Advertisement

Experimental Techniques

, Volume 40, Issue 3, pp 959–971 | Cite as

Removing Quasi-Periodic Noise in Strain Maps by Filtering in the Fourier Domain

  • M. Grédiac
  • F. Sur
  • B. Blaysat
Article

Abstract

Quasi-periodic noise due to various reasons often corrupts strainmaps obtained with full-field measuring systems. The aim of this didactic paper is to show how to remove this noise by changing some Fourier coefficients involved in the two-dimensional (2D) Fourier transform of these strain maps. The basics of the 2D Fourier transform of images, which is a common tool in image processing but that is only scarcely employed in the experimental mechanics community, are first briefly recalled. Several procedures employed for removing undesirable frequencies in strain maps are then discussed. Three different examples illustrate the benefit of this approach.

Keywords

Fourier Transform Grid Method Image Processing Strain Measurement Strain Map Restoration 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Grédiac, M., and Hild, F. (eds), Full-Field Measurements and Identification in Solid Mechanics, Wiley, p. 496, (2012). ISBN: 9781848212947.Google Scholar
  2. 2.
    Badulescu, C., Grédiac, M., and Mathias, J.-D., “Investigation of the Grid Method for Accurate In-Plane Strain Measurement,” Measurement Science and Technology 20: 095102 (2009).CrossRefGoogle Scholar
  3. 3.
    Aizenberg, I., and Butakoff, C., “A Windowed Gaussian Notch Filter for Quasi-Periodic Noise Removal,” Image and Vision Computing 26(10): 1347–1353 (2008).CrossRefGoogle Scholar
  4. 4.
    Sutton, M.A., Orteu, J.-J., and Schreier, H.W., Image Correlation for Shape, Motion and Deformation Measurements—Basic Concepts, Theory and Applications, Springer, New York (2009).Google Scholar
  5. 5.
    Dautriat, J., Bornert, M., Gland, N., Dimanov, A., and Raphanel, J., “Localized Deformation Induced by Heterogeneities in Porous Carbonate Analysed by Multi-Scale Digital Image Correlation,” Tectonophysics 503: 100–116 (2011).CrossRefGoogle Scholar
  6. 6.
    Avril, S., Feissel, P., Pierron, F., and Villon, P., “Estimation of the Strain Field from Full-Field Displacement Noisy Data,” European Journal of Computational Mechanics 17(5–7): 857–868 (2008).Google Scholar
  7. 7.
    Lebrun, M., Colom, M., Buades, A., and Morel, J.-M., “Secrets of Image Denoising Cuisine,” Acta Numerica 21: 475–576 (2012).CrossRefGoogle Scholar
  8. 8.
    Milanfar, P., “A Tour of Modern Image Filtering: New Insights and Methods, Both Practical and Theoretical,” IEEE Signal Processing Magazine 30(1): 106–128 (2013).CrossRefGoogle Scholar
  9. 9.
    Fehrenbach, J., Weiss, P., and Lorenzo, C., “Variational Algorithms to Remove Stationary Noise: Applications to Microscopy Imaging,” IEEE Transactions on Image Processing 21(10): 4420–4430 (2012).CrossRefGoogle Scholar
  10. 10.
    Sur, F., and Grédiac, M., “Automated Removal of Quasi-Periodic Noise through Frequency Domain Statistics,” Journal of Electronic Imaging 24(1): 013003 (2015). DOI: 10.1117/1.JEI.24.1.013003.CrossRefGoogle Scholar
  11. 11.
    Grédiac, M., Toussaint, E., Petit, C., Millien, A., and Nguyen, D.C., “A Comparative Study of the Heterogeneous Local Mechanical Response of Two Types of Asphalt Mixes,” Materials and Structures 47(9): 1513–1529 (2014).CrossRefGoogle Scholar
  12. 12.
    van der Schaaf, A., and van Hateren, J., “Modelling the Power Spectra of Natural Images: Statistics and Information,” Vision Research 36(17): 2759–2770 (1996).CrossRefGoogle Scholar
  13. 13.
    Gonzalez, R.C., and Woods, R.E., Digital Image Processing, 3rd Edition, Prentice Hall, Upper Saddle River, NJ (2008).Google Scholar
  14. 14.
    The MathWorks Inc., MATLAB. version 8.3 (R2014a), The MathWorks Inc., (2014).Google Scholar
  15. 15.
    Gonzalez, R.C., Woods, R.E., and Eddins, S.L., Digital Image Processing Using MATLAB, 2nd Edition, Gatesmark Publishing, Knoxville, TN (2009).Google Scholar
  16. 16.
    Kaur, S., and Singh, R., “An Efficient Method for Periodic Vertical Banding Noise Removal in Satellite Images,” International Journal of Computer Science and Engineering 4(10): 1710–1721 (2012).Google Scholar
  17. 17.
    Wang, J., and Liu, D.C., “2D FFT Periodic Noise Removal on Strain Images,” Proceedings of the 4th International Conference on Bioinformatics and Biomedical Engineering (iCBBE), Chengdu, China, pp 1–4, (2010).Google Scholar
  18. 18.
    Al Hudhud, G.A., and Turner, M., “Digital Removal of Power Frequency Artifacts Using a Fourier Space Median Filter,” IEEE Signal Processing Letters 12(8): 573–576 (2005).CrossRefGoogle Scholar
  19. 19.
    Grédiac, M., and Sur, F., “Effect of Sensor Noise on the Resolution and Spatial Resolution of the Displacement and Strain Maps Obtained with the Grid Method,” Strain 50(1): 1–27 (2014). Paper invited for the 50th anniversary of the journal.Google Scholar
  20. 20.
    Sur, F., and Grédiac, M., “Towards Deconvolution to Enhance the Grid Method for In-Plane Strain Measurement,” Inverse Problems and Imaging 8(1): 259–291 (2014).CrossRefGoogle Scholar

Copyright information

© The Society for Experimental Mechanics, Inc 2016

Authors and Affiliations

  1. 1.Clermont Université,Université Blaise Pascal, Institut PascalClermont-FerrandFrance
  2. 2.Laboratoire Lorrain de Recherche en Informatique et ses ApplicationsUniversité de LorraineVandoeuvre-lès-Nancy CedexFRANCE

Personalised recommendations