Food and Bioprocess Technology

, Volume 2, Issue 2, pp 167–176 | Cite as

Retrospective Shading Correction of Confocal Laser Scanning Microscopy Beef Images for Three-Dimensional Visualization

  • Cheng-Jin Du
  • Da-Wen Sun


Because of the inherent imperfections of the image formation process, confocal laser scanning microscopy (CLSM) images are often corrupted by spurious intensity variations not present in the original scene, which is usually referred to as shading or intensity inhomogeneity. In this paper, a retrospective shading correction method for CLSM beef images was developed using a hybrid of image processing algorithms. A partial-differential-equation-based diffusion technique was applied, firstly, to reduce the additive shading component. To reduce the computational burden, a thresholding segmentation method was then presented to separate the muscle tissues from the background. After that, a robust, automatic, and fast method was applied for reduction of multiplicative shading component. The corrected images were finally used to construct a three-dimensional beef image, which could provide a valuable source of knowledge about beef microstructure that cannot be obtained via traditional two-dimensional images.


Beef Confocal laser scanning microscopy Partial differential equation Shading correction Three-dimensional reconstruction 



basis coefficient


cost function


intensity value


Hessian matrix of the vector channel I i

\(f_ \pm \)

weighting functions to obtain regularization behavior

\(I_{\log } ,M_{\log } ,I_{\log }^\prime \)

log-transform of I, M, I′, respectively


acquired image


additive shading component


estimated true image

\(G_\sigma \)

Gaussian smoothed version of the structure tensor G


low-degree polynomial basis

\(D_\alpha \)

mixed partial derivative operator


multiplicative shading component

\(t_\alpha ^\beta \)

scalar equal to β-percentile of all elements of the matrix \(I_{\log }^\alpha \)


spatial gradient of the ith channel


structure tensor


tensor field


variable of the height of an image


variable of the width of an image

\(w_\alpha \)

weight function

\(\hat \eta _n (v)\)

estimated function fitted to the first n bins


frequency function of pixel intensities


root mean squared error


threshold value

ζ, γ

parameters of an exponential function


a set of all partial derivative


maximum gray level value



The authors wish to acknowledge the Government of Ireland Postdoctoral Fellowship in Science, Engineering and Technology, funded by the Irish Research Council for Science, Engineering and Technology, and the Academy Exchange Scheme Fellowship, funded by both Royal Irish and Hungarian Academies of Sciences. Furthermore, we would like to thank Prof. Ferenc Firtha and Prof. Jozsef Felfoldi (Physics–Control Department, Faculty of Food Science, Corvinus University of Budapest, Somlói út 14–16, H-1118 Budapest, Hungary) for their help, supporting me in my 2-week visit to their department and providing useful information.


  1. Atkinson, K. (1989). An introduction to numerical analysis (2nd ed.). New York: Wiley.Google Scholar
  2. Aubert, G., & Kornprobst, P. (2002). Mathematical problems in image processing: PDE’s and the calculus of variations. Applied mathematical sciences, vol. 147. New York: Springer.Google Scholar
  3. Black, M. J., Sapiro, G., Marimont, D. H., & Heeger, D. (1998). Robust anisotropic diffusion. IEEE Transactions on Image Processing, 7(3), 421–432.CrossRefGoogle Scholar
  4. Canny, J. (1986). A computational approach to edge detection. IEEE Transactions on Pattern Analysis and Machine Intelligence, 8, 679–714.CrossRefGoogle Scholar
  5. Catmull, E. (1975). Computer display of curved surfaces. Proceedings of IEEE Conference on computer graphics pattern recognition data structures, Los Angeles, IEEE, NY, 75CHO981-1C, pp. 11–17.Google Scholar
  6. Gonzalez, R., & Woods, E. (2002). Digital image processing (2nd ed.). Prentice Hall: Upper Saddle River, NJ.Google Scholar
  7. Ko, S., & Gunasekaran, S. (2007). Error correction of confocal microscopy images for in situ food microstructure evaluation. Journal of Food Engineering, 79, 935–944.CrossRefGoogle Scholar
  8. Lee S.-C., & Bajcsy, P. (2006). Spatial intensity correction of fluorescent confocal laser scanning microscope images. European Conference on Computer Vision workshop on Computer Vision Approaches to Medical Image Analysis (ECCV/CVAMIA 06), Graz, Austria.Google Scholar
  9. Lichtenbelt, B., Crane, R., & Naqvi, S. (1998). Introduction to volume rendering (Hewlett-Packard Professional Books). Upper Saddle River, NJ: Prentice Hall.Google Scholar
  10. Likar, B., Maintz, J. B., Viergever, M. A., & Pernus, F. (2000). Retrospective shading correction based on entropy minimization. Journal of Microscopy, 197(3), 285–295.CrossRefGoogle Scholar
  11. Milchenko, M. V., Pianykh, O. S., & Tyler, J. M. (2006). The fast automatic algorithm for correction of MR bias field. Journal of Magnetic Resonance Imaging, 24(4), 891–900.CrossRefGoogle Scholar
  12. Model, M. A., & Burkhardt, J. K. (2001). A standard for calibration and shading correction of a fluorescence microscope. Cytometry, 44(4), 309–316.CrossRefGoogle Scholar
  13. Perona, P., & Malik, J. (1990). Scale-space and edge detection using anisotropic diffusion. IEEE Transactions on Pattern Analysis and Machine Intelligence, 12(7), 629–639.CrossRefGoogle Scholar
  14. Pisano, E., Zong, S., Hemminger, M., De Luca, M., Johnsoton, R., Muller, K., et al. (1998). Contrast limited adaptive histogram equalization image processing to improve the detection of simulated spiculations in dense mammograms. Journal of Digital Imaging, 11(4), 193–200.CrossRefGoogle Scholar
  15. Prachaiyo, P., & McLandsborough, L. A. (2000). A microscopic method to visualize Escherichia coli interaction with beef muscle. Journal of Food Protection, 63(4), 427–433.Google Scholar
  16. Rainville, E. D. (1946). Symbolic relations among classical polynomials. The American Mathematical Monthly, 53(6), 299–305.CrossRefGoogle Scholar
  17. Rasband, W. S. (2007). ImageJ, U.S. National Institutes of Health, Bethesda, MD, USA. Retrieved from
  18. Russ, J. C. (1995). The image processing handbook (2nd ed.). Boca Raton, FL: IEEE Press.Google Scholar
  19. Sandison, D., & Webb, W. (1994). Background rejection and signal-to-noise optimization in the confocal and alternative fluorescence microscopes. Applied Optics, 33, 603–610.CrossRefGoogle Scholar
  20. Tomaževič, D., Likar, B., & Pernuš, F. (2002). Comparative evaluation of retrospective shading correction methods. Journal of Microscopy, 208(3), 212–223.CrossRefGoogle Scholar
  21. Tschumperle, D., & Deriche, R. (2005). Vector-valued image regularization with PDEs: A common framework for different applications. IEEE Transactions on Pattern Analysis and Machine Intelligence, 27(4), 506–517.CrossRefGoogle Scholar
  22. Weisstein, E.W. (2007). Least squares fitting-exponential. Mathworld—a Wolfram web resource. Retrieved from
  23. Young, I.T., Gerbrands, J. J., & Vliet, L. J. (1999). Image processing fundamentals. In V. K. Madisetti, & D. B. Williams (Eds.)The digital signal processing handbook. Boca Raton, FL: CRC Press.Google Scholar

Copyright information

© Springer Science + Business Media, LLC 2007

Authors and Affiliations

  1. 1.Biosystems Engineering, School of Agriculture, Food Science and Veterinary Medicine, College of Life Sciences, University College DublinNational University of IrelandDublin 2Ireland

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