Abstract

We present a novel joint nonuniform illumination estimation and deblurring method for bar code signals based on a penalized nonlinear squares objective function. The objective function is based on the proper parameterization of a bar code signal and nonuniform illumination as well as a regularization on the illumination using a smoothness penalty. By the minimization of the objective function, the proposed method simultaneously estimates the bar code signal and illumination in the spatial domain. In simulations and experiments, the proposed method showed improved performance compared with two conventional bar code decoding methods without deblurring or nonuniform illumination correction. In a few iterations, the proposed method was able to decode test bar code signals that were not decodable due to blurring or nonuniform illumination.

© 2007 Optical Society of America

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  1. E. Joseph and T. Pavlids, "Deblurring of bilevel waveforms," IEEE Trans. Image Process. 2, 223-235 (1993).
    [CrossRef] [PubMed]
  2. E. Joseph and T. Pavlids, "Bar code waveform recognition using peak locations," IEEE Trans. Pattern Anal. Mach. Intell. 16, 630-640 (1994).
    [CrossRef]
  3. S. Esedoglu, "Blind deconvolution of bar code signals," Inverse Probl. 20, 121-135 (2004).
    [CrossRef]
  4. E. Marom, S. Krešić-Jurić, and L. Bergstein, "Analysis of speckle noise in bar-code scanning systems," J. Opt. Soc. Am. A 18, 889-901 (2001).
    [CrossRef]
  5. E. Marom, S. Krešić-Jurić, and L. Bergstein, "Speckle noise in bar-code scanning systems-power spectral density and SNR," Appl. Opt. 42, 161-174 (2003).
    [CrossRef] [PubMed]
  6. S. Krešić-Jurić, "Edge detection in bar code signals corrupted by integrated time-varying speckle," Pattern Recogn. 38, 2483-2493 (2005).
    [CrossRef]
  7. L. Qu and Y. C. Tu, "Change point estimation of bilevel functions," J. Mod. Appl. Stat. Meth. 5, 347-355 (2006).
  8. R. C. Palmer, The bar code book: reading, printing and specification of bar code symbols (Helmers Publishing Inc. 1999).
  9. J. S. Chen and G. Medioni, "Detection, localization and estimation of edges," IEEE Trans. Pattern Anal. Mach. Intell. 11, 191-198 (1989).
    [CrossRef]
  10. M. D. Sanner, "Ambient illumination bar code reader," U. S. Patent 4,874,933 (1989).
  11. J. Debiez and F. Lerat, "Intelligent light source," U. S. Patent 6,774,893 B2 (2004).
  12. R. Shams and P. Sadeghi, "Bar code recognition in highly distorted and low resolution images," in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2007) pp. 737-740.
  13. D. A. Forsyth and J. Ponce, Computer vision: A modern approach (Prentice Hall, 2003).
  14. T. Chen, W. Yin, X. S. Zhou, D. Comaniciu, and T. S. Huang, "Total variation models for variable lighting face recognition," IEEE Trans. Pattern Anal. Mach. Intell. 28, 1519-1524 (2006).
    [CrossRef] [PubMed]
  15. D. Tomazevic, B. Likar, and F. Pernus, "Comparative evaluation of retrospective shading correction methods," J. Microsc. 208, 212-223 (2002).
    [CrossRef] [PubMed]
  16. Z. Hou, "A review on MR image inhomogeneity correction," Int. J. Biomed. Imaging 2006, 1-11 (2006).
    [CrossRef]
  17. B. Likar, J. B. A. Maintz, M. A. Viergever, and F. Pernus, "Retrospective shading correction based on entropy minimization," J. Microsc. 197, 285-295 (2000).
    [CrossRef] [PubMed]
  18. B. H. Brinkmann, A. Manduca, and R. A. Robb, "Optimized homomorphic unsharp masking for MR grayscale inhomogeneity correction," IEEE Trans. Med. Imag. 17, 161-171 (1998).
    [CrossRef]
  19. J. G. Sled, A. P. Zijdenbos, and A. C. Evans, "A nonparametric method for automatic correction of intensity nonuniformity in MRI data," IEEE Trans. Med. Imag. 17, 87-97 (1998).
    [CrossRef]
  20. M. S. Brown and Y. C. Tsoi, "Geometric and shading correction for images of printed materials using boundary," IEEE Trans. Image Process. 15, 1544-1554 (2006).
    [CrossRef] [PubMed]
  21. M. Unser, "Splines: A perfect fit for signal and image processing," IEEE Signal Process. Mag. 16, 22-38 (1999).
    [CrossRef]
  22. D. G. Bailey, "Super-resolution of bar codes," J. Electron. Imag. 10, 213-220 (2001).
    [CrossRef]
  23. Y. C. Eldar, A. Ben-Tal, and A. Nemirovski, "Robust mean-squared error estimation in the presence of model uncertainties," IEEE Trans. Signal Process. 53, 168-181 (2005).
    [CrossRef]
  24. M. Gulliksson, "KKT conditions for rank-deficient nonlinear least-squares problems with rank-deficient nonlinear constraints," J. Optim. Theor. Appl. 100, 145-160 (1999).
    [CrossRef]
  25. P. E. Gill and W. Murray, "Algorithms for the solution of the nonlinear least-squares problem," SIAM J. Numer. Anal. 15, 977-992 (1978).
    [CrossRef]
  26. J. Eriksson, P. A. Wedin, M. E. Gulliksson, and I. Soderkvist, "Regularization methods for uniformly rankdeficient nonlinear least-squares problems," J. Optim. Theor. Appl. 127, 1-26 (2005).
    [CrossRef]
  27. E. Kreyszig, Advanced Engineering Mathematics, 8th ed. (Wiley, 1998).
  28. J. A. Fessler, "Penalized weighted least-squares image reconstruction for positron emission tomography," IEEE.Trans. Med. Imag. 13, 290-300 (1997).
    [CrossRef]
  29. J. Kim, Intensity-based image registration using robust similarity measure and constrained optimization: Applications for radiation therapy, Ph.D. dissertation, The University of Michigan, Ann Arbor, 2004.
    [PubMed]
  30. P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic Press, 1981).
  31. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++, 2nd ed. (Cambridge, 2005).

2006 (4)

L. Qu and Y. C. Tu, "Change point estimation of bilevel functions," J. Mod. Appl. Stat. Meth. 5, 347-355 (2006).

Z. Hou, "A review on MR image inhomogeneity correction," Int. J. Biomed. Imaging 2006, 1-11 (2006).
[CrossRef]

T. Chen, W. Yin, X. S. Zhou, D. Comaniciu, and T. S. Huang, "Total variation models for variable lighting face recognition," IEEE Trans. Pattern Anal. Mach. Intell. 28, 1519-1524 (2006).
[CrossRef] [PubMed]

M. S. Brown and Y. C. Tsoi, "Geometric and shading correction for images of printed materials using boundary," IEEE Trans. Image Process. 15, 1544-1554 (2006).
[CrossRef] [PubMed]

2005 (2)

S. Krešić-Jurić, "Edge detection in bar code signals corrupted by integrated time-varying speckle," Pattern Recogn. 38, 2483-2493 (2005).
[CrossRef]

Y. C. Eldar, A. Ben-Tal, and A. Nemirovski, "Robust mean-squared error estimation in the presence of model uncertainties," IEEE Trans. Signal Process. 53, 168-181 (2005).
[CrossRef]

2004 (1)

S. Esedoglu, "Blind deconvolution of bar code signals," Inverse Probl. 20, 121-135 (2004).
[CrossRef]

2003 (1)

2002 (1)

D. Tomazevic, B. Likar, and F. Pernus, "Comparative evaluation of retrospective shading correction methods," J. Microsc. 208, 212-223 (2002).
[CrossRef] [PubMed]

2001 (2)

E. Marom, S. Krešić-Jurić, and L. Bergstein, "Analysis of speckle noise in bar-code scanning systems," J. Opt. Soc. Am. A 18, 889-901 (2001).
[CrossRef]

D. G. Bailey, "Super-resolution of bar codes," J. Electron. Imag. 10, 213-220 (2001).
[CrossRef]

2000 (1)

B. Likar, J. B. A. Maintz, M. A. Viergever, and F. Pernus, "Retrospective shading correction based on entropy minimization," J. Microsc. 197, 285-295 (2000).
[CrossRef] [PubMed]

1999 (2)

M. Unser, "Splines: A perfect fit for signal and image processing," IEEE Signal Process. Mag. 16, 22-38 (1999).
[CrossRef]

M. Gulliksson, "KKT conditions for rank-deficient nonlinear least-squares problems with rank-deficient nonlinear constraints," J. Optim. Theor. Appl. 100, 145-160 (1999).
[CrossRef]

1998 (2)

B. H. Brinkmann, A. Manduca, and R. A. Robb, "Optimized homomorphic unsharp masking for MR grayscale inhomogeneity correction," IEEE Trans. Med. Imag. 17, 161-171 (1998).
[CrossRef]

J. G. Sled, A. P. Zijdenbos, and A. C. Evans, "A nonparametric method for automatic correction of intensity nonuniformity in MRI data," IEEE Trans. Med. Imag. 17, 87-97 (1998).
[CrossRef]

1997 (1)

J. A. Fessler, "Penalized weighted least-squares image reconstruction for positron emission tomography," IEEE.Trans. Med. Imag. 13, 290-300 (1997).
[CrossRef]

1994 (1)

E. Joseph and T. Pavlids, "Bar code waveform recognition using peak locations," IEEE Trans. Pattern Anal. Mach. Intell. 16, 630-640 (1994).
[CrossRef]

1993 (1)

E. Joseph and T. Pavlids, "Deblurring of bilevel waveforms," IEEE Trans. Image Process. 2, 223-235 (1993).
[CrossRef] [PubMed]

1989 (1)

J. S. Chen and G. Medioni, "Detection, localization and estimation of edges," IEEE Trans. Pattern Anal. Mach. Intell. 11, 191-198 (1989).
[CrossRef]

1978 (1)

P. E. Gill and W. Murray, "Algorithms for the solution of the nonlinear least-squares problem," SIAM J. Numer. Anal. 15, 977-992 (1978).
[CrossRef]

Appl. Opt. (1)

IEEE Signal Process. Mag. (1)

M. Unser, "Splines: A perfect fit for signal and image processing," IEEE Signal Process. Mag. 16, 22-38 (1999).
[CrossRef]

IEEE Trans. Image Process. (2)

M. S. Brown and Y. C. Tsoi, "Geometric and shading correction for images of printed materials using boundary," IEEE Trans. Image Process. 15, 1544-1554 (2006).
[CrossRef] [PubMed]

E. Joseph and T. Pavlids, "Deblurring of bilevel waveforms," IEEE Trans. Image Process. 2, 223-235 (1993).
[CrossRef] [PubMed]

IEEE Trans. Med. Imag. (2)

B. H. Brinkmann, A. Manduca, and R. A. Robb, "Optimized homomorphic unsharp masking for MR grayscale inhomogeneity correction," IEEE Trans. Med. Imag. 17, 161-171 (1998).
[CrossRef]

J. G. Sled, A. P. Zijdenbos, and A. C. Evans, "A nonparametric method for automatic correction of intensity nonuniformity in MRI data," IEEE Trans. Med. Imag. 17, 87-97 (1998).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (3)

E. Joseph and T. Pavlids, "Bar code waveform recognition using peak locations," IEEE Trans. Pattern Anal. Mach. Intell. 16, 630-640 (1994).
[CrossRef]

J. S. Chen and G. Medioni, "Detection, localization and estimation of edges," IEEE Trans. Pattern Anal. Mach. Intell. 11, 191-198 (1989).
[CrossRef]

T. Chen, W. Yin, X. S. Zhou, D. Comaniciu, and T. S. Huang, "Total variation models for variable lighting face recognition," IEEE Trans. Pattern Anal. Mach. Intell. 28, 1519-1524 (2006).
[CrossRef] [PubMed]

IEEE Trans. Signal Process. (1)

Y. C. Eldar, A. Ben-Tal, and A. Nemirovski, "Robust mean-squared error estimation in the presence of model uncertainties," IEEE Trans. Signal Process. 53, 168-181 (2005).
[CrossRef]

Int. J. Biomed. Imaging (1)

Z. Hou, "A review on MR image inhomogeneity correction," Int. J. Biomed. Imaging 2006, 1-11 (2006).
[CrossRef]

Inverse Probl. (1)

S. Esedoglu, "Blind deconvolution of bar code signals," Inverse Probl. 20, 121-135 (2004).
[CrossRef]

J. Electron. Imag. (1)

D. G. Bailey, "Super-resolution of bar codes," J. Electron. Imag. 10, 213-220 (2001).
[CrossRef]

J. Microsc. (2)

B. Likar, J. B. A. Maintz, M. A. Viergever, and F. Pernus, "Retrospective shading correction based on entropy minimization," J. Microsc. 197, 285-295 (2000).
[CrossRef] [PubMed]

D. Tomazevic, B. Likar, and F. Pernus, "Comparative evaluation of retrospective shading correction methods," J. Microsc. 208, 212-223 (2002).
[CrossRef] [PubMed]

J. Mod. Appl. Stat. Meth. (1)

L. Qu and Y. C. Tu, "Change point estimation of bilevel functions," J. Mod. Appl. Stat. Meth. 5, 347-355 (2006).

J. Opt. Soc. Am. A (1)

E. Marom, S. Krešić-Jurić, and L. Bergstein, "Analysis of speckle noise in bar-code scanning systems," J. Opt. Soc. Am. A 18, 889-901 (2001).
[CrossRef]

J. Optim. Theor. Appl. (1)

M. Gulliksson, "KKT conditions for rank-deficient nonlinear least-squares problems with rank-deficient nonlinear constraints," J. Optim. Theor. Appl. 100, 145-160 (1999).
[CrossRef]

Pattern Recogn. (1)

S. Krešić-Jurić, "Edge detection in bar code signals corrupted by integrated time-varying speckle," Pattern Recogn. 38, 2483-2493 (2005).
[CrossRef]

SIAM J. Numer. Anal. (1)

P. E. Gill and W. Murray, "Algorithms for the solution of the nonlinear least-squares problem," SIAM J. Numer. Anal. 15, 977-992 (1978).
[CrossRef]

Trans. Med. Imag. (1)

J. A. Fessler, "Penalized weighted least-squares image reconstruction for positron emission tomography," IEEE.Trans. Med. Imag. 13, 290-300 (1997).
[CrossRef]

Other (10)

J. Kim, Intensity-based image registration using robust similarity measure and constrained optimization: Applications for radiation therapy, Ph.D. dissertation, The University of Michigan, Ann Arbor, 2004.
[PubMed]

P. E. Gill, W. Murray, and M. H. Wright, Practical Optimization (Academic Press, 1981).

W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in C++, 2nd ed. (Cambridge, 2005).

J. Eriksson, P. A. Wedin, M. E. Gulliksson, and I. Soderkvist, "Regularization methods for uniformly rankdeficient nonlinear least-squares problems," J. Optim. Theor. Appl. 127, 1-26 (2005).
[CrossRef]

E. Kreyszig, Advanced Engineering Mathematics, 8th ed. (Wiley, 1998).

R. C. Palmer, The bar code book: reading, printing and specification of bar code symbols (Helmers Publishing Inc. 1999).

M. D. Sanner, "Ambient illumination bar code reader," U. S. Patent 4,874,933 (1989).

J. Debiez and F. Lerat, "Intelligent light source," U. S. Patent 6,774,893 B2 (2004).

R. Shams and P. Sadeghi, "Bar code recognition in highly distorted and low resolution images," in Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (IEEE, 2007) pp. 737-740.

D. A. Forsyth and J. Ponce, Computer vision: A modern approach (Prentice Hall, 2003).

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Figures (13)

Fig. 1.
Fig. 1.

2D image and 1D signal for UPC bar code representing ‘012345678905‘: (a) 2D UPC bar code image; (b) 1D ideal bar code signal.

Fig. 2.
Fig. 2.

Synthetic blurred bar code signals with nonuniform illuminations: (a) synthetic blurred bar code signal; (b) synthetic nonuniform illuminations; (c) synthetic observation with the Gaussian illumination; (d) synthetic observation with the linear illumination.

Fig. 3.
Fig. 3.

Fitted signals for the observation in Fig. 2(c) using the three methods, plus the estimated illumination by the proposed method: (a) fitted bar code signal using the edge method; (b) fitted bar code signal using the NLS-UI method; (c) fitted bar code signal using the proposed method; (d) estimated illumination by the proposed method.

Fig. 4.
Fig. 4.

Estimated lengths of patterns for the signal shown in Fig. 2(c) using the three methods: (a) the edge method; (b) the NLS-UI method; (c) the proposed method.

Fig. 5.
Fig. 5.

Estimated nonuniform illuminations for the signals shown in Fig. 2(c) and Fig. 2(d) with different λ values: (a) for the signal shown in Fig. 2(c); (b) for the signal shown in Fig. 2(d).

Fig. 6.
Fig. 6.

Change of the objective functions and ME during iterations for the signals shown in Fig. 2(c) and Fig. 2(d): (a) the objective function for the signal shown in Fig. 2(c); (b) the ME for the signal shown in Fig. 2(c); (c) the objective function for the signal shown in Fig. 2(d); (d) the ME for the signal shown in Fig. 2(d).

Fig. 7.
Fig. 7.

Bar code images under nonuniform illumination: (a) bar code image whose central part is brighter due to nonuniform illumination; (b) bar code image whose left part is brighter due to nonuniform illumination; (c) horizontal line scan of the image in (a); (d) horizontal line scan of the image in (b).

Fig. 8.
Fig. 8.

Fitted signals for the observation in Fig. 7(c)) using the three methods, plus the estimated illumination using the proposed method: (a) the edge method; (b) the NLS-UI method; (c) the proposed method; (d) estimated illumination by the proposed method with λ= 10.

Fig. 9.
Fig. 9.

Fitted signals for the observation in Fig. 7(d) by the three methods, plus the estimated illumination by the proposed method: (a) the edge method; (b) the NLS-UI method; (c) the proposed method; (d) estimated illumination by the proposed method with λ= 10.

Fig. 10.
Fig. 10.

Estimated lengths of patterns by the three methods for the signal in Fig. 7(c): (a) the edge method; (b) the NLS-UI method; (c) the proposed method.

Fig. 11.
Fig. 11.

Estimated lengths of patterns by the three methods for the signal in Fig. 7(d): (a) the edge method; (b) the NLS-UI method; (c) the proposed method.

Fig. 12.
Fig. 12.

Estimated nonuniform illuminations for the signals shown in Fig. 7(c) and Fig. 7(d) with different λ values: (a) for the signal shown in Fig. 7(c); (b) for the signal shown in Fig. 7(d).

Fig. 13.
Fig. 13.

Change of the objective functions during iterations for the signals shown in Fig. 7(c) and Fig. 7(d): (a) for the signal shown in Fig. 7(c); (b) for the signal shown in Fig. 7(d).

Tables (3)

Tables Icon

Table 1. Average ME values of the three methods for the signal shown in Fig. 2(c) with different size blurring kernels and SNR values (the unit for ME value is 10-3).

Tables Icon

Table 2. Average ME values of the three methods for the signal shown in Fig. 2(d) with different size blurring kernels and SNR values (the unit for ME value is 10-3).

Tables Icon

Table 3. Decode rate values of the three methods for the signal shown in Fig. 2(c) with different size blurring kernels and SNR values (the unit for decode rate is %.)

Equations (24)

Equations on this page are rendered with MathJax. Learn more.

y ( t ) = I ( t ) [ G ( t ) x ( t ) + c ] + n ( t ) ,
x ( t ; e ) = i = 1 K ( 1 ) i 1 u ( t e i ) ,
G ( t ; σ ) = 1 2 π σ 2 e t 2 2 σ 2 .
I ( t ; b ) = j = 1 L b j β 3 ( t l j ) ,
θ ̂ = arg min θ F ( θ ) ,
F ( θ ) = 1 2 i = 1 M [ f i ( θ ) ] 2 ,
f i ( θ ) = y ( t i ) I ( t i ; b ) [ G ( t i ; σ ) x ( t i ; e ) ] ,
θ F ( θ ) | θ = θ ̂ = J ( θ ) T f ( θ ) | θ = θ ̂ = 0 ,
[ J ( θ ) ] ij = f i ( θ ) θ j .
θ 2 F ( θ ˜ ) J ( θ ˜ ) T J ( θ ˜ ) ,
[ θ 2 F ( θ ) ] ij = 2 F ( θ ) θ i θ j .
I ( t i ; b 1 ) [ G ( t i ; σ 1 ) x ( t i ; e i ) + c 1 ] = I ( t i ; b 2 ) [ G ( t i ; σ 2 ) x ( t i ; e 2 ) + c 2 ] , i = 1 , , M .
h J ( θ ˜ ) T = 0 ,
θ s T J s ( θ ˜ s ) T J ( θ ˜ s ) θ s > 0 ,
θ s T J s ( θ ˜ s ) T J ( θ ˜ s ) θ s = θ u T J u ( θ ˜ u ) T J ( θ ˜ u ) θ u ,
J ( θ ˜ ) = J ( θ ˜ u ) ,
θ u T J ( θ ˜ ) T J ( θ ˜ ) θ u > 0 .
Φ ( θ ) = 1 2 i = 0 M [ f i ( θ ) ] 2 + λ R ( θ ) ,
R ( θ ) = 1 2 θ T R θ = j = 1 L 1 ( b j b j + 1 ) 2 ,
θ 2 Φ ( θ ˜ ) J ( θ ˜ ) T J ( θ ˜ ) + λ R .
θ T J ( θ ˜ ) T J ( θ ˜ ) θ + λ θ T R θ > 0 .
θ k + 1 = θ k H ( θ k ) 1 J ( θ k ) T f ( θ k ) , k = 1,2 ,
Δ ̂ i = t ̂ i + 1 t ̂ i i = 1,2 , , K 1 ,
ME = max i t ̂ i t i true , i = 1,2 , , K ,

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