Abstract

Mathematical phantoms developed to synthesize realistic complex backgrounds such as those obtained when imaging biological tissue, play a key role in the quantitative assessment of image quality for medical and biomedical imaging. We present a modeling framework for the synthesis of realistic tissue samples. The technique is demonstrated using radiological breast tissue. The model employs a two-component image decomposition consisting of a slowly, spatially varying mean-background and a residual texture image. Each component is synthesized independently. The approach and results presented here constitute an important step towards developing methods for the quantitative assessment of image quality in medical and biomedical imaging, and more generally image science.

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References

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  1. B.R. Hunt, and T. M. Cannon, "Nonstationary assumptions for Gaussian models of images," IEEE Trans. on Sys., Man, and Cybern., 876-882 (1976).
  2. R.N. Strickland, and H.I. Hahn, "Wavelet transforms for detecting microcalcifications in mammograms," IEEE Trans. on Med. Imaging 15, 218-229 (1996).
    [CrossRef]
  3. K.J. Myers, J.P. Rolland, H.H. Barrett, and R.F. Wagner, "Aperture optimization for emission imaging: effect of a spatially varying background," J. Opt. Soc. Am. A. 7, 1279-1293 (1990).
    [CrossRef] [PubMed]
  4. J.P. Rolland, "Factors influencing lesion detection in medical imaging," Ph.D. Dissertation, University of Arizona, (1990).
  5. J.P. Rolland, and H.H. Barrett, "Effect of random background inhomogeneity on observer detection performance," J. Opt. Soc. Am. A. 9, 649-658 (1992).
    [CrossRef] [PubMed]
  6. M.G.A. Thomson, and D.H. Foster, "Role of second- and third-order statistics in the discriminability of natural images," J. Opt. Soc. Am. A. 14(9), 2081-2090 (1997).
    [CrossRef]
  7. C. Caldwell, and M. Yaffe, "Fractal analysis of mammographic parenchemal pattern," Phys. Med. Biol. 35, 235-247 (1990).
    [CrossRef] [PubMed]
  8. F.O. Bochud, F. R. Verdun, C. Hessler, and J.F. Valley, "Detectability on radiological images: the influence of anatomical noise," Proc. SPIE 2436, 156-165 (1995).
    [CrossRef]
  9. B. Zheng, Y.H. Chang, and D. Gur, "Adpative computer-aided diagnosis scheme of digitized mammograms," Acad. Radiol. 3 (10), 806-814 (1996).
    [CrossRef] [PubMed]
  10. M.F. Barnsley, Fractals Everywhere. (Academic Press, San Diego, CA, 1988)
  11. J.W. Byng, M J. Yaffe, G.A. Lockwood, L.E. Little, D.L. Tritchler, and N.F. Boyd, "Automated analysis of mammographic densities and breast carcinoma risk," Cancer 80(1), 66-74 (1997).
    [CrossRef] [PubMed]
  12. B. Dubuc, C.R. Carmes, C. Tricot, and S.W. Zucker, "The variation method: a technique to estimate the fractal dimension of surfaces," Proc. SPIE 845, 241-248 (1987).
    [CrossRef]
  13. J.N. Wolfe, "Breast patterns as an index of risk for developing breast cancer," Am. J. Roentgenol. 126, 1130-1139 (1976).
  14. The Nijmegen database is available by anonymous FTP from <A HREF="ftp://figment.csee.usf.edu/pub/mammograms/nijmegen-images">ftp://figment.csee.usf.edu/pub/mammograms/nijmegen-images</A>
  15. A. Papoulis. Probablity, Random Variables, and Stochastic Processes. (Mc Graw-Hill, NY, 1991).
  16. H.H. Barrett, J. Yao, J.P. Rolland, and K.J Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. USA 90, 9758-9765 (1993).
    [CrossRef] [PubMed]
  17. J.P. Rolland and L.Yu, "A four-layer pyramid framework for statistical texture synthesis," (in preparation).
  18. P.P. Vaidyanathan. Multivariate systems and filter banks. (Prentice Hall, NJ, 1993).
  19. D.J. Heeger, and J.R. Bergen, "Pyramid-based texture analysis/synthesis," Compt. Graph., 229-238 (1995).
  20. E.P. Simoncelli, and E.H. Adelson, "Subband transforms." In Subbands Image Coding, (Kluwer Academic Publishers, J.W. Woods, eds., MA 1991).
  21. E.P. Simoncelli, W.T. Freeman, E.H. Adelson, and D.J. Heeger, "Shiftable multi-scale transforms," IEEE Trans. on Info. Theory, Special Issue on Wavelets 38, 587607 (1992).
  22. P. Perona, "Deformable kernels for early vision," IEEE Trans. Pattern Analysis and Machine Intelligence, 17(5), 448-499 (1995).
    [CrossRef]
  23. J. W. Woods. Subband Image Coding. (Kluwer Academic Publishers, MA,1991).
  24. W.K. Pratt, Digital Image Processing. (John Wiley & Sons, NY, 1991).
  25. K.R. Castleman, Digital Image Processing. (Prentice Hall, NJ,1996).
  26. P.D. Welch, "The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms," IEEE Trans. Audio Electroacoust. 15, 70-73 (1967).
    [CrossRef]
  27. K.M. Hanson, "Detectability in computed tomographic images," Med. Phys. 6(5), 441-451 (1979).
    [CrossRef] [PubMed]

Other (27)

B.R. Hunt, and T. M. Cannon, "Nonstationary assumptions for Gaussian models of images," IEEE Trans. on Sys., Man, and Cybern., 876-882 (1976).

R.N. Strickland, and H.I. Hahn, "Wavelet transforms for detecting microcalcifications in mammograms," IEEE Trans. on Med. Imaging 15, 218-229 (1996).
[CrossRef]

K.J. Myers, J.P. Rolland, H.H. Barrett, and R.F. Wagner, "Aperture optimization for emission imaging: effect of a spatially varying background," J. Opt. Soc. Am. A. 7, 1279-1293 (1990).
[CrossRef] [PubMed]

J.P. Rolland, "Factors influencing lesion detection in medical imaging," Ph.D. Dissertation, University of Arizona, (1990).

J.P. Rolland, and H.H. Barrett, "Effect of random background inhomogeneity on observer detection performance," J. Opt. Soc. Am. A. 9, 649-658 (1992).
[CrossRef] [PubMed]

M.G.A. Thomson, and D.H. Foster, "Role of second- and third-order statistics in the discriminability of natural images," J. Opt. Soc. Am. A. 14(9), 2081-2090 (1997).
[CrossRef]

C. Caldwell, and M. Yaffe, "Fractal analysis of mammographic parenchemal pattern," Phys. Med. Biol. 35, 235-247 (1990).
[CrossRef] [PubMed]

F.O. Bochud, F. R. Verdun, C. Hessler, and J.F. Valley, "Detectability on radiological images: the influence of anatomical noise," Proc. SPIE 2436, 156-165 (1995).
[CrossRef]

B. Zheng, Y.H. Chang, and D. Gur, "Adpative computer-aided diagnosis scheme of digitized mammograms," Acad. Radiol. 3 (10), 806-814 (1996).
[CrossRef] [PubMed]

M.F. Barnsley, Fractals Everywhere. (Academic Press, San Diego, CA, 1988)

J.W. Byng, M J. Yaffe, G.A. Lockwood, L.E. Little, D.L. Tritchler, and N.F. Boyd, "Automated analysis of mammographic densities and breast carcinoma risk," Cancer 80(1), 66-74 (1997).
[CrossRef] [PubMed]

B. Dubuc, C.R. Carmes, C. Tricot, and S.W. Zucker, "The variation method: a technique to estimate the fractal dimension of surfaces," Proc. SPIE 845, 241-248 (1987).
[CrossRef]

J.N. Wolfe, "Breast patterns as an index of risk for developing breast cancer," Am. J. Roentgenol. 126, 1130-1139 (1976).

The Nijmegen database is available by anonymous FTP from <A HREF="ftp://figment.csee.usf.edu/pub/mammograms/nijmegen-images">ftp://figment.csee.usf.edu/pub/mammograms/nijmegen-images</A>

A. Papoulis. Probablity, Random Variables, and Stochastic Processes. (Mc Graw-Hill, NY, 1991).

H.H. Barrett, J. Yao, J.P. Rolland, and K.J Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. USA 90, 9758-9765 (1993).
[CrossRef] [PubMed]

J.P. Rolland and L.Yu, "A four-layer pyramid framework for statistical texture synthesis," (in preparation).

P.P. Vaidyanathan. Multivariate systems and filter banks. (Prentice Hall, NJ, 1993).

D.J. Heeger, and J.R. Bergen, "Pyramid-based texture analysis/synthesis," Compt. Graph., 229-238 (1995).

E.P. Simoncelli, and E.H. Adelson, "Subband transforms." In Subbands Image Coding, (Kluwer Academic Publishers, J.W. Woods, eds., MA 1991).

E.P. Simoncelli, W.T. Freeman, E.H. Adelson, and D.J. Heeger, "Shiftable multi-scale transforms," IEEE Trans. on Info. Theory, Special Issue on Wavelets 38, 587607 (1992).

P. Perona, "Deformable kernels for early vision," IEEE Trans. Pattern Analysis and Machine Intelligence, 17(5), 448-499 (1995).
[CrossRef]

J. W. Woods. Subband Image Coding. (Kluwer Academic Publishers, MA,1991).

W.K. Pratt, Digital Image Processing. (John Wiley & Sons, NY, 1991).

K.R. Castleman, Digital Image Processing. (Prentice Hall, NJ,1996).

P.D. Welch, "The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms," IEEE Trans. Audio Electroacoust. 15, 70-73 (1967).
[CrossRef]

K.M. Hanson, "Detectability in computed tomographic images," Med. Phys. 6(5), 441-451 (1979).
[CrossRef] [PubMed]

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Figures (5)

Fig. 1.
Fig. 1.

Mammography breast image decomposition: (a) The original sample. (b) The slowly, spatially varying mean-background. (c) The residual texture image.

Fig. 2.
Fig. 2.

Illustration of the steerable pyramid transform used in the texture synthesis algorithm. The input image in the upper left corner would be either the texture sample or the white noise image. The output image in the upper right corner will be either the reconstruction of a decomposed image if only one input image is considered, or a synthesis image if two pyramid layers are combined as described in section 4. The left hand side of the pyramid is used for decomposing the two images and the right hand side of the pyramid is used for image reconstruction or synthesis.

Fig. 3.
Fig. 3.

Syntheses of a residual mammographic texture image: (a) a typical sample of a uniformly distributed white noise image used as a starting point for one synthesis; (b) original mammographic residual texture; (c) synthesis 1; (d) synthesis 2.

Fig. 4.
Fig. 4.

Average greylevel histograms over 18 images of an ensemble for five ensemble sets: (a) the original sample mammograms; (b) the mean backgrounds; (c) the lumpy backgrounds that best matched the mean backgrounds in visual appearance; (d) the residual texture images; and (e) the texture synthesis images.

Fig. 5.
Fig. 5.

Average Power spectra over 18 images of an ensemble for five ensemble sets: (a) the original sample mammograms; (b) the mean backgrounds; (c) the lumpy backgrounds that best matched the mean backgrounds in visual appearance; (d) the residue texture images; and (e) the texture synthesis images.

Equations (4)

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W ( ρ ) = W ( 0 ) exp ( 2 π 2 r b 2 ρ 2 ) ,
b ( r ) = j = 1 K b 0 πr b 2 exp [ r r j 2 r b 2 ] ,
W ( 0 ) = K ¯ A d b 0 2 ,
M i ( x , y ) = β L i ( x , y ) + ( 1 β ) T i ( x , y ) ,

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