Abstract

We sought to determine whether the detection and the identification of texture modulations are mediated by a common mechanism. On each trial two textures were presented, one of which contained a modulation in orientation (OM), spatial frequency (FM), or contrast (CM). Observers were required to indicate whether the modulated texture was presented in the first or the second interval as well as the nature of the texture modulation. The results showed that for two of the three pairwise matchings (OM–FM and OM–CM) detection and identification performance were nearly identical, suggesting a common underlying mechanism. However, when FM and CM textures were paired, discrimination thresholds were significantly higher than detection thresholds. In the context of the filter–rectify–filter model of texture perception, our results suggest that the mechanisms underlying detection are labeled with respect to their first-order input; i.e., the identities of these mechanisms are available to higher levels of processing. Several possible explanations for the misidentification of FM and CM at detection threshold are considered.

© 2003 Optical Society of America

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References

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  1. H. Wilson, “Non-Fourier cortical processes in texture, form, and motion perception,” Cereb. Cortex 13, 445–477 (1999).
    [CrossRef]
  2. C. L. Baker, “Central neural mechanisms for detecting second-order motion,” Curr. Opin. Neurobiol. 9, 461–466 (1999).
    [CrossRef] [PubMed]
  3. A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
    [CrossRef] [PubMed]
  4. S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
    [CrossRef] [PubMed]
  5. J. Malik, P. Perona, “Preattentive texture discrimination with early vision mechanisms,” J. Opt. Soc. Am. A 7, 923–932 (1990).
    [CrossRef] [PubMed]
  6. J. R. Bergen, M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 253–271.
  7. M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
    [CrossRef] [PubMed]
  8. F. A. A. Kingdom, D. R. T. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
    [CrossRef] [PubMed]
  9. R. Gray, D. Regan, “Spatial frequency discrimination and detection characteristics for gratings defined by orientation texture,” Vision Res. 38, 2601–2617 (1998).
    [CrossRef]
  10. N. Prins, A. J. Mussap, “Alignment of orientation-modulated textures,” Vision Res. 40, 3567–3573 (2000).
    [CrossRef] [PubMed]
  11. N. Graham, A. Sutter, C. Venkatesan, “Spatial-frequency- and orientation-selectivity of simple and complex channels in region segregation,” Vision Res. 33, 1893–1911 (1993).
    [CrossRef] [PubMed]
  12. S. A. Arsenault, F. Wilkinson, F. A. A. Kingdom, “Modulation frequency and orientation tuning of second-order texture mechanisms,” J. Opt. Soc. Am. A 16, 427–435 (1999).
    [CrossRef]
  13. N. Graham, A. Sutter, “Spatial summation in simple (Fourier) and complex (non-Fourier) texture channels,” Vision Res. 38, 231–257 (1999).
    [CrossRef]
  14. N. Prins, F. A. A. Kingdom, “Orientation- and frequency-modulated textures at low depths of modulation are processed by off-orientation and off-frequency texture mechanisms,” Vision Res. 42, 705–713 (2002).
    [CrossRef] [PubMed]
  15. We model the spectral amplitude distribution here as H(f, θ)=exp(-0.5[(f-f0)/(f0σf)]2)exp(-0.5[(θ-θ0)/σθ]2), where f is frequency, f0 is the dc spatial frequency (5 cpd), σf is a constant determining spatial-frequency bandwidth and set at a value of 0.41, θ is orientation, θ0 is the dc orientation of the texture (0°, horizontal), and σθ is a constant determining orientation bandwidth and set at 25.5. This function describes the average spectral content of the textures used here quite well.14
  16. A. B. Watson, J. C. Robson, “Discrimination at threshold: labeled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
    [CrossRef]
  17. N. Prins, A. J. Mussap, “Adaptation reveals a neural code for the visual location of orientation change,” Perception 30, 669–680 (2001).
    [CrossRef] [PubMed]
  18. P. G. Hoel, S. C. Port, C. J. Stone, Introduction to Statistical Theory (Houghton Mifflin, Boston, Mass., 1971).
  19. F. A. Wichmann, N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness of fit,” Percept. Psychophys. 63, 1293–1313 (2001).
    [CrossRef]
  20. The statistical test employed to assess goodness of fit indicated a poor fit for the identification curve of NP in the OM–CM condition (p<0.01). However, as the reader may verify by inspection of Fig. 4, the data appear to fit the curve quite well. As it turns out, the poor goodness of fit is due almost entirely to one data point, namely, identification performance for OM textures at the second-highest value of modulation amplitude. This suggests that the poor fit is likely a spurious result. The p value of the deviance score calculated when this data point is omitted is 0.57.
  21. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
    [PubMed]
  22. L. A. Olzak, J. P. Thomas, “Neural recoding in human pattern vision: model and mechanisms,” Vision Res. 39, 231–256 (1999).
    [CrossRef] [PubMed]

2002 (1)

N. Prins, F. A. A. Kingdom, “Orientation- and frequency-modulated textures at low depths of modulation are processed by off-orientation and off-frequency texture mechanisms,” Vision Res. 42, 705–713 (2002).
[CrossRef] [PubMed]

2001 (2)

N. Prins, A. J. Mussap, “Adaptation reveals a neural code for the visual location of orientation change,” Perception 30, 669–680 (2001).
[CrossRef] [PubMed]

F. A. Wichmann, N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness of fit,” Percept. Psychophys. 63, 1293–1313 (2001).
[CrossRef]

2000 (2)

S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
[CrossRef] [PubMed]

N. Prins, A. J. Mussap, “Alignment of orientation-modulated textures,” Vision Res. 40, 3567–3573 (2000).
[CrossRef] [PubMed]

1999 (5)

H. Wilson, “Non-Fourier cortical processes in texture, form, and motion perception,” Cereb. Cortex 13, 445–477 (1999).
[CrossRef]

C. L. Baker, “Central neural mechanisms for detecting second-order motion,” Curr. Opin. Neurobiol. 9, 461–466 (1999).
[CrossRef] [PubMed]

L. A. Olzak, J. P. Thomas, “Neural recoding in human pattern vision: model and mechanisms,” Vision Res. 39, 231–256 (1999).
[CrossRef] [PubMed]

S. A. Arsenault, F. Wilkinson, F. A. A. Kingdom, “Modulation frequency and orientation tuning of second-order texture mechanisms,” J. Opt. Soc. Am. A 16, 427–435 (1999).
[CrossRef]

N. Graham, A. Sutter, “Spatial summation in simple (Fourier) and complex (non-Fourier) texture channels,” Vision Res. 38, 231–257 (1999).
[CrossRef]

1998 (1)

R. Gray, D. Regan, “Spatial frequency discrimination and detection characteristics for gratings defined by orientation texture,” Vision Res. 38, 2601–2617 (1998).
[CrossRef]

1996 (1)

F. A. A. Kingdom, D. R. T. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

1995 (1)

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

1993 (1)

N. Graham, A. Sutter, C. Venkatesan, “Spatial-frequency- and orientation-selectivity of simple and complex channels in region segregation,” Vision Res. 33, 1893–1911 (1993).
[CrossRef] [PubMed]

1991 (1)

M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
[CrossRef] [PubMed]

1990 (1)

1981 (1)

A. B. Watson, J. C. Robson, “Discrimination at threshold: labeled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[CrossRef]

1968 (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

Arsenault, S. A.

Baker, C. L.

C. L. Baker, “Central neural mechanisms for detecting second-order motion,” Curr. Opin. Neurobiol. 9, 461–466 (1999).
[CrossRef] [PubMed]

Bergen, J. R.

M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
[CrossRef] [PubMed]

J. R. Bergen, M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 253–271.

Campbell, F. W.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

Chubb, C.

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

Dakin, S. C.

S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
[CrossRef] [PubMed]

Graham, N.

N. Graham, A. Sutter, “Spatial summation in simple (Fourier) and complex (non-Fourier) texture channels,” Vision Res. 38, 231–257 (1999).
[CrossRef]

N. Graham, A. Sutter, C. Venkatesan, “Spatial-frequency- and orientation-selectivity of simple and complex channels in region segregation,” Vision Res. 33, 1893–1911 (1993).
[CrossRef] [PubMed]

Gray, R.

R. Gray, D. Regan, “Spatial frequency discrimination and detection characteristics for gratings defined by orientation texture,” Vision Res. 38, 2601–2617 (1998).
[CrossRef]

Hill, N. J.

F. A. Wichmann, N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness of fit,” Percept. Psychophys. 63, 1293–1313 (2001).
[CrossRef]

Hoel, P. G.

P. G. Hoel, S. C. Port, C. J. Stone, Introduction to Statistical Theory (Houghton Mifflin, Boston, Mass., 1971).

Keeble, D. R. T.

F. A. A. Kingdom, D. R. T. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

Kingdom, F. A. A.

N. Prins, F. A. A. Kingdom, “Orientation- and frequency-modulated textures at low depths of modulation are processed by off-orientation and off-frequency texture mechanisms,” Vision Res. 42, 705–713 (2002).
[CrossRef] [PubMed]

S. A. Arsenault, F. Wilkinson, F. A. A. Kingdom, “Modulation frequency and orientation tuning of second-order texture mechanisms,” J. Opt. Soc. Am. A 16, 427–435 (1999).
[CrossRef]

F. A. A. Kingdom, D. R. T. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

Landy, M. S.

M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
[CrossRef] [PubMed]

J. R. Bergen, M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 253–271.

Malik, J.

Mareschal, I.

S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
[CrossRef] [PubMed]

Mussap, A. J.

N. Prins, A. J. Mussap, “Adaptation reveals a neural code for the visual location of orientation change,” Perception 30, 669–680 (2001).
[CrossRef] [PubMed]

N. Prins, A. J. Mussap, “Alignment of orientation-modulated textures,” Vision Res. 40, 3567–3573 (2000).
[CrossRef] [PubMed]

Olzak, L. A.

L. A. Olzak, J. P. Thomas, “Neural recoding in human pattern vision: model and mechanisms,” Vision Res. 39, 231–256 (1999).
[CrossRef] [PubMed]

Perona, P.

Port, S. C.

P. G. Hoel, S. C. Port, C. J. Stone, Introduction to Statistical Theory (Houghton Mifflin, Boston, Mass., 1971).

Prins, N.

N. Prins, F. A. A. Kingdom, “Orientation- and frequency-modulated textures at low depths of modulation are processed by off-orientation and off-frequency texture mechanisms,” Vision Res. 42, 705–713 (2002).
[CrossRef] [PubMed]

N. Prins, A. J. Mussap, “Adaptation reveals a neural code for the visual location of orientation change,” Perception 30, 669–680 (2001).
[CrossRef] [PubMed]

N. Prins, A. J. Mussap, “Alignment of orientation-modulated textures,” Vision Res. 40, 3567–3573 (2000).
[CrossRef] [PubMed]

Regan, D.

R. Gray, D. Regan, “Spatial frequency discrimination and detection characteristics for gratings defined by orientation texture,” Vision Res. 38, 2601–2617 (1998).
[CrossRef]

Robson, J. C.

A. B. Watson, J. C. Robson, “Discrimination at threshold: labeled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[CrossRef]

Robson, J. G.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

Sperling, G.

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

Stone, C. J.

P. G. Hoel, S. C. Port, C. J. Stone, Introduction to Statistical Theory (Houghton Mifflin, Boston, Mass., 1971).

Sutter, A.

N. Graham, A. Sutter, “Spatial summation in simple (Fourier) and complex (non-Fourier) texture channels,” Vision Res. 38, 231–257 (1999).
[CrossRef]

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

N. Graham, A. Sutter, C. Venkatesan, “Spatial-frequency- and orientation-selectivity of simple and complex channels in region segregation,” Vision Res. 33, 1893–1911 (1993).
[CrossRef] [PubMed]

Thomas, J. P.

L. A. Olzak, J. P. Thomas, “Neural recoding in human pattern vision: model and mechanisms,” Vision Res. 39, 231–256 (1999).
[CrossRef] [PubMed]

Venkatesan, C.

N. Graham, A. Sutter, C. Venkatesan, “Spatial-frequency- and orientation-selectivity of simple and complex channels in region segregation,” Vision Res. 33, 1893–1911 (1993).
[CrossRef] [PubMed]

Watson, A. B.

A. B. Watson, J. C. Robson, “Discrimination at threshold: labeled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[CrossRef]

Wichmann, F. A.

F. A. Wichmann, N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness of fit,” Percept. Psychophys. 63, 1293–1313 (2001).
[CrossRef]

Wilkinson, F.

Wilson, H.

H. Wilson, “Non-Fourier cortical processes in texture, form, and motion perception,” Cereb. Cortex 13, 445–477 (1999).
[CrossRef]

Cereb. Cortex (1)

H. Wilson, “Non-Fourier cortical processes in texture, form, and motion perception,” Cereb. Cortex 13, 445–477 (1999).
[CrossRef]

Curr. Opin. Neurobiol. (1)

C. L. Baker, “Central neural mechanisms for detecting second-order motion,” Curr. Opin. Neurobiol. 9, 461–466 (1999).
[CrossRef] [PubMed]

J. Opt. Soc. Am. A (2)

J. Physiol. (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 197, 551–566 (1968).
[PubMed]

Percept. Psychophys. (1)

F. A. Wichmann, N. J. Hill, “The psychometric function: I. Fitting, sampling, and goodness of fit,” Percept. Psychophys. 63, 1293–1313 (2001).
[CrossRef]

Perception (1)

N. Prins, A. J. Mussap, “Adaptation reveals a neural code for the visual location of orientation change,” Perception 30, 669–680 (2001).
[CrossRef] [PubMed]

Vision Res. (11)

A. Sutter, G. Sperling, C. Chubb, “Measuring the spatial frequency selectivity of second-order texture mechanisms,” Vision Res. 35, 915–924 (1995).
[CrossRef] [PubMed]

S. C. Dakin, I. Mareschal, “Sensitivity to contrast modulation depends on carrier spatial frequency and orientation,” Vision Res. 40, 311–329 (2000).
[CrossRef] [PubMed]

M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
[CrossRef] [PubMed]

F. A. A. Kingdom, D. R. T. Keeble, “A linear systems approach to the detection of both abrupt and smooth spatial variations in orientation-defined textures,” Vision Res. 36, 409–420 (1996).
[CrossRef] [PubMed]

R. Gray, D. Regan, “Spatial frequency discrimination and detection characteristics for gratings defined by orientation texture,” Vision Res. 38, 2601–2617 (1998).
[CrossRef]

N. Prins, A. J. Mussap, “Alignment of orientation-modulated textures,” Vision Res. 40, 3567–3573 (2000).
[CrossRef] [PubMed]

N. Graham, A. Sutter, C. Venkatesan, “Spatial-frequency- and orientation-selectivity of simple and complex channels in region segregation,” Vision Res. 33, 1893–1911 (1993).
[CrossRef] [PubMed]

N. Graham, A. Sutter, “Spatial summation in simple (Fourier) and complex (non-Fourier) texture channels,” Vision Res. 38, 231–257 (1999).
[CrossRef]

N. Prins, F. A. A. Kingdom, “Orientation- and frequency-modulated textures at low depths of modulation are processed by off-orientation and off-frequency texture mechanisms,” Vision Res. 42, 705–713 (2002).
[CrossRef] [PubMed]

L. A. Olzak, J. P. Thomas, “Neural recoding in human pattern vision: model and mechanisms,” Vision Res. 39, 231–256 (1999).
[CrossRef] [PubMed]

A. B. Watson, J. C. Robson, “Discrimination at threshold: labeled detectors in human vision,” Vision Res. 21, 1115–1122 (1981).
[CrossRef]

Other (4)

We model the spectral amplitude distribution here as H(f, θ)=exp(-0.5[(f-f0)/(f0σf)]2)exp(-0.5[(θ-θ0)/σθ]2), where f is frequency, f0 is the dc spatial frequency (5 cpd), σf is a constant determining spatial-frequency bandwidth and set at a value of 0.41, θ is orientation, θ0 is the dc orientation of the texture (0°, horizontal), and σθ is a constant determining orientation bandwidth and set at 25.5. This function describes the average spectral content of the textures used here quite well.14

J. R. Bergen, M. S. Landy, “Computational modeling of visual texture segregation,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 253–271.

P. G. Hoel, S. C. Port, C. J. Stone, Introduction to Statistical Theory (Houghton Mifflin, Boston, Mass., 1971).

The statistical test employed to assess goodness of fit indicated a poor fit for the identification curve of NP in the OM–CM condition (p<0.01). However, as the reader may verify by inspection of Fig. 4, the data appear to fit the curve quite well. As it turns out, the poor goodness of fit is due almost entirely to one data point, namely, identification performance for OM textures at the second-highest value of modulation amplitude. This suggests that the poor fit is likely a spurious result. The p value of the deviance score calculated when this data point is omitted is 0.57.

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Figures (4)

Fig. 1
Fig. 1

FRF mechanism. A schematic FRF mechanism is shown atop a frequency-modulated texture. The amplitude of modulation is 0.2 octave. The excitatory center of the FRF shown covers a texture region in which the center spatial frequency is 0.2 octave below the texture’s dc spatial frequency (5 cpd) and the inhibitory surrounds cover texture regions in which the center spatial frequency is 0.2 octave above the dc spatial frequency. The texture is first filtered with simple first-order luminance filters selective for orientation and spatial frequency. One example Gabor-shaped filter, maximally tuned to a spatial frequency of 3.5 cpd, is shown on the right. The rectified output from the first-stage filter is consequently integrated by the larger second-stage filter. The center region leads to activation of the FRF mechanism (+), whereas the surround leads to inhibition of the FRF mechanism (-). Shown within the receptive fields of the second-stage filter is the full-wave-rectified output from the first-stage (luminance) filter, on the far right of the figure.

Fig. 2
Fig. 2

a, Idealized amplitude spectrum of an unmodulated texture at dc spatial frequency (5 cpd) and dc orientation (horizontal). Besides a scaling factor, this corresponds also to the difference between the amplitude spectra of the two regions of a CM texture. b, Absolute difference between the idealized amplitude spectra of the two texture regions of an OM texture at an amplitude of modulation of 4°. c, Absolute difference between the idealized amplitude spectra of the two texture regions of an FM texture at an amplitude of modulation of 0.1 octave. FRF mechanisms tuned to orientations/spatial frequencies at the peaks in the spectral-difference distribution will be maximally responsive to the texture modulation.

Fig. 3
Fig. 3

Example textures. a, CM texture; modulation amplitude is 25%. b, OM texture; modulation amplitude is 8°. c, FM texture; modulation amplitude is 0.2 octave.

Fig. 4
Fig. 4

Detection and identification performance. Plotted are proportion correct detection and identification as a function of depth of modulation for (a) OM–FM pairing of textures, (b) OM–CM pairing of textures, and (c) FM–CM pairing of textures. Abscissas are linear with respect to depth of modulation in normalized units. Insets show modeled proportions of correct detection [i.e., ωd(snorm, αd, βd) of formula (3); heavy curve] and proportions of correct identification [i.e., ωi(snorm, αi, βi) of formula (4); light curve] produced by the underlying mechanisms for visual comparison. Abscissas of insets are linearly scaled versions of those of the main figures.

Tables (1)

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Table 1 Model Fitsa

Equations (12)

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

L(x, y)=L0+Lm cos{2πf[x sin(θ)+y cos(θ)]+ϕ}×exp[-(x2+y2)/(2σe2)],
σe=(fπ)-1[0.5 ln(2)]1/2(21.5+1)(21.5-1)-1,
snorm=(s/α)β/2,
P(correct|snorm)=γ+(1-γ)ωd(snorm, αd, βd),
P(A|{A, snorm})=ωi(snorm, αi, βi)+[1-ωi(snorm, αi, βi)]PA,
P(A|{A, snorm})=PA+(1-PA)ωi(snorm, αi, βi).
P(B|{B, snorm})=(1-PA)+PAωi(snorm, αi, βi).
P(correct|snorm)=0.5+(1-0.5)ωc(snorm, αc, βc),
P(A|{A, snorm})=PA+(1-PA)ωc(snorm, αc, βc),P(B|{B, snorm})=(1-PA)+PAωc(snorm, αc, βc).
P(correct|snorm)=0.5+(1-0.5)ωd(snorm, αd, βd),
P(A|{A, snorm})=PA+(1-PA)ωi(snorm, αi, βi),P(B|{B, snorm})=(1-PA)+PAωi(snorm, αi, βi).
λ=-2 loge[L(X|α˜c, β˜c, P˜A)/L(X|α˜d, β˜d, α˜i, β˜i, P˜A)],

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