Abstract

We estimated human observer linear templates underlying the detection of a realistic, spherical mass signal with mammographic backgrounds. Five trained naïve observers participated in two-alternative forced-choice (2-AFC) detection experiments with the signal superimposed on synthetic, clustered lumpy backgrounds (CLBs) in one condition and on nonstationary real mammographic backgrounds in another. Human observer linear templates were estimated using a genetic algorithm. A variety of common model observer templates were computed, and their shapes and associated performances were compared with those of the human observer. The estimated linear templates are not significantly different for stationary CLBs and real mammographic backgrounds. The estimated performance of the linear template compared with that of the human observers is within 5% in terms of percent correct (Pc) for the 2-AFC task. Channelized Hotelling models can fit human performance, but the templates differ considerably from the human linear template. Due to different local statistics, detection efficiency is significantly higher on nonstationary real backgrounds than on globally stationary synthetic CLBs. This finding emphasizes that nonstationary backgrounds need to be described by their local statistics.

© 2007 Optical Society of America

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References

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  2. P. F. Judy, R. G. Swensson, R. D. Nawfel, and K. H. Chan, "Contrast detail curves for liver CT," Med. Phys. 19, 1167-1174 (1992).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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  20. A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Lesion detection in digital mammograms," Proc. SPIE 4320, 555-560 (2001).
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    [CrossRef]
  22. 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).
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  24. C. Castella, K. Kinkel, F. Descombes, M. P. Eckstein,P.-E. Sottas, F. R. Verdun, and F. O. Bochud, "Mammographic texture synthesis using genetic programming and clustered lumpy background," Proc. SPIE 6146, 238-249 (2006).
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    [CrossRef]
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    [CrossRef] [PubMed]
  31. H. H. Barrett, J. Yao, J. P. Rolland, and K. J. Myers, "Model observers for assessment of image quality," Proc. Natl. Acad. Sci. U.S.A. 90, 9758-9765 (1993).
    [CrossRef] [PubMed]
  32. H. H. Barrett, C. K. Abbey, and 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]
  33. F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds," J. Opt. Soc. Am. A 17, 193-205 (2000).
    [CrossRef]
  34. K. J. Myers and H. H. Barrett, "The addition of a channel mechanism to the ideal-observer model," J. Opt. Soc. Am. A 4, 2447-2457 (1987).
    [CrossRef] [PubMed]
  35. C. K. Abbey and H. H. Barrett, "Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability," J. Opt. Soc. Am. A 18, 473-487 (2001).
    [CrossRef]
  36. C. K. Abbey and H. H. Barrett, "Linear iterative reconstruction algorithms: study of observers performance," in Proceedings of the 14th International Conference on Information Processing in Medical Imaging, Y.Bizais, C.Barillot, and R.Di Paola, eds. (Kluwer Academic, 1995), pp. 65-76.
  37. C. K. Abbey, H. H. Barrett, and D. W. Wilson, "Observer signal-to-noise ratios for the ML-EM algorithm," Proc. SPIE 2712, 47-58 (1996).
    [CrossRef]
  38. A. Papoulis, Probability, Random Variables, and Stochastic Processes (McGraw-Hill, 1991).
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    [CrossRef] [PubMed]
  40. S. Muller, "Full-field digital mammography designed as a complete system," Eur. J. Radiol. 31, 25-34 (1999).
    [CrossRef] [PubMed]
  41. J. Eng, "JLABROC4: Maximum likelihood estimation of a binormal ROC curve from continuously distributed test results," Version 1.0.1 (The Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins University), http://www.rad.jhmi.edu/jeng/javarad/roc/main.html.
  42. A. E. Burgess and B. Colborne, "Visual signal detection. IV. Observer inconsistency," J. Opt. Soc. Am. A 5, 617-627 (1988).
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2007 (1)

C. Castella, K. Kinkel, F. Descombes, M. P. Eckstein, P. Sottas, F. R. Verdun, and F. O. Bochud, "Mass detection on real and synthetic mammograms: human observer templates and local statistics," Proc. SPIE 6515, 65150U (2007).
[CrossRef]

2006 (2)

C. Castella, K. Kinkel, F. Descombes, M. P. Eckstein,P.-E. Sottas, F. R. Verdun, and F. O. Bochud, "Mammographic texture synthesis using genetic programming and clustered lumpy background," Proc. SPIE 6146, 238-249 (2006).

Y. Zhang, C. K. Abbey, and M. P. Eckstein, "Adaptative detection mechanisms in globally statistically nonstationary-oriented noise," J. Opt. Soc. Am. A 7, 1549-1558 (2006).
[CrossRef]

2004 (1)

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Search for lesions in mammograms: non-Gaussian observer response," Med. Phys. 31, 24-36 (2004).
[CrossRef] [PubMed]

2003 (1)

A. E. Burgess and P. F. Judy, "Detection in power-law noise: spectrum exponents and CD diagram slopes," Proc. SPIE 5034, 57-62 (2003).
[CrossRef]

2002 (6)

C. K. Abbey and M. P. Eckstein, "Classification image analysis: estimation and statistical inference for two-alternative forced-choice experiments," J. Vision 2, 66-78 (2002).
[CrossRef]

C. K. Abbey and M. P. Eckstein, "Optimal shifted estimates of human-observer templates in two-alternative forced choice experiments," IEEE Trans. Med. Imaging 21, 429-440 (2002).
[CrossRef] [PubMed]

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]

A. J. Ahumada, Jr., "Classification image weights and internal noise level estimation," J. Vision 2, 121-131 (2002).
[CrossRef]

J. A. Solomon, "Noise reveals visual mechanisms of detection and discrimination," J. Vision 2, 105-120 (2002).
[CrossRef]

R. F. Murray, P. J. Bennett, and A. B. Sekuler, "Optimal methods for calculating classification images: weighted sums," J. Vision 2, 79-104 (2002).
[CrossRef]

2001 (2)

2000 (2)

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds," J. Opt. Soc. Am. A 17, 193-205 (2000).
[CrossRef]

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, P. R. Granfors, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full breast digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).
[CrossRef] [PubMed]

1999 (3)

S. Muller, "Full-field digital mammography designed as a complete system," Eur. J. Radiol. 31, 25-34 (1999).
[CrossRef] [PubMed]

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Statistical texture synthesis of mammographic images with clustered lumpy backgrounds," Opt. Express 4, 33-43 (1999).
[CrossRef] [PubMed]

F. O. Bochud, J.-F. Valley, F. R. Verdun, C. Hessler, and P. Schnyder, "Estimation of the noisy component of anatomical backgrounds," Med. Phys. 26, 1365-1370 (1999).
[CrossRef] [PubMed]

1998 (1)

1996 (3)

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

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]

C. Herrmann, E. Buhr, and D. Hoeschen, "Bildrauschen und Diagnose von Rundherden in Thoraxaufnahme," Z. Med. Phys. 6, 80-86 (1996).

1994 (3)

S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, and R. D. Nawfel, "Flattening of the contrast-detail curve for large lesions on liver CT images," Med. Phys. 21, 1547-1555 (1994).
[CrossRef] [PubMed]

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

D. Whitley, "A genetic algorithm tutorial," Stat. Comput. 4, 65-85 (1994).
[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. U.S.A. 90, 9758-9765 (1993).
[CrossRef] [PubMed]

1992 (2)

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]

P. F. Judy, R. G. Swensson, R. D. Nawfel, and K. H. Chan, "Contrast detail curves for liver CT," Med. Phys. 19, 1167-1174 (1992).
[CrossRef] [PubMed]

1990 (1)

1988 (1)

1987 (3)

1985 (1)

1984 (1)

1981 (1)

A. E. Burgess, R. F. Wagner, R. J. Jennings, and H. B. Barlow, "Efficiency of human visual signal discrimination," Science 214, 93-94 (1981).
[CrossRef]

1954 (1)

W. W. Peterson, T. G. Birdsall, and W. C. Fox, "The theory of signal detectability," IEEE Trans. Inf. Theory 4, 171-212 (1954).
[CrossRef]

Eur. J. Radiol. (1)

S. Muller, "Full-field digital mammography designed as a complete system," Eur. J. Radiol. 31, 25-34 (1999).
[CrossRef] [PubMed]

IEEE Trans. Inf. Theory (1)

W. W. Peterson, T. G. Birdsall, and W. C. Fox, "The theory of signal detectability," IEEE Trans. Inf. Theory 4, 171-212 (1954).
[CrossRef]

IEEE Trans. Med. Imaging (1)

C. K. Abbey and M. P. Eckstein, "Optimal shifted estimates of human-observer templates in two-alternative forced choice experiments," IEEE Trans. Med. Imaging 21, 429-440 (2002).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (13)

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]

Y. Zhang, C. K. Abbey, and M. P. Eckstein, "Adaptative detection mechanisms in globally statistically nonstationary-oriented noise," J. Opt. Soc. Am. A 7, 1549-1558 (2006).
[CrossRef]

H. H. Barrett, C. K. Abbey, and 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]

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Visual signal detection in structured backgrounds. III. Calculation of figures of merit for model observers in statistically nonstationary backgrounds," J. Opt. Soc. Am. A 17, 193-205 (2000).
[CrossRef]

K. J. Myers and H. H. Barrett, "The addition of a channel mechanism to the ideal-observer model," J. Opt. Soc. Am. A 4, 2447-2457 (1987).
[CrossRef] [PubMed]

C. K. Abbey and H. H. Barrett, "Human- and model-observer performance in ramp-spectrum noise: effects of regularization and object variability," J. Opt. Soc. Am. A 18, 473-487 (2001).
[CrossRef]

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

R. D. Fiete, H. H. Barrett, W. E. Smith, and K. J. Myers, "The Hotelling trace criterion and its correlation with human observer performance," J. Opt. Soc. Am. A 4, 945-953 (1987).
[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]

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]

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

A. E. Burgess and B. Colborne, "Visual signal detection. IV. Observer inconsistency," J. Opt. Soc. Am. A 5, 617-627 (1988).
[CrossRef] [PubMed]

J. Vision (4)

A. J. Ahumada, Jr., "Classification image weights and internal noise level estimation," J. Vision 2, 121-131 (2002).
[CrossRef]

J. A. Solomon, "Noise reveals visual mechanisms of detection and discrimination," J. Vision 2, 105-120 (2002).
[CrossRef]

R. F. Murray, P. J. Bennett, and A. B. Sekuler, "Optimal methods for calculating classification images: weighted sums," J. Vision 2, 79-104 (2002).
[CrossRef]

C. K. Abbey and M. P. Eckstein, "Classification image analysis: estimation and statistical inference for two-alternative forced-choice experiments," J. Vision 2, 66-78 (2002).
[CrossRef]

Med. Phys. (5)

F. O. Bochud, J.-F. Valley, F. R. Verdun, C. Hessler, and P. Schnyder, "Estimation of the noisy component of anatomical backgrounds," Med. Phys. 26, 1365-1370 (1999).
[CrossRef] [PubMed]

F. O. Bochud, C. K. Abbey, and M. P. Eckstein, "Search for lesions in mammograms: non-Gaussian observer response," Med. Phys. 31, 24-36 (2004).
[CrossRef] [PubMed]

P. F. Judy, R. G. Swensson, R. D. Nawfel, and K. H. Chan, "Contrast detail curves for liver CT," Med. Phys. 19, 1167-1174 (1992).
[CrossRef] [PubMed]

S. E. Seltzer, P. F. Judy, R. G. Swensson, K. H. Chan, and R. D. Nawfel, "Flattening of the contrast-detail curve for large lesions on liver CT images," Med. Phys. 21, 1547-1555 (1994).
[CrossRef] [PubMed]

S. Vedantham, A. Karellas, S. Suryanarayanan, D. Albagli, S. Han, E. J. Tkaczyk, C. E. Landberg, B. Opsahl-Ong, P. R. Granfors, I. Levis, C. J. D'Orsi, and R. E. Hendrick, "Full breast digital mammography with an amorphous silicon-based flat panel detector: physical characteristics of a clinical prototype," Med. Phys. 27, 558-567 (2000).
[CrossRef] [PubMed]

Opt. Express (1)

Proc. Natl. Acad. Sci. U.S.A. (1)

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

Proc. Soc. Inf. Display (1)

P. G. J. Barten, "The SQRI method: a new method for the evaluation of visible resolution on a display," Proc. Soc. Inf. Display 28, 253-262 (1987).

Proc. SPIE (6)

C. Castella, K. Kinkel, F. Descombes, M. P. Eckstein,P.-E. Sottas, F. R. Verdun, and F. O. Bochud, "Mammographic texture synthesis using genetic programming and clustered lumpy background," Proc. SPIE 6146, 238-249 (2006).

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]

C. Castella, K. Kinkel, F. Descombes, M. P. Eckstein, P. Sottas, F. R. Verdun, and F. O. Bochud, "Mass detection on real and synthetic mammograms: human observer templates and local statistics," Proc. SPIE 6515, 65150U (2007).
[CrossRef]

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

A. E. Burgess, F. L. Jacobson, and P. F. Judy, "Lesion detection in digital mammograms," Proc. SPIE 4320, 555-560 (2001).
[CrossRef]

A. E. Burgess and P. F. Judy, "Detection in power-law noise: spectrum exponents and CD diagram slopes," Proc. SPIE 5034, 57-62 (2003).
[CrossRef]

Science (1)

A. E. Burgess, R. F. Wagner, R. J. Jennings, and H. B. Barlow, "Efficiency of human visual signal discrimination," Science 214, 93-94 (1981).
[CrossRef]

Stat. Comput. (1)

D. Whitley, "A genetic algorithm tutorial," Stat. Comput. 4, 65-85 (1994).
[CrossRef]

Z. Med. Phys. (1)

C. Herrmann, E. Buhr, and D. Hoeschen, "Bildrauschen und Diagnose von Rundherden in Thoraxaufnahme," Z. Med. Phys. 6, 80-86 (1996).

Other (5)

J. Beutel, H. L. Kundel, and R. L. Van Metter, Handbook of Medical Imaging Volume 1. Physics and Psychophysics (SPIE, 2000).

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

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

C. K. Abbey and H. H. Barrett, "Linear iterative reconstruction algorithms: study of observers performance," in Proceedings of the 14th International Conference on Information Processing in Medical Imaging, Y.Bizais, C.Barillot, and R.Di Paola, eds. (Kluwer Academic, 1995), pp. 65-76.

J. Eng, "JLABROC4: Maximum likelihood estimation of a binormal ROC curve from continuously distributed test results," Version 1.0.1 (The Russell H. Morgan Department of Radiology and Radiological Science, Johns Hopkins University), http://www.rad.jhmi.edu/jeng/javarad/roc/main.html.

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Figures (10)

Fig. 1
Fig. 1

Channels used for (a) the SQR model, (b) the S-DOG model, and (c) the D-DOG model. The gray area represents the signal frequency profile.

Fig. 2
Fig. 2

Dimensions of the original signal (S) and attenuation function used for the surrounding background. Display screen pixel size is 0.25 mm .

Fig. 3
Fig. 3

(a) Normalized profile of the signal used in the psychophysical experiments. (b) Fourier space representation. Display screen pixel size is 0.25 mm .

Fig. 4
Fig. 4

Examples of (a) signal-present real background and (b) signal-absent CLB. The amplitude of the signal has been increased for printing purposes.

Fig. 5
Fig. 5

Human observer template obtained when pooling the five observers’ data. (a) CLBs. (b) Real backgrounds. Profiles of both templates in (c) the spatial domain and in (d) the Fourier domain. Display screen pixel size is 0.25 mm .

Fig. 6
Fig. 6

Results of the 2-AFC experiments performed on the CLBs and real backgrounds. (a) Performance of each human observer and the corresponding linear templates presented in terms of Pc. (b) ROC curve computed with the templates obtained from the pooled data (the dim bands around the curves show the 95% confidence intervals).

Fig. 7
Fig. 7

Model observer templates presented as 2D images. (a) ROI, (b) NPW, (c) NPWE, (d) SQR, (e) S-DOG, (f) D-DOG.

Fig. 8
Fig. 8

Radial frequency profiles of the model observer templates estimated for the detection task with real backgrounds. The frequency profiles of the signal and the human linear template are shown for comparison. (a) NPWE and SQR models. (b) S-DOG and D-DOG models. Similar results are obtained with CLB images.

Fig. 9
Fig. 9

Performance of the various model observers in the 2-AFC experiment and comparison with human data (dotted lines). The performance is given by the AUC for all model observers and for the percentage of correct responses for the pooled human observers. NPWE* and D-DOG* values correspond to the NPWE and D-DOG with noise added in the model, respectively, in order to match human observer performance on CLBs.

Fig. 10
Fig. 10

(a) Noise power spectrum of the real backgrounds and the CLBs. Slope in the linear part is 3.23 for the real images and 3.17 for the CLBs. (b) Distribution of the local variance across real backgrounds and CLB images. The local variance is defined as the variance computed for a 40 × 40 pixel area around the center of the image.

Tables (2)

Tables Icon

Table 1 Definitions and Values of the Variables Used in the CLB Model

Tables Icon

Table 2 Weighted wRMSD between the Frequency Profiles of the HLT Estimated from the Pooled Observer Data for Real Images and the Other Model Observer Templates a

Equations (16)

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λ = w t g + ϵ ,
o i = s t e p ( λ + λ ) = s t e p ( w t Δ g i + Δ ϵ i ) .
p ( o i = 1 ) p i = Φ ( w t Δ g i 2 σ ) ,
p i = Φ ( w t Δ g i 2 ) .
Pr ( o i Δ g i , w ) = p i o i ( 1 p i ) 1 o i ,
L i ( w ) = f joint ( o i , Δ g i ; w ) = Pr ( o i Δ g i ; w ) f marg ( Δ g i ) ,
l ( w ) = ln ( i = 1 N T L i ( w ) ) = i = 1 N T [ o i ln ( p i ( w ) ) + ( 1 o i ) ln ( 1 p i ( w ) ) + ln ( f marg ( Δ g i ) ) ] .
Q ( w ) = i = 1 N T [ o i ln ( p i ( w ) ) + ( 1 o i ) ln ( 1 p i ( w ) ) ] .
w = j = 1 N C β j t j ,
p i = Φ ( ( j = 1 N c β j t j T ) Δ g i 2 ) Φ ( j = 1 N c β j X i j 2 ) ,
E ( ρ ) = ρ n exp ( c ρ 2 ) ,
w N P W = E t Es ,
w H O T = K b 1 s ,
w C H = T ( T t K b T + K ϵ ) 1 T t s ,
g ( r ) = k = 1 K , small n = 1 N k , small b small ( r r k , small r k n , small , R θ k , small ) + k = 1 K , large n = 1 N k , large b large ( r r k , large r k n , large , R θ k , large ) ,
b ( r , R θ ) = exp ( α R θ r β L ( R θ r ) ) .

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