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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
Article

Abstract

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.

Keywords

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

Nomenclature

ci

basis coefficient

F

cost function

v

intensity value

Hi

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

I

acquired image

A

additive shading component

I′

estimated true image

\(G_\sigma \)

Gaussian smoothed version of the structure tensor G

Bi

low-degree polynomial basis

\(D_\alpha \)

mixed partial derivative operator

M

multiplicative shading component

\(t_\alpha ^\beta \)

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

Ii

spatial gradient of the ith channel

G

structure tensor

T

tensor field

y

variable of the height of an image

x

variable of the width of an image

\(w_\alpha \)

weight function

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

estimated function fitted to the first n bins

η(v)

frequency function of pixel intensities

E(n)

root mean squared error

τ

threshold value

ζ, γ

parameters of an exponential function

Ω

a set of all partial derivative

G

maximum gray level value

Notes

Acknowledgment

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.

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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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