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.

© 1997 Optical Society of America

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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, MJ. 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 ftp://figment.csee.usf.edu /pub/mammograms/nijmegen-images
  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]

1997 (2)

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]

J.W. Byng, MJ. 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]

1996 (2)

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]

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

1995 (3)

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]

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

P. Perona, “Deformable kernels for early vision,” IEEE Trans. Pattern Analysis and Machine Intelligence,  17(5), 448–499 (1995).
[Crossref]

1993 (1)

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]

1992 (2)

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).

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]

1990 (2)

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]

C. Caldwell and M. Yaffe, “Fractal analysis of mammographic parenchemal pattern,” Phys. Med. Biol. 35, 235–247 (1990).
[Crossref] [PubMed]

1987 (1)

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]

1979 (1)

K.M. Hanson, “Detectability in computed tomographic images,” Med. Phys. 6(5), 441–451 (1979).
[Crossref] [PubMed]

1976 (2)

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

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

1967 (1)

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]

Adelson, E.H.

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).

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

Barnsley, M.F.

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

Barrett, H.H.

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 H.H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A. 9, 649–658 (1992).
[Crossref] [PubMed]

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]

Bergen, J.R.

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

Bochud, F.O.

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]

Boyd, N.F.

J.W. Byng, MJ. 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]

Byng, J.W.

J.W. Byng, MJ. 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]

Caldwell, C.

C. Caldwell and M. Yaffe, “Fractal analysis of mammographic parenchemal pattern,” Phys. Med. Biol. 35, 235–247 (1990).
[Crossref] [PubMed]

Cannon, T. M.

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

Carmes, C.R.

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]

Castleman, K.R.

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

Chang, Y.H.

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]

Dubuc, B.

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]

Foster, D.H.

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]

Freeman, W.T.

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).

Gur, D.

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]

Hahn, H.I.

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

Hanson, K.M.

K.M. Hanson, “Detectability in computed tomographic images,” Med. Phys. 6(5), 441–451 (1979).
[Crossref] [PubMed]

Heeger, D.J.

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

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).

Hessler, C.

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]

Hunt, B.R.

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

Little, L.E.

J.W. Byng, MJ. 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]

Lockwood, G.A.

J.W. Byng, MJ. 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]

Myers, K.J

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]

Myers, K.J.

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]

Papoulis, A.

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

Perona, P.

P. Perona, “Deformable kernels for early vision,” IEEE Trans. Pattern Analysis and Machine Intelligence,  17(5), 448–499 (1995).
[Crossref]

Pratt, W.K.

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

Rolland, J.P.

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 H.H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A. 9, 649–658 (1992).
[Crossref] [PubMed]

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 L. Yu, “A four-layer pyramid framework for statistical texture synthesis,” (in preparation).

Simoncelli, E.P.

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).

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

Strickland, R.N.

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

Thomson, M.G.A.

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]

Tricot, C.

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]

Tritchler, D.L.

J.W. Byng, MJ. 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]

Vaidyanathan, P.P.

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

Valley, J.F.

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]

Verdun, F. R.

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]

Wagner, R.F.

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]

Welch, P.D.

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]

Wolfe, J.N.

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

Woods, J. W.

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

Yaffe, M.

C. Caldwell and M. Yaffe, “Fractal analysis of mammographic parenchemal pattern,” Phys. Med. Biol. 35, 235–247 (1990).
[Crossref] [PubMed]

Yaffe, MJ.

J.W. Byng, MJ. 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]

Yao, J.

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]

Yu, L.

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

Zheng, B.

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]

Zucker, S.W.

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]

Acad. Radiol. (1)

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]

Am. J.Roentgenol. (1)

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

Cancer (1)

J.W. Byng, MJ. 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]

Compt. Graph.. (1)

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

IEEE Trans. Audio Electroacoust. (1)

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]

IEEE Trans. on Info. Theory (1)

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).

IEEE Trans. on Med. Imaging (1)

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

IEEE Trans. on Sys., Man, and Cybern. (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).

IEEE Trans. Pattern Analysis and Machine Intelligence (1)

P. Perona, “Deformable kernels for early vision,” IEEE Trans. Pattern Analysis and Machine Intelligence,  17(5), 448–499 (1995).
[Crossref]

J. Opt. Soc. Am. A. (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]

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]

Med. Phys. (1)

K.M. Hanson, “Detectability in computed tomographic images,” Med. Phys. 6(5), 441–451 (1979).
[Crossref] [PubMed]

Phys. Med. Biol. (1)

C. Caldwell and M. Yaffe, “Fractal analysis of mammographic parenchemal pattern,” Phys. Med. Biol. 35, 235–247 (1990).
[Crossref] [PubMed]

Proc. Natl. Acad. Sci. USA (1)

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]

Proc. SPIE (2)

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]

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]

Other (10)

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

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

The Nijmegen database is available by anonymous FTP from ftp://figment.csee.usf.edu /pub/mammograms/nijmegen-images

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

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).

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

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).

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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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

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.

Download Full Size | PPT Slide | PDF

Equations (4)

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

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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