Abstract

In a texture pair (TP) yielding a vertical or horizontal edge, the local (luminance or color) contrast or the local orientation of the individual textels is traded off with the global strength of the luminance-, color-, or orientation-defined TP edge so as to keep the latter at the detection threshold. Local and global contrasts are defined along the same (within-domain conditions) or along distinct physical dimensions (transdomain conditions). In the latter case local luminance or color contrast is traded off against global orientation. In all cases TP’s are presented for 66.7 or 333.3 ms. Textels differ from the background in either luminance or color so that the TP’s are respectively equichromatic or equiluminant. TP edge strength is modulated by means of swapping variable proportions of textels between the two textures in the TP. The observed local–global relationships are fitted with a version of the equivalent noise model for contrast coding modified to include the presentation time factor. The extension of the standard model in the time domain is meant to allow comparison between equivalent noise estimates for variable duration stimuli. Model fits of the within-domain data yield equivalent noise energy values significantly different for color- and luminance-defined TP’s but are not applicable for the transdomain experiments, which indicates that global orientation processing is independent of both local luminance and local color contrast insofar as the latter are above the detection threshold. Finally, this study points to the equivalence among the local–global, the equivalent noise, and the statistical approaches to texture segregation.

© 1999 Optical Society of America

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References

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  1. A. Gorea, “Visual texture,” in Early Vision and Beyond, T. V. Papathomas, C. Chubb, A. Gorea, E. Kowler, eds. (MIT, Cambridge, Mass., 1995), pp. 55–57.
  2. J. R. Bergen, “Theories of visual texture perception,” in Spatial Vision, D. Regan, ed. (CRC Press, New York, 1991), pp. 114–139.
  3. 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, Cambridge, Mass., 1991), pp. 253–271.
  4. D. Sagi, “The psychophysics of texture segmentation,” in Early Vision and Beyond, T. V. Papathomas, C. Chubb, A. Gorea, E. Kowler, eds. (MIT, Cambridge, Mass., 1995), pp. 70–78.
  5. D. Navon, “Forest before trees: the precedence of global features in visual perception,” Cogn. Psychol. 9, 353–383 (1977).
    [CrossRef]
  6. D. Navon, “The forest revisited: more on global precedence,” Psychol. Res. 43, 1–32 (1981).
    [CrossRef]
  7. R. A. Kinchla, J. M. Wolfe, “The order of visual processing: ‘top-down,’ ‘bottom-up’ or ‘middle-out,’” Percept. Psychophys. 25, 225–231 (1979).
    [CrossRef] [PubMed]
  8. D. Marr, Vision (Freeman, San Francisco, Calif., 1982).
  9. B. Julesz, “Visual pattern discrimination,” IRE Trans. Inf. Theory 8, 84–92 (1962).
    [CrossRef]
  10. J. Beck, “Perceptual grouping produced by changes in orientation and shape,” Science 154, 538–540 (1966).
    [CrossRef] [PubMed]
  11. B. Julesz, “Textons, the elements of texture perception and their interactions,” Nature (London) 290, 91–97 (1981).
    [CrossRef]
  12. R. Rosenholtz, “Texture and image segmentation,” Perception Suppl. 26, 111 (1997).
  13. C. Chubb, M. S. Landy, “Orthogonal distribution analysis: a new approach to the study of texture perception,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT, Cambridge, Mass., 1990), pp. 291–301.
  14. S. C. Dakin, R. J. Watt, “The computation of orientation statistics from visual texture,” Vision Res. 37, 3181–3192 (1997).
    [CrossRef]
  15. D. G. Pelli, “Effects of visual noise,” Ph.D. dissertation (University of Cambridge, Cambridge, UK, 1981).
  16. D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, New York, 1990), pp. 3–24.
  17. A. J. Ahumada, A. B. Watson, “Equivalent-noise model for contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1133–1139 (1985).
    [CrossRef] [PubMed]
  18. A. J. Ahumada, “Putting the visual system noise back in the picture,” J. Opt. Soc. Am. A 4, 2372–2378 (1987).
    [CrossRef] [PubMed]
  19. A. J. Ahumada, B. L. Beard, “Parafoveal target detectability reversal predicted by local luminance and gain control,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S380 (1997).
  20. H. B. Barlow, “Retinal noise and absolute threshold,” J. Opt. Soc. Am. 46, 634–639 (1956).
    [CrossRef] [PubMed]
  21. H. B. Barlow, “Increment thresholds at low intensities considered as signal/noise discrimination,” J. Physiol. (London) 136, 469–488 (1957).
  22. This approach appears to characterize the rather complex visual processing stream without loss of generality. Threshold predictions based on this single, generic front-end filter (whose Fourier transform is the contrast transfer function of the visual system as a whole) are quite comparable with those yielded by more realistic models involving the parallel processing of the input image through a bank of front-end filters tuned to different spatial frequencies and orientations.17,18
  23. Assume that there are 2 textels of luminance L0+ΔL and L0-ΔL, with L0 being the luminance of the background. Their contrast relative both to L0 and to each other is c=ΔL/L0. The overall luminance in a TP is LT1=pd(L0+ΔL)+(1-p)d(L0-ΔL)+(1-d)L0=dΔL(2p-1)+L0 for one texture and LT2=pd(L0-ΔL)+(1-p)d(L0+ΔL)+(1-d)L0=-dΔL(2p-1)+L0 for the other texture. The global TP contrast is given by (LT1-LT2)/(LT1+LT2)=c(P-1)d, with P=2p, so that 50% swapped textels (p=0.5) yields 0% global contrast. As noted in the text, the status of the density parameter, d, is not clear when one is averaging second-order features such as orientation; mean orientation contrast could well be a nonmonotonic function of density.
  24. In experiments in which presentation time, T, is a parameter (as was the case here), local contrast should be replaced by local energy, which can be approximated by CLT insofar as T is smaller than the temporal integration constant (see Section 6).
  25. B. A. Dosher, Z.-L. Lu, “Mechanisms of perceptual learning,” Invest. Ophthalmol. Visual Sci. Suppl. 39, S912 (1998).
  26. Z.-L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
    [CrossRef] [PubMed]
  27. In the terminology of Gorea and Papathomas,28,29 these TP’s are of the type luminance (or color) across orientation (L×O or C×O) and orientation across luminance (or color) (O×L or O×C). More generally, A×B TP’s are those whose edges are defined by two (or more) values of attribute A with two (or more) values of the remaining attribute, B, randomized over the whole TP.
  28. A. Gorea, T. V. Papathomas, “Texture segregation by chromatic and achromatic visual pathways: an analogy with motion perception,” J. Opt. Soc. Am. 8, 386–393 (1991).
    [CrossRef]
  29. A. Gorea, T. V. Papathomas, “Extending a class of motion stimuli to study multiattribute texture perception,” Behav. Res. Methods Instrum. 23, 5–8 (1991).
    [CrossRef]
  30. Once the extraction of the TP edge is achieved, specifying edge orientation (vertical or horizontal) or edge location (±3.2-deg location discrimination) is a trivial task in the sense that these tasks do not limit texture segregation: They both yield 100% performance, provided that the edge itself is 100% visible; thus performances below 100% in any of the two tasks reflect only edge extraction limitations. Moreover, in the remainder of this paper the only comparative discussion between the luminance/color and the orientation data shall bear on the generality of the generic equivalent noise model and not on the details of the fits. The equivalent noises estimated for the luminance/color domains, on the one hand, and for the orientation domain, on the other, are not commensurable and therefore are not to be related even when estimated by means of identical procedures.
  31. A. Gorea, T. V. Papathomas, I. Kovacs, “Motion perception with spatiotemporally matched chromatic and achromatic information reveals a ‘slow’ and a ‘fast’ motion system,” Vision Res. 33, 2515–2534 (1993).
    [CrossRef] [PubMed]
  32. T. V. Papathomas, A. Gorea, A. Feher, T. E. Conway, “Attention-based texture segregation,” Percept. Psychophys. (to be published).
  33. C. Agonie, A. Gorea, “Equivalent luminance contrast of red–green drifting stimuli: dependency on luminance–color interactions and on the psychophysical task,” J. Opt. Soc. Am. A 10, 1341–1352 (1993).
    [CrossRef] [PubMed]
  34. The distribution of the two-valued attributes (luminance, color, or orientation) in the textures used here is binomial. The upper confidence limit of the binomial distribution with respect to p is given by p+zpq/N, where q=1-p; N is the number of events considered (in this particular case, the number of textels); and z, the standard score in the normal distribution, with the upper α/2 proportion of cases cut off. For p=0.5,N=400, and α=0.05, this expression yields a p′ value of 0.549. When converted into P′-1=2p′-1 (see Ref. 23), it becomes 0.098. The linear function delimiting the shaded area is given by 0.098CLd, which is the limit below which the measured global contrast at threshold cannot be distinguished from random variations of the binomial distribution around p=0.5.
  35. A. Gorea, C. W. Tyler, “New look at Bloch’s law for contrast,” J. Opt. Soc. Am. A 3, 52–61 (1986).
    [CrossRef] [PubMed]
  36. D. H. Kelly, D. van Norren, “Two-band model of heterochromatic flicker,” J. Opt. Soc. Am. 67, 1081–1091 (1977).
    [CrossRef] [PubMed]
  37. S. S. Wolfson, M. S. Landy, “Examining edge- and region-based texture analysis mechanisms,” Vision Res. 38, 439–446 (1998).
    [CrossRef] [PubMed]
  38. E. Matin, A. Drivas, “Acuity for orientation measured with a sequential recognition task and signal detection methods,” Percept. Psychophys. 25, 161–168 (1979).
    [CrossRef] [PubMed]
  39. D. W. Heeley, B. Timney, “Meridional anisotropies of orientation discrimination for sine wave gratings,” Vision Res. 28, 337–344 (1988).
    [CrossRef] [PubMed]
  40. B. G. Smith, J. P. Thomas, “Why are some spatial discriminations independent of contrast,” J. Opt. Soc. Am. A 6, 713–724 (1989).
    [CrossRef] [PubMed]
  41. D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 30, 1429–1437 (1990).
    [CrossRef] [PubMed]
  42. R. E. Näsänen, H. T. Kukkonen, J. M. Rovamo, “Modeling spatial integration and contrast invariance in visual pattern discrimination,” Invest. Ophthalmol. Visual Sci. 37, 260–266 (1997).
  43. Obviously, the process responsible for the decision as to whether a signal is present receives inputs from both the external signal and noise and the internal noise.16 Simulating it with an integrator that acts on a window of fixed duration is only a first approximation toward incorporating the effect of time into the model. It is assumed that the decision stage acts on the probabilistic sum of the outputs of several temporal integrators, each characterized by a critical integration time, τ.35 For obvious reasons, TD must be larger than the average integration time τ.
  44. D. Regan, “Orientation discrimination for bars defined by orientation texture,” Perception 24, 1131–1138 (1995).
    [CrossRef] [PubMed]
  45. H. C. Nothdurft, “Sensitivity for structure gradient in texture discrimination tasks,” Vision Res. 25, 1957–1968 (1985).
    [CrossRef] [PubMed]
  46. D. Sagi, B. Julesz, “Short-range limitation on detection of feature differences,” Spatial Vision 2, 39–49 (1987).
    [CrossRef] [PubMed]
  47. P. Hammond, D. P. Andrews, C. R. James, “Invariance of orientational and directional tuning in visual cortical cells of the adult cat,” Brain Res. 96, 56–59 (1975).
    [CrossRef] [PubMed]
  48. G. Sclar, R. D. Freeman, “Orientation selectivity in the cat’s striate cortex is invariant with stimulus contrast,” Exp. Brain Res. 46, 457–461 (1982).
    [CrossRef]
  49. L. Chao-yi, O. Creutzfeldt, “The representation of contrast and other stimulus parameters by single neurons in area 17 of the cat,” Pfluegers Arch. 401, 304–314 (1984).
    [CrossRef]
  50. J. M. Foley, “Human luminance pattern-vision mechanisms: masking experiments require a new model,” J. Opt. Soc. Am. A 11, 1710–1719 (1994).
    [CrossRef]
  51. 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]
  52. J. M. Foley, W. Schwartz, “Spatial attention: effect of position uncertainty and number of distractor patterns on the threshold-versus-contrast function for contrast discrimination,” J. Opt. Soc. Am. A 15, 1036–1047 (1998).
    [CrossRef]
  53. H. R. Wilson, “A transducer function for threshold and suprathreshold human vision,” Biol. Cybern. 38, 171–178 (1980).
    [CrossRef] [PubMed]
  54. G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
    [CrossRef] [PubMed]

1998

B. A. Dosher, Z.-L. Lu, “Mechanisms of perceptual learning,” Invest. Ophthalmol. Visual Sci. Suppl. 39, S912 (1998).

Z.-L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

S. S. Wolfson, M. S. Landy, “Examining edge- and region-based texture analysis mechanisms,” Vision Res. 38, 439–446 (1998).
[CrossRef] [PubMed]

J. M. Foley, W. Schwartz, “Spatial attention: effect of position uncertainty and number of distractor patterns on the threshold-versus-contrast function for contrast discrimination,” J. Opt. Soc. Am. A 15, 1036–1047 (1998).
[CrossRef]

1997

A. J. Ahumada, B. L. Beard, “Parafoveal target detectability reversal predicted by local luminance and gain control,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S380 (1997).

R. E. Näsänen, H. T. Kukkonen, J. M. Rovamo, “Modeling spatial integration and contrast invariance in visual pattern discrimination,” Invest. Ophthalmol. Visual Sci. 37, 260–266 (1997).

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]

R. Rosenholtz, “Texture and image segmentation,” Perception Suppl. 26, 111 (1997).

S. C. Dakin, R. J. Watt, “The computation of orientation statistics from visual texture,” Vision Res. 37, 3181–3192 (1997).
[CrossRef]

1995

D. Regan, “Orientation discrimination for bars defined by orientation texture,” Perception 24, 1131–1138 (1995).
[CrossRef] [PubMed]

1994

1993

A. Gorea, T. V. Papathomas, I. Kovacs, “Motion perception with spatiotemporally matched chromatic and achromatic information reveals a ‘slow’ and a ‘fast’ motion system,” Vision Res. 33, 2515–2534 (1993).
[CrossRef] [PubMed]

C. Agonie, A. Gorea, “Equivalent luminance contrast of red–green drifting stimuli: dependency on luminance–color interactions and on the psychophysical task,” J. Opt. Soc. Am. A 10, 1341–1352 (1993).
[CrossRef] [PubMed]

1991

A. Gorea, T. V. Papathomas, “Texture segregation by chromatic and achromatic visual pathways: an analogy with motion perception,” J. Opt. Soc. Am. 8, 386–393 (1991).
[CrossRef]

A. Gorea, T. V. Papathomas, “Extending a class of motion stimuli to study multiattribute texture perception,” Behav. Res. Methods Instrum. 23, 5–8 (1991).
[CrossRef]

1990

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 30, 1429–1437 (1990).
[CrossRef] [PubMed]

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

1989

1988

D. W. Heeley, B. Timney, “Meridional anisotropies of orientation discrimination for sine wave gratings,” Vision Res. 28, 337–344 (1988).
[CrossRef] [PubMed]

1987

D. Sagi, B. Julesz, “Short-range limitation on detection of feature differences,” Spatial Vision 2, 39–49 (1987).
[CrossRef] [PubMed]

A. J. Ahumada, “Putting the visual system noise back in the picture,” J. Opt. Soc. Am. A 4, 2372–2378 (1987).
[CrossRef] [PubMed]

1986

1985

A. J. Ahumada, A. B. Watson, “Equivalent-noise model for contrast detection and discrimination,” J. Opt. Soc. Am. A 2, 1133–1139 (1985).
[CrossRef] [PubMed]

H. C. Nothdurft, “Sensitivity for structure gradient in texture discrimination tasks,” Vision Res. 25, 1957–1968 (1985).
[CrossRef] [PubMed]

1984

L. Chao-yi, O. Creutzfeldt, “The representation of contrast and other stimulus parameters by single neurons in area 17 of the cat,” Pfluegers Arch. 401, 304–314 (1984).
[CrossRef]

1982

G. Sclar, R. D. Freeman, “Orientation selectivity in the cat’s striate cortex is invariant with stimulus contrast,” Exp. Brain Res. 46, 457–461 (1982).
[CrossRef]

1981

B. Julesz, “Textons, the elements of texture perception and their interactions,” Nature (London) 290, 91–97 (1981).
[CrossRef]

D. Navon, “The forest revisited: more on global precedence,” Psychol. Res. 43, 1–32 (1981).
[CrossRef]

1980

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

1979

R. A. Kinchla, J. M. Wolfe, “The order of visual processing: ‘top-down,’ ‘bottom-up’ or ‘middle-out,’” Percept. Psychophys. 25, 225–231 (1979).
[CrossRef] [PubMed]

E. Matin, A. Drivas, “Acuity for orientation measured with a sequential recognition task and signal detection methods,” Percept. Psychophys. 25, 161–168 (1979).
[CrossRef] [PubMed]

1977

D. Navon, “Forest before trees: the precedence of global features in visual perception,” Cogn. Psychol. 9, 353–383 (1977).
[CrossRef]

D. H. Kelly, D. van Norren, “Two-band model of heterochromatic flicker,” J. Opt. Soc. Am. 67, 1081–1091 (1977).
[CrossRef] [PubMed]

1975

P. Hammond, D. P. Andrews, C. R. James, “Invariance of orientational and directional tuning in visual cortical cells of the adult cat,” Brain Res. 96, 56–59 (1975).
[CrossRef] [PubMed]

1966

J. Beck, “Perceptual grouping produced by changes in orientation and shape,” Science 154, 538–540 (1966).
[CrossRef] [PubMed]

1962

B. Julesz, “Visual pattern discrimination,” IRE Trans. Inf. Theory 8, 84–92 (1962).
[CrossRef]

1957

H. B. Barlow, “Increment thresholds at low intensities considered as signal/noise discrimination,” J. Physiol. (London) 136, 469–488 (1957).

1956

Agonie, C.

Ahumada, A. J.

Andrews, D. P.

P. Hammond, D. P. Andrews, C. R. James, “Invariance of orientational and directional tuning in visual cortical cells of the adult cat,” Brain Res. 96, 56–59 (1975).
[CrossRef] [PubMed]

Barlow, H. B.

H. B. Barlow, “Increment thresholds at low intensities considered as signal/noise discrimination,” J. Physiol. (London) 136, 469–488 (1957).

H. B. Barlow, “Retinal noise and absolute threshold,” J. Opt. Soc. Am. 46, 634–639 (1956).
[CrossRef] [PubMed]

Beard, B. L.

A. J. Ahumada, B. L. Beard, “Parafoveal target detectability reversal predicted by local luminance and gain control,” Invest. Ophthalmol. Visual Sci. Suppl. 38, S380 (1997).

Beck, J.

J. Beck, “Perceptual grouping produced by changes in orientation and shape,” Science 154, 538–540 (1966).
[CrossRef] [PubMed]

Bergen, J. R.

J. R. Bergen, “Theories of visual texture perception,” in Spatial Vision, D. Regan, ed. (CRC Press, New York, 1991), pp. 114–139.

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, Cambridge, Mass., 1991), pp. 253–271.

Buchanan-Smith, H. M.

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 30, 1429–1437 (1990).
[CrossRef] [PubMed]

Chao-yi, L.

L. Chao-yi, O. Creutzfeldt, “The representation of contrast and other stimulus parameters by single neurons in area 17 of the cat,” Pfluegers Arch. 401, 304–314 (1984).
[CrossRef]

Chen, C.-C.

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]

Chubb, C.

C. Chubb, M. S. Landy, “Orthogonal distribution analysis: a new approach to the study of texture perception,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT, Cambridge, Mass., 1990), pp. 291–301.

Conway, T. E.

T. V. Papathomas, A. Gorea, A. Feher, T. E. Conway, “Attention-based texture segregation,” Percept. Psychophys. (to be published).

Creutzfeldt, O.

L. Chao-yi, O. Creutzfeldt, “The representation of contrast and other stimulus parameters by single neurons in area 17 of the cat,” Pfluegers Arch. 401, 304–314 (1984).
[CrossRef]

Dakin, S. C.

S. C. Dakin, R. J. Watt, “The computation of orientation statistics from visual texture,” Vision Res. 37, 3181–3192 (1997).
[CrossRef]

Dosher, B. A.

B. A. Dosher, Z.-L. Lu, “Mechanisms of perceptual learning,” Invest. Ophthalmol. Visual Sci. Suppl. 39, S912 (1998).

Z.-L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

Drivas, A.

E. Matin, A. Drivas, “Acuity for orientation measured with a sequential recognition task and signal detection methods,” Percept. Psychophys. 25, 161–168 (1979).
[CrossRef] [PubMed]

Feher, A.

T. V. Papathomas, A. Gorea, A. Feher, T. E. Conway, “Attention-based texture segregation,” Percept. Psychophys. (to be published).

Foley, J. M.

Freeman, R. D.

G. Sclar, R. D. Freeman, “Orientation selectivity in the cat’s striate cortex is invariant with stimulus contrast,” Exp. Brain Res. 46, 457–461 (1982).
[CrossRef]

Gorea, A.

A. Gorea, T. V. Papathomas, I. Kovacs, “Motion perception with spatiotemporally matched chromatic and achromatic information reveals a ‘slow’ and a ‘fast’ motion system,” Vision Res. 33, 2515–2534 (1993).
[CrossRef] [PubMed]

C. Agonie, A. Gorea, “Equivalent luminance contrast of red–green drifting stimuli: dependency on luminance–color interactions and on the psychophysical task,” J. Opt. Soc. Am. A 10, 1341–1352 (1993).
[CrossRef] [PubMed]

A. Gorea, T. V. Papathomas, “Texture segregation by chromatic and achromatic visual pathways: an analogy with motion perception,” J. Opt. Soc. Am. 8, 386–393 (1991).
[CrossRef]

A. Gorea, T. V. Papathomas, “Extending a class of motion stimuli to study multiattribute texture perception,” Behav. Res. Methods Instrum. 23, 5–8 (1991).
[CrossRef]

A. Gorea, C. W. Tyler, “New look at Bloch’s law for contrast,” J. Opt. Soc. Am. A 3, 52–61 (1986).
[CrossRef] [PubMed]

T. V. Papathomas, A. Gorea, A. Feher, T. E. Conway, “Attention-based texture segregation,” Percept. Psychophys. (to be published).

A. Gorea, “Visual texture,” in Early Vision and Beyond, T. V. Papathomas, C. Chubb, A. Gorea, E. Kowler, eds. (MIT, Cambridge, Mass., 1995), pp. 55–57.

Hammond, P.

P. Hammond, D. P. Andrews, C. R. James, “Invariance of orientational and directional tuning in visual cortical cells of the adult cat,” Brain Res. 96, 56–59 (1975).
[CrossRef] [PubMed]

Heeley, D. W.

D. W. Heeley, H. M. Buchanan-Smith, “Recognition of stimulus orientation,” Vision Res. 30, 1429–1437 (1990).
[CrossRef] [PubMed]

D. W. Heeley, B. Timney, “Meridional anisotropies of orientation discrimination for sine wave gratings,” Vision Res. 28, 337–344 (1988).
[CrossRef] [PubMed]

James, C. R.

P. Hammond, D. P. Andrews, C. R. James, “Invariance of orientational and directional tuning in visual cortical cells of the adult cat,” Brain Res. 96, 56–59 (1975).
[CrossRef] [PubMed]

Julesz, B.

D. Sagi, B. Julesz, “Short-range limitation on detection of feature differences,” Spatial Vision 2, 39–49 (1987).
[CrossRef] [PubMed]

B. Julesz, “Textons, the elements of texture perception and their interactions,” Nature (London) 290, 91–97 (1981).
[CrossRef]

B. Julesz, “Visual pattern discrimination,” IRE Trans. Inf. Theory 8, 84–92 (1962).
[CrossRef]

Kelly, D. H.

Kinchla, R. A.

R. A. Kinchla, J. M. Wolfe, “The order of visual processing: ‘top-down,’ ‘bottom-up’ or ‘middle-out,’” Percept. Psychophys. 25, 225–231 (1979).
[CrossRef] [PubMed]

Kovacs, I.

A. Gorea, T. V. Papathomas, I. Kovacs, “Motion perception with spatiotemporally matched chromatic and achromatic information reveals a ‘slow’ and a ‘fast’ motion system,” Vision Res. 33, 2515–2534 (1993).
[CrossRef] [PubMed]

Kukkonen, H. T.

R. E. Näsänen, H. T. Kukkonen, J. M. Rovamo, “Modeling spatial integration and contrast invariance in visual pattern discrimination,” Invest. Ophthalmol. Visual Sci. 37, 260–266 (1997).

Landy, M. S.

S. S. Wolfson, M. S. Landy, “Examining edge- and region-based texture analysis mechanisms,” Vision Res. 38, 439–446 (1998).
[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, Cambridge, Mass., 1991), pp. 253–271.

C. Chubb, M. S. Landy, “Orthogonal distribution analysis: a new approach to the study of texture perception,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT, Cambridge, Mass., 1990), pp. 291–301.

Lennie, P.

G. Sclar, J. H. R. Maunsell, P. Lennie, “Coding of image contrast in central visual pathways of the macaque monkey,” Vision Res. 30, 1–10 (1990).
[CrossRef] [PubMed]

Lu, Z.-L.

B. A. Dosher, Z.-L. Lu, “Mechanisms of perceptual learning,” Invest. Ophthalmol. Visual Sci. Suppl. 39, S912 (1998).

Z.-L. Lu, B. A. Dosher, “External noise distinguishes attention mechanisms,” Vision Res. 38, 1183–1198 (1998).
[CrossRef] [PubMed]

Marr, D.

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

Matin, E.

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Other

T. V. Papathomas, A. Gorea, A. Feher, T. E. Conway, “Attention-based texture segregation,” Percept. Psychophys. (to be published).

The distribution of the two-valued attributes (luminance, color, or orientation) in the textures used here is binomial. The upper confidence limit of the binomial distribution with respect to p is given by p+zpq/N, where q=1-p; N is the number of events considered (in this particular case, the number of textels); and z, the standard score in the normal distribution, with the upper α/2 proportion of cases cut off. For p=0.5,N=400, and α=0.05, this expression yields a p′ value of 0.549. When converted into P′-1=2p′-1 (see Ref. 23), it becomes 0.098. The linear function delimiting the shaded area is given by 0.098CLd, which is the limit below which the measured global contrast at threshold cannot be distinguished from random variations of the binomial distribution around p=0.5.

In the terminology of Gorea and Papathomas,28,29 these TP’s are of the type luminance (or color) across orientation (L×O or C×O) and orientation across luminance (or color) (O×L or O×C). More generally, A×B TP’s are those whose edges are defined by two (or more) values of attribute A with two (or more) values of the remaining attribute, B, randomized over the whole TP.

Once the extraction of the TP edge is achieved, specifying edge orientation (vertical or horizontal) or edge location (±3.2-deg location discrimination) is a trivial task in the sense that these tasks do not limit texture segregation: They both yield 100% performance, provided that the edge itself is 100% visible; thus performances below 100% in any of the two tasks reflect only edge extraction limitations. Moreover, in the remainder of this paper the only comparative discussion between the luminance/color and the orientation data shall bear on the generality of the generic equivalent noise model and not on the details of the fits. The equivalent noises estimated for the luminance/color domains, on the one hand, and for the orientation domain, on the other, are not commensurable and therefore are not to be related even when estimated by means of identical procedures.

This approach appears to characterize the rather complex visual processing stream without loss of generality. Threshold predictions based on this single, generic front-end filter (whose Fourier transform is the contrast transfer function of the visual system as a whole) are quite comparable with those yielded by more realistic models involving the parallel processing of the input image through a bank of front-end filters tuned to different spatial frequencies and orientations.17,18

Assume that there are 2 textels of luminance L0+ΔL and L0-ΔL, with L0 being the luminance of the background. Their contrast relative both to L0 and to each other is c=ΔL/L0. The overall luminance in a TP is LT1=pd(L0+ΔL)+(1-p)d(L0-ΔL)+(1-d)L0=dΔL(2p-1)+L0 for one texture and LT2=pd(L0-ΔL)+(1-p)d(L0+ΔL)+(1-d)L0=-dΔL(2p-1)+L0 for the other texture. The global TP contrast is given by (LT1-LT2)/(LT1+LT2)=c(P-1)d, with P=2p, so that 50% swapped textels (p=0.5) yields 0% global contrast. As noted in the text, the status of the density parameter, d, is not clear when one is averaging second-order features such as orientation; mean orientation contrast could well be a nonmonotonic function of density.

In experiments in which presentation time, T, is a parameter (as was the case here), local contrast should be replaced by local energy, which can be approximated by CLT insofar as T is smaller than the temporal integration constant (see Section 6).

D. G. Pelli, “Effects of visual noise,” Ph.D. dissertation (University of Cambridge, Cambridge, UK, 1981).

D. G. Pelli, “The quantum efficiency of vision,” in Vision: Coding and Efficiency, C. Blakemore, ed. (Cambridge U. Press, New York, 1990), pp. 3–24.

C. Chubb, M. S. Landy, “Orthogonal distribution analysis: a new approach to the study of texture perception,” in Computational Models of Visual Processing, M. S. Landy, J. A. Movshon, eds. (MIT, Cambridge, Mass., 1990), pp. 291–301.

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

A. Gorea, “Visual texture,” in Early Vision and Beyond, T. V. Papathomas, C. Chubb, A. Gorea, E. Kowler, eds. (MIT, Cambridge, Mass., 1995), pp. 55–57.

J. R. Bergen, “Theories of visual texture perception,” in Spatial Vision, D. Regan, ed. (CRC Press, New York, 1991), pp. 114–139.

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, Cambridge, Mass., 1991), pp. 253–271.

D. Sagi, “The psychophysics of texture segmentation,” in Early Vision and Beyond, T. V. Papathomas, C. Chubb, A. Gorea, E. Kowler, eds. (MIT, Cambridge, Mass., 1995), pp. 70–78.

Obviously, the process responsible for the decision as to whether a signal is present receives inputs from both the external signal and noise and the internal noise.16 Simulating it with an integrator that acts on a window of fixed duration is only a first approximation toward incorporating the effect of time into the model. It is assumed that the decision stage acts on the probabilistic sum of the outputs of several temporal integrators, each characterized by a critical integration time, τ.35 For obvious reasons, TD must be larger than the average integration time τ.

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Figures (4)

Fig. 1
Fig. 1

Illustration of two types of texture pair (TP) used in the present study. For the top four TP’s segregation is based on global differences in luminance contrast. The bottom four TP’s illustrate the case of a global orientation difference. Replacing the two shades of gray of the textels with two equiluminant hues (in this case, red and green) would yield a global color contrast discrimination task for the top four TP’s and a chromatically defined orientation discrimination task for the bottom four. Local textel contrast, or local textel orientation difference, is maximal for panels (a), (c), (e), (g), and it is reduced in panels (b), (d), (f), and (h). Left-hand TP’s [(a)–(d)] yield zero dilution, that is, all the textels in each texture of the TP are identical along the discriminant dimension, namely, luminance polarity or orientation. The right-hand TP’s [(e)–(h)] illustrate the 50% dilution case: 25% of the textels on each side of the TP are randomly swapped. Illustrations are not to actual scale, and textel density is larger than in the experiments.

Fig. 2
Fig. 2

Global luminance contrast (open symbols) and global chromatic contrast (filled symbols) thresholds as a function of local contrast for (a) 66.7-ms and (b) 333.3-ms presentations. Local contrast for the chromatic condition is expressed in equivalent luminance contrast units. Different symbols are for different observers. Smooth curves are best fits with Eq. (4) of the average data (not shown); dashed and solid curves are for the luminance and chromatic conditions, respectively. Vertical thin bars are ±1 SE of the mean data. Vertical arrows show the estimated equivalent noise contrasts for the luminance-defined (dashed) and color-defined (solid) textures. The oblique line limiting the gray areas in each plot represents the upper 95% confidence interval of the binomial distribution for a 100% dilution (see text).

Fig. 3
Fig. 3

Global orientation thresholds as a function of the local orientation differences for [(a), left] 66.7-ms and [(b), right] 333.3-ms presentations. In (b) the data obtained for the two durations are presented together. Open and filled symbols are for luminance- and color-defined textels, respectively. In (a) the circles and squares are for the two observers, TEC and TVP, respectively. In (b) the circles and triangles are for observer TEC under 66.7- and 333-ms presentations; squares and diamonds are for observer TVP for the same durations. Smooth curves are best fits with Eq. (4) of the average data (not shown); dashed and solid curves are for the luminance and chromatic conditions, respectively. In (a) the vertical arrows show the estimated equivalent noise contrasts for the luminance-defined (dashed) and color-defined (solid) textures. In (b) the solid arrow shows the equivalent orientation noise estimated from the average of all the data. The upper 95% confidence interval of the binomial distribution for a 100% dilution (see text) are out of the range of the plot.

Fig. 4
Fig. 4

Global orientation thresholds as a function of either local luminance contrast (open symbols) or local chromatic contrast (in EqLC units; filled symbols) for (a) 66.7-ms and (b) 333.3-ms presentations. Different symbols are for different observers. Straight dashed lines (for the luminance condition) and straight solid lines (for the chromatic condition) are best fits to the descending (slope, -1) and the flat (slope, 0) ranges of the data. Vertical arrows show the intersection points of these lines. There is no descending range for the luminance-defined textures under the 333-ms presentation, so this intersection point is not defined in (b).

Tables (2)

Tables Icon

Table 1 Estimated Parameters of Eqs. (7) for the Best Fit of the Global versus Local Trade-Off in Luminance and Colora

Tables Icon

Table 2 Estimated Parameters of Eq. (6) for the Best Fit of the Local versus Global Trade-Off in Orientationa

Equations (8)

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

CG=CLd|1-P|,
CG_θ=f(CL),
N2=(rms)2=CL2d.
K=CG_θ(CL2d+NEq2)1/2.
K=CL1|1-P|d(CL22d+NEq22)1/2,
K=TSCG_θ(TS2CL2d+TD2NEq2)1/2.
K=TSCG_θ(TS2CL2d+TD2NEq2)1/2forTSTD,
K=CG_θ(CL2d+NEq2)1/2forTS>TD.

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