Abstract

We present a model of human preattentive texture perception. This model consists of three stages: (1) convolution of the image with a bank of even-symmetric linear filters followed by half-wave rectification to give a set of responses modeling outputs of V1 simple cells, (2) inhibition, localized in space, within and among the neural-response profiles that results in the suppression of weak responses when there are strong responses at the same or nearby locations, and (3) texture-boundary detection by using wide odd-symmetric mechanisms. Our model can predict the salience of texture boundaries in any arbitrary gray-scale image. A computer implementation of this model has been tested on many of the classic stimuli from psychophysical literature. Quantitative predictions of the degree of discriminability of different texture pairs match well with experimental measurements of discriminability in human observers.

© 1990 Optical Society of America

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References

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  1. B. Julesz, “Textons, the elements of texture perception and their interactions,” Nature (London) 290, 91–97 (1981).
    [CrossRef]
  2. J. Bergen, B. Julesz, “Rapid discrimination of visual patterns,” IEEE Trans. Syst. Man Cybern. 13, 857–863 (1983).
    [CrossRef]
  3. B. Julesz, “Texton gradients: the texton theory revisited,” Biol. Cybern. 54, 245–251 (1986).
    [CrossRef] [PubMed]
  4. J. Beck, “Similarity grouping and peripheral discriminability under uncertainty,” Am. J. Psychol. 85, 1–19 (1972).
    [CrossRef] [PubMed]
  5. J. Beck, “Textural segmentation,” in Organization and Representation in Perception, J. Beck, ed. (Erlbaum, Hillsdale, N.J., 1982).
  6. J. Beck, K. Prazdny, A. Rosenfeld, Human and Machine Vision(Academic, New York, 1983), pp. 1–38.
  7. H. Voorhees, T. Poggio, “Computing texture boundaries from images,” Nature (London) 333, 364–367 (1988).
    [CrossRef]
  8. J. Enns, “Seeing textons in context,” Percept. Psychophys. 39, 143–147 (1986).
    [CrossRef] [PubMed]
  9. J. Beck, A. Sutter, R. Ivry, “Spatial frequency channels and perceptual grouping in texture segmentation,” Comput. Vision Graphics Image Process. 37, 299–325 (1987).
    [CrossRef]
  10. R. Gurnsey, R. Browse, “Micropattern properties and presentation conditions influencing visual texture discrimination,” Percept. Psychophys. 41, 239–252 (1987).
    [CrossRef] [PubMed]
  11. T. Caelli, “Three processing characteristics of visual texture segmentation,” Spatial Vision 1, 19–30 (1985).
    [CrossRef] [PubMed]
  12. J. Coggins, A. K. Jain, “A spatial filtering approach to texture analysis,” Pattern Recogn. Lett. 3, 195–203 (1985).
    [CrossRef]
  13. M. Turner, “Texture discrimination by gabor functions,” Biol. Cybern. 55, 71–82 (1986).
    [PubMed]
  14. J. Bergen, E. Adelson, “Early vision and texture perception,” Nature (London) 333, 363–364 (1988).
    [CrossRef]
  15. A. Sutter, J. Beck, N. Graham, “Contrast and spatial variables in texture segregation: testing a simple spatial-frequency channels model,” Percept. Psychophys. 46, 312–332 (1989).
    [CrossRef] [PubMed]
  16. I. Fogel, D. Sagi, “Gabor filters as texture discriminators,” Biol. Cybern. 61, 103–113 (1989).
    [CrossRef]
  17. B. J. Kröse, A Description of Visual Structure, Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1986).
  18. B. Julesz, B. Kröse, “Features and spatial filters,” Nature (London) 333, 302–303 (1988).
    [CrossRef]
  19. B. Julesz, AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (personal communication).
  20. H. Spitzer, S. Hochstein, “Simple- and complex-cell response dependences on stimulation parameters, and A complex cell receptive-field model,” J. Neurophysiol. 53, 1244–1286 (1985).
    [PubMed]
  21. H. C. Nothdurft, “Sensitivity for structure gradient for texture discrimination tasks,” Vision Res. 25, 1957–1968 (1985).
    [CrossRef]
  22. A. Treisman, “Preattentive processing in vision,” Comput. Vision Graphics Image Process. 31, 156–177 (1985).
    [CrossRef]
  23. P. R. Kube, On Image Texture, Ph.D. dissertation (University of California, Berkeley, Berkeley, Calif., 1988).
  24. J. D. Daugman, “Two dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1980).
    [CrossRef]
  25. R. Young, “The Gaussian derivative theory of spatial vision: analysis of cortical cell receptive field line-weighting profiles,” Tech. Rep. GMR-4920 (General Motors Research, Warren, Mich., 1985).
  26. A. Parker, M. J. Hawken, “Two-dimensional spatial structure of receptive fields in monkey striate cortex,” J. Opt. Soc. Am. A 5, 598–605 (1988).
    [CrossRef] [PubMed]
  27. D. Field, J. Nachmias, “Phase reversal discrimination,” J. Vis. Res. 24, 333–340 (1984).
    [CrossRef]
  28. D. Burr, C. Morrone, D. Spinelli, “Evidence of edge and bar detectors in human vision,” Vision Res. 29, 419–431 (1989).
    [CrossRef]
  29. We have used a linear sampling of the frequency space instead of the more common logarithmic sampling. The way we combine the output of the different channels makes this choice immaterial, provided that the sampling is dense enough.
  30. H. Voorhees, “Finding texture boundaries in images,” Tech. Rep. 968 (Massachusetts Institute of Technology, Artificial Intelligence Laboratory, Cambridge, Mass., 1987).
  31. B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third order statistics,” Biol. Cybern. 31, 137–140 (1978).
    [CrossRef] [PubMed]
  32. R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retinal Res. 4, 263–347 (1984).
    [CrossRef]
  33. N. Graham, J. Beck, A. Sutter, “Two nonlinearities in texture segregation,” Invest. Ophtalmol. Vis. Sci. 30, 161 (1989).
  34. D. Albrecht, D. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
    [PubMed]
  35. K. Toyama, M. Kimura, K. Tanaka, “Organization of cat visual cortex as investigated by cross-correlation techniques,” J. Neurophysiol. 46, 202–214 (1981).
    [PubMed]
  36. K. De Valois, R. Tootell, “Spatial-frequency-specific inhibition in car striate cortex cells,” J. Physiol. 336, 359–376 (1983).
  37. A. M. Sillito, P. C. Murphy, Neurotransmitters and Cortical Function: From Molecules to Mind (Plenum, New York, 1988), Chap. 11.
  38. D. Tolhurst, “Adaptation to square wave gratings: inhibition between spatial frequency channels in the human visual system,” J. Physiol. 226, 231–248 (1972).
    [PubMed]
  39. A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the car striate cortex,” Visual Neurosci. 2, 41–55 (1989).
    [CrossRef]
  40. I. Rentschler, M. Hubner, T. Caelli, “On the discrimination of compound Gabor signals and textures,” Vision Res. 28, 279–291 (1988).
    [CrossRef] [PubMed]
  41. Data are from Ref. 17. The tabulated data correspond to δtb(Table 3.1, p. 39; stimulus onset asynchrony, 320).
  42. B. Kröse, “Local structure analyzers as determinants of preattentive pattern discrimination,” Biol. Cybern. 55, 289–298 (1987).
    [CrossRef] [PubMed]
  43. Data are from Ref. 10. The tabulated data correspond to mean overall discriminability (pairs 1.1, 1.2, 1.3, 3.1) averaged over foreground/background and different stimulus durations.
  44. J. Malik, P. Perona, “A computational model of texture perception,” Tech. Rep. UCB/CSD 89/491 (Computer Science Division, University of California, Berkeley, Berkeley, Calif., 1989).
  45. B. Julesz, AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (personal communication).
  46. B. Rubenstein, D. Sagi, “Texture variability across the orientation spectrum can yield asymmetry in texture discrimination,” Perception 18, 517 (1989).
  47. J. Malik, P. Perona, “A computational model of human texture perception,” Invest. Ophthalmol. Vis. Sci. 30, 161 (1989).

1989

A. Sutter, J. Beck, N. Graham, “Contrast and spatial variables in texture segregation: testing a simple spatial-frequency channels model,” Percept. Psychophys. 46, 312–332 (1989).
[CrossRef] [PubMed]

I. Fogel, D. Sagi, “Gabor filters as texture discriminators,” Biol. Cybern. 61, 103–113 (1989).
[CrossRef]

D. Burr, C. Morrone, D. Spinelli, “Evidence of edge and bar detectors in human vision,” Vision Res. 29, 419–431 (1989).
[CrossRef]

N. Graham, J. Beck, A. Sutter, “Two nonlinearities in texture segregation,” Invest. Ophtalmol. Vis. Sci. 30, 161 (1989).

A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the car striate cortex,” Visual Neurosci. 2, 41–55 (1989).
[CrossRef]

B. Rubenstein, D. Sagi, “Texture variability across the orientation spectrum can yield asymmetry in texture discrimination,” Perception 18, 517 (1989).

J. Malik, P. Perona, “A computational model of human texture perception,” Invest. Ophthalmol. Vis. Sci. 30, 161 (1989).

1988

A. Parker, M. J. Hawken, “Two-dimensional spatial structure of receptive fields in monkey striate cortex,” J. Opt. Soc. Am. A 5, 598–605 (1988).
[CrossRef] [PubMed]

I. Rentschler, M. Hubner, T. Caelli, “On the discrimination of compound Gabor signals and textures,” Vision Res. 28, 279–291 (1988).
[CrossRef] [PubMed]

B. Julesz, B. Kröse, “Features and spatial filters,” Nature (London) 333, 302–303 (1988).
[CrossRef]

H. Voorhees, T. Poggio, “Computing texture boundaries from images,” Nature (London) 333, 364–367 (1988).
[CrossRef]

J. Bergen, E. Adelson, “Early vision and texture perception,” Nature (London) 333, 363–364 (1988).
[CrossRef]

1987

J. Beck, A. Sutter, R. Ivry, “Spatial frequency channels and perceptual grouping in texture segmentation,” Comput. Vision Graphics Image Process. 37, 299–325 (1987).
[CrossRef]

R. Gurnsey, R. Browse, “Micropattern properties and presentation conditions influencing visual texture discrimination,” Percept. Psychophys. 41, 239–252 (1987).
[CrossRef] [PubMed]

B. Kröse, “Local structure analyzers as determinants of preattentive pattern discrimination,” Biol. Cybern. 55, 289–298 (1987).
[CrossRef] [PubMed]

1986

B. Julesz, “Texton gradients: the texton theory revisited,” Biol. Cybern. 54, 245–251 (1986).
[CrossRef] [PubMed]

M. Turner, “Texture discrimination by gabor functions,” Biol. Cybern. 55, 71–82 (1986).
[PubMed]

J. Enns, “Seeing textons in context,” Percept. Psychophys. 39, 143–147 (1986).
[CrossRef] [PubMed]

1985

H. Spitzer, S. Hochstein, “Simple- and complex-cell response dependences on stimulation parameters, and A complex cell receptive-field model,” J. Neurophysiol. 53, 1244–1286 (1985).
[PubMed]

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

A. Treisman, “Preattentive processing in vision,” Comput. Vision Graphics Image Process. 31, 156–177 (1985).
[CrossRef]

T. Caelli, “Three processing characteristics of visual texture segmentation,” Spatial Vision 1, 19–30 (1985).
[CrossRef] [PubMed]

J. Coggins, A. K. Jain, “A spatial filtering approach to texture analysis,” Pattern Recogn. Lett. 3, 195–203 (1985).
[CrossRef]

1984

D. Field, J. Nachmias, “Phase reversal discrimination,” J. Vis. Res. 24, 333–340 (1984).
[CrossRef]

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retinal Res. 4, 263–347 (1984).
[CrossRef]

1983

K. De Valois, R. Tootell, “Spatial-frequency-specific inhibition in car striate cortex cells,” J. Physiol. 336, 359–376 (1983).

J. Bergen, B. Julesz, “Rapid discrimination of visual patterns,” IEEE Trans. Syst. Man Cybern. 13, 857–863 (1983).
[CrossRef]

1982

D. Albrecht, D. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

1981

K. Toyama, M. Kimura, K. Tanaka, “Organization of cat visual cortex as investigated by cross-correlation techniques,” J. Neurophysiol. 46, 202–214 (1981).
[PubMed]

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

1980

J. D. Daugman, “Two dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1980).
[CrossRef]

1978

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third order statistics,” Biol. Cybern. 31, 137–140 (1978).
[CrossRef] [PubMed]

1972

D. Tolhurst, “Adaptation to square wave gratings: inhibition between spatial frequency channels in the human visual system,” J. Physiol. 226, 231–248 (1972).
[PubMed]

J. Beck, “Similarity grouping and peripheral discriminability under uncertainty,” Am. J. Psychol. 85, 1–19 (1972).
[CrossRef] [PubMed]

Adelson, E.

J. Bergen, E. Adelson, “Early vision and texture perception,” Nature (London) 333, 363–364 (1988).
[CrossRef]

Albrecht, D.

D. Albrecht, D. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

Beck, J.

A. Sutter, J. Beck, N. Graham, “Contrast and spatial variables in texture segregation: testing a simple spatial-frequency channels model,” Percept. Psychophys. 46, 312–332 (1989).
[CrossRef] [PubMed]

N. Graham, J. Beck, A. Sutter, “Two nonlinearities in texture segregation,” Invest. Ophtalmol. Vis. Sci. 30, 161 (1989).

J. Beck, A. Sutter, R. Ivry, “Spatial frequency channels and perceptual grouping in texture segmentation,” Comput. Vision Graphics Image Process. 37, 299–325 (1987).
[CrossRef]

J. Beck, “Similarity grouping and peripheral discriminability under uncertainty,” Am. J. Psychol. 85, 1–19 (1972).
[CrossRef] [PubMed]

J. Beck, K. Prazdny, A. Rosenfeld, Human and Machine Vision(Academic, New York, 1983), pp. 1–38.

J. Beck, “Textural segmentation,” in Organization and Representation in Perception, J. Beck, ed. (Erlbaum, Hillsdale, N.J., 1982).

Bergen, J.

J. Bergen, E. Adelson, “Early vision and texture perception,” Nature (London) 333, 363–364 (1988).
[CrossRef]

J. Bergen, B. Julesz, “Rapid discrimination of visual patterns,” IEEE Trans. Syst. Man Cybern. 13, 857–863 (1983).
[CrossRef]

Bonds, A. B.

A. B. Bonds, “Role of inhibition in the specification of orientation selectivity of cells in the car striate cortex,” Visual Neurosci. 2, 41–55 (1989).
[CrossRef]

Browse, R.

R. Gurnsey, R. Browse, “Micropattern properties and presentation conditions influencing visual texture discrimination,” Percept. Psychophys. 41, 239–252 (1987).
[CrossRef] [PubMed]

Burr, D.

D. Burr, C. Morrone, D. Spinelli, “Evidence of edge and bar detectors in human vision,” Vision Res. 29, 419–431 (1989).
[CrossRef]

Caelli, T.

I. Rentschler, M. Hubner, T. Caelli, “On the discrimination of compound Gabor signals and textures,” Vision Res. 28, 279–291 (1988).
[CrossRef] [PubMed]

T. Caelli, “Three processing characteristics of visual texture segmentation,” Spatial Vision 1, 19–30 (1985).
[CrossRef] [PubMed]

Coggins, J.

J. Coggins, A. K. Jain, “A spatial filtering approach to texture analysis,” Pattern Recogn. Lett. 3, 195–203 (1985).
[CrossRef]

Daugman, J. D.

J. D. Daugman, “Two dimensional spectral analysis of cortical receptive field profiles,” Vision Res. 20, 847–856 (1980).
[CrossRef]

De Valois, K.

K. De Valois, R. Tootell, “Spatial-frequency-specific inhibition in car striate cortex cells,” J. Physiol. 336, 359–376 (1983).

Enns, J.

J. Enns, “Seeing textons in context,” Percept. Psychophys. 39, 143–147 (1986).
[CrossRef] [PubMed]

Enroth-Cugell, C.

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retinal Res. 4, 263–347 (1984).
[CrossRef]

Field, D.

D. Field, J. Nachmias, “Phase reversal discrimination,” J. Vis. Res. 24, 333–340 (1984).
[CrossRef]

Fogel, I.

I. Fogel, D. Sagi, “Gabor filters as texture discriminators,” Biol. Cybern. 61, 103–113 (1989).
[CrossRef]

Gilbert, E. N.

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third order statistics,” Biol. Cybern. 31, 137–140 (1978).
[CrossRef] [PubMed]

Graham, N.

N. Graham, J. Beck, A. Sutter, “Two nonlinearities in texture segregation,” Invest. Ophtalmol. Vis. Sci. 30, 161 (1989).

A. Sutter, J. Beck, N. Graham, “Contrast and spatial variables in texture segregation: testing a simple spatial-frequency channels model,” Percept. Psychophys. 46, 312–332 (1989).
[CrossRef] [PubMed]

Gurnsey, R.

R. Gurnsey, R. Browse, “Micropattern properties and presentation conditions influencing visual texture discrimination,” Percept. Psychophys. 41, 239–252 (1987).
[CrossRef] [PubMed]

Hamilton, D.

D. Albrecht, D. Hamilton, “Striate cortex of monkey and cat: contrast response function,” J. Neurophysiol. 48, 217–237 (1982).
[PubMed]

Hawken, M. J.

Hochstein, S.

H. Spitzer, S. Hochstein, “Simple- and complex-cell response dependences on stimulation parameters, and A complex cell receptive-field model,” J. Neurophysiol. 53, 1244–1286 (1985).
[PubMed]

Hubner, M.

I. Rentschler, M. Hubner, T. Caelli, “On the discrimination of compound Gabor signals and textures,” Vision Res. 28, 279–291 (1988).
[CrossRef] [PubMed]

Ivry, R.

J. Beck, A. Sutter, R. Ivry, “Spatial frequency channels and perceptual grouping in texture segmentation,” Comput. Vision Graphics Image Process. 37, 299–325 (1987).
[CrossRef]

Jain, A. K.

J. Coggins, A. K. Jain, “A spatial filtering approach to texture analysis,” Pattern Recogn. Lett. 3, 195–203 (1985).
[CrossRef]

Julesz, B.

B. Julesz, B. Kröse, “Features and spatial filters,” Nature (London) 333, 302–303 (1988).
[CrossRef]

B. Julesz, “Texton gradients: the texton theory revisited,” Biol. Cybern. 54, 245–251 (1986).
[CrossRef] [PubMed]

J. Bergen, B. Julesz, “Rapid discrimination of visual patterns,” IEEE Trans. Syst. Man Cybern. 13, 857–863 (1983).
[CrossRef]

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

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third order statistics,” Biol. Cybern. 31, 137–140 (1978).
[CrossRef] [PubMed]

B. Julesz, AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (personal communication).

B. Julesz, AT&T Bell Laboratories, Murray Hill, New Jersey 07974 (personal communication).

Kimura, M.

K. Toyama, M. Kimura, K. Tanaka, “Organization of cat visual cortex as investigated by cross-correlation techniques,” J. Neurophysiol. 46, 202–214 (1981).
[PubMed]

Kröse, B.

B. Julesz, B. Kröse, “Features and spatial filters,” Nature (London) 333, 302–303 (1988).
[CrossRef]

B. Kröse, “Local structure analyzers as determinants of preattentive pattern discrimination,” Biol. Cybern. 55, 289–298 (1987).
[CrossRef] [PubMed]

Kröse, B. J.

B. J. Kröse, A Description of Visual Structure, Ph.D. dissertation (Delft University of Technology, Delft, The Netherlands, 1986).

Kube, P. R.

P. R. Kube, On Image Texture, Ph.D. dissertation (University of California, Berkeley, Berkeley, Calif., 1988).

Malik, J.

J. Malik, P. Perona, “A computational model of human texture perception,” Invest. Ophthalmol. Vis. Sci. 30, 161 (1989).

J. Malik, P. Perona, “A computational model of texture perception,” Tech. Rep. UCB/CSD 89/491 (Computer Science Division, University of California, Berkeley, Berkeley, Calif., 1989).

Morrone, C.

D. Burr, C. Morrone, D. Spinelli, “Evidence of edge and bar detectors in human vision,” Vision Res. 29, 419–431 (1989).
[CrossRef]

Murphy, P. C.

A. M. Sillito, P. C. Murphy, Neurotransmitters and Cortical Function: From Molecules to Mind (Plenum, New York, 1988), Chap. 11.

Nachmias, J.

D. Field, J. Nachmias, “Phase reversal discrimination,” J. Vis. Res. 24, 333–340 (1984).
[CrossRef]

Nothdurft, H. C.

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

Parker, A.

Perona, P.

J. Malik, P. Perona, “A computational model of human texture perception,” Invest. Ophthalmol. Vis. Sci. 30, 161 (1989).

J. Malik, P. Perona, “A computational model of texture perception,” Tech. Rep. UCB/CSD 89/491 (Computer Science Division, University of California, Berkeley, Berkeley, Calif., 1989).

Poggio, T.

H. Voorhees, T. Poggio, “Computing texture boundaries from images,” Nature (London) 333, 364–367 (1988).
[CrossRef]

Prazdny, K.

J. Beck, K. Prazdny, A. Rosenfeld, Human and Machine Vision(Academic, New York, 1983), pp. 1–38.

Rentschler, I.

I. Rentschler, M. Hubner, T. Caelli, “On the discrimination of compound Gabor signals and textures,” Vision Res. 28, 279–291 (1988).
[CrossRef] [PubMed]

Rosenfeld, A.

J. Beck, K. Prazdny, A. Rosenfeld, Human and Machine Vision(Academic, New York, 1983), pp. 1–38.

Rubenstein, B.

B. Rubenstein, D. Sagi, “Texture variability across the orientation spectrum can yield asymmetry in texture discrimination,” Perception 18, 517 (1989).

Sagi, D.

B. Rubenstein, D. Sagi, “Texture variability across the orientation spectrum can yield asymmetry in texture discrimination,” Perception 18, 517 (1989).

I. Fogel, D. Sagi, “Gabor filters as texture discriminators,” Biol. Cybern. 61, 103–113 (1989).
[CrossRef]

Shapley, R.

R. Shapley, C. Enroth-Cugell, “Visual adaptation and retinal gain controls,” Prog. Retinal Res. 4, 263–347 (1984).
[CrossRef]

Sillito, A. M.

A. M. Sillito, P. C. Murphy, Neurotransmitters and Cortical Function: From Molecules to Mind (Plenum, New York, 1988), Chap. 11.

Spinelli, D.

D. Burr, C. Morrone, D. Spinelli, “Evidence of edge and bar detectors in human vision,” Vision Res. 29, 419–431 (1989).
[CrossRef]

Spitzer, H.

H. Spitzer, S. Hochstein, “Simple- and complex-cell response dependences on stimulation parameters, and A complex cell receptive-field model,” J. Neurophysiol. 53, 1244–1286 (1985).
[PubMed]

Sutter, A.

N. Graham, J. Beck, A. Sutter, “Two nonlinearities in texture segregation,” Invest. Ophtalmol. Vis. Sci. 30, 161 (1989).

A. Sutter, J. Beck, N. Graham, “Contrast and spatial variables in texture segregation: testing a simple spatial-frequency channels model,” Percept. Psychophys. 46, 312–332 (1989).
[CrossRef] [PubMed]

J. Beck, A. Sutter, R. Ivry, “Spatial frequency channels and perceptual grouping in texture segmentation,” Comput. Vision Graphics Image Process. 37, 299–325 (1987).
[CrossRef]

Tanaka, K.

K. Toyama, M. Kimura, K. Tanaka, “Organization of cat visual cortex as investigated by cross-correlation techniques,” J. Neurophysiol. 46, 202–214 (1981).
[PubMed]

Tolhurst, D.

D. Tolhurst, “Adaptation to square wave gratings: inhibition between spatial frequency channels in the human visual system,” J. Physiol. 226, 231–248 (1972).
[PubMed]

Tootell, R.

K. De Valois, R. Tootell, “Spatial-frequency-specific inhibition in car striate cortex cells,” J. Physiol. 336, 359–376 (1983).

Toyama, K.

K. Toyama, M. Kimura, K. Tanaka, “Organization of cat visual cortex as investigated by cross-correlation techniques,” J. Neurophysiol. 46, 202–214 (1981).
[PubMed]

Treisman, A.

A. Treisman, “Preattentive processing in vision,” Comput. Vision Graphics Image Process. 31, 156–177 (1985).
[CrossRef]

Turner, M.

M. Turner, “Texture discrimination by gabor functions,” Biol. Cybern. 55, 71–82 (1986).
[PubMed]

Victor, J. D.

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third order statistics,” Biol. Cybern. 31, 137–140 (1978).
[CrossRef] [PubMed]

Voorhees, H.

H. Voorhees, T. Poggio, “Computing texture boundaries from images,” Nature (London) 333, 364–367 (1988).
[CrossRef]

H. Voorhees, “Finding texture boundaries in images,” Tech. Rep. 968 (Massachusetts Institute of Technology, Artificial Intelligence Laboratory, Cambridge, Mass., 1987).

Young, R.

R. Young, “The Gaussian derivative theory of spatial vision: analysis of cortical cell receptive field line-weighting profiles,” Tech. Rep. GMR-4920 (General Motors Research, Warren, Mich., 1985).

Am. J. Psychol.

J. Beck, “Similarity grouping and peripheral discriminability under uncertainty,” Am. J. Psychol. 85, 1–19 (1972).
[CrossRef] [PubMed]

Biol. Cybern.

B. Julesz, “Texton gradients: the texton theory revisited,” Biol. Cybern. 54, 245–251 (1986).
[CrossRef] [PubMed]

M. Turner, “Texture discrimination by gabor functions,” Biol. Cybern. 55, 71–82 (1986).
[PubMed]

I. Fogel, D. Sagi, “Gabor filters as texture discriminators,” Biol. Cybern. 61, 103–113 (1989).
[CrossRef]

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third order statistics,” Biol. Cybern. 31, 137–140 (1978).
[CrossRef] [PubMed]

B. Kröse, “Local structure analyzers as determinants of preattentive pattern discrimination,” Biol. Cybern. 55, 289–298 (1987).
[CrossRef] [PubMed]

Comput. Vision Graphics Image Process.

A. Treisman, “Preattentive processing in vision,” Comput. Vision Graphics Image Process. 31, 156–177 (1985).
[CrossRef]

J. Beck, A. Sutter, R. Ivry, “Spatial frequency channels and perceptual grouping in texture segmentation,” Comput. Vision Graphics Image Process. 37, 299–325 (1987).
[CrossRef]

IEEE Trans. Syst. Man Cybern.

J. Bergen, B. Julesz, “Rapid discrimination of visual patterns,” IEEE Trans. Syst. Man Cybern. 13, 857–863 (1983).
[CrossRef]

Invest. Ophtalmol. Vis. Sci.

N. Graham, J. Beck, A. Sutter, “Two nonlinearities in texture segregation,” Invest. Ophtalmol. Vis. Sci. 30, 161 (1989).

Invest. Ophthalmol. Vis. Sci.

J. Malik, P. Perona, “A computational model of human texture perception,” Invest. Ophthalmol. Vis. Sci. 30, 161 (1989).

J. Neurophysiol.

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Data are from Ref. 17. The tabulated data correspond to δtb(Table 3.1, p. 39; stimulus onset asynchrony, 320).

Data are from Ref. 10. The tabulated data correspond to mean overall discriminability (pairs 1.1, 1.2, 1.3, 3.1) averaged over foreground/background and different stimulus durations.

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We have used a linear sampling of the frequency space instead of the more common logarithmic sampling. The way we combine the output of the different channels makes this choice immaterial, provided that the sampling is dense enough.

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Figures (11)

Fig. 1
Fig. 1

Simplified schematics of our model for texture perception. The image (bottom) is filtered using the kernels F1Fm and is half-wave rectified to give the set of simple-cell responses R1Rn. The postinhibition responses PIR1 … PIRn are computed by thresholding the Ri and taking the maximum of the result over small neighborhoods. The thresholds depend on the activity of all channels. The texture gradient is computed by taking the maximum of the responses of wide odd-symmetric filters acting on the postinhibition responses PIRi.

Fig. 2
Fig. 2

Point-spread functions of some of the filters used in our simulation. The filters were designed after Young25 by summing Gaussian functions G(x0, y0, σx, σy) ≐ 1/2πσxσy exp{−(xx0/σx)2 + (yy0/σy)2]} and have zero-mean value. a, Linear combination of three circular concentric Gaussian functions, DOG2(σ) ≐ a · G(0, 0, σi, σi) + b · G(0, 0, σ, σ) + c · G(0, 0, σo, σo) with variance σi:σ:σo in a ratio of 0.62:1:1.6 and a:b:c in a ratio of 1:−2:1. b, Linear combination of two circular concentric Gaussian functions, DOG1(σ) = a · G(0, 0, σi, σi) + b · G(0, 0, σo, σo), with variance σi:σ:σo in a ratio of 0.71:1:1.14 and coefficients a:b in a ratio of 1:−1. c, Linear combination of three offset identical Gaussian functions DOOG2(σ, r, θ) = a · G(0, ya, σx, σy) + b · G(0, yb, σx, σy) + c · G(0, yc, σx, σy). Variances are σy = σ, σx = r · σ, offsets are ya = −yc = σ, yb = 0, and coefficients are a:b:c in a ratio of −1:2:−1 for the filter with an axis of symmetry along the x direction (θ = 0). The other DOOG2( ) filters are obtained by rotation about the center of the middle Gaussian. The scaling coefficients aDOG1:aDOG2:aDOG2 were in a ratio of 3:4.15:2, which was designed to equalize the dynamic range of the respective responses.

Fig. 3
Fig. 3

Some textures (top row) and half-wave-rectified responses of one of the filters to each (bottom row). The point-spread function of each filter is shown at the bottom-right corner of the response image. The filter shapes are as in Fig. 2; the frequency parameters correspond to a 4 deg × 4 deg image. The response images are composed of two square regions, an upper one depicting R+, the positive part of the response, and a lower one showing R. a, Texture from Ref. 10, Fig. 6, pair 2.2 (top) and the response of an 8-c/deg DOG1 filter (bottom); σ ≈ 0.5 × (length of texel line segments). b, Texture from Ref. 10, Fig. 6, pair 2.1 (top) and the response of a 5-c/deg DOG1 filter (bottom); σ ≈ 2 × (width of texel line segments). c, Arrow–triangle texture (top), for which the arrow texel is obtained from the triangle by shifting one of its legs, and the response to a 5-c/deg DOG2 filter (bottom); σ ≈ 0.3 × (length of triangle’s hypotenuse). d, Texture from Ref. 30, Fig. 4.2b (top) and the response to a 13-c/deg DOOG2 filter (bottom); σy ≈ (width of bars), σx:σy = 3, and orientation 120 deg.

Fig. 4
Fig. 4

a, Texture pair that was constructed by adding to a uniform gray field the zero-mean micropatterns M (right) and −M (left). The two textures are easily discriminable, though it may be shown that spatially averaged responses for any linear filter followed by either half- or full-wave rectification are identical for both and thus insufficient for the discrimination. b, Cross section of M along the x axis. c, d, Cross sections of the responses to M and −M in one channel (corresponding to convolution with Fi = M followed by positive half-wave rectification). The areas under c and d are equal. For any zero-mean filter F(∫ ∫ F = 0) we have ∫ ∫(M * F) = 0; hence ∫ ∫(M * F)+ = ∫ ∫(M * F) = ∫ ∫(−M * F)+.

Fig. 5
Fig. 5

Detail of the portrait of Adele Bloch-Bauer by Gustav Klimt (left) and the texture boundaries that were found (right). The essential boundaries of the five perceived groups have been detected.

Fig. 6
Fig. 6

Texture pair composed of y mirror-symmetric micropatterns. Segmentation is not preattentive. Compare with Fig. 4.

Fig. 7
Fig. 7

Nine textures that were used in our experiments.

Fig. 8
Fig. 8

Texture gradient as a function of column number. For the 128 × 128 textures in Fig. 7 the texture gradient is averaged along the vertical direction on the central middle portion of each column and plotted with respect to the horizontal coordinate. Such plots are shown for the most (L +) and least (R-mirror-R) discriminable textures. The value of the texture gradient at its central peak is taken to be the prediction of our model and is reported in Table 3, column 3.

Fig. 9
Fig. 9

Textures from left to right: the +L texture, the same after removal of Laplacian pyramid level 3 (+L −3), the same after removal of Laplacian pyramid levels 2, 3, and 4 (+L −234). The Laplacian pyramid was generated by taking differences of contiguous levels of a Gaussian pyramid. Level 0 of the Gaussian pyramid was the image itself; level i was the image convolved with a rotationally symmetric Gaussian of unitary norm, and σ is equal to 2i pixels. The original image is 128 × 128 pixels in size. In our experiment the (+ L) image and the (+ L −3) image were scaled by ⅔ and ⅘, respectively, to reach roughly the same perceptual segmentability as the (+L −234) image.

Fig. 10
Fig. 10

Texture gradient for the three textures in Fig. 9. The average gradient over the central middle portion of each column of the picture is plotted. The values of the maxima are 134 for the (+ L) image, 114 for the (+ L −3) image, and 126 for the (+ L −234) image. These values have to be scaled by 3/2 to be compared with the values in Fig. 8.

Fig. 11
Fig. 11

Texture (Δ) (center) and two textures obtained by its bandpass filtering (left and right). Our simulations suggested that segmentation of Texture (Δ) does not rely on outputs of filters of 3–4, 10–11, and 15 c/deg. The two bandpassed images were obtained by filtering the original texture with radially symmetric window (brick wall) filters passing the corresponding bands (left) and a comparable number of complementary bands (right). Our model predicts that the left image should be much less segmentable than the one to the right. The bands used were (3–9 30–42 48–57) for the left image and (9–30 42–48) for the right image (frequency units here are in pixels and refer to 128 × 128 pixel-square images, which is not to be confused with the c/deg units that are used in the rest of this paper).

Tables (5)

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Table 1 Inhibitory Coefficients αjiA for Model Aa

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Table 2 Radii of the Inhibition Neighborhoods Iji for Models A and Ba

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Table 3 Comparison of Predictions from Texture Segmentation Algorithm with Two Sets of Psychophysical Dataa

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Table 4 Comparison of the Predictions from Models A-D with Segmentability Measurements for Two Sets of Experimental Dataa

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Table 5 Comparison of the Discriminability Ranking Given by Models A–D with That for Experimental Data

Equations (3)

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R 2 k = ( I * F k ) + ( x , y ) , R 2 k + 1 = ( I * F k ) ( x , y ) .
T i ( x 0 , y 0 ) = max j max x , y I j i ( x 0 , y 0 ) α j i R j ( x , y ) .
PIR i ( x 0 , y 0 ) max x , y S i ( x 0 , y 0 ) 1 1 α i i [ R i ( x , y ) T i ( x , y ) ] + .

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