Abstract

Modern imaging systems rely on complicated hardware and sophisticated image-processing methods to produce images. Owing to this complexity in the imaging chain, there are numerous variables in both the hardware and the software that need to be determined. We advocate a task-based approach to measuring and optimizing image quality in which one analyzes the ability of an observer to perform a task. Ideally, a task-based measure of image quality would account for all sources of variation in the imaging system, including object variability. Often, researchers ignore object variability even though it is known to have a large effect on task performance. The more accurate the statistical description of the objects, the more believable the task-based results will be. We have developed methods to fit statistical models of objects, using only noisy image data and a well-characterized imaging system. The results of these techniques could eventually be used to optimize both the hardware and the software components of imaging systems.

© 2003 Optical Society of America

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References

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  1. 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]
  2. H. H. Barrett, J. L. Denny, R. F. Wagner, 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]
  3. H. H. Barrett, C. K. Abbey, E. Clarkson, “Objective assessment of image quality. III. ROC metrics, ideal observers, and likelihood-generating functions,” J. Opt. Soc. Am. A 15, 1520–1535 (1998).
    [CrossRef]
  4. Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
    [CrossRef] [PubMed]
  5. C. K. Abbey, H. H. Barrett, “Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability,” J. Opt. Soc. Am. A 18, 473–488 (2001).
    [CrossRef]
  6. O. Schwartz, E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neuroscience 4, 819–825 (2001).
    [PubMed]
  7. H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I (Academic, New York, 1968).
  8. S. C. Zhu, Y. Wu, D. Mumford, “Filters, random fields and maximum entropy (FRAME),” Int. J. Comput. Vision 27, 1–20 (1998).
    [CrossRef]
  9. E. P. Simoncelli, B. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1217 (2001).
    [CrossRef] [PubMed]
  10. H. H. Barrett, C. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
    [CrossRef]
  11. J. P. Rolland, H. H. Barrett, “Effect of random background inhomogeneity on observer detection performance,” J. Opt. Soc. Am. A 9, 649–658 (1992).
    [CrossRef] [PubMed]
  12. F. Bochud, C. K. Abbey, M. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999); http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  13. H. H. Barrett, K. J. Myers, Foundations of Image Science (Wiley, New York, to be published).
  14. E. Clarkson, M. A. Kupinski, H. H. Barrett, “Transformation of characteristic functionals through imaging systems,” Opt. Express 10, 536–539 (2002); http://www.opticsexpress.org .
    [CrossRef] [PubMed]
  15. C. P. Robert, G. Casella, Monte Carlo Statistical Methods (Springer-Verlag, New York, 1999).
  16. W. R. Gilks, S. Richardson, D. J. Spiegelhalter, eds., Markov Chain Monte Carlo in Practice (Chapman & Hall, Boca Raton, Fla., 1996).
  17. K. J. Myers, H. H. Barrett, “Addition of a channel mechanism to the ideal-observer model,” J. Opt. Soc. Am. A 4, 2447–2457 (1987).
    [CrossRef] [PubMed]

2002 (1)

2001 (3)

C. K. Abbey, H. H. Barrett, “Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability,” J. Opt. Soc. Am. A 18, 473–488 (2001).
[CrossRef]

O. Schwartz, E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neuroscience 4, 819–825 (2001).
[PubMed]

E. P. Simoncelli, B. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1217 (2001).
[CrossRef] [PubMed]

1999 (1)

1998 (2)

1995 (2)

1992 (1)

1990 (1)

1987 (1)

Abbey, C.

H. H. Barrett, C. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

Abbey, C. K.

Barrett, H. H.

E. Clarkson, M. A. Kupinski, H. H. Barrett, “Transformation of characteristic functionals through imaging systems,” Opt. Express 10, 536–539 (2002); http://www.opticsexpress.org .
[CrossRef] [PubMed]

C. K. Abbey, H. H. Barrett, “Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability,” J. Opt. Soc. Am. A 18, 473–488 (2001).
[CrossRef]

H. H. Barrett, C. K. Abbey, E. Clarkson, “Objective assessment of image quality. III. ROC metrics, ideal observers, and likelihood-generating functions,” J. Opt. Soc. Am. A 15, 1520–1535 (1998).
[CrossRef]

H. H. Barrett, J. L. Denny, R. F. Wagner, 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]

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

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]

K. J. Myers, H. H. Barrett, “Addition of a channel mechanism to the ideal-observer model,” J. Opt. Soc. Am. A 4, 2447–2457 (1987).
[CrossRef] [PubMed]

H. H. Barrett, K. J. Myers, Foundations of Image Science (Wiley, New York, to be published).

H. H. Barrett, C. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

Bochud, F.

Casella, G.

C. P. Robert, G. Casella, Monte Carlo Statistical Methods (Springer-Verlag, New York, 1999).

Clarkson, E.

Denny, J. L.

Eckstein, M.

F. Bochud, C. K. Abbey, M. Eckstein, “Statistical texture synthesis of mammographic images with clustered lumpy backgrounds,” Opt. Express 4, 33–43 (1999); http://www.opticsexpress.org .
[CrossRef] [PubMed]

H. H. Barrett, C. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

Gallas, B.

H. H. Barrett, C. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

Kersten, D.

Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
[CrossRef] [PubMed]

Knill, D. C.

Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
[CrossRef] [PubMed]

Kupinski, M. A.

Liu, Z.

Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
[CrossRef] [PubMed]

Mumford, D.

S. C. Zhu, Y. Wu, D. Mumford, “Filters, random fields and maximum entropy (FRAME),” Int. J. Comput. Vision 27, 1–20 (1998).
[CrossRef]

Myers, K. J.

Olshausen, B.

E. P. Simoncelli, B. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1217 (2001).
[CrossRef] [PubMed]

Robert, C. P.

C. P. Robert, G. Casella, Monte Carlo Statistical Methods (Springer-Verlag, New York, 1999).

Rolland, J. P.

Schwartz, O.

O. Schwartz, E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neuroscience 4, 819–825 (2001).
[PubMed]

Simoncelli, E. P.

O. Schwartz, E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neuroscience 4, 819–825 (2001).
[PubMed]

E. P. Simoncelli, B. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1217 (2001).
[CrossRef] [PubMed]

Van Trees, H. L.

H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I (Academic, New York, 1968).

Wagner, R. F.

Wu, Y.

S. C. Zhu, Y. Wu, D. Mumford, “Filters, random fields and maximum entropy (FRAME),” Int. J. Comput. Vision 27, 1–20 (1998).
[CrossRef]

Zhu, S. C.

S. C. Zhu, Y. Wu, D. Mumford, “Filters, random fields and maximum entropy (FRAME),” Int. J. Comput. Vision 27, 1–20 (1998).
[CrossRef]

Annu. Rev. Neurosci. (1)

E. P. Simoncelli, B. Olshausen, “Natural image statistics and neural representation,” Annu. Rev. Neurosci. 24, 1193–1217 (2001).
[CrossRef] [PubMed]

Int. J. Comput. Vision (1)

S. C. Zhu, Y. Wu, D. Mumford, “Filters, random fields and maximum entropy (FRAME),” Int. J. Comput. Vision 27, 1–20 (1998).
[CrossRef]

J. Opt. Soc. Am. A (6)

Nat. Neuroscience (1)

O. Schwartz, E. P. Simoncelli, “Natural signal statistics and sensory gain control,” Nat. Neuroscience 4, 819–825 (2001).
[PubMed]

Opt. Express (2)

Vision Res. (1)

Z. Liu, D. C. Knill, D. Kersten, “Object classification for human and ideal observers,” Vision Res. 35, 549–568 (1995).
[CrossRef] [PubMed]

Other (5)

H. L. Van Trees, Detection, Estimation, and Modulation Theory, Part I (Academic, New York, 1968).

H. H. Barrett, C. Abbey, B. Gallas, M. Eckstein, “Stabilized estimates of Hotelling-observer detection performance in patient-structured noise,” in Medical Imaging: Image Perception, H. L. Kundel, ed., Proc. SPIE3340, 27–43 (1998).
[CrossRef]

H. H. Barrett, K. J. Myers, Foundations of Image Science (Wiley, New York, to be published).

C. P. Robert, G. Casella, Monte Carlo Statistical Methods (Springer-Verlag, New York, 1999).

W. R. Gilks, S. Richardson, D. J. Spiegelhalter, eds., Markov Chain Monte Carlo in Practice (Chapman & Hall, Boca Raton, Fla., 1996).

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Figures (3)

Fig. 1
Fig. 1

Examples of two-dimensional lumpy objects with different parameters θ.

Fig. 2
Fig. 2

Examples of two-dimensional clustered lumpy objects with different parameters θ.

Fig. 3
Fig. 3

Simulation results for lumpy objects. (a)–(c) Three of the images used to fit the lumpy object model parameters. (d)–(f) Three images generated by using the fitted model parameters. The top row of images are not meant to look exactly like the bottom row of images; they are simply meant to appear statistically similar.

Equations (52)

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g=Hf+n,
Ψg(ρ)=exp(-2πigρ)g.
Ψf(ξ)=exp(-2πiξf)f,
v=Tg=T(Hf+n),
f=f(r)=n=1NΛ(r-cn|a, s),
Ψf(ξ|θ)=exp(-2πiξf)f|θ
=exp-2πiξ(r)n=1NΛ(r-cn|a,s)dr{cn},N
Ψf(ξ|θ)=n=1Nexp-2πiξ(r)Λ(r-cn|a,s)drcnN
=ΨΛ(ξ|θ)NN
=exp(-N¯)N=0N¯NN!ΨΛ(ξ|θ)N
=exp{-N¯[1-ΨΛ(ξ|θ)]},
ΨΛ(ξ|θ)=exp-2πiξ(r)Λ(r-c|a,s)drc.
f=f(r)=n=1Nk=1KnΛ([Rϕn](r-cn-Δnk)|α),
Λ(r, ϕ|γ, β, lx, ly)=exp-γrβly2 cos(ϕ)2+lx2 sin(ϕ)2lx2ly21/2.
f=f(r)=n=1NΩ(r-cn, {Δnk}, ϕn, Kn|α),
Ω(r-cn, {Δnk}, ϕn, Kn|α)=k=1KnΛ([Rϕn](r-cn-Δnk)|α),
Ψf(ξ|θ)=exp{-N¯[1-ΨΩ(ξ|θ)]},
ΨΩ(ξ|θ)=exp{-K¯[1-ΨΛ(ξ|c, ϕ, θ)]}c,ϕ,
Ψf(ξ|θ)=exp[-N¯(1-exp{-K¯[1-ΨΛ(ξ|c, ϕ, θ)]}c,ϕ)].
g¯=Hf
Ψg¯(ρ|θ)=exp(-2πiρg¯)g¯|θ
=p(g¯|θ)m=1M exp(-2πiρmg¯m)dg¯,
Ψg¯(ρ|θ)=exp(-2πi(Hρ)f)f|θ
=Ψf(Hρ|θ).
Ψn(ρ|K)=exp(-2π2ρKρ).
Ψg(ρ|θ, K)=Ψf(Hρ|θ)Ψn(ρ|K).
pr(g|g¯)=m=1M exp(-g¯m)g¯mgmgm!,
pr(g|θ)=pr(g|g¯)pr(g¯|θ)dg¯
=pr(g¯|θ)m=1M exp(-g¯m)g¯mgmgm!dg¯.
Ψg(ρ|θ)=pr(g¯|θ)m=1M exp[-g¯m+g¯m exp(-2πiρm)]dg¯,
[Γ(ρ)]m=-1+exp(-2πiρm)-2πi.
Ψg(ρ|θ)=Ψg¯(Γ(ρ)|θ)=Ψf(HΓ(ρ)|θ).
Ψv(ω|θ)=Ψf(HΓ(Tω)|θ),
pr({gl}|θ)=l=1Ldfpr(gl|f)pr(f|θ).
Ψv(ω)=exp(-2πiωv)v.
Ψˆv(ω)=1Ll=1L exp(-2πiωvl).
C(ω, ω)=Ψˆv(ω)Ψˆv*(ω){vl}-Ψv(ω)Ψv*(ω)
=1L2l=1Ll=1Lexp(-2πiωvl)×exp(2πiωvl)vl,vl-Ψv(ω)Ψv*(ω).
exp[-2πi(ω-ω)vl]vl=Ψv(ω-ω)
exp(-2πiωvl)vlexp(2πiωvl)vl=Ψv(ω)Ψv*(ω).
C(ω, ω)=1L[Ψv(ω-ω)-Ψv(ω)Ψv*(ω)].
V(ω)=1L[1-|Ψv(ω)|2].
Wmse(θ)=|Ψˆv(ω)-Ψv(ω|θ)|21L[1-|Ψv(ω|θ)|2]dω,
λ(θ|{v(l)})=l=1L log[pˆr(v(l)|θ)].
Wmse(θ)=|Ψv(ω|θ)-Ψˆv(ω)|21L[1-|Ψv(ω|θ)|2]dω
=|Ψv(ω|θ)-Ψˆv(ω)|21L[1-|Ψv(ω|θ)|2]pr(ω)pr(ω)dω
1Jj=1J|Ψv(ψj|θ)-Ψˆv(ωj)|21L[1-|Ψv(ωj|θ)|2]1pr(ωj),
ΨΛ(ξ|θ)=p(c)exp-2πidrξ(r)Λ(r-c)dc,
ΨΛ(ω|θ)=p(c)exp-2πim=1Mhm(r)Γ(Tω)m×Λ(r-c)drdc
=p(c)exp-2πim=1MΓ(Tω)m×hm(r)Λ(r-c)drdc.
Hx=m=1Mhm(r)xm.
g¯m=γhm(r)f(r)dr,

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