Skip to main content
SpringerLink
Log in

Bi-dimensional empirical mode decomposition (BEMD) algorithm based on particle swarm optimization-fractal interpolation

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

The performance of interpolation algorithm used in bi-dimensional empirical mode decomposition directly affects its popularization and application. Therefore, the research on interpolation algorithm is more reasonable, accurate and fast. So far, in the interpolation algorithm adopted by the bi-dimensional empirical mode decomposition, an adaptive interpolation algorithm can be proposed according to the image characteristics. In view of this, this paper proposes an image interpolation algorithm based on the particle swarm and fractal. Its procedure includes: to analyze the given image by using the fractal brown function, to pick up the feature quantity from the image, and then to operate the adaptive image interpolation in terms of the obtained feature quantity. The parameters involved in the interpolation process are optimized by particle swarm optimization algorithm, and the optimal parameters are obtained, which can solve the problem of low efficiency and low precision of interpolation algorithm used in bi-dimensional empirical mode decomposition. It solves the problem that the image cannot be decomposed to obtain accurate and reliable bi-dimensional intrinsic modal function, and realize the fast decomposition of the image. It lays the foundation for the further popularization and application of the bi-dimensional empirical mode decomposition algorithm.

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
Fig. 19
Fig. 20

Similar content being viewed by others

References

  1. Akima H, Gebhardt A, Petzoldt T (2013) “akima: interpolation of irregularly spaced data,” R package version 0.5–11, URL http://CRAN.R-project.org/package=akima

  2. Al-Baddai S, Al-Subari K, Tomé AM (2016) A Green’s function-based bi-dimensional empirical mode decomposition. Inf Sci 348:305–321. https://doi.org/10.1016/j.ins.2016.01.089

    Article  MATH  Google Scholar 

  3. Bernini MB, Federico A, Kaufmann GH (2008) Noise reduction in digital speckle pattern interferometry using bi-dimensional empirical mode decomposition. Appl Opt 47(14):2592–2598. https://doi.org/10.1364/AO.47.002592

    Article  Google Scholar 

  4. Bernini MB, Federico A, Kaufmann GH (2009) Normalization of fringe patterns using the bi-dimensional empirical mode decomposition and the Hilbert transform. Appl Opt 48(36):6862–6869. https://doi.org/10.1364/AO.48.006862

    Article  Google Scholar 

  5. Bhuiyan SMA, Attoh-Okine NO, Barner KE (2009) Bi-dimensional empirical mode decomposition using various interpolation techniques. Adv Adapt Data Anal 1(2):309–338. https://doi.org/10.1142/S1793536909000084

    Article  MathSciNet  Google Scholar 

  6. Bornert M, Doumalin P, Dupré JC (2017) Shortcut in DIC error assessment induced by image interpolation used for subpixel shifting. Opt Lasers Eng 91:124–133

    Article  Google Scholar 

  7. Clerc M (2010) Particle swarm optimization. Wiley, Hoboken, pp 321–389

    Google Scholar 

  8. De Boor C, Höllig K, Sabin M (1987) High accuracy geometric Hermite interpolation. Comput Aided Geom Des 4(4):269–278. https://doi.org/10.1016/0167-8396(87)90002-1

    Article  MathSciNet  MATH  Google Scholar 

  9. Falconer K, Fractal geometry: mathematical foundations and applications. Hoboken: Wiley, 2004, pp. 109–139

  10. Falconer K (2012) Fractals: theory and applications in engineering: theory and applications in engineering. Springer Science & Business Media, Berlin, pp 201–289

    Google Scholar 

  11. Goldberg DE (2013) The design of innovation: lessons from and for competent genetic algorithms. Springer Science & Business Media, Berlin, pp 138–165

    Google Scholar 

  12. Grefenstette JJ (2013) Genetic algorithms and their applications: proceedings of the second international conference on genetic algorithms. Psychology Press, London, pp 309–337

    Book  Google Scholar 

  13. Grefenstette JJ (2013) Genetic algorithms and their applications: proceedings of the second international conference on genetic algorithms. Psychology Press, London, pp 109–138

    Book  Google Scholar 

  14. He Z, Wang Q, Shen Y (2013) Multivariate gray model-based BEMD for hyperspectral image classification. IEEE Trans Instrum Meas 62(5):889–904. https://doi.org/10.1109/TIM.2013.2246917

    Article  Google Scholar 

  15. Ke Y, Sukthankar R (2004) PCA-SIFT: A more distinctive representation for local image descriptors. Proceedings of the 2004 IEEE Computer Society Conference on. IEEE, USA, p 506–513

  16. Lei D, Xiaolin H, Feng L (2011) Support vector machines-based method for restraining end effects of B-spline empirical mode decomposition. J Vib Meas Diagn 31(3): 344–347. 3: 1–19

  17. Li T, Wang Y (2011) Biological image fusion using a NSCT based variable-weight method. Inform Fusion 12(2):85–92. https://doi.org/10.1016/j.inffus.2010.03.007

    Article  Google Scholar 

  18. Lin DC, Guo ZL, An FP (2012) Elimination of end effects in empirical mode decomposition by mirror image coupled with support vector regression. Mech Syst Signal Process 31(1):13–28. https://doi.org/10.1016/j.ymssp.2012.02.012

    Article  Google Scholar 

  19. Linderhed A (2005) Variable sampling of the empirical mode decomposition of two-dimensional signals. Int J Wavelets Multiresolution Inf Process 3(3):435–452. https://doi.org/10.1142/S0219691305000932

    Article  MATH  Google Scholar 

  20. Liu Z, Wang H, Peng S (2004) Texture segmentation using directional empirical mode decomposition. In: Proc. ICIP'04, USA, p 279–282

  21. Nunes JC, Bouaouue Y, Delechelle E (2003) Image analysis by bi-dimensional empirical mode decomposition. Image Vis Comput 21(12):1019–1026. https://doi.org/10.1016/S0262-8856(03)00094-5

    Article  Google Scholar 

  22. Nunes JC, Guyot S, Delechelle E (2005) Texture analysis based on local analysis of the bi-dimensional empirical mode decomposition. Mach Vis Appl 16(3):177–188. https://doi.org/10.1007/s00138-004-0170-5

    Article  Google Scholar 

  23. Panichella A, Dit B, Oliveto R (2013) How to effectively use topic models for software engineering tasks? An approach based on genetic algorithms. In: Proceedings of the 2013 International Conference on Software Engineering, USA, p 522–531

  24. Rubin SG, Khosla PK (1977) Polynomial interpolation methods for viscous flow calculations. J Comput Phys 24(3):217–244. https://doi.org/10.1016/0021-9991(77)90036-5

    Article  MathSciNet  MATH  Google Scholar 

  25. Sadeghi B, Yu R, Wang R (2018) Shifting interpolation kernel toward orthogonal projection. IEEE Trans Signal Process 66(1):101–112

    Article  MathSciNet  MATH  Google Scholar 

  26. Sastry K, Goldberg DE, Kendall G (2014) Genetic algorithms. Springer US, Berlin, pp 93–117

    Google Scholar 

  27. Scrucca L (2013) GA: a package for genetic algorithms in R [J]. J Stat Softw 53(4):1–37

    Article  Google Scholar 

  28. Steeb WH (2014) The nonlinear workbook: chaos, fractals, cellular automata, genetic algorithms, gene expression programming, support vector machine, wavelets, hidden Markov models, fuzzy logic with C++, Java and SymbolicC++ programs. World Scientific Publishing Co Inc, Singapore, pp 307–334

    Book  Google Scholar 

  29. Torres IC, Rubio JMA, Ipsen R (2012) Using fractal image analysis to characterize microstructure of low-fat stirred yoghurt manufactured with microparticulated whey protein. J Food Eng 109(4):721–729. https://doi.org/10.1016/j.jfoodeng.2011.11.016

    Article  Google Scholar 

  30. Wang Z, Bovik AC (2009) Mean squared error: love it or leave it? A new look at signal fidelity measures. IEEE Signal Process Mag 26(1):98–117

    Article  Google Scholar 

  31. Wielgus M, Patorski K (2011) Evaluation of amplitude encoded fringe patterns using the bi-dimensional empirical mode decomposition and the 2D Hilbert transform generalizations. Appl Opt 50(28):5513–5523. https://doi.org/10.1364/AO.50.005513

    Article  Google Scholar 

  32. Wu Z, Huang NE, Chen X (2009) The multi-dimensional ensemble empirical mode decomposition method. Adv Adapt Data Anal 1(3):339–372. https://doi.org/10.1142/S1793536909000187

    Article  MathSciNet  Google Scholar 

  33. Xu G, Cheng Q, Zuo R (2016) Application of improved bi-dimensional empirical mode decomposition (BEMD) based on Perona–Malik to identify copper anomaly association in the southwestern Fujian. J Geochem Explor 164:65–74. https://doi.org/10.1016/j.gexplo.2015.09.013

    Article  Google Scholar 

  34. Yin S, Cao L, Ling Y (2010) One color contrast enhanced infrared and visible image fusion method. Infrared Phys Technol 53(2):146–150. https://doi.org/10.1016/j.infrared.2009.10.007

    Article  Google Scholar 

  35. Zhao J, Zhao P, Chen Y (2016) Using an improved BEMD method to analyse the characteristic scale of aeromagnetic data in the Gejiu region of Yunnan, China. Comput Geosci 88(2016):132–141. https://doi.org/10.1016/j.cageo.2015.12.016

    Article  Google Scholar 

  36. Zhou Y, Li H (2011) Adaptive noise reduction method for DSPI fringes based on bi-dimensional ensemble empirical mode decomposition. Opt Express 19(19):18207–18215. https://doi.org/10.1364/OE.19.018207

    Article  Google Scholar 

Download references

Acknowledgements

This work is supported by National Science Foundation Project of P. R. China (No. 61701188).

Author information

Authors and Affiliations

  1. School of Physics and Electronic Electrical Engineering, Huaiyin Normal University, Huaian, 223300, JS, China

    Feng-Ping An

  2. School of Information and Electronics, Beijing Institute of Technology, Beijing, 100081, BJ, China

    Feng-Ping An & Zhi-Wen Liu

Authors
  1. Feng-Ping An
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhi-Wen Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Feng-Ping An.

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

An, FP., Liu, ZW. Bi-dimensional empirical mode decomposition (BEMD) algorithm based on particle swarm optimization-fractal interpolation. Multimed Tools Appl 78, 17239–17264 (2019). https://doi.org/10.1007/s11042-018-7097-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-018-7097-8

Keywords

Search

Navigation