for image enhancement. Informatica 45, 89–102 (2021)

    Article  Google Scholar 

  7. Chao, L.T.: A new adaptive center weighted median filter for suppressing impulsive noise in images. Inf. Sci. 177, 1073–1087 (2007)

    Article  Google Scholar 

  8. Crnojevic, V., Senk, V., Tropovski, Z.: Advanced impulse detection based on pixel-wise MAD. IEEE Signal Process. Lett. 11(7), 589–592 (2004)

    Article  Google Scholar 

  9. Dong, Y., Xu, S.: A new directional weighted median filter for removal of random valued impulsive noise. IEEE Signal Process. Lett. 14(3), 193–196 (2007)

    Article  Google Scholar 

  10. Cai, J.F., Chan, R.H., Nikolova, M.: Fast two-phase image deblurring under impulse noise. J. Math. Imaging Vision 36(1), 46–53 (2010)

    Article  MathSciNet  Google Scholar 

  11. Weickert, J.: Anisotropic Diffusion in Image Processing, vol. 1. Teubner Stuttgart (1998)

    MATH  Google Scholar 

  12. Perona, P., Malik, J.: Scale space and edge detection using anisotropic diffusion. IEEE Trans. Pattern Anal. Mach. Intell. 12(8), 629–639 (1990)

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Alvarez, L., Lions, P., Morel, J.M.: Image selective smoothing and edge-detection by nonlinear diffusion. II. SIAM J. Numer. Anal. 29, 845–866 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  15. Zimmermann, H.: Fuzzy Set Theory and Its Applications. Springer, Berlin (2001)

    Book  Google Scholar 

  16. Ross, T.J.: Fuzzy Logic with Engineering Applications. Wiley, Chichester (2009)

    Google Scholar 

  17. Shojafar, M., Javanmardi, S., Abolfazli, S., Cordeschi, N.: FUGE: a joint meta heuristic approach to cloud job scheduling algorithm using fuzzy theory and a genetic method. Clust. Comput. 18, 829–844 (2015)

    Article  Google Scholar 

  18. Javanmardi, S., Shojafar, M., Shariatmadari, S., Ahrabi, S.S.: FR trust: a fuzzy reputation based model for trust management in semantic P2P grids. Int. J. Grid Util. Comput. 6(1), 57–66 (2015)

    Article  Google Scholar 

  19. Nadernejad, E., Korhonen, J., Forchhammer, S., Burini, N.: Enhancing perceived quality of compressed images and video with anisotropic diffusion and fuzzy filtering. Signal Process. 28(3), 222–240 (2012)

    Google Scholar 

  20. Wang, H., Fei, B.: A modified fuzzy C-means classification method using a multiscale diffusion filtering scheme. Med. Image Anal. 13(2), 193–202 (2009)

    Article  MathSciNet  Google Scholar 

  21. Schulte, S., Witte, V.D., Nachtegael, M., Weken, D.V., Kerre, E.E.: Fuzzy random impulse noise reduction method. Fuzzy Sets Syst. 158, 270–283 (2007)

    Article  MathSciNet  Google Scholar 

  22. Schulte, S., Witte, V.D., Kerre, E.E.: A fuzzy noise reduction method for color images. IEEE Trans. Image Process. 16(5), 1425–1436 (2007)

    Article  MathSciNet  Google Scholar 

  23. Fu, S., Ruanb, Q., Wanga, W., Gaoa, F., Cheng, H.: A feature-dependent fuzzy bidirectional flow for adaptive image sharpening. Neurocomputing 70, 883–895 (2007)

    Article  Google Scholar 

  24. Aja, S., Alberola, C., Ruiz, J.: Fuzzy anisotropic diffusion for speckle filtering. In: 2001 IEEE international conference on acoustics, speech and signal processing, vol. 2, pp. 31261–31264. May 7–11 (2001)

  25. Puvanathasan, P., Bizheva, K.: Interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in optical coherence tomography images. Opt. Express 17(2), 733–746 (2009)

    Article  Google Scholar 

  26. Yuanfeng, L., Yan, Z.: Accelerating Fuzzy Adaptive Anisotropic Diffusion on GPU. In: 2011 tenth IEEE international conference on electronic measurement and instruments, pp. 175–180. August 16–19 (2011)

  27. Molina, C.L., De Baets, B., Bustince, H.: Generating fuzzy edge images from gradient magnitudes. Comput. Vis. Image Underst. 115(11), 1571–1580 (2011)

    Article  Google Scholar 

  28. Zhang, Y., Cheng, H.D., Tian, J., Huang, J., Tang, X.: Fractional subpixel diffusion and fuzzy logic approach for ultrasound speckle reduction. Patt. Recogn. 43(8), 2962–2970 (2010)

    Article  MATH  Google Scholar 

  29. Khan, N.U., Arya, K.V., Pattanaik, M.: Fuzzy based diffusion coefficient function in anisotropic diffusion for impulse noise removal. In: Eighth Indian conference on vision, graphics and image processing, December 16–19 (2012)

  30. Roy, A., Laskar, R.H.: Region adaptive fuzzy filter: an approach for removal of random-valued impulse noise. IEEE Trans. Ind. Electron. 65(9), 7268–7278 (2018)

    Article  Google Scholar 

  31. Khan, N.U., Arya, K.V.: A new fuzzy rule based pixel organization scheme for optimal edge detection and impulse noise removal. Multimed. Tools Appl. 79, 33811–33837 (2020)

    Article  Google Scholar 

  32. Chen, Y., Barcelos, C., Mair, B.: Smoothing and edge detection by time-varying coupled nonlinear diffusion equations. Comput. Vis. Image Underst. 82, 85–100 (2001)

    Article  MATH  Google Scholar 

  33. Black, M.J., Sapiro, G., Marimont, D.H., Heeger, D.: Robust anisotropic diffusion. IEEE Trans. Image Process. 7(3), 421–432 (1998)

    Article  Google Scholar 

  34. Arya, K.V., Gupta, P., Kalra, P.K., Mitra, P.: Image registration using robust M-estimators. Patt. Recogn. Lett. 28(15), 1957–1968 (2007)

    Article  Google Scholar 

  35. You, Y., Kaveh, M.: Fourth-order partial differential equations for noise removal. IEEE Trans. Image Process. 9(10), 1723–1730 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  36. Gilboa, G., Sochen, N., Zeevi, Y.Y.: Forward and backward diffusion processes for adaptive image enhancement and de-noising. IEEE Trans. Image Process. 11(7), 689–703 (2002)

    Article  Google Scholar 

  37. Smolka, B.: Combined forward and backward anisotropic diffusion filtering of color images. Lecture Notes on Computer Science 2449, pp. 314–320 (2002)

  38. Fang, D., Nanning, Z., Jianru, X.: Image smoothing and sharpening based on nonlinear diffusion equation. Signal Process. 88, 2850–2855 (2008)

    Article  MATH  Google Scholar 

  39. Gilboa, G., Sochen, N., Zeevi, Y.Y.: Image enhancement and de-noising by complex diffusion processes. IEEE Trans. Pattern Anal. Mach. Intell. 26(8), 1020–1036 (2004)

    Article  Google Scholar 

  40. Chen, Q., Montesinos, P., Sun, Q.S., Xia, D.S.: Ramp preserving Perona–Malik model. Signal Process. 90(6), 1963–1975 (2010)

    Article  MATH  Google Scholar 

  41. Tschumperle, D., Deriche, R.: Vector-valued image regularization with PDEs: a common framework for different applications. IEEE Trans. Pattern Anal. Mach. Intell. 27(4), 506–517 (2005)

    Article  Google Scholar 

  42. Yu, J., Wang, Y., Shen, Y.: Noise reduction and edge detection via kernel anisotropic diffusion. Patt. Recogn. Lett. 29, 1496–1503 (2008)

    Article  Google Scholar 

  43. Chao, S.M., Tsai, D.M.: An improved anisotropic diffusion model for detail and edge preserving smoothing. Patt. Recogn. Lett. 31, 2012–2023 (2010)

    Article  Google Scholar 

  44. Khan, N.U., Arya, K.V., Pattanaik, M.: Histogram statistics based variance controlled adaptive threshold in anisotropic diffusion for low contrast image enhancement. Signal Process. 93, 1684–1693 (2012)

    Google Scholar 

  45. Wu, J., Tang, C.: PDE-based random-valued impulse noise removal based on new class of controlling functions. IEEE Trans. Image Process. 20(9), 2428–2438 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  46. Khan, N.U., Arya, K.V., Pattanaik, M.: Edge preservation of impulse noise filtered images by improved anisotropic diffusion. Multimed. Tools Appl. 73, 573–597 (2014)

    Article  Google Scholar 

  47. Nnolim, U.A.: Improved partial differential equation based enhancement for underwater images using local global contrast operators and fuzzy homomorphic processes. IET Image Proc. 11, 1059–1067 (2017)

    Article  Google Scholar 

  48. Du, S., Ibrahim, M., Shehata, M., Badawy, W.: Automatic license plate recognition (ALPR): a state-of-the-art review. IEEE Trans. Circ. Syst. Video Technol. 23(2), 311–325 (2013)

    Article  Google Scholar 

  49. Zhang, Y., Li, X., Gao, X., Zhang, C.: A simple algorithm of superpixel segmentation with boundary constraint. IEEE Trans. Circ. Syst. Video Technol. 27(7), 1502–1514 (2017)

    Google Scholar 

  50. Abdou, I.E., Pratt, W.K.: Quantitative design and evaluation of enhancement/thresholding edge detectors. Proc. IEEE 67(5), 753–763 (1979)

    Article  Google Scholar 

  51. Wang, Z., Bovik, A.C., Shaikh, H.R., Simoncelli, E.P.: Image quality assessment: from error visibility to structural similarity. IEEE Trans. Image Process. 13, 600–612 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Jaypee University of Information Technology, Waknaghat, Solan, HP, India

    Niveditta Thakur, Nafis Uddin Khan & Sunil Datt Sharma

Authors
  1. Niveditta Thakur
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nafis Uddin Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sunil Datt Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nafis Uddin Khan.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Thakur, N., Khan, N.U. & Sharma, S.D. An efficient fuzzy inference system based approximated anisotropic diffusion for image de-noising. Cluster Comput 25, 4303–4323 (2022). https://doi.org/10.1007/s10586-022-03642-y

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10586-022-03642-y

Keywords

Search

Navigation