Abstract

We report a method for evaluating the performance of model observers for decompressed images in analytical form using compression noise statistics. It derives test statistics and detectabilities for the ideal observer, the nonprewhitening observer, the Hotelling observer, and the channelized Hotelling observer (CHO) on decompressed images. The derived CHO performance is validated using the Joint Photographic Experts Group (JPEG) compression algorithm. The validation results show that the derived CHO receiver operating characteristics (ROCs) and areas under ROC curves predict accurately their corresponding estimated values. These analytical-form quality measures of decompressed images provide a way to optimize compression algorithms analytically, subject to a model-observer performance criterion. They also provide a theoretical foundation for efforts to create a model observer for decompressed images.

© 2007 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |

  1. H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).
  2. M. Eckstein, C. Abbey, and F. Bochud, "A practical guide to model observers for visual detection in synthetic and natural noisy images," in Handbook of Medical Imaging, J.Beutel, H.Kundel, and R.van Metter, eds. (SPIE Press, 2000), Vol. 1, Chap. 10, pp. 593-628.
  3. H. Barrett, J. Yao, J. Rolland, and K. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
    [CrossRef] [PubMed]
  4. A. Burgess, X. Li, and C. Abbey, "Visual signal detectability with two noise components: anomalous masking effects," J. Opt. Soc. Am. A 14, 2420-2442 (1997).
    [CrossRef]
  5. C. Abbey and 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. M. Eckstein, C. Abbey, F. Bochud, J. Bartroff, and J. Whiting, "The effect of image compression in model and human performance," Proc. SPIE 3663, 284-295 (1999).
    [CrossRef]
  7. C. A. Morioka, M. P. Eckstein, J. L. Bartroff, J. Hansleiter, G. Aharanov, and J. S. Whiting, "Observer performance for JPEG versus wavelet image compression of x-ray coronary angiograms," Opt. Express 5, 8-19 (1999).
    [CrossRef] [PubMed]
  8. B. Schmanske and M. Loew, "Bit-plane-channelized Hotelling observer for predicting task performance using lossy-compressed images," Proc. SPIE 5034, 77-88 (2003).
    [CrossRef]
  9. B. Schmanske, "Task-based assessment of quality applied to compressed radiological images," Ph.D. dissertation (George Washington University, 2003).
  10. D. Li, "Statistics of transform coding and assessment of decompressed image quality," Ph.D. dissertation (George Washington University, 2007).
  11. D. Li and M. Loew, "Closed-form quality measures for compressed medical images: Statistical preliminaries for transform coding," 25th Annual International Conference of IEEE Engineering in Medicine and Biology Society (IEEE, 2003).
  12. D. Li and M. Loew, "Closed-form quality measures for compressed medical images: compression noise statistics of transform coding," Proc. SPIE 5372, 218-229 (2004).
    [CrossRef]
  13. D. Li and M. Loew, "Model-observer based quality measures for decompressed medical images," IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE, 2004), pp. 832-835, Vol. 1.
  14. D. Li and M. Loew, "Closed-form compression noise in images with known statistics," Proc. SPIE 5749, 211-222 (2005).
    [CrossRef]
  15. K. Sayood, Introduction to Data Compression, 2nd ed. (Morgan Kaufmann, 2000).
  16. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, 1991).
  17. G. Wallace, "The JPEG still picture compression standard," Commun. ACM 34, 30-44 (1991).
    [CrossRef]
  18. W. B. Pennebaker and J. L. Mitchell, JPEG: Still Image Data Compression Standard (Van Nostrand Reinhold, 1993).
  19. B. D. Gallas, "Signal detection in lumpy noise," Ph.D. dissertation (University of Arizona, 2001).
  20. C. K. Abbey, M. P. Eckstein, S. S. Shimozaki, A. H. Baydush, D. M. Catarious, and C. E. Floyd, "Human-observer templates for detection of a simulated lesion in mammographic images," Proc. SPIE 4686, 25-36 (2002).
    [CrossRef]

2005

D. Li and M. Loew, "Closed-form compression noise in images with known statistics," Proc. SPIE 5749, 211-222 (2005).
[CrossRef]

2004

D. Li and M. Loew, "Closed-form quality measures for compressed medical images: compression noise statistics of transform coding," Proc. SPIE 5372, 218-229 (2004).
[CrossRef]

2003

B. Schmanske and M. Loew, "Bit-plane-channelized Hotelling observer for predicting task performance using lossy-compressed images," Proc. SPIE 5034, 77-88 (2003).
[CrossRef]

2002

C. K. Abbey, M. P. Eckstein, S. S. Shimozaki, A. H. Baydush, D. M. Catarious, and C. E. Floyd, "Human-observer templates for detection of a simulated lesion in mammographic images," Proc. SPIE 4686, 25-36 (2002).
[CrossRef]

2001

1999

1997

1993

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

1991

G. Wallace, "The JPEG still picture compression standard," Commun. ACM 34, 30-44 (1991).
[CrossRef]

Commun. ACM

G. Wallace, "The JPEG still picture compression standard," Commun. ACM 34, 30-44 (1991).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Express

Proc. Natl. Acad. Sci. U.S.A.

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

Proc. SPIE

M. Eckstein, C. Abbey, F. Bochud, J. Bartroff, and J. Whiting, "The effect of image compression in model and human performance," Proc. SPIE 3663, 284-295 (1999).
[CrossRef]

C. K. Abbey, M. P. Eckstein, S. S. Shimozaki, A. H. Baydush, D. M. Catarious, and C. E. Floyd, "Human-observer templates for detection of a simulated lesion in mammographic images," Proc. SPIE 4686, 25-36 (2002).
[CrossRef]

B. Schmanske and M. Loew, "Bit-plane-channelized Hotelling observer for predicting task performance using lossy-compressed images," Proc. SPIE 5034, 77-88 (2003).
[CrossRef]

D. Li and M. Loew, "Closed-form quality measures for compressed medical images: compression noise statistics of transform coding," Proc. SPIE 5372, 218-229 (2004).
[CrossRef]

D. Li and M. Loew, "Closed-form compression noise in images with known statistics," Proc. SPIE 5749, 211-222 (2005).
[CrossRef]

Other

K. Sayood, Introduction to Data Compression, 2nd ed. (Morgan Kaufmann, 2000).

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 3rd ed. (McGraw-Hill, 1991).

D. Li and M. Loew, "Model-observer based quality measures for decompressed medical images," IEEE International Symposium on Biomedical Imaging: Nano to Macro (IEEE, 2004), pp. 832-835, Vol. 1.

B. Schmanske, "Task-based assessment of quality applied to compressed radiological images," Ph.D. dissertation (George Washington University, 2003).

D. Li, "Statistics of transform coding and assessment of decompressed image quality," Ph.D. dissertation (George Washington University, 2007).

D. Li and M. Loew, "Closed-form quality measures for compressed medical images: Statistical preliminaries for transform coding," 25th Annual International Conference of IEEE Engineering in Medicine and Biology Society (IEEE, 2003).

H. Barrett and K. Myers, Foundations of Image Science (Wiley, 2004).

M. Eckstein, C. Abbey, and F. Bochud, "A practical guide to model observers for visual detection in synthetic and natural noisy images," in Handbook of Medical Imaging, J.Beutel, H.Kundel, and R.van Metter, eds. (SPIE Press, 2000), Vol. 1, Chap. 10, pp. 593-628.

W. B. Pennebaker and J. L. Mitchell, JPEG: Still Image Data Compression Standard (Van Nostrand Reinhold, 1993).

B. D. Gallas, "Signal detection in lumpy noise," Ph.D. dissertation (University of Arizona, 2001).

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 (9)

Fig. 1
Fig. 1

Image transform coding process.

Fig. 2
Fig. 2

Example of 2AFC experiment.

Fig. 3
Fig. 3

Image transform coding with additive quantization noise.

Fig. 4
Fig. 4

2AFC tests for original and decompressed lumpy-background images.

Fig. 5
Fig. 5

Comparison of covariance matrices of lumpy-background decompressed images.

Fig. 6
Fig. 6

Original and decompressed signal images.

Fig. 7
Fig. 7

Derived and estimated covariance matrices of compression noise for JPEG lumpy-background images.

Fig. 8
Fig. 8

Laguerre–Gauss channel profile.

Fig. 9
Fig. 9

ROC curves for CHO on lumpy-background images with circle disk signal.

Tables (3)

Tables Icon

Table 1 Decision Outcomes of 2AFC Experiments

Tables Icon

Table 2 Relative MSE (Percent) between Covariance Matrices of Lumpy-Background Decompressed Images with Different Present Signals

Tables Icon

Table 3 AUCs of CHO for Decompressed Images

Equations (33)

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

AUC = 0 1 TPF d ( FPF )
d A = 2 erf 1 ( 2 AUC 1 ) .
Y = A X
X r = A T Y q ,
Q = Y q Y
R = X r X ,
E [ R ] = A T m Q
Cov ( R ) = A T Cov ( Q ) A ,
P R ( R ) = n D n p Y ( A R + T n ) A ,
p R ( R ) = exp { ( ( R E [ R ] ) T Cov ( R ) ( R E [ R ] ) 2 ) } ( 2 π ) N b B 2 Cov ( R ) ,
X = { N signal absent S 0 + N signal present .
X r = { N + R 1 signal absent S + N + R 2 signal present ,
E [ X r ] = { E [ N ] + E [ R 1 ] signal absent S + E [ N ] + E [ R 2 ] signal present
Cov ( X r ) = { Cov ( N + R 1 ) signal absent Cov ( N + R 2 ) signal present ,
p ( X r T i ) = exp [ ( X r m i ) Cov ( X r T i ) 1 ( X r m i ) 2 ] ( 2 π ) L Cov ( X r T i ) ,
λ ideal ( X ) = log ( P ( X r T 2 ) P ( X r T 1 ) ) .
λ ideal ( X r ) = ( S 0 + E [ R 2 ] E [ R 1 ] ) T { Cov ( N ) + [ Cov ( R 1 ) + Cov ( R 2 ) ] 2 } 1 X r ,
d ideal 2 = ( S 0 + E [ R 2 ] E [ R 1 ] ) T { Cov ( N ) + [ Cov ( R 1 ) + Cov ( R 2 ) ] 2 } 1 ( S 0 + E [ R 2 ] E [ R 1 ] ) .
λ ideal ( X r ) = S 0 T { Cov ( N ) + [ Cov ( R 1 ) + Cov ( R 2 ) ] 2 } 1 X r
d ideal 2 = S 0 T { Cov ( N ) + [ Cov ( R 1 ) + Cov ( R 2 ) ] 2 } 1 S 0 .
λ hot = S T { Cov ( N ) + [ Cov ( R 1 ) + Cov ( R 2 ) ] 2 } 1 X r
d hot 2 = S T { Cov ( N ) + [ Cov ( R 1 ) + Cov ( R 2 ) ] 2 } 1 S ,
λ NPW ( X r ) = S T X r
d NPW 2 = 2 ( S T S ) 2 ( S T { Cov ( N ) + [ Cov ( R 1 ) + Cov ( R 2 ) ] 2 } S ) ,
λ chot ( X r ) = S T ( T T [ Cov ( N ) + { Cov ( R 1 ) + Cov ( R 2 ) ] 2 } T ) 1 T T X r
d chot 2 = S T T ( T T { Cov ( N ) + [ Cov ( R 1 ) + Cov ( R 2 ) ] 2 } T ) 1 T T S ,
{ Cov ( N ) + [ Cov ( R 1 ) + Cov ( R 2 ) ] 2 } Cov ( N ) + Cov ( R 1 ) ,
D rmse = i = 1 L j = 1 L [ C 1 ( i , j ) C 2 ( i , j ) ] 2 i = 1 L j = 1 L C 2 ( i , j ) 2 ,
X = p Re ( F 1 WF N ) ,
P Y ( Y ) = exp [ Y T Cov ( Y ) 1 Y 2 ] ( 2 π ) L Cov ( Y ) ,
P Y ( y i ) = exp ( y i 2 2 σ y i 2 ) 2 π σ y i 2 ,
P Y ( y i , y j ) = exp { [ y i 2 σ y i 2 2 ρ i , j y i y j ( σ y i σ y j ) + y j 2 σ y j 2 ] 2 ( 1 ρ i , j 2 ) } ( 2 π σ y i σ y j 1 ρ i , j 2 ) ,
L n ( x ) = m = 0 n ( 1 ) m ( n m ) x m m ! .

Metrics