Abstract

We report contrast detection, contrast increment, contrast masking, orientation discrimination, and spatial frequency discrimination thresholds for spatially localized stimuli at 4° of eccentricity. Our stimulus geometry emphasizes interactions among overlapping visual filters and differs from that used in previous threshold measurements, which also admits interactions among distant filters. We quantitatively account for all measurements by simulating a small population of overlapping visual filters interacting through divisive inhibition. We depart from previous models of this kind in the parameters of divisive inhibition and in using a statistically efficient decision stage based on Fisher information. The success of this unified account suggests that, contrary to Bowne [Vision Res. 30, 449 (1990)], spatial vision thresholds reflect a single level of processing, perhaps as early as primary visual cortex.

© 2000 Optical Society of America

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1999 (4)

P. Adorjan, J. B. Levitt, J. S. Lund, K. Obermayer, “A model for the intracortical origin of orientation preference and tuning in macaque striate cortex,” Visual Neurosci. 16, 303–318 (1999).
[CrossRef]

D. K. Lee, L. Itti, C. Koch, J. Braun, “Attention activates winner-take-all competition among visual filters,” Nat. Neurosci. 2, 375–381 (1999).
[CrossRef] [PubMed]

S. Deneve, P. E. Latham, A. Pouget, “Reading population codes: a neural implementation of ideal observers [in process citation],” Nat. Neurosci. 2, 740–745 (1999).
[CrossRef] [PubMed]

A. Das, C. D. Gilbert, “Topography of contextual modulations mediated by short-range interactions in pri-mary visual cortex,” Nature 399, 655–661 (1999).
[CrossRef] [PubMed]

1998 (4)

M. Carandini, J. A. Movshon, D. Ferster, “Pattern adaptation and cross-orientation interactions in the primary visual cortex,” Neuropharmacology 37, 501–511 (1998).
[CrossRef] [PubMed]

A. Pouget, K. Zhang, S. Deneve, P. E. Latham, “Statistically efficient estimation using population coding,” Neural Comput. 10, 373–401 (1998).
[CrossRef] [PubMed]

U. Polat, K. Mizobe, M. W. Pettet, T. Kasamatsu, A. M. Norcia, “Collinear stimuli regulate visual responses depending on cell’s contrast threshold,” Nature 391, 580–584 (1998).
[CrossRef] [PubMed]

M. Ito, G. Westheimer, C. D. Gilbert, “Attention and perceptual learning modulate contextual influences on visual perception,” Neuron 20, 1191–1197 (1998).
[CrossRef] [PubMed]

1997 (14)

J. B. Levitt, J. S. Lund, “Contrast dependence of contextual effects in primate visual cortex,” Nature 387, 73–76 (1997).
[CrossRef] [PubMed]

J. M. Foley, C. C. Chen, “Analysis of the effect of pattern adaptation on pattern pedestal effects: a two-process model,” Vision Res. 37, 2779–2788 (1997).
[CrossRef] [PubMed]

W. S. Geisler, D. G. Albrecht, “Visual cortex neurons in monkeys and cats: detection, discrimination, and identification,” Visual Neurosci. 14, 897–919 (1997).
[CrossRef]

M. Carandini, D. J. Heeger, J. A. Movshon, “Linearity and normalization in simple cells of the macaque primary visual cortex,” J. Neurosci. 17, 8621–8644 (1997).
[PubMed]

M. Carandini, D. L. Ringach, “Predictions of a recurrent model of orientation selectivity,” Vision Res. 37, 3061–3071 (1997).
[CrossRef]

B. Ahmed, J. D. Allison, R. J. Douglas, K. A. Martin, “An intracellular study of the contrast-dependence of neuronal activity in cat visual cortex,” Cereb. Cortex 7, 559–570 (1997).
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C. W. Tyler, “Color bit-stealing to enhance the luminance resolution of digital displays on a single pixel basis,” Spatial Vis. 10, 369–377 (1997).
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J. M. Crook, Z. F. Kisvarday, U. T. Eysel, “GABA-induced inactivation of functionally characterized sites in cat striate cortex: effects on orientation tuning and direction selectivity,” Visual Neurosci. 14, 141–158 (1997).
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1996 (10)

M. A. Garcia-Perez, V. Sierra-Vazquez, “Do channels shift their tuning towards lower spatial frequencies in the periphery?” Vision Res. 36, 3339–3372 (1996).
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M. N. Shadlen, K. H. Britten, W. T. Newsome, J. A. Movshon, “A computational analysis of the relationship between neuronal and behavioral responses to visual motion,” J. Neurosci. 16, 1486–1510 (1996).
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M. C. Teich, R. G. Turcott, R. M. Siegel, “Temporal correlation in cat striate-cortex neural spike trains,” IEEE Eng. Med. Biol. Mag.Sept.–Oct.1996, pp. 79–87.

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S. Magnussen, M. W. Greenlee, J. P. Thomas, “Parallel processing in visual short-term memory,” J. Exp. Psychol. Human Percept. Perform. 22, 202–212 (1996).
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U. Polat, A. M. Norcia, “Neurophysiological evidence for contrast dependent long-range facilitation and suppression in the human visual cortex,” Vision Res. 36, 2099–2109 (1996).
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1995 (8)

M. K. Kapadia, M. Ito, C. D. Gilbert, G. Westheimer, “Improvement in visual sensitivity by changes in local context: parallel studies in human observers and in V1 of alert monkeys,” Neuron 15, 843–856 (1995).
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A. M. Sillito, K. L. Grieve, H. E. Jones, J. Cudeiro, J. Davis, “Visual cortical mechanisms detecting focal orientation discontinuities,” Nature 378, 492–496 (1995).
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M. B. Ben-Av, D. Sagi, “Perceptual grouping by similarity and proximity: experimental results can be predicted by intensity autocorrelations,” Vision Res. 35, 853–866 (1995).
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P. Verghese, L. S. Stone, “Combining speed information across space,” Vision Res. 35, 2811–2823 (1995).
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I. A. Shevelev, R. V. Novikova, N. A. Lazareva, A. S. Tikhomirov, G. A. Sharaev, “Sensitivity to cross-like figures in the cat striate neurons,” Neuroscience 69, 51–57 (1995).
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W. S. Geisler, D. G. Albrecht, “Bayesian analysis of identification performance in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
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1994 (7)

E. Zohary, M. N. Shadlen, W. T. Newsome, “Correlated neuronal discharge rate and its implications for psychophysical performance,” Nature 370, 140–143 (1994); erratum 371, 358 (1994).
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T. B. Lawton, C. W. Tyler, “On the role of X and simple cells in human contrast processing,” Vision Res. 34, 659–667 (1994).
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U. Polat, D. Sagi, “The architecture of perceptual spatial interactions,” Vision Res. 34, 73–78 (1994).
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1993 (6)

U. Polat, D. Sagi, “Lateral interactions between spatial channels: suppression and facilitation revealed by lateral masking experiments,” Vision Res. 33, 993–999 (1993).
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D. J. Field, A. Hayes, R. F. Hess, “Contour integration by the human visual system: evidence for a local association field,” Vision Res. 33, 173–193 (1993).
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H. R. Wilson, R. Humanski, “Spatial frequency adaptation and contrast gain control,” Vision Res. 33, 1133–1149 (1993).
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H. R. Wilson, “Nonlinear processes in visual pattern discrimination,” Proc. Natl. Acad. Sci. USA 90, 9785–9790 (1993).
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H. S. Seung, H. Sompolinsky, “Simple models for reading neuronal population codes,” Proc. Natl. Acad. Sci. USA 90, 10749–10753 (1993).
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W. R. Softky, C. Koch, “The highly irregular firing of cortical cells is inconsistent with temporal integration of random EPSPs,” J. Neurosci. 13, 334–350 (1993).
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1992 (7)

H. P. Snippe, J. J. Koenderink, “Information in channel-coded systems: correlated receivers,” Biol. Cybern. 67, 183–190 (1992).
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G. C. DeAngelis, J. G. Robson, I. Ohzawa, R. D. Freeman, “Organization of suppression in receptive fields of neurons in cat visual cortex,” J. Neurophysiol. 68, 144–163 (1992).
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W. S. Geisler, D. G. Albrecht, “Cortical neurons: isolation of contrast gain control,” Vision Res. 32, 1409–1410 (1992).
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D. J. Heeger, “Normalization of cell responses in cat striate cortex,” Visual Neurosci. 9, 181–197 (1992).
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J. J. Knierim, D. C. van Essen, “Neuronal responses to static texture patterns in area V1 of the alert macaque monkey,” J. Neurophysiol. 67, 961–980 (1992).
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M. W. Greenlee, “Spatial frequency discrimination of band-limited periodic targets: effects of stimulus contrast, bandwidth and retinal eccentricity,” Vision Res. 32, 275–283 (1992).
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1991 (8)

L. A. Olzak, J. P. Thomas, “When orthogonal orientations are not processed independently,” Vision Res. 31, 51–57 (1991).
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H. R. Wilson, “Model of peripheral and amblyopic hyperacuity,” Vision Res. 31, 967–982 (1991).
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A. B. Bonds, “Temporal dynamics of contrast gain in single cells of the cat striate cortex,” Visual Neurosci. 6, 239–255 (1991).
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1990 (3)

S. F. Bowne, “Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination,” Vision Res. 30, 449–461 (1990).
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1989 (2)

J. Bolz, C. D. Gilbert, T. N. Wiesel, “Pharmacological analysis of cortical circuitry,” Trends Neurosci. 12, 292–296 (1989).
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L. C. Katz, C. D. Gilbert, T. N. Wiesel, “Local circuits and ocular dominance columns in monkey striate cortex,” J. Neurosci. 9, 1389–1399 (1989).
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1988 (1)

D. Ferster, “Spatially opponent excitation and inhibition in simple cells of the cat visual cortex,” J. Neurosci. 8, 1172–1180 (1988).
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1987 (3)

D. Ferster, C. Koch, “Neuronal connections underlying orientation selectivity in cat visual cortex,” Trends Neurosci. 10, 187–192 (1987).
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N. Graham, J. G. Robson, “Summation of very close spatial frequencies: the importance of spatial probability summation,” Vision Res. 27, 1997–2007 (1987).
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1986 (4)

H. R. Wilson, “Responses of spatial mechanisms can explain hyperacuity,” Vision Res. 26, 453–469 (1986).
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A. S. Ramoa, M. Shadlen, B. C. Skottun, R. D. Freeman, “A comparison of inhibition in orientation and spatial frequency selectivity of cat visual cortex,” Nature 321, 237–239 (1986).
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D. Ferster, “Orientation selectivity of synaptic potentials in neurons of cat primary visual cortex,” J. Neurosci. 6, 1284–1301 (1986).
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G. G. Blasdel, G. Salama, “Voltage-sensitive dyes reveal a modular organization in monkey striate cortex,” Nature 321, 579–585 (1986).
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1985 (2)

1984 (5)

1983 (4)

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H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983).
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1982 (3)

R. L. DeValois, D. G. Albrecht, L. G. Thorell, “Spatial-frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
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J. Hirsch, R. Hylton, “Limits of spatial-frequency discrimination as evidence of neural interpolation,” J. Opt. Soc. Am. 72, 1367–1374 (1982).
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1981 (2)

D. A. Pollen, S. F. Ronner, “Phase relationships between adjacent simple cells in the visual cortex,” Science 212, 1409–1411 (1981).
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1980 (2)

H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171–178 (1980).
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1979 (1)

H. R. Wilson, J. R. Bergen, “A four mechanism model for threshold spatial vision,” Vision Res. 19, 19–32 (1979).
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1975 (1)

C. F. Stromeyer, S. Klein, “Evidence against narrow-band spatial frequency channels in human vision: the detectability of frequency modulated gratings,” Vision Res. 15, 899–910 (1975).
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1974 (4)

J. Nachmias, R. V. Sansbury, “Letter: grating contrast: discrimination may be better than detection,” Vision Res. 14, 1039–1042 (1974).
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1973 (1)

L. Maffei, A. Fiorentini, “The visual cortex as a spatial frequency analyser,” Vision Res. 13, 1255–1267 (1973).
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1971 (2)

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1970 (1)

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1969 (1)

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1968 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. (London) 195, 215–243 (1968).

1962 (1)

D. H. Hubel, T. N. Wiesel, “Receptive fields, binocular interaction and functional architecture in the cat’s visual cortex,” J. Physiol. (London) 160, 106–154 (1962).

1953 (1)

N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, “Equation of state calculations by fast computing machines,” J. Chem. Phys. 21, 1087–1092 (1953).
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Figures (9)

Fig. 1
Fig. 1

Model architecture, represented schematically in the style of Wilson and collaborators. The model consists of three successive stages: (1) A bank of linear visual filters tuned to different orientations and spatial frequencies, (2) nonlinear interactions between visual filters in the form of a power law and divisive inhibition, and (3) addition of independent noise and a statistically efficient decision based on the entire filter population.

Fig. 2
Fig. 2

Visual filters used in the model. Filters are defined in terms of their separable Gaussian tuning functions for the orientation θ and logarithm of the spatial period λ of a sinusoidal grating stimulus (left). The spatial shape of the visual filter can be reconstructed though an inverse Fourier transform. Both even- and odd-symmetric filters are shown (middle and right). Their shape is very similar to the multilobed functions used by other models. Pairs of reconstructed even- and odd-symmetric filters can be used to numerically compute the response to arbitrary stimuli. However, the response to stimuli based on sinusoidal gratings (e.g., Gabor patches) can be obtained directly from the Gaussian tuning functions.

Fig. 3
Fig. 3

Fisher information with respect to stimulus orientation, contrast, and spatial frequency. Fisher information is the inverse of the variance of an unbiased and efficient estimator of the stimulus parameter [Subsection 2.B.4. and Eq. (7)]. Each surface point represents the information encoded in the response of one model unit. The volume under the surface represents the total information encoded by a population of units with independent noise and tuned to 24 orientations and 24 spatial periods. Arrows indicate the spatial period λS and orientation θS=0 of the stimulus. Note that the unit tuned optimally for the stimulus does not contribute to the Fisher information for orientation or spatial period.

Fig. 4
Fig. 4

Experimental results of seven psychophysical observers. Three observers completed all five experiments (LB, LZ, and SC), and others completed either two or three experiments (AW, AZ, IR, and MI). All experiments involve a temporal 2AFC discrimination between Gabor stimuli at 4° of eccentricity (insets). Exp 1: contrast increment threshold, ΔC, as a function of contrast, C. Exps. 2 and 3: orientation and relative spatial frequency discrimination threshold, Δθ and Δω/ω, as a function of contrast, C. Exp. 4: contrast threshold elevation, ΔC/Cth, as a function of mask orientation, θ (Cth is the detection contrast threshold, leftmost point of Exp. 1). Exp. 5: contrast threshold elevation, ΔC/Cth, as a function of mask spatial period, λ.

Fig. 5
Fig. 5

Measured and predicted thresholds for three observers (LB, LZ, and SC). Measured thresholds (symbols with error bars) are represented by the mean and standard deviation for each observer. Predicted thresholds are represented by the optimal model fit (solid curve) and the family of all model fits with up to 5% higher fit error (gray regions). Predicted thresholds are close to measured thresholds, often to within the accuracy of the measurement. In general, the gray regions closely hug the measured thresholds, demonstrating that the model fit is robust and not accidental. The narrow parts of the gray regions indicate which parts of the data constitute particularly tight constraints for the model.

Fig. 6
Fig. 6

Functional properties of the optimal model for observer SC. (a) The effective contrast response function exhibits the sigmoidal shape postulated by most psychophysical models. (b) and (c) The effective tuning functions for orientation and spatial frequency are approximately Gaussian but are 30%–40% narrower than the original tuning functions (dashed curves). (d) and (e) Relative weights with which different filters contribute to divisive inhibition. Inhibition derives from filters tuned to similar orientations (difference less than 40°). The range of spatial frequencies contributing to divisive inhibition is broad but only poorly constrained by the data.

Fig. 7
Fig. 7

Measured and predicted thresholds for two variants of the model (observer SC). The first column shows the fit of the standard model, for comparison. The second column shows the fit of a model variant using flat noise instead of proportional noise. The quality of the fit is comparable to that of the standard model, except in that it is less robust with respect to contrast-masking experiments (as indicated by relatively broad gray regions). The third column shows a model variant using a suboptimal decision based on the Minkowski norm. The fit is inferior to that of the standard model, in particular with respect to the contrast-masking experiments. Thus the statistically efficient decision contributes significantly to the success of the standard model.

Fig. 8
Fig. 8

Differential contrast dependence of thresholds. The model has been manually tuned such as to simultaneously predict increment contrast thresholds (a, Exp. 1) following Guilford’s law (ΔCC0.75), but contrast-independent orientation thresholds (b, Exp. 2) (ΔθC-0.03). Looking at the internals of the model reveals that, although the unit responses, Rλ,θ, increase for units of all orientations (c), the increase is more pronounced at the tails of the orientation tuning curve (d). As a result, the slope of the tuning curve at ±15° increases more slowly than its height. Specifically, as contrast increases from C=0.2 to C=0.9 curves, Rλ,θ increases by a factor of 3, whereas Rλ,θ/θ increases only by a factor of 1.75 (for θ±15°). As a result, the Fisher information with respect to contrast, which is approximately proportional to (Rλ,θ/θ)2/Rλ,θ, does not increase with C.

Fig. 9
Fig. 9

Approximation of the error surface near the point of best fit, X0. The error surface is approximated by a paraboloid based on the Hessian matrix at X0. With this approximation, all points at which the fit error e(X)e(X0)+ are within an ellipsoid (thick curve). The actual isocontour at which e(X)e(X0)+ is indicated by the arrow. For each parameter, the tolerance range within which e(X)e(X0)+ is obtained by projecting the ellipsoid onto the associated axis (dotted lines).

Tables (1)

Tables Icon

Table 1 Best-Fit Model Parameters

Equations (68)

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Eλ,θ(CS, λS, θS)
=CSA exp-[log(λS)-log(λ)]22σλ2-(θS-θ)22σθ2,
Rλ,θ=(Eλ, θ)γ(S)δ+(λ,θ)Λ×ΘWλ,θ(λ, θ)(Eλ, θ)δ+η,
Wλ,θ(λ, θ)=exp-[log(λ)-log(λ)]22Λλ2-(θ-θ)22Λθ2
Vλ,θ2=Rλ,θα,
Prop.Corr.=
12+12erf|mean[T(ζ1)]-mean[T(ζ2)]|2{var[T(ζ1)]+var[T(ζ2)]},
Prop.Corr.=12+12erf|ζ1-ζ2|2[1/J(ζ1)+1/J(ζ2)].
Jλ,θ(ζ)=Rλ,θζ21Rλ,θα+α22Rλ,θ2.
J(ζ)=λ,θJλ,θ(ζ).
D(ζ1, ζ2)=(λ,θ)Λ×ΘRλ,θ(ζ2)Vλ,θ(ζ2)-Rλ,θ(ζ1)Vλ,θ(ζ1)Q1/Q,
Jλ,θ(Rλ,θ/θ)2Rλ,θ.
p(x|ζ)=1σ2πexp-(x-μ)22σ2,
p(x|ζ)=p(x|ζ)(x-μ)2σ3 σ+x-μσ2 μ-σσ.
E[f(x)]=-+f(x)p(x|ζ)dx,
J(ζ)=Eζlog p(X|ζ)2
=Ep(X|ζ)2p(X|ζ)2
=E(X-μ)2σ3 σ+X-μσ2 μ-σσ2
=1σ6[(μ2σ2μ2-2μ3σμσ+2μσ3μσ+μ4σ2-2μ2σ2σ2+σ4σ2)+(-2μσ2μ2+6μ2σμσ-2σ3μσ-4μ3σ2+4μσ2σ2)E[X]+(σ2μ2-6μσμσ+6μ2σ2-2σ2σ2)E[X2]+(2σμσ-4μσ2)E[X3]+(σ2)E[X4]]
=μ2+2σ2σ2,
J(ζ)=μ2μ2μ2-α+α22.
Ri=Acfexp-(θ-θi)22σθ2exp-(ω-ωi)22σω2,
Vi2=βRi,
Ric=fRic,Riθ=-Riθ-θiσθ2,
Riω=-Riω-ωiσω2.
Jiζ=1Ri2Riζ2Riβ+121Ri2Riζ2Riβ,
Jicf2c2Riβ,Jiθ(θ-θi)2σθ4Riβ,
Jiω(ω-ωi)2σω4Riβ.
Ri=Acf/2exp-(θ-θi)24σθ2exp-(ω-ωi)24σω2,
Vi2=β4,
Ric=fRi2c,Riθ=-Riθ-θi2σθ2
Riω=-Riω-ωi2σω2,
Jiζ=4βRiζ2,Jic=f2c2Ri2β,
Jiθ=(θ-θi)2σθ4Ri2β,Jiω=(ω-ωi)2σω4Ri2β.
Δζ=|ζ1-ζ2|=k1/J(ζ1)+1/J(ζ2)2kJ[(ζ1+ζ2)/2];k=2 erf-112.
Δcc2kβAf2cf,Δθ2ekβσθ2Acf,
Δω2ekβσω2Acf.
Jtot=θi,ωiJi=1ΔθΔωθi,ωiJiΔθΔωρσθσωJidθdω,
12πσθ2exp-(θ-θi)22σθ2dθ=1,
12πσθ2(θ-θi)22σθ2exp-(θ-θi)22σθ2dθ=12,
JtotcρσθσωJicdθdω=2πσθσωAf2cfρβc2,
Δcc2π kβAf2cfρ,
JtotθρσθσωJiθdθdω=2πσωAcfρβσθ,
Δθ2π kβσθ2Acfρ,
JtotωρσθσωJiωdθdω=2πσθAcfρβσω,
Δω2π kβσω2Acfρ.
ΔRi=RiζΔζ=Vi,ΔRiVi=1ViRiζΔζ=1.
1=iΔRiViQ1/Q.
ΔRiVi=1βRiζΔζ=JiζΔζ.
1=iΔRiVi21/2=ΔζiJiζ1/2,Δζ=1Jtotζ.
ΔζMinkowski=iΔRiViQ-1/Q=N-1/Q(Jζ)-1/2
ΔζFisher=iJiζ-1/2=N-1/2=(Jζ)-1/2.
ti(X)=ti(X0)+JtiT(X-X0),
e(X)=e(X0)+JeT(X-X0)+(X-X0)THe(X-X0),
EjTXsubjectto(X-X0)THe(X-X0).
EjTX-λ[(X-X0)THe(X-X0)-].
Ej-2λHe(X-X0)=0.
X=X0±EjTHe-1EjHe-1Ej,
EjTX=EjTX0±EjTHe-1Ej,
σj=EjTHe-1Ej.
He=VD1/2D1/2V-1.
(X-X0)TVD1/2D1/2VT(X-X0),
[D1/2VT(X-X0)]T[D1/2VT(X-X0)],
WTW,i.e.,W2,W=D1/2VT(X-X0).
ti(X)=ti(X0)+JtiTV-TD-1/2D1/2VT(X-X0),
ti(X)=ti(X0)+KTW
W=±KK.
tiextr=ti(X0)±K.

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