Abstract

A multiresolution-analysis-based local contrast transform is proposed to enhance local structures in x-ray images. The local contrast is defined as a ratio of the local intensity variation to the local mean. With wavelet multiresolution decomposition, the detail coefficients and approximation coefficients are interpreted, respectively, as local variations and local averages in virtue of the localization property of wavelet transform. Based on the local contrast transform, an algorithm is developed to modify coefficients before wavelet synthesis. An across-scale local contrast is obtained when the scale associated with the local variation is different from that of the local mean. The nonlinearity and local adaptiveness properties of local contrast transform result in structural enhancement in local dark regions in the reconstructed images. We applied this technique to deboned poultry inspection using x-ray images. Because of its high x-ray absorption, a foreign inclusion appears as a low-intensity object in an x-ray image, thus resulting in contrast enhancement in the reconstructed multiresolution images.

© 2001 Optical Society of America

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References

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  1. T. F. Schatzki, R. Young, R. P. Haff, J. G. Eye, G. R. Wright, “Visual detection of particulates in x-ray images of processed meat products,” Opt. Eng. 35, 2286–2291 (1996).
    [CrossRef]
  2. R. Zwiggelaar, C. R. Bull, M. J. Mooney, “X-ray simulations for imaging applications in the agricultural and food industries,” J. Agric. Eng. Res. 63, 161–170 (1996).
    [CrossRef]
  3. R. M. Haralick, L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, Reading, Mass., 1993), pp. 571–572.
  4. P. Buser, M. Imbert, Vision (MIT, Cambridge, Mass., 1992), pp. 94–98.
  5. M. V. Klein, T. E. Purtak, Optics (Wiley, New York, 1986), pp. 519–522.
  6. R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992), pp. 161–195.
  7. J. P. Antoine, R. Muenzi, B. Piette, “Image analysis with 2D continuous wavelet transform: detection of position, orientation, and visual contrast of simple objects,” in Wavelets and Applications, Y. Meyer, ed. (Masson, Paris, 1991), pp. 144–159.
  8. A. Toet, “Multiscale contrast enhancement with applications to image fusion,” Opt. Eng. 31, 1026–1031 (1992).
    [CrossRef]
  9. A. V. Bronnikov, G. Duifhis, “Wavelet-base image enhancement in x-ray imaging and tomography,” Appl. Opt. 37, 4437–4448 (1998).
    [CrossRef]
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    [CrossRef]
  11. S. Thurnhofer, S. K. Mitra, “Edge-enhanced image zooming,” Opt. Eng. 35, 1862–1870 (1996).
    [CrossRef]
  12. S. Thurnhofer, S. K. Mitra, “Detail-enhanced error diffusion,” Opt. Eng. 35, 2592–2598 (1996).
    [CrossRef]
  13. S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
    [CrossRef]
  14. S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
    [CrossRef]
  15. Z. Chen, M. A. Karim, “Forest representation of wavelet transform and feature detection,” Opt. Eng. 39, 1194–1202 (2000).
    [CrossRef]
  16. Z. Chen, M. A. Karim, “Frequency-refined multiresolution processing using wavelet splitting,” Opt. Commun. 173(1), 81–94 (2000).
    [CrossRef]

2000 (2)

Z. Chen, M. A. Karim, “Forest representation of wavelet transform and feature detection,” Opt. Eng. 39, 1194–1202 (2000).
[CrossRef]

Z. Chen, M. A. Karim, “Frequency-refined multiresolution processing using wavelet splitting,” Opt. Commun. 173(1), 81–94 (2000).
[CrossRef]

1998 (1)

1996 (4)

T. F. Schatzki, R. Young, R. P. Haff, J. G. Eye, G. R. Wright, “Visual detection of particulates in x-ray images of processed meat products,” Opt. Eng. 35, 2286–2291 (1996).
[CrossRef]

R. Zwiggelaar, C. R. Bull, M. J. Mooney, “X-ray simulations for imaging applications in the agricultural and food industries,” J. Agric. Eng. Res. 63, 161–170 (1996).
[CrossRef]

S. Thurnhofer, S. K. Mitra, “Edge-enhanced image zooming,” Opt. Eng. 35, 1862–1870 (1996).
[CrossRef]

S. Thurnhofer, S. K. Mitra, “Detail-enhanced error diffusion,” Opt. Eng. 35, 2592–2598 (1996).
[CrossRef]

1995 (1)

S. Choi, R. R. Schultz, R. L. Stevenson, Y. Huang, R. Liu, “Contrast enhancement of missile video sequences via image stabilization and product correlation,” Opt. Eng. 34, 3495–3507 (1995).
[CrossRef]

1992 (2)

A. Toet, “Multiscale contrast enhancement with applications to image fusion,” Opt. Eng. 31, 1026–1031 (1992).
[CrossRef]

S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
[CrossRef]

1989 (1)

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

Antoine, J. P.

J. P. Antoine, R. Muenzi, B. Piette, “Image analysis with 2D continuous wavelet transform: detection of position, orientation, and visual contrast of simple objects,” in Wavelets and Applications, Y. Meyer, ed. (Masson, Paris, 1991), pp. 144–159.

Bronnikov, A. V.

Bull, C. R.

R. Zwiggelaar, C. R. Bull, M. J. Mooney, “X-ray simulations for imaging applications in the agricultural and food industries,” J. Agric. Eng. Res. 63, 161–170 (1996).
[CrossRef]

Buser, P.

P. Buser, M. Imbert, Vision (MIT, Cambridge, Mass., 1992), pp. 94–98.

Chen, Z.

Z. Chen, M. A. Karim, “Forest representation of wavelet transform and feature detection,” Opt. Eng. 39, 1194–1202 (2000).
[CrossRef]

Z. Chen, M. A. Karim, “Frequency-refined multiresolution processing using wavelet splitting,” Opt. Commun. 173(1), 81–94 (2000).
[CrossRef]

Choi, S.

S. Choi, R. R. Schultz, R. L. Stevenson, Y. Huang, R. Liu, “Contrast enhancement of missile video sequences via image stabilization and product correlation,” Opt. Eng. 34, 3495–3507 (1995).
[CrossRef]

Duifhis, G.

Eye, J. G.

T. F. Schatzki, R. Young, R. P. Haff, J. G. Eye, G. R. Wright, “Visual detection of particulates in x-ray images of processed meat products,” Opt. Eng. 35, 2286–2291 (1996).
[CrossRef]

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992), pp. 161–195.

Haff, R. P.

T. F. Schatzki, R. Young, R. P. Haff, J. G. Eye, G. R. Wright, “Visual detection of particulates in x-ray images of processed meat products,” Opt. Eng. 35, 2286–2291 (1996).
[CrossRef]

Haralick, R. M.

R. M. Haralick, L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, Reading, Mass., 1993), pp. 571–572.

Huang, Y.

S. Choi, R. R. Schultz, R. L. Stevenson, Y. Huang, R. Liu, “Contrast enhancement of missile video sequences via image stabilization and product correlation,” Opt. Eng. 34, 3495–3507 (1995).
[CrossRef]

Hwang, W. L.

S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
[CrossRef]

Imbert, M.

P. Buser, M. Imbert, Vision (MIT, Cambridge, Mass., 1992), pp. 94–98.

Karim, M. A.

Z. Chen, M. A. Karim, “Forest representation of wavelet transform and feature detection,” Opt. Eng. 39, 1194–1202 (2000).
[CrossRef]

Z. Chen, M. A. Karim, “Frequency-refined multiresolution processing using wavelet splitting,” Opt. Commun. 173(1), 81–94 (2000).
[CrossRef]

Klein, M. V.

M. V. Klein, T. E. Purtak, Optics (Wiley, New York, 1986), pp. 519–522.

Liu, R.

S. Choi, R. R. Schultz, R. L. Stevenson, Y. Huang, R. Liu, “Contrast enhancement of missile video sequences via image stabilization and product correlation,” Opt. Eng. 34, 3495–3507 (1995).
[CrossRef]

Mallat, S.

S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
[CrossRef]

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

Mitra, S. K.

S. Thurnhofer, S. K. Mitra, “Detail-enhanced error diffusion,” Opt. Eng. 35, 2592–2598 (1996).
[CrossRef]

S. Thurnhofer, S. K. Mitra, “Edge-enhanced image zooming,” Opt. Eng. 35, 1862–1870 (1996).
[CrossRef]

Mooney, M. J.

R. Zwiggelaar, C. R. Bull, M. J. Mooney, “X-ray simulations for imaging applications in the agricultural and food industries,” J. Agric. Eng. Res. 63, 161–170 (1996).
[CrossRef]

Muenzi, R.

J. P. Antoine, R. Muenzi, B. Piette, “Image analysis with 2D continuous wavelet transform: detection of position, orientation, and visual contrast of simple objects,” in Wavelets and Applications, Y. Meyer, ed. (Masson, Paris, 1991), pp. 144–159.

Piette, B.

J. P. Antoine, R. Muenzi, B. Piette, “Image analysis with 2D continuous wavelet transform: detection of position, orientation, and visual contrast of simple objects,” in Wavelets and Applications, Y. Meyer, ed. (Masson, Paris, 1991), pp. 144–159.

Purtak, T. E.

M. V. Klein, T. E. Purtak, Optics (Wiley, New York, 1986), pp. 519–522.

Schatzki, T. F.

T. F. Schatzki, R. Young, R. P. Haff, J. G. Eye, G. R. Wright, “Visual detection of particulates in x-ray images of processed meat products,” Opt. Eng. 35, 2286–2291 (1996).
[CrossRef]

Schultz, R. R.

S. Choi, R. R. Schultz, R. L. Stevenson, Y. Huang, R. Liu, “Contrast enhancement of missile video sequences via image stabilization and product correlation,” Opt. Eng. 34, 3495–3507 (1995).
[CrossRef]

Shapiro, L. G.

R. M. Haralick, L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, Reading, Mass., 1993), pp. 571–572.

Stevenson, R. L.

S. Choi, R. R. Schultz, R. L. Stevenson, Y. Huang, R. Liu, “Contrast enhancement of missile video sequences via image stabilization and product correlation,” Opt. Eng. 34, 3495–3507 (1995).
[CrossRef]

Thurnhofer, S.

S. Thurnhofer, S. K. Mitra, “Edge-enhanced image zooming,” Opt. Eng. 35, 1862–1870 (1996).
[CrossRef]

S. Thurnhofer, S. K. Mitra, “Detail-enhanced error diffusion,” Opt. Eng. 35, 2592–2598 (1996).
[CrossRef]

Toet, A.

A. Toet, “Multiscale contrast enhancement with applications to image fusion,” Opt. Eng. 31, 1026–1031 (1992).
[CrossRef]

Woods, R. E.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992), pp. 161–195.

Wright, G. R.

T. F. Schatzki, R. Young, R. P. Haff, J. G. Eye, G. R. Wright, “Visual detection of particulates in x-ray images of processed meat products,” Opt. Eng. 35, 2286–2291 (1996).
[CrossRef]

Young, R.

T. F. Schatzki, R. Young, R. P. Haff, J. G. Eye, G. R. Wright, “Visual detection of particulates in x-ray images of processed meat products,” Opt. Eng. 35, 2286–2291 (1996).
[CrossRef]

Zwiggelaar, R.

R. Zwiggelaar, C. R. Bull, M. J. Mooney, “X-ray simulations for imaging applications in the agricultural and food industries,” J. Agric. Eng. Res. 63, 161–170 (1996).
[CrossRef]

Appl. Opt. (1)

IEEE Trans. Inf. Theory (1)

S. Mallat, W. L. Hwang, “Singularity detection and processing with wavelets,” IEEE Trans. Inf. Theory 38, 617–643 (1992).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. Mallat, “A theory for multiresolution signal decomposition: the wavelet representation,” IEEE Trans. Pattern Anal. Mach. Intell. 11, 674–693 (1989).
[CrossRef]

J. Agric. Eng. Res. (1)

R. Zwiggelaar, C. R. Bull, M. J. Mooney, “X-ray simulations for imaging applications in the agricultural and food industries,” J. Agric. Eng. Res. 63, 161–170 (1996).
[CrossRef]

Opt. Commun. (1)

Z. Chen, M. A. Karim, “Frequency-refined multiresolution processing using wavelet splitting,” Opt. Commun. 173(1), 81–94 (2000).
[CrossRef]

Opt. Eng. (6)

Z. Chen, M. A. Karim, “Forest representation of wavelet transform and feature detection,” Opt. Eng. 39, 1194–1202 (2000).
[CrossRef]

T. F. Schatzki, R. Young, R. P. Haff, J. G. Eye, G. R. Wright, “Visual detection of particulates in x-ray images of processed meat products,” Opt. Eng. 35, 2286–2291 (1996).
[CrossRef]

A. Toet, “Multiscale contrast enhancement with applications to image fusion,” Opt. Eng. 31, 1026–1031 (1992).
[CrossRef]

S. Choi, R. R. Schultz, R. L. Stevenson, Y. Huang, R. Liu, “Contrast enhancement of missile video sequences via image stabilization and product correlation,” Opt. Eng. 34, 3495–3507 (1995).
[CrossRef]

S. Thurnhofer, S. K. Mitra, “Edge-enhanced image zooming,” Opt. Eng. 35, 1862–1870 (1996).
[CrossRef]

S. Thurnhofer, S. K. Mitra, “Detail-enhanced error diffusion,” Opt. Eng. 35, 2592–2598 (1996).
[CrossRef]

Other (5)

R. M. Haralick, L. G. Shapiro, Computer and Robot Vision (Addison-Wesley, Reading, Mass., 1993), pp. 571–572.

P. Buser, M. Imbert, Vision (MIT, Cambridge, Mass., 1992), pp. 94–98.

M. V. Klein, T. E. Purtak, Optics (Wiley, New York, 1986), pp. 519–522.

R. C. Gonzalez, R. E. Woods, Digital Image Processing (Addison-Wesley, Reading, Mass., 1992), pp. 161–195.

J. P. Antoine, R. Muenzi, B. Piette, “Image analysis with 2D continuous wavelet transform: detection of position, orientation, and visual contrast of simple objects,” in Wavelets and Applications, Y. Meyer, ed. (Masson, Paris, 1991), pp. 144–159.

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Figures (8)

Fig. 1
Fig. 1

Representation of a three-level orthogonal wavelet transform.

Fig. 2
Fig. 2

Illustration of a three-level wavelet analysis and synthesis. (a) Analysis, and (b) synthesis.

Fig. 3
Fig. 3

An original x-ray image f(x, y), in size of 288 × 456, of a chicken fillet containing bone fragments.

Fig. 4
Fig. 4

Representation of a three-level wavelet transform of f(x, y) in which the gray levels at the subbands were adjusted for display purposes.

Fig. 5
Fig. 5

Multiresolution approximations of f(x, y) and the corresponding expanded versions: (a) A 3, (b) A 2, (c) A 1, and (d) A 0 = f(x, y); (a′) expand(A 3), (b′) expand(A 2), and (c′) expand(A 1).

Fig. 6
Fig. 6

Results of local multiresolution contrast enhancement by use of Eqs. (11) and (15): (a) A 2*, (b) A 1*, and (c) A 0*.

Fig. 7
Fig. 7

Another original sample of chicken fillet containing bone fragments.

Fig. 8
Fig. 8

Results of local multiresolution contrast enhancement of Fig. 7, which were obtained with the same procedures used in Figs. 3 6.

Equations (36)

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

Cb=Io-IbIb.
Cm=Imax-IminImax+Imin,
Vj-12=Vj-1  Vj-1=Vj  Wj  Vj  Wj=Vj  Vj  Vj  Wj  Wj  Vj× Wj  Wj=Vj2  Wj2,
Φx, y=ϕxϕy,
Ψhx, y=ϕxψy,
Ψvx, y=ψxϕy,
Ψdx, y=ψxψy,
Vj2=spanΦj;m,nx, y; m, nZ,
Wj2=λ=h,v,dWj2λ=spanΨj;m,nλx, y; m, nZ,  λ=h, v, d,
Wj2λ=spanΨj;m,nλx, y; m, nZ, λ=h, v, d,
Φj;m,nx, y=2jϕ2jx-mϕ2jy-n,
aj;m,n=fx, y,  Φj;m,nx, y,
hj;m,n=fx, y,  Ψj;m,nhx, y,
vj;m,n=fx, y,  Ψj;m,nvx, y,
dj;m,n=fx, y,  Ψj;m,ndx, y,  jZ, m, nZ,
fx, y  AJ, Hj, Vj, Dj,  jJ, J-1,, 1,
AJ=aJ;m,n; m, nZ, Hj=hj;m,n; m, nZ, Vj=vj;m,n; m, nZ,  Dj=dj;m,n; m, nZ.
Aj+1, Hj+1, Vj+1, Dj+1=analysisAj,
Aj=synthesisAj+1, Hj+1, Vj+1, Dj+1.
Cs,sx, y=intensity variation in Nsx, yintensity mean in Nsx, y,
Cs,sx, y=intensity variation in Nsx, yintensity mean in Nsx, y.
AJ*=AJmeanAJ,
HJ*=HJmeanAJ,
VJ*=VJmeanAJ,
DJ*=DJmeanAJ,
expandAj+1=synthesisAj+1, 0, 0, 0,j=J-1,, 1,
Hj*=HjexpandAj+1,  j=J-1,, 1,
Vj*=VjexpandAj+1,  j=J-1,, 1,
Dj*=DjexpandAj+1,  j=J-1,, 1,
Aj*=synthesisAj+1*, Hj+1*, Vj+1*, Dj+1*,j=J-1,, 0.
j,m,n|aj;m,n|2+|hj;m,n|2+|vj;m,n|2+|dj;m,n|2= |fx, y|2dxdy.
fx, y=synthesisA1, H1, V1, D1.
f*x, y=synthesisA1*, H1*, V1*, D1*.
-x1+m2jxx2+m2j,  mZ,
-y1+n2jyy2+n2j,  mZ.
Hj*m, n=Hjm, nexpandAj+1m, n|,|expandAj+1m, n|>εHjm, n,otherwise,

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