Abstract

Realistic anatomical images are useful for assessment and improvement of medical image quality. The use of synthesized images has the advantage of providing the user with a large number of independent samples, in a controlled environment. We propose a method to generate medical textures that are fully defined by a set of adjustable parameters and a random number generator, and which statistical properties are analytically tractable. This method, called the “clustered lumpy background”, is a generalization of the original lumpy background described by Rolland and Barrett (1992). A detailed application of the method in the case of mammography is presented. It is shown that the synthesized images are visually very similar and that their first and second order statistics can be considered as being equivalent.

© Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. A. Petrosian, H. P. Chan, M. A. Helvie, M. M. Goodsitt and D. D. Adler, "Computer-aided diagnosis in mammography: classification of mass and normal tissue by texture analysis," Phys. Med. Biol. 39, 2273-2288 (1994).
    [CrossRef] [PubMed]
  2. H. P. Chan, W. Wei, M. A. Helvie, B. Sahiner, D.D. Adler, M. M. Goodsitt and N. Petrick, "Computer-aided classification of mammographic masses and normal tissue: linear discriminant analysis in texture space," Phys. Med. Biol. 40, 857-876 (1995).
    [CrossRef] [PubMed]
  3. P. Caligiuri, M. L. Giger and M. Favus, "Multifractal radiographic analysis of osteoporosis," Med. Phys. 21, 503- 508 (1994).
    [CrossRef] [PubMed]
  4. G. Revesz, H. L. Kundel and M. A. Graber, "The influence of structured noise on the detection of radiologic abnormalities," Am. J. Roentgenol. 9, 479-486 (1974).
  5. J. Moshita, K. Doi, S. Katsuragawa, L. Monnier-Cholley and H. MacMahon, "Computer aided diagnostic for interstitial infiltrates in chest radiographs: Optical-density dependence of texture measures," Med. Phys. 22, 1515- 1523 (1995).
    [CrossRef]
  6. J. W. Allison, L.L. Barr, R. J. Massoth, G. P. Berg, B. H. Krasner and B. S. Garra, "Understanding the process of quantitative ultrasonic tissue characterization," RadioGraphics 14, 1099-1108 (1994).
    [PubMed]
  7. T. Kobayashi, X. W. Xu, H. MacMahon, C. E. Metz and K. Doi, "Effect of a computer-aided diagnosis scheme on radiologists performance in detection of lung nodules on radiographs," Radiology 199, 843-848 (1996).
    [PubMed]
  8. E. Samei, M. J. Flynn and W. R. Eyler, "Simulation of subtle lung Nodules in projection chest radiography," Radiology 202, 117-124 (1997).
    [PubMed]
  9. A. J. Mendez, P. G. Tahoces, M. J. Lado, M. Souto and J. J. Vidal, "Computer-aided diagnosis: automatic detection of malignant masses in digitized mammograms," Med. Phys. 25, 957-964, (1998).
    [CrossRef] [PubMed]
  10. W. Zhang, K. Doi, M. L. Giger, Y. Wu, R. M. Nishikawa and R. A. Schmidt, "Computerized detection of clustered microcalcifications in digital mammograms using a shift-invariant artificial neural network," Med. Phys. 21, 517-524 (1994).
    [CrossRef] [PubMed]
  11. C. Kimme-Smith, M. McCombs, R. H. Gold and L. W. Bassett, "Mammography fixed grid versus reciprocating grid: Evaluation using cadaveric breasts as test objects," Med. Phys. 23, 141-147 (1996).
    [CrossRef] [PubMed]
  12. R. F. Wagner and K. E. Weaver, "An assortment of image quality indices for radiographic film-screen combinations - can they be resolved?," proceedings SPIE 35, 83-94 (1972).
    [CrossRef]
  13. A. E. Burgess, "Statistically defined backgrounds: Performance of a modified nonprewhitening observer model," J. Opt. Soc. Am. A 11, 1237-1242 (1994).
    [CrossRef]
  14. M. P. Eckstein, C. K. Abbey and J. S. Whiting, "Human versus model observers in anatomic backgrounds," proceedings SPIE 3340, 16-26 (1998).
    [CrossRef]
  15. H. H. Barrett, "Objective assessment of image quality: effects of quantum noise and object variability," J. Opt. Soc. Am. A 7, 1266-1278 (1990).
    [CrossRef] [PubMed]
  16. A. E. Burgess and H. Ghandeharian, "Visual signal detection. I. Ability to use phase information," J. Opt. Soc. Am. A 1, 900-905 (1984).
    [CrossRef] [PubMed]
  17. K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton and G. W. Seeley, "Effect of noise correlation on detectability of disk signals in medical imaging," J. Opt. Soc. Am. A 2, 1752-1759 (1985).
    [CrossRef] [PubMed]
  18. M. P. Eckstein and J. S. Whiting, "Visual signal detection in structured backgrounds. I. Effect of number of possible spatial locations and signal contrast," J. Opt. Soc. Am. A 13, 1777-1787 (1996).
    [CrossRef]
  19. 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]
  20. C. K. Abbey, H. H. Barrett, and D. W. Wilson, "Observer signal-to-noise ratios for the ML-EM algorithm," proceedings SPIE 2712, 47-58 (1996).
    [CrossRef] [PubMed]
  21. J. P. Rolland and R. N. Strickland, "An approach to the synthesis of biological tissue," Opt. Express 1, 414-423 (1997). http://epubs.osa.org/oearchive/source/2850.htm
    [CrossRef] [PubMed]
  22. E. P. Simoncelli, W. T. Freeman, E. H. Adelson and D. J. Heeger, "Shiftable multi-scale transforms," Trans. on Info. Theory, Special Issue on Wavelets 38, 587-607 (1992).
  23. B. Picinbono, Random Signals and systems (Prentice Hall International, 1993), p.182.
  24. A. Papoulis, Probability, random variables, and stochastic processes (McGraw-Hill, Inc, 1991), p.453.
  25. A. Papoulis, Probability, random variables, and stochastic processes (McGraw-Hill, Inc, 1991), p.419.
  26. J. P. Rolland, Factors influencing lesion detection in medical imaging (Ph.D. dissertation, University of Arizona, 1990).
  27. F. O. Bochud, F. R. Verdun, C. Hessler and J. F. Valley, "Detectability on radiological images: The effect of the anatomical noise," proceedings SPIE 2436, 156-164 (1995).
    [CrossRef]
  28. H. H. Barrett, J. L. Denny, R. F. Wagner and K. J. Myers, "Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance," J. Opt. Soc. Am. A 12, 834-852 (1995).
    [CrossRef]
  29. A. E. Burgess, X. Li, and C. K. Abbey, "Visual signal detectability with two noise components: anomalous masking effects," J. Opt. Soc. Am. A 14, 2420-2442 (1997).
    [CrossRef]
  30. J. C. Dainty and R. Shaw, Image Science (Academic, London, 1974).

Other

A. Petrosian, H. P. Chan, M. A. Helvie, M. M. Goodsitt and D. D. Adler, "Computer-aided diagnosis in mammography: classification of mass and normal tissue by texture analysis," Phys. Med. Biol. 39, 2273-2288 (1994).
[CrossRef] [PubMed]

H. P. Chan, W. Wei, M. A. Helvie, B. Sahiner, D.D. Adler, M. M. Goodsitt and N. Petrick, "Computer-aided classification of mammographic masses and normal tissue: linear discriminant analysis in texture space," Phys. Med. Biol. 40, 857-876 (1995).
[CrossRef] [PubMed]

P. Caligiuri, M. L. Giger and M. Favus, "Multifractal radiographic analysis of osteoporosis," Med. Phys. 21, 503- 508 (1994).
[CrossRef] [PubMed]

G. Revesz, H. L. Kundel and M. A. Graber, "The influence of structured noise on the detection of radiologic abnormalities," Am. J. Roentgenol. 9, 479-486 (1974).

J. Moshita, K. Doi, S. Katsuragawa, L. Monnier-Cholley and H. MacMahon, "Computer aided diagnostic for interstitial infiltrates in chest radiographs: Optical-density dependence of texture measures," Med. Phys. 22, 1515- 1523 (1995).
[CrossRef]

J. W. Allison, L.L. Barr, R. J. Massoth, G. P. Berg, B. H. Krasner and B. S. Garra, "Understanding the process of quantitative ultrasonic tissue characterization," RadioGraphics 14, 1099-1108 (1994).
[PubMed]

T. Kobayashi, X. W. Xu, H. MacMahon, C. E. Metz and K. Doi, "Effect of a computer-aided diagnosis scheme on radiologists performance in detection of lung nodules on radiographs," Radiology 199, 843-848 (1996).
[PubMed]

E. Samei, M. J. Flynn and W. R. Eyler, "Simulation of subtle lung Nodules in projection chest radiography," Radiology 202, 117-124 (1997).
[PubMed]

A. J. Mendez, P. G. Tahoces, M. J. Lado, M. Souto and J. J. Vidal, "Computer-aided diagnosis: automatic detection of malignant masses in digitized mammograms," Med. Phys. 25, 957-964, (1998).
[CrossRef] [PubMed]

W. Zhang, K. Doi, M. L. Giger, Y. Wu, R. M. Nishikawa and R. A. Schmidt, "Computerized detection of clustered microcalcifications in digital mammograms using a shift-invariant artificial neural network," Med. Phys. 21, 517-524 (1994).
[CrossRef] [PubMed]

C. Kimme-Smith, M. McCombs, R. H. Gold and L. W. Bassett, "Mammography fixed grid versus reciprocating grid: Evaluation using cadaveric breasts as test objects," Med. Phys. 23, 141-147 (1996).
[CrossRef] [PubMed]

R. F. Wagner and K. E. Weaver, "An assortment of image quality indices for radiographic film-screen combinations - can they be resolved?," proceedings SPIE 35, 83-94 (1972).
[CrossRef]

A. E. Burgess, "Statistically defined backgrounds: Performance of a modified nonprewhitening observer model," J. Opt. Soc. Am. A 11, 1237-1242 (1994).
[CrossRef]

M. P. Eckstein, C. K. Abbey and J. S. Whiting, "Human versus model observers in anatomic backgrounds," proceedings SPIE 3340, 16-26 (1998).
[CrossRef]

H. H. Barrett, "Objective assessment of image quality: effects of quantum noise and object variability," J. Opt. Soc. Am. A 7, 1266-1278 (1990).
[CrossRef] [PubMed]

A. E. Burgess and H. Ghandeharian, "Visual signal detection. I. Ability to use phase information," J. Opt. Soc. Am. A 1, 900-905 (1984).
[CrossRef] [PubMed]

K. J. Myers, H. H. Barrett, M. C. Borgstrom, D. D. Patton and G. W. Seeley, "Effect of noise correlation on detectability of disk signals in medical imaging," J. Opt. Soc. Am. A 2, 1752-1759 (1985).
[CrossRef] [PubMed]

M. P. Eckstein and J. S. Whiting, "Visual signal detection in structured backgrounds. I. Effect of number of possible spatial locations and signal contrast," J. Opt. Soc. Am. A 13, 1777-1787 (1996).
[CrossRef]

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]

C. K. Abbey, H. H. Barrett, and D. W. Wilson, "Observer signal-to-noise ratios for the ML-EM algorithm," proceedings SPIE 2712, 47-58 (1996).
[CrossRef] [PubMed]

J. P. Rolland and R. N. Strickland, "An approach to the synthesis of biological tissue," Opt. Express 1, 414-423 (1997). http://epubs.osa.org/oearchive/source/2850.htm
[CrossRef] [PubMed]

E. P. Simoncelli, W. T. Freeman, E. H. Adelson and D. J. Heeger, "Shiftable multi-scale transforms," Trans. on Info. Theory, Special Issue on Wavelets 38, 587-607 (1992).

B. Picinbono, Random Signals and systems (Prentice Hall International, 1993), p.182.

A. Papoulis, Probability, random variables, and stochastic processes (McGraw-Hill, Inc, 1991), p.453.

A. Papoulis, Probability, random variables, and stochastic processes (McGraw-Hill, Inc, 1991), p.419.

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

F. O. Bochud, F. R. Verdun, C. Hessler and J. F. Valley, "Detectability on radiological images: The effect of the anatomical noise," proceedings SPIE 2436, 156-164 (1995).
[CrossRef]

H. H. Barrett, J. L. Denny, R. F. Wagner and K. J. Myers, "Objective assessment of image quality. II. Fisher information, Fourier crosstalk, and figures of merit for task performance," J. Opt. Soc. Am. A 12, 834-852 (1995).
[CrossRef]

A. E. Burgess, X. Li, and C. K. Abbey, "Visual signal detectability with two noise components: anomalous masking effects," J. Opt. Soc. Am. A 14, 2420-2442 (1997).
[CrossRef]

J. C. Dainty and R. Shaw, Image Science (Academic, London, 1974).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (3)

Fig. 1.
Fig. 1.

Measured power spectra of real mammograms (extreme values I and II; as measured on images of pixel size = 0.04mm, image size = 1024 pixels) and of CLB images (as measured on images of pixel size = 0.3mm, image size = 128 pixels). These spectra are averaged over all angles and displayed versus radial spatial frequency

Fig. 2.
Fig. 2.

Definition of the chosen blob. (a) Profile of the blob defined by Eq. (8) with a rotation angle (θ) set to 45°. (b) The characteristic length L in Eq. (8) is equal to the “radius” of the ellipse having half-axes Lx and Ly.

Fig. 3.
Fig. 3.

Examples of simulated (row a) and real mammograms (row b). Pixel size: 0.3mm. 128×128 pixels.

Tables (3)

Tables Icon

Table 1. Definition of the variables involved in the description of the CLB.

Tables Icon

Table 2. Parameters of the clustered lumpy background for a 128×128 pixel image.

Tables Icon

Table 3. First order statistics of real and synthesized mammograms (the variation indicates ± one standard deviation).

Equations (27)

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

h ( r ) = { 1 π sin π r r w + ( 1 r r w ) cos π r r w r r w 0 r > r w ,
W window ( f ) = h ˜ ( f f 1 ) 2 W true ( f 1 ) d f 1 ,
g ( r ) = k = 1 K b ( r r k ) ,
g ( r ) = k = 1 K n = 1 N k b ( 1 a kn ( r r k r kn ) , R θ kn ) ,
W ( f ) = K ¯ N ¯ A ( W b ( f ) + N ¯ W s ( f ) ) ,
W b ( f ) = 1 2 π 0 2 π b ˜ θ ( f ) 2 ,
W s ( f ) = 1 2 π 0 2 π ϕ ˜ ( f ) 2 b ˜ θ ( f ) 2 ,
b ( r , R θ ) = exp ( α R θ r β L ( R θ r ) ) ,
g ( r ) = k = 1 K n = 1 N k b ( r r k r kn , R θ k ) r k , r kn , θ k N K
= k = 1 K n = 1 1 2 πA N k 0 2 π k A d r k Θ d r kn ϕ ( r kn ) b ( r r k r kn , R θ k ) N K
= k = 1 K n = 1 N k I b A N K = K ¯ N ¯ I b A ,
c ( r , r′ ) = g ( r ) g ( r′ ) g ( r ) g ( r′ ) .
g ( r ) g ( r′ ) = k = 1 K n = 1 N k k′ = 1 K n′ = 1 N k′ b ( r r k r kn , R θ k ) b ( r′ r k′ r k′n′ , R θ k′ ) )
= k = 1 K n = 1 N k b ( r r k r kn , R θ k ) b ( r′ r k r kn , R θ k ) )
+ k = 1 K n = 1 N k n′ = 1 n′ n N k′ b ( r r k r kn , R θ k ) b ( r′ r k r kn′ , R θ k ) )
+ k = 1 K k′ = 1 k′ k K n = 1 K k n′ = 1 N k′ b ( r r k r kn , R θ k ) b ( r′ r k′ r k′n′ , R θ k′ ) ) .
T 1 = k = 1 K n = 1 N k b ( r r k r kn , R θ k ) b ( r′ r k r kn , R θ k ) r k , θ k r kn N k K
= k = 1 K n = 1 N k 1 2 πA 0 2 π k A d r k Θ d r kn ϕ ( r kn ) b ( r r k r kn , R θ k ) b ( r′ r k r kn , R θ k ) N k K
= k = 1 K n = 1 N k 1 2 πA 0 2 π k Θ d r kn ϕ ( r kn ) R b θ k ( r r′ ) N k K = K ¯ N ¯ A R b ( r r′ ) ,
T 2 = k = 1 K n = 1 N k n′ = 1 n′ n N k′ b ( r r k r kn , R θ k ) b ( r′ r k r kn , R θ k ) r k , θ k r kn , r kn′ N k K
= k = 1 K n = 1 N k n′ = 1 n′ n N k′ b ( r r k r kn , R θ k ) r kn b ( r′ r k r kn , R θ k ) r kn′ r k θ k N k K
= k = 1 K n = 1 N k n′ = 1 n′ n N k′ S θ k ( r r k ) S θ k ( r′ r k ) r k θ k N k K
= k = 1 K n = 1 N k n′ = 1 n′ n N k′ 1 A R s ( r r′ ) N k K
= KN ¯ 2 A R s ( r r′ ) ,
T 3 = k = 1 K k′ = 1 k′ k K n = 1 N k b ( r r k r kn , R θ k ) r k r kn θ k N n′ = 1 N k′ b ( r′ r k′ r k′n′ , R θ k′ ) r k′ r k′n′ θ k′ N K
= k = 1 K k′ = 1 k′ k K n = 1 N k I A N k n′ = 1 N k′ I A N k K = K ( K 1 ) ( N ¯ I A ) 2 K = ( K ¯ N ¯ I A ) 2 ,
c ( r , r′ ) = c ( r r′ ) = K ¯ N ¯ A ( R b ( r r′ ) + N ¯ R s ( r r′ ) ) .

Metrics