Abstract

Many visual tasks can be carried out by using several sources of information. The most accurate estimates of scene properties require the observer to utilize all available information and to combine the information sources in an optimal manner. Two experiments are described that required the observers to judge the relative locations of two texture-defined edges (a vernier task). The edges were signaled by a change across the edge of two texture properties [either frequency and orientation (Experiment 1) or contrast and orientation (Experiment 2)]. The reliability of each cue was controlled by varying the distance over which the change (in frequency, orientation, or contrast) occurred—a kind of “texture blur.” In some conditions, the position of the edge signaled by one cue was shifted relative to the other (“perturbation analysis”). An ideal-observer model, previously used in studies of depth perception and color constancy, was fitted to the data. Although the fit can be rejected relative to some more elaborate models, especially given the large quantity of data, this model does account for most trends in the data. A second, suboptimal model that switches between the available cues from trial to trial does a poor job of accounting for the data.

© 2001 Optical Society of America

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2000 (2)

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

P. V. McGraw, D. Whitaker, D. R. Badcock, “Localising conflicting visual attributes,” Invest. Ophthalmol. Visual Sci. Suppl. 41, S804 (2000).

1999 (4)

S. C. Dakin, “Orientation variance as a quantifier of structure in texture,” Spatial Vision 12, 1–30 (1999).
[CrossRef] [PubMed]

E. Brenner, M. S. Landy, “Interaction between the perceived shape of two objects,” Vision Res. 39, 933–945 (1999).
[CrossRef]

I. Fine, R. A. Jacobs, “Modeling the combination of motion, stereo, and vergence angle cues to visual depth,” Neural Comput. 11, 1297–1330 (1999).
[CrossRef] [PubMed]

N. E. Scott-Samuel, M. A. Georgeson, “Does early nonlinearity account for second-order motion?” Vision Res. 39, 2853–2865 (1999).
[CrossRef] [PubMed]

1997 (3)

J. Rivest, I. Boutet, J. Intriligator, “Perceptual learning of orientation discrimination by more than one attribute,” Vision Res. 37, 273–281 (1997).
[CrossRef] [PubMed]

J. R. Li, L. T. Maloney, M. S. Landy, “Combination of consistent and inconsistent depth cues,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S903 (1997).

R. Gray, D. Regan, “Vernier step acuity and bisection acuity for texture-defined form,” Vision Res. 37, 1713–1723 (1997).
[CrossRef]

1996 (1)

J. Rivest, P. Cavanagh, “Localizing contours defined by more than one attribute,” Vision Res. 36, 53–66 (1996).
[CrossRef] [PubMed]

1995 (4)

P. Cavanagh, S. Saida, J. Rivest, “The contribution of color to depth perceived from motion parallax,” Vision Res. 35, 1871–1878 (1995).
[CrossRef] [PubMed]

M. S. Landy, L. T. Maloney, E. B. Johnston, M. J. Young, “Measurement and modeling of depth cue combination: in defense of weak fusion,” Vision Res. 35, 389–412 (1995).
[CrossRef] [PubMed]

S. S. Wolfson, M. S. Landy, “Discrimination of orientation-defined texture edges,” Vision Res. 35, 2863–2877 (1995).
[CrossRef] [PubMed]

F. A. A. Kingdom, D. Keeble, B. Moulden, “Sensitivity to orientation modulation in micropattern-based texture,” Vision Res. 35, 79–91 (1995).
[CrossRef] [PubMed]

1994 (3)

E. B. Johnston, B. G. Cumming, M. S. Landy, “Integration of stereopsis and motion shape cues,” Vision Res. 34, 2259–2275 (1994).
[CrossRef] [PubMed]

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

H. R. Wilson, J. Kim, “A model of motion coherence and transparency,” Visual Neurosci. 11, 1205–1220 (1994).
[CrossRef]

1993 (2)

D. W. Massaro, M. M. Cohen, “The paradigm and the fuzzy logical model of perception are alive and well,” J. Exp. Psychol. Gen. 122, 115–124 (1993).
[CrossRef] [PubMed]

M. J. Young, M. S. Landy, L. T. Maloney, “A perturbation analysis of depth perception from combinations of texture and motion cues,” Vision Res. 33, 2685–2696 (1993).
[CrossRef] [PubMed]

1992 (1)

J. E. Cutting, N. Bruno, N. P. Brady, C. Moore, “Selectivity, scope, and simplicity of models: a lesson from fitting judgments of perceived depth,” J. Exp. Psychol. Gen. 121, 364–381 (1992).
[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)

D. W. Massaro, D. Friedman, “Models of integration given multiple sources of information,” Psychol. Rev. 97, 225–252 (1990).
[CrossRef] [PubMed]

1988 (1)

D. W. Massaro, “Ambiguity in perception and experimentation,” J. Exp. Psychol. Gen. 117, 417–421 (1988).
[CrossRef] [PubMed]

1985 (2)

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

D. R. Badcock, G. Westheimer, “Spatial location and hyperacuity: the centre/surround localization contribution function has two substrates,” Vision Res. 25, 1259–1267 (1985).
[CrossRef] [PubMed]

1984 (1)

M. S. Landy, Y. Cohen, G. Sperling, “Hips: a unix-based image processing system,” Comput. Vision Graph. Image Process. 25, 331–347 (1984).
[CrossRef]

1981 (1)

1974 (1)

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Aut. Control AC-19, 716–723 (1974).
[CrossRef]

Akaike, H.

H. Akaike, “A new look at the statistical model identification,” IEEE Trans. Aut. Control AC-19, 716–723 (1974).
[CrossRef]

Aloimonos, J.

J. Aloimonos, D. A. Shulman, Integration of Visual Modules: an Extension of the Marr Paradigm (Academic, New York, 1989).

Badcock, D. R.

P. V. McGraw, D. Whitaker, D. R. Badcock, “Localising conflicting visual attributes,” Invest. Ophthalmol. Visual Sci. Suppl. 41, S804 (2000).

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

D. R. Badcock, G. Westheimer, “Spatial location and hyperacuity: the centre/surround localization contribution function has two substrates,” Vision Res. 25, 1259–1267 (1985).
[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.

Boes, D. C.

A. M. Mood, F. A. Graybill, D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. (McGraw-Hill, New York, 1974).

Boutet, I.

J. Rivest, I. Boutet, J. Intriligator, “Perceptual learning of orientation discrimination by more than one attribute,” Vision Res. 37, 273–281 (1997).
[CrossRef] [PubMed]

Boynton, R. M.

Brady, N. P.

J. E. Cutting, N. Bruno, N. P. Brady, C. Moore, “Selectivity, scope, and simplicity of models: a lesson from fitting judgments of perceived depth,” J. Exp. Psychol. Gen. 121, 364–381 (1992).
[CrossRef] [PubMed]

Brenner, E.

E. Brenner, M. S. Landy, “Interaction between the perceived shape of two objects,” Vision Res. 39, 933–945 (1999).
[CrossRef]

M. S. Landy, E. Brenner, “Motion-disparity interaction and the scaling of stereoscopic disparity,” in Vision and Attention, L. R. Harris, M. R. M. Jenkin, eds. (Springer- Verlag, New York, 2001), Chap. 7.

Bruno, N.

J. E. Cutting, N. Bruno, N. P. Brady, C. Moore, “Selectivity, scope, and simplicity of models: a lesson from fitting judgments of perceived depth,” J. Exp. Psychol. Gen. 121, 364–381 (1992).
[CrossRef] [PubMed]

Buck, S. L.

Bülthoff, H. H.

A. L. Yuille, H. H. Bülthoff, “Bayesian decision theory and psychophysics,” in Perception as Bayesian Inference, D. C. Knill, W. Richards, eds. (Cambridge U. Press, Cambridge, UK, 1996), pp. 123–161.

Cavanagh, P.

J. Rivest, P. Cavanagh, “Localizing contours defined by more than one attribute,” Vision Res. 36, 53–66 (1996).
[CrossRef] [PubMed]

P. Cavanagh, S. Saida, J. Rivest, “The contribution of color to depth perceived from motion parallax,” Vision Res. 35, 1871–1878 (1995).
[CrossRef] [PubMed]

Clark, J. J.

J. J. Clark, A. L. Yuille, Data Fusion for Sensory Information Processing Systems (Kluwer Academic, Boston, 1990).

Cohen, M. M.

D. W. Massaro, M. M. Cohen, “The paradigm and the fuzzy logical model of perception are alive and well,” J. Exp. Psychol. Gen. 122, 115–124 (1993).
[CrossRef] [PubMed]

Cohen, Y.

M. S. Landy, Y. Cohen, G. Sperling, “Hips: a unix-based image processing system,” Comput. Vision Graph. Image Process. 25, 331–347 (1984).
[CrossRef]

Cumming, B. G.

E. B. Johnston, B. G. Cumming, M. S. Landy, “Integration of stereopsis and motion shape cues,” Vision Res. 34, 2259–2275 (1994).
[CrossRef] [PubMed]

Cutting, J. E.

J. E. Cutting, N. Bruno, N. P. Brady, C. Moore, “Selectivity, scope, and simplicity of models: a lesson from fitting judgments of perceived depth,” J. Exp. Psychol. Gen. 121, 364–381 (1992).
[CrossRef] [PubMed]

Dakin, S. C.

S. C. Dakin, “Orientation variance as a quantifier of structure in texture,” Spatial Vision 12, 1–30 (1999).
[CrossRef] [PubMed]

Derrington, A. M.

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
[CrossRef] [PubMed]

Fine, I.

I. Fine, R. A. Jacobs, “Modeling the combination of motion, stereo, and vergence angle cues to visual depth,” Neural Comput. 11, 1297–1330 (1999).
[CrossRef] [PubMed]

Friedman, D.

D. W. Massaro, D. Friedman, “Models of integration given multiple sources of information,” Psychol. Rev. 97, 225–252 (1990).
[CrossRef] [PubMed]

Frome, F. S.

Georgeson, M. A.

N. E. Scott-Samuel, M. A. Georgeson, “Does early nonlinearity account for second-order motion?” Vision Res. 39, 2853–2865 (1999).
[CrossRef] [PubMed]

Gray, R.

R. Gray, D. Regan, “Vernier step acuity and bisection acuity for texture-defined form,” Vision Res. 37, 1713–1723 (1997).
[CrossRef]

Graybill, F. A.

A. M. Mood, F. A. Graybill, D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. (McGraw-Hill, New York, 1974).

Hon, A. K.

A. K. Hon, L. T. Maloney, M. S. Landy, “The influence function for visual interpolation,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 409–419 (1997).

Intriligator, J.

J. Rivest, I. Boutet, J. Intriligator, “Perceptual learning of orientation discrimination by more than one attribute,” Vision Res. 37, 273–281 (1997).
[CrossRef] [PubMed]

Jacobs, R. A.

I. Fine, R. A. Jacobs, “Modeling the combination of motion, stereo, and vergence angle cues to visual depth,” Neural Comput. 11, 1297–1330 (1999).
[CrossRef] [PubMed]

Johnston, E. B.

M. S. Landy, L. T. Maloney, E. B. Johnston, M. J. Young, “Measurement and modeling of depth cue combination: in defense of weak fusion,” Vision Res. 35, 389–412 (1995).
[CrossRef] [PubMed]

E. B. Johnston, B. G. Cumming, M. S. Landy, “Integration of stereopsis and motion shape cues,” Vision Res. 34, 2259–2275 (1994).
[CrossRef] [PubMed]

Kaufman, L.

L. Kaufman, Sight and Mind (Oxford, New York, 1974).

Keeble, D.

F. A. A. Kingdom, D. Keeble, B. Moulden, “Sensitivity to orientation modulation in micropattern-based texture,” Vision Res. 35, 79–91 (1995).
[CrossRef] [PubMed]

Kendall, M. K.

M. K. Kendall, A. Stuart, The Advanced Theory of Statistics: Vol. 2. Inference and Relationship, 4th ed. (Macmillan, New York, 1979).

Kim, J.

H. R. Wilson, J. Kim, “A model of motion coherence and transparency,” Visual Neurosci. 11, 1205–1220 (1994).
[CrossRef]

Kingdom, F. A. A.

F. A. A. Kingdom, D. Keeble, B. Moulden, “Sensitivity to orientation modulation in micropattern-based texture,” Vision Res. 35, 79–91 (1995).
[CrossRef] [PubMed]

Knill, D. C.

D. C. Knill, W. Richards, Perception as Bayesian Inference (Cambridge U. Press, Cambridge, UK, 1996).

Landy, M. S.

E. Brenner, M. S. Landy, “Interaction between the perceived shape of two objects,” Vision Res. 39, 933–945 (1999).
[CrossRef]

J. R. Li, L. T. Maloney, M. S. Landy, “Combination of consistent and inconsistent depth cues,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S903 (1997).

S. S. Wolfson, M. S. Landy, “Discrimination of orientation-defined texture edges,” Vision Res. 35, 2863–2877 (1995).
[CrossRef] [PubMed]

M. S. Landy, L. T. Maloney, E. B. Johnston, M. J. Young, “Measurement and modeling of depth cue combination: in defense of weak fusion,” Vision Res. 35, 389–412 (1995).
[CrossRef] [PubMed]

E. B. Johnston, B. G. Cumming, M. S. Landy, “Integration of stereopsis and motion shape cues,” Vision Res. 34, 2259–2275 (1994).
[CrossRef] [PubMed]

M. J. Young, M. S. Landy, L. T. Maloney, “A perturbation analysis of depth perception from combinations of texture and motion cues,” Vision Res. 33, 2685–2696 (1993).
[CrossRef] [PubMed]

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

M. S. Landy, Y. Cohen, G. Sperling, “Hips: a unix-based image processing system,” Comput. Vision Graph. Image Process. 25, 331–347 (1984).
[CrossRef]

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.

L. T. Maloney, M. S. Landy, “A statistical framework for robust fusion of depth information,” in Visual Communications and Image Processing IV, W. A. Pearlman, ed., Proc. SPIE1199, 1154–1163 (1989).

M. S. Landy, “Combining multiple cues for texture edge localization,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 506–517 (1993).

M. S. Landy, E. Brenner, “Motion-disparity interaction and the scaling of stereoscopic disparity,” in Vision and Attention, L. R. Harris, M. R. M. Jenkin, eds. (Springer- Verlag, New York, 2001), Chap. 7.

A. K. Hon, L. T. Maloney, M. S. Landy, “The influence function for visual interpolation,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 409–419 (1997).

Ledgeway, T.

T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

Li, J. R.

J. R. Li, L. T. Maloney, M. S. Landy, “Combination of consistent and inconsistent depth cues,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S903 (1997).

Maloney, L. T.

J. R. Li, L. T. Maloney, M. S. Landy, “Combination of consistent and inconsistent depth cues,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S903 (1997).

M. S. Landy, L. T. Maloney, E. B. Johnston, M. J. Young, “Measurement and modeling of depth cue combination: in defense of weak fusion,” Vision Res. 35, 389–412 (1995).
[CrossRef] [PubMed]

M. J. Young, M. S. Landy, L. T. Maloney, “A perturbation analysis of depth perception from combinations of texture and motion cues,” Vision Res. 33, 2685–2696 (1993).
[CrossRef] [PubMed]

A. K. Hon, L. T. Maloney, M. S. Landy, “The influence function for visual interpolation,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 409–419 (1997).

L. T. Maloney, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, Cambridge, UK, 1999), pp. 387–422.

L. T. Maloney, J. N. Yang, “The illuminant estimation hypothesis and surface color perception,” in Colour Vision:From Light to Object, R. Mausfeld, D. Heyer, eds. (Oxford U. Press, Oxford, UK, to be published).

L. T. Maloney, M. S. Landy, “A statistical framework for robust fusion of depth information,” in Visual Communications and Image Processing IV, W. A. Pearlman, ed., Proc. SPIE1199, 1154–1163 (1989).

Marr, D.

D. Marr, Vision (Freeman, San Francisco, Calif., 1982).

Massaro, D. W.

D. W. Massaro, M. M. Cohen, “The paradigm and the fuzzy logical model of perception are alive and well,” J. Exp. Psychol. Gen. 122, 115–124 (1993).
[CrossRef] [PubMed]

D. W. Massaro, D. Friedman, “Models of integration given multiple sources of information,” Psychol. Rev. 97, 225–252 (1990).
[CrossRef] [PubMed]

D. W. Massaro, “Ambiguity in perception and experimentation,” J. Exp. Psychol. Gen. 117, 417–421 (1988).
[CrossRef] [PubMed]

McGraw, P. V.

P. V. McGraw, D. Whitaker, D. R. Badcock, “Localising conflicting visual attributes,” Invest. Ophthalmol. Visual Sci. Suppl. 41, S804 (2000).

Mood, A. M.

A. M. Mood, F. A. Graybill, D. C. Boes, Introduction to the Theory of Statistics, 3rd ed. (McGraw-Hill, New York, 1974).

Moore, C.

J. E. Cutting, N. Bruno, N. P. Brady, C. Moore, “Selectivity, scope, and simplicity of models: a lesson from fitting judgments of perceived depth,” J. Exp. Psychol. Gen. 121, 364–381 (1992).
[CrossRef] [PubMed]

Moulden, B.

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N. Prins, A. J. Mussap, “Alignment of orientation-modulated textures,” Vision Res. 40, 3567–3573 (2000).
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R. Gray, D. Regan, “Vernier step acuity and bisection acuity for texture-defined form,” Vision Res. 37, 1713–1723 (1997).
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D. C. Knill, W. Richards, Perception as Bayesian Inference (Cambridge U. Press, Cambridge, UK, 1996).

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J. Rivest, I. Boutet, J. Intriligator, “Perceptual learning of orientation discrimination by more than one attribute,” Vision Res. 37, 273–281 (1997).
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J. Rivest, P. Cavanagh, “Localizing contours defined by more than one attribute,” Vision Res. 36, 53–66 (1996).
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P. Cavanagh, S. Saida, J. Rivest, “The contribution of color to depth perceived from motion parallax,” Vision Res. 35, 1871–1878 (1995).
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P. Cavanagh, S. Saida, J. Rivest, “The contribution of color to depth perceived from motion parallax,” Vision Res. 35, 1871–1878 (1995).
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N. E. Scott-Samuel, M. A. Georgeson, “Does early nonlinearity account for second-order motion?” Vision Res. 39, 2853–2865 (1999).
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J. Aloimonos, D. A. Shulman, Integration of Visual Modules: an Extension of the Marr Paradigm (Academic, New York, 1989).

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T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
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M. S. Landy, Y. Cohen, G. Sperling, “Hips: a unix-based image processing system,” Comput. Vision Graph. Image Process. 25, 331–347 (1984).
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S. S. Wolfson, M. S. Landy, “Discrimination of orientation-defined texture edges,” Vision Res. 35, 2863–2877 (1995).
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M. S. Landy, L. T. Maloney, E. B. Johnston, M. J. Young, “Measurement and modeling of depth cue combination: in defense of weak fusion,” Vision Res. 35, 389–412 (1995).
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P. V. McGraw, D. Whitaker, D. R. Badcock, “Localising conflicting visual attributes,” Invest. Ophthalmol. Visual Sci. Suppl. 41, S804 (2000).

J. R. Li, L. T. Maloney, M. S. Landy, “Combination of consistent and inconsistent depth cues,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S903 (1997).

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I. Fine, R. A. Jacobs, “Modeling the combination of motion, stereo, and vergence angle cues to visual depth,” Neural Comput. 11, 1297–1330 (1999).
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S. C. Dakin, “Orientation variance as a quantifier of structure in texture,” Spatial Vision 12, 1–30 (1999).
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E. Brenner, M. S. Landy, “Interaction between the perceived shape of two objects,” Vision Res. 39, 933–945 (1999).
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M. S. Landy, L. T. Maloney, E. B. Johnston, M. J. Young, “Measurement and modeling of depth cue combination: in defense of weak fusion,” Vision Res. 35, 389–412 (1995).
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M. J. Young, M. S. Landy, L. T. Maloney, “A perturbation analysis of depth perception from combinations of texture and motion cues,” Vision Res. 33, 2685–2696 (1993).
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E. B. Johnston, B. G. Cumming, M. S. Landy, “Integration of stereopsis and motion shape cues,” Vision Res. 34, 2259–2275 (1994).
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N. Prins, A. J. Mussap, “Alignment of orientation-modulated textures,” Vision Res. 40, 3567–3573 (2000).
[CrossRef] [PubMed]

S. S. Wolfson, M. S. Landy, “Discrimination of orientation-defined texture edges,” Vision Res. 35, 2863–2877 (1995).
[CrossRef] [PubMed]

F. A. A. Kingdom, D. Keeble, B. Moulden, “Sensitivity to orientation modulation in micropattern-based texture,” Vision Res. 35, 79–91 (1995).
[CrossRef] [PubMed]

A. M. Derrington, D. R. Badcock, “Separate detectors for simple and complex grating patterns?” Vision Res. 25, 1869–1878 (1985).
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T. Ledgeway, A. T. Smith, “Evidence for separate motion-detecting mechanisms for first- and second-order motion in human vision,” Vision Res. 34, 2727–2740 (1994).
[CrossRef] [PubMed]

N. E. Scott-Samuel, M. A. Georgeson, “Does early nonlinearity account for second-order motion?” Vision Res. 39, 2853–2865 (1999).
[CrossRef] [PubMed]

P. Cavanagh, S. Saida, J. Rivest, “The contribution of color to depth perceived from motion parallax,” Vision Res. 35, 1871–1878 (1995).
[CrossRef] [PubMed]

J. Rivest, I. Boutet, J. Intriligator, “Perceptual learning of orientation discrimination by more than one attribute,” Vision Res. 37, 273–281 (1997).
[CrossRef] [PubMed]

J. Rivest, P. Cavanagh, “Localizing contours defined by more than one attribute,” Vision Res. 36, 53–66 (1996).
[CrossRef] [PubMed]

D. R. Badcock, G. Westheimer, “Spatial location and hyperacuity: the centre/surround localization contribution function has two substrates,” Vision Res. 25, 1259–1267 (1985).
[CrossRef] [PubMed]

R. Gray, D. Regan, “Vernier step acuity and bisection acuity for texture-defined form,” Vision Res. 37, 1713–1723 (1997).
[CrossRef]

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H. R. Wilson, J. Kim, “A model of motion coherence and transparency,” Visual Neurosci. 11, 1205–1220 (1994).
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M. S. Landy, “Combining multiple cues for texture edge localization,” in Human Vision, Visual Processing, and Digital Display IV, J. P. Allebach, B. E. Rogowitz, eds., Proc. SPIE1913, 506–517 (1993).

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A. K. Hon, L. T. Maloney, M. S. Landy, “The influence function for visual interpolation,” in Human Vision and Electronic Imaging II, B. E. Rogowitz, T. N. Pappas, eds., Proc. SPIE3016, 409–419 (1997).

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.

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M. S. Landy, E. Brenner, “Motion-disparity interaction and the scaling of stereoscopic disparity,” in Vision and Attention, L. R. Harris, M. R. M. Jenkin, eds. (Springer- Verlag, New York, 2001), Chap. 7.

J. J. Clark, A. L. Yuille, Data Fusion for Sensory Information Processing Systems (Kluwer Academic, Boston, 1990).

D. Marr, Vision (Freeman, San Francisco, Calif., 1982).

J. Aloimonos, D. A. Shulman, Integration of Visual Modules: an Extension of the Marr Paradigm (Academic, New York, 1989).

L. T. Maloney, M. S. Landy, “A statistical framework for robust fusion of depth information,” in Visual Communications and Image Processing IV, W. A. Pearlman, ed., Proc. SPIE1199, 1154–1163 (1989).

D. C. Knill, W. Richards, Perception as Bayesian Inference (Cambridge U. Press, Cambridge, UK, 1996).

A. L. Yuille, H. H. Bülthoff, “Bayesian decision theory and psychophysics,” in Perception as Bayesian Inference, D. C. Knill, W. Richards, eds. (Cambridge U. Press, Cambridge, UK, 1996), pp. 123–161.

L. T. Maloney, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, Cambridge, UK, 1999), pp. 387–422.

L. T. Maloney, J. N. Yang, “The illuminant estimation hypothesis and surface color perception,” in Colour Vision:From Light to Object, R. Mausfeld, D. Heyer, eds. (Oxford U. Press, Oxford, UK, to be published).

M. K. Kendall, A. Stuart, The Advanced Theory of Statistics: Vol. 2. Inference and Relationship, 4th ed. (Macmillan, New York, 1979).

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