Abstract

We suggest that intrinsic two-dimensional (i2D) features, computationally defined as the outputs of nonlinear operators that model the activity of end-stopped neurons, play a role in preattentive texture discrimination. We first show that for discriminable textures with identical power spectra the predictions of traditional models depend on the type of nonlinearity and fail for energy measures. We then argue that the concept of intrinsic dimensionality, and the existence of end-stopped neurons, can help us to understand the role of the nonlinearities. Furthermore, we show examples in which models without strong i2D selectivity fail to predict the correct ranking order of perceptual segregation. Our arguments regarding the importance of i2D features resemble the arguments of Julesz and co-workers regarding textons such as terminators and crossings. However, we provide a computational framework that identifies textons with the outputs of nonlinear operators that are selective to i2D features.

© 1998 Optical Society of America

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    [CrossRef] [PubMed]
  2. B. Julesz, “Textons, the elements of texture perception, and their interactions,” Nature 290, 91–97 (1981).
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    [CrossRef]
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    [PubMed]
  7. C. Zetzsche, W. Schönecker, “Orientation selective filters lead to entropy reduction in the processing of natural images,” Perception 16, 229 (1987).
  8. U. Kriegeskotten-Thiede, C. Zetzsche, “Local amplitude of filter outputs predicts the influence of micropattern spacing, orientation, and elongation on texture discrimination,” Perception 17, 398 (1988).
  9. I. Fogel, D. Sagi, “Gabor filters as texture discriminators,” Biol. Cybern. 61, 103–113 (1989).
    [CrossRef]
  10. 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]
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  13. M. S. Landy, J. R. Bergen, “Texture segregation and orientation gradient,” Vision Res. 31, 679–691 (1991).
    [CrossRef] [PubMed]
  14. N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
    [CrossRef] [PubMed]
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  16. T. M. Caelli, “Three processing characteristics of visual texture segmentation,” Spatial Vis. 1, 19–30 (1985).
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  17. T. M. Caelli, “An adaptive computational model for texture segmentation,” IEEE Trans. Semicond. Manuf. 18, 9–17 (1988).
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    [CrossRef]
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    [CrossRef]
  20. B. Julesz, “Early vision and focal attention,” Review Mod. Phys. 63, 735–772 (1991).
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  27. C. Zetzsche, E. Barth, “Image surface predicates and the neural encoding of two-dimensional signal variation,” in Human Vision and Electronic Imaging: Models, Methods, and Applications, B. Rogowitz, ed., Proc. SPIE1249, 160–177 (1990).
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    [CrossRef]
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  30. C. Zetzsche, E. Barth, B. Wegmann, “The importance of intrinsically two-dimensional image features in biological vision and picture coding,” in Digital Images and Human Vision, A. Watson, ed. (MIT Press, Cambridge, Mass., 1993), pp. 109–138.
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  32. G. Krieger, C. Zetzsche, E. Barth, “2D-detectors in biological vision: Volterra–Wiener kernels for end-stopped, dot-responsive, and motion-specific cells,” Perception 22 (Suppl.), 143 (1993).
  33. G. Krieger, C. Zetzsche, E. Barth, “Nonlinear image operators for the detection of local intrinsic dimensionality,” in Proceedings of the IEEE Workshop Nonlinear Signal and Image Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995), pp. 182–185.
  34. G. Krieger, C. Zetzsche, “Nonlinear image operators for the evaluation of local intrinsic dimensionality,” Special issue on Nonlinear Image Processing, IEEE Trans. Image Process. 5, 1026–1042 (1996).
    [CrossRef]
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  39. I. Rentschler, B. Treutwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature 313, 308–310 (1985).
    [CrossRef] [PubMed]
  40. I. Rentschler, M. Huebner, T. Caelli, “On the discrimination of compound Gabor signals and textures,” Vision Res. 28, 279–291 (1988).
    [CrossRef] [PubMed]
  41. S. A. Klein, C. W. Tyler, “Phase discrimination of compound gratings: generalized autocorrelation analysis,” J. Opt. Soc. Am. A 3, 868–879 (1986).
    [CrossRef] [PubMed]
  42. C. Zetzsche, B. Wegmann, “Coding properties of local amplitude and phase of two-dimensional filter outputs,” Perception 17, 396 (1988).
  43. T. M. Caelli, B. Julesz, E. Gilbert, “On perceptual analysers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).
    [CrossRef] [PubMed]
  44. D. S. Simmons, D. H. Foster, “Segmenting textures of curved-line elements,” in Artificial and Biological Vision Systems, G. A. Orban, H.-H. Nagel, eds. (Springer-Verlag, Berlin, 1992), pp. 324–349.
  45. B. S. Rubenstein, D. Sagi, “Preattentive texture segmentation: the role of line terminations, size, and filter wavelength,” Percept. Psychophys. 58, 489–509 (1996).
    [CrossRef] [PubMed]
  46. E. Barth, G. Krieger, I. Rentschler, B. Treutwein, “Receptor-horizontal cell interactions may induce endstopping,” Invest. Ophthalmol. Visual Sci. 37 (Suppl.), 1056 (1996).
  47. E. Barth, C. Zetzsche, “Endstopped operators based on iterated nonlinear center-surround inhibition,” in Human Vision and Electronic Imaging III, B. Rogowitz, ed., Proc. SPIE3299, pp. 41–53 (1998).
  48. E. Barth, M. Ferraro, C. Zetzsche, I. Rentschler, “Computational models for the topological selectivity in early and primitive vision systems,” OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.
  49. K. Koffka, Principles of Gestalt Psychology (Harcourt, Brace, New York, 1935).
  50. B. Julesz, “Spatial nonlinearities in the instantaneous perception of textures with identical power spectra,” Philos. Trans. R. Soc. London Ser. B 290, 83–94 (1980).
    [CrossRef]
  51. J. Elder, S. Zucker, “The effect of contour closure on the rapid discrimination of two-dimensional shapes,” Vision Res. 33, 981–991 (1993).
    [CrossRef] [PubMed]
  52. J. Elder, S. Zucker, “A measure of closure,” Vision Res. 34, 3361–3369 (1994).
    [CrossRef] [PubMed]
  53. E. Barth, C. Zetzsche, I. Rentschler, “End-stopping may yield textons,” Perception 24 (Suppl.), 19 (1995).

1997 (1)

1996 (4)

G. Krieger, C. Zetzsche, “Nonlinear image operators for the evaluation of local intrinsic dimensionality,” Special issue on Nonlinear Image Processing, IEEE Trans. Image Process. 5, 1026–1042 (1996).
[CrossRef]

J. A. Solomon, A. B. Watson, “Cinematica: a system for calibrated, Macintosh-driven displays from within Mathematica,” Behav. Res. Methods Instrum. Comput. 28, 607–610 (1996).
[CrossRef] [PubMed]

B. S. Rubenstein, D. Sagi, “Preattentive texture segmentation: the role of line terminations, size, and filter wavelength,” Percept. Psychophys. 58, 489–509 (1996).
[CrossRef] [PubMed]

E. Barth, G. Krieger, I. Rentschler, B. Treutwein, “Receptor-horizontal cell interactions may induce endstopping,” Invest. Ophthalmol. Visual Sci. 37 (Suppl.), 1056 (1996).

1995 (1)

E. Barth, C. Zetzsche, I. Rentschler, “End-stopping may yield textons,” Perception 24 (Suppl.), 19 (1995).

1994 (1)

J. Elder, S. Zucker, “A measure of closure,” Vision Res. 34, 3361–3369 (1994).
[CrossRef] [PubMed]

1993 (4)

A. Gorea, T. V. Papathomas, “Double opponency as a generalized concept in texture segregation illustrated with stimuli defined by color, luminance, and orientation,” J. Opt. Soc. Am. A 10, 1450–1462 (1993).
[CrossRef]

J. Elder, S. Zucker, “The effect of contour closure on the rapid discrimination of two-dimensional shapes,” Vision Res. 33, 981–991 (1993).
[CrossRef] [PubMed]

E. Barth, T. Caelli, C. Zetzsche, “Image encoding, labelling and reconstruction from differential geometry,” CVGIP: Graph. Models Image Process. 55, 428–446 (1993).

G. Krieger, C. Zetzsche, E. Barth, “2D-detectors in biological vision: Volterra–Wiener kernels for end-stopped, dot-responsive, and motion-specific cells,” Perception 22 (Suppl.), 143 (1993).

1992 (2)

F. Heitger, L. Rosenthaler, R. von der Heydt, E. Peterhans, O. Kübler, “Simulation of neural contour mechanisms: from simple to end-stopped cells,” Vision Res. 32, 63–981 (1992).
[CrossRef]

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

1991 (3)

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

B. Julesz, “Early vision and focal attention,” Review Mod. Phys. 63, 735–772 (1991).
[CrossRef]

C. Zetzsche, E. Barth, “Detection of intrinsic signal dimensionality in images and optic flow fields,” Perception 20, 71 (1991).

1990 (4)

H. C. Nothdurft, “Texton segregation by associated differences in global and local luminance distribution,” Proc. R. Soc. London Ser. B 239, 295–320 (1990).
[CrossRef]

C. Zetzsche, E. Barth, “Fundamental limits of linear filters in the visual processing of two-dimensional signals,” Vision Res. 30, 1111–1117 (1990).
[CrossRef] [PubMed]

A. C. Bovik, M. Clark, W. S. Geisler, “Multi-channel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

J. Malik, P. Perona, “Preattentive texture discrimination with early vision mechanisms,” J. Opt. Soc. Am. A 7, 923–932 (1990).
[CrossRef] [PubMed]

1989 (3)

H. R. Wilson, W. A. Richards, “Mechanisms of contour curvature discrimination,” J. Opt. Soc. Am. A 6, 106–115 (1989).
[CrossRef] [PubMed]

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

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]

1988 (8)

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

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

U. Kriegeskotten-Thiede, C. Zetzsche, “Local amplitude of filter outputs predicts the influence of micropattern spacing, orientation, and elongation on texture discrimination,” Perception 17, 398 (1988).

T. M. Caelli, “An adaptive computational model for texture segmentation,” IEEE Trans. Semicond. Manuf. 18, 9–17 (1988).

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

C. Zetzsche, B. Wegmann, “Coding properties of local amplitude and phase of two-dimensional filter outputs,” Perception 17, 396 (1988).

C. Zetzsche, “Statistical properties of the representation of natural images at different levels in the visual system,” Perception 17, 359 (1988).

J. J. Koenderink, W. Richards, “Two-dimensional curvature operators,” J. Opt. Soc. Am. A 5, 1136–1141 (1988).
[CrossRef]

1987 (2)

A. Dobbins, S. W. Zucker, M. S. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438–441 (1987).
[CrossRef] [PubMed]

C. Zetzsche, W. Schönecker, “Orientation selective filters lead to entropy reduction in the processing of natural images,” Perception 16, 229 (1987).

1986 (3)

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

T. M. Caelli, M. Hübner, I. Rentschler, “On the discrimination of micropatterns and textures,” Hum. Neurobiol. 5, 129–136 (1986).
[PubMed]

S. A. Klein, C. W. Tyler, “Phase discrimination of compound gratings: generalized autocorrelation analysis,” J. Opt. Soc. Am. A 3, 868–879 (1986).
[CrossRef] [PubMed]

1985 (3)

I. Rentschler, B. Treutwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature 313, 308–310 (1985).
[CrossRef] [PubMed]

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

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

1981 (1)

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

1980 (1)

B. Julesz, “Spatial nonlinearities in the instantaneous perception of textures with identical power spectra,” Philos. Trans. R. Soc. London Ser. B 290, 83–94 (1980).
[CrossRef]

1978 (1)

T. M. Caelli, B. Julesz, E. Gilbert, “On perceptual analysers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).
[CrossRef] [PubMed]

1975 (1)

B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
[CrossRef] [PubMed]

Adelson, E. H.

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

Barth, E.

E. Barth, G. Krieger, I. Rentschler, B. Treutwein, “Receptor-horizontal cell interactions may induce endstopping,” Invest. Ophthalmol. Visual Sci. 37 (Suppl.), 1056 (1996).

E. Barth, C. Zetzsche, I. Rentschler, “End-stopping may yield textons,” Perception 24 (Suppl.), 19 (1995).

E. Barth, T. Caelli, C. Zetzsche, “Image encoding, labelling and reconstruction from differential geometry,” CVGIP: Graph. Models Image Process. 55, 428–446 (1993).

G. Krieger, C. Zetzsche, E. Barth, “2D-detectors in biological vision: Volterra–Wiener kernels for end-stopped, dot-responsive, and motion-specific cells,” Perception 22 (Suppl.), 143 (1993).

C. Zetzsche, E. Barth, “Detection of intrinsic signal dimensionality in images and optic flow fields,” Perception 20, 71 (1991).

C. Zetzsche, E. Barth, “Fundamental limits of linear filters in the visual processing of two-dimensional signals,” Vision Res. 30, 1111–1117 (1990).
[CrossRef] [PubMed]

C. Zetzsche, E. Barth, “Image surface predicates and the neural encoding of two-dimensional signal variation,” in Human Vision and Electronic Imaging: Models, Methods, and Applications, B. Rogowitz, ed., Proc. SPIE1249, 160–177 (1990).

C. Zetzsche, E. Barth, B. Wegmann, “The importance of intrinsically two-dimensional image features in biological vision and picture coding,” in Digital Images and Human Vision, A. Watson, ed. (MIT Press, Cambridge, Mass., 1993), pp. 109–138.

G. Krieger, C. Zetzsche, E. Barth, “Nonlinear image operators for the detection of local intrinsic dimensionality,” in Proceedings of the IEEE Workshop Nonlinear Signal and Image Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995), pp. 182–185.

E. Barth, C. Zetzsche, “Endstopped operators based on iterated nonlinear center-surround inhibition,” in Human Vision and Electronic Imaging III, B. Rogowitz, ed., Proc. SPIE3299, pp. 41–53 (1998).

E. Barth, M. Ferraro, C. Zetzsche, I. Rentschler, “Computational models for the topological selectivity in early and primitive vision systems,” OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.

Beck, J.

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

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]

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

J. R. Bergen, “Theories of visual texture perception,” in Vision and Visual Disfunction, D. Regan, ed. (Macmillan, New York, 1991), Vol. 10B, pp. 114–134.

Bovik, A. C.

A. C. Bovik, M. Clark, W. S. Geisler, “Multi-channel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

Caelli, T.

D. Carević, T. Caelli, “Application of partial modelling techniques for texture segmentation,” J. Opt. Soc. Am. A 14, 2924–2937 (1997).
[CrossRef]

E. Barth, T. Caelli, C. Zetzsche, “Image encoding, labelling and reconstruction from differential geometry,” CVGIP: Graph. Models Image Process. 55, 428–446 (1993).

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

Caelli, T. M.

T. M. Caelli, “An adaptive computational model for texture segmentation,” IEEE Trans. Semicond. Manuf. 18, 9–17 (1988).

T. M. Caelli, M. Hübner, I. Rentschler, “On the discrimination of micropatterns and textures,” Hum. Neurobiol. 5, 129–136 (1986).
[PubMed]

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

T. M. Caelli, B. Julesz, E. Gilbert, “On perceptual analysers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).
[CrossRef] [PubMed]

Carevic, D.

Clark, M.

A. C. Bovik, M. Clark, W. S. Geisler, “Multi-channel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

Coggins, J. M.

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

Cynader, M. S.

A. Dobbins, S. W. Zucker, M. S. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438–441 (1987).
[CrossRef] [PubMed]

Dobbins, A.

A. Dobbins, S. W. Zucker, M. S. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438–441 (1987).
[CrossRef] [PubMed]

Elder, J.

J. Elder, S. Zucker, “A measure of closure,” Vision Res. 34, 3361–3369 (1994).
[CrossRef] [PubMed]

J. Elder, S. Zucker, “The effect of contour closure on the rapid discrimination of two-dimensional shapes,” Vision Res. 33, 981–991 (1993).
[CrossRef] [PubMed]

Ferraro, M.

E. Barth, M. Ferraro, C. Zetzsche, I. Rentschler, “Computational models for the topological selectivity in early and primitive vision systems,” OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.

Fogel, I.

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

Foster, D. H.

D. S. Simmons, D. H. Foster, “Segmenting textures of curved-line elements,” in Artificial and Biological Vision Systems, G. A. Orban, H.-H. Nagel, eds. (Springer-Verlag, Berlin, 1992), pp. 324–349.

Geisler, W. S.

A. C. Bovik, M. Clark, W. S. Geisler, “Multi-channel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

Gilbert, E.

T. M. Caelli, B. Julesz, E. Gilbert, “On perceptual analysers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).
[CrossRef] [PubMed]

Gorea, A.

Graham, N.

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

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]

Heitger, F.

F. Heitger, L. Rosenthaler, R. von der Heydt, E. Peterhans, O. Kübler, “Simulation of neural contour mechanisms: from simple to end-stopped cells,” Vision Res. 32, 63–981 (1992).
[CrossRef]

Hübner, M.

T. M. Caelli, M. Hübner, I. Rentschler, “On the discrimination of micropatterns and textures,” Hum. Neurobiol. 5, 129–136 (1986).
[PubMed]

Huebner, M.

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

Jain, A. K.

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

Julesz, B.

B. Julesz, “Early vision and focal attention,” Review Mod. Phys. 63, 735–772 (1991).
[CrossRef]

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

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

B. Julesz, “Spatial nonlinearities in the instantaneous perception of textures with identical power spectra,” Philos. Trans. R. Soc. London Ser. B 290, 83–94 (1980).
[CrossRef]

T. M. Caelli, B. Julesz, E. Gilbert, “On perceptual analysers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).
[CrossRef] [PubMed]

B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
[CrossRef] [PubMed]

Klein, S. A.

Koenderink, J. J.

Koffka, K.

K. Koffka, Principles of Gestalt Psychology (Harcourt, Brace, New York, 1935).

Krieger, G.

E. Barth, G. Krieger, I. Rentschler, B. Treutwein, “Receptor-horizontal cell interactions may induce endstopping,” Invest. Ophthalmol. Visual Sci. 37 (Suppl.), 1056 (1996).

G. Krieger, C. Zetzsche, “Nonlinear image operators for the evaluation of local intrinsic dimensionality,” Special issue on Nonlinear Image Processing, IEEE Trans. Image Process. 5, 1026–1042 (1996).
[CrossRef]

G. Krieger, C. Zetzsche, E. Barth, “2D-detectors in biological vision: Volterra–Wiener kernels for end-stopped, dot-responsive, and motion-specific cells,” Perception 22 (Suppl.), 143 (1993).

G. Krieger, C. Zetzsche, E. Barth, “Nonlinear image operators for the detection of local intrinsic dimensionality,” in Proceedings of the IEEE Workshop Nonlinear Signal and Image Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995), pp. 182–185.

Kriegeskotten-Thiede, U.

U. Kriegeskotten-Thiede, C. Zetzsche, “Local amplitude of filter outputs predicts the influence of micropattern spacing, orientation, and elongation on texture discrimination,” Perception 17, 398 (1988).

Kröse, B.

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

Kübler, O.

F. Heitger, L. Rosenthaler, R. von der Heydt, E. Peterhans, O. Kübler, “Simulation of neural contour mechanisms: from simple to end-stopped cells,” Vision Res. 32, 63–981 (1992).
[CrossRef]

Landy, M. S.

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

Liedtke, C.-E.

D. Wermser, C.-E. Liedtke, “Texture analysis using a model of the visual system,” in Proceedings of the Sixth International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1982), pp. 1078–1080.

Malik, J.

Nothdurft, H. C.

H. C. Nothdurft, “Texton segregation by associated differences in global and local luminance distribution,” Proc. R. Soc. London Ser. B 239, 295–320 (1990).
[CrossRef]

Papathomas, T. V.

Papoulis, A.

A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill, New York, 1962).

Perona, P.

Peterhans, E.

F. Heitger, L. Rosenthaler, R. von der Heydt, E. Peterhans, O. Kübler, “Simulation of neural contour mechanisms: from simple to end-stopped cells,” Vision Res. 32, 63–981 (1992).
[CrossRef]

Rentschler, I.

E. Barth, G. Krieger, I. Rentschler, B. Treutwein, “Receptor-horizontal cell interactions may induce endstopping,” Invest. Ophthalmol. Visual Sci. 37 (Suppl.), 1056 (1996).

E. Barth, C. Zetzsche, I. Rentschler, “End-stopping may yield textons,” Perception 24 (Suppl.), 19 (1995).

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

T. M. Caelli, M. Hübner, I. Rentschler, “On the discrimination of micropatterns and textures,” Hum. Neurobiol. 5, 129–136 (1986).
[PubMed]

I. Rentschler, B. Treutwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature 313, 308–310 (1985).
[CrossRef] [PubMed]

E. Barth, M. Ferraro, C. Zetzsche, I. Rentschler, “Computational models for the topological selectivity in early and primitive vision systems,” OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.

Richards, W.

Richards, W. A.

Rosenthaler, L.

F. Heitger, L. Rosenthaler, R. von der Heydt, E. Peterhans, O. Kübler, “Simulation of neural contour mechanisms: from simple to end-stopped cells,” Vision Res. 32, 63–981 (1992).
[CrossRef]

Rubenstein, B. S.

B. S. Rubenstein, D. Sagi, “Preattentive texture segmentation: the role of line terminations, size, and filter wavelength,” Percept. Psychophys. 58, 489–509 (1996).
[CrossRef] [PubMed]

Sagi, D.

B. S. Rubenstein, D. Sagi, “Preattentive texture segmentation: the role of line terminations, size, and filter wavelength,” Percept. Psychophys. 58, 489–509 (1996).
[CrossRef] [PubMed]

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

Schönecker, W.

C. Zetzsche, W. Schönecker, “Orientation selective filters lead to entropy reduction in the processing of natural images,” Perception 16, 229 (1987).

Simmons, D. S.

D. S. Simmons, D. H. Foster, “Segmenting textures of curved-line elements,” in Artificial and Biological Vision Systems, G. A. Orban, H.-H. Nagel, eds. (Springer-Verlag, Berlin, 1992), pp. 324–349.

Solomon, J. A.

J. A. Solomon, A. B. Watson, “Cinematica: a system for calibrated, Macintosh-driven displays from within Mathematica,” Behav. Res. Methods Instrum. Comput. 28, 607–610 (1996).
[CrossRef] [PubMed]

Sutter, A.

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

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]

Treutwein, B.

E. Barth, G. Krieger, I. Rentschler, B. Treutwein, “Receptor-horizontal cell interactions may induce endstopping,” Invest. Ophthalmol. Visual Sci. 37 (Suppl.), 1056 (1996).

I. Rentschler, B. Treutwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature 313, 308–310 (1985).
[CrossRef] [PubMed]

Turner, M. R.

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

Tyler, C. W.

von der Heydt, R.

F. Heitger, L. Rosenthaler, R. von der Heydt, E. Peterhans, O. Kübler, “Simulation of neural contour mechanisms: from simple to end-stopped cells,” Vision Res. 32, 63–981 (1992).
[CrossRef]

Watson, A. B.

J. A. Solomon, A. B. Watson, “Cinematica: a system for calibrated, Macintosh-driven displays from within Mathematica,” Behav. Res. Methods Instrum. Comput. 28, 607–610 (1996).
[CrossRef] [PubMed]

Wegmann, B.

C. Zetzsche, B. Wegmann, “Coding properties of local amplitude and phase of two-dimensional filter outputs,” Perception 17, 396 (1988).

C. Zetzsche, E. Barth, B. Wegmann, “The importance of intrinsically two-dimensional image features in biological vision and picture coding,” in Digital Images and Human Vision, A. Watson, ed. (MIT Press, Cambridge, Mass., 1993), pp. 109–138.

Wermser, D.

D. Wermser, C.-E. Liedtke, “Texture analysis using a model of the visual system,” in Proceedings of the Sixth International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1982), pp. 1078–1080.

Wilson, H. R.

Zetzsche, C.

G. Krieger, C. Zetzsche, “Nonlinear image operators for the evaluation of local intrinsic dimensionality,” Special issue on Nonlinear Image Processing, IEEE Trans. Image Process. 5, 1026–1042 (1996).
[CrossRef]

E. Barth, C. Zetzsche, I. Rentschler, “End-stopping may yield textons,” Perception 24 (Suppl.), 19 (1995).

G. Krieger, C. Zetzsche, E. Barth, “2D-detectors in biological vision: Volterra–Wiener kernels for end-stopped, dot-responsive, and motion-specific cells,” Perception 22 (Suppl.), 143 (1993).

E. Barth, T. Caelli, C. Zetzsche, “Image encoding, labelling and reconstruction from differential geometry,” CVGIP: Graph. Models Image Process. 55, 428–446 (1993).

C. Zetzsche, E. Barth, “Detection of intrinsic signal dimensionality in images and optic flow fields,” Perception 20, 71 (1991).

C. Zetzsche, E. Barth, “Fundamental limits of linear filters in the visual processing of two-dimensional signals,” Vision Res. 30, 1111–1117 (1990).
[CrossRef] [PubMed]

C. Zetzsche, “Statistical properties of the representation of natural images at different levels in the visual system,” Perception 17, 359 (1988).

U. Kriegeskotten-Thiede, C. Zetzsche, “Local amplitude of filter outputs predicts the influence of micropattern spacing, orientation, and elongation on texture discrimination,” Perception 17, 398 (1988).

C. Zetzsche, B. Wegmann, “Coding properties of local amplitude and phase of two-dimensional filter outputs,” Perception 17, 396 (1988).

C. Zetzsche, W. Schönecker, “Orientation selective filters lead to entropy reduction in the processing of natural images,” Perception 16, 229 (1987).

C. Zetzsche, E. Barth, “Image surface predicates and the neural encoding of two-dimensional signal variation,” in Human Vision and Electronic Imaging: Models, Methods, and Applications, B. Rogowitz, ed., Proc. SPIE1249, 160–177 (1990).

C. Zetzsche, E. Barth, B. Wegmann, “The importance of intrinsically two-dimensional image features in biological vision and picture coding,” in Digital Images and Human Vision, A. Watson, ed. (MIT Press, Cambridge, Mass., 1993), pp. 109–138.

G. Krieger, C. Zetzsche, E. Barth, “Nonlinear image operators for the detection of local intrinsic dimensionality,” in Proceedings of the IEEE Workshop Nonlinear Signal and Image Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995), pp. 182–185.

E. Barth, M. Ferraro, C. Zetzsche, I. Rentschler, “Computational models for the topological selectivity in early and primitive vision systems,” OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.

E. Barth, C. Zetzsche, “Endstopped operators based on iterated nonlinear center-surround inhibition,” in Human Vision and Electronic Imaging III, B. Rogowitz, ed., Proc. SPIE3299, pp. 41–53 (1998).

Zucker, S.

J. Elder, S. Zucker, “A measure of closure,” Vision Res. 34, 3361–3369 (1994).
[CrossRef] [PubMed]

J. Elder, S. Zucker, “The effect of contour closure on the rapid discrimination of two-dimensional shapes,” Vision Res. 33, 981–991 (1993).
[CrossRef] [PubMed]

Zucker, S. W.

A. Dobbins, S. W. Zucker, M. S. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438–441 (1987).
[CrossRef] [PubMed]

Behav. Res. Methods Instrum. Comput. (1)

J. A. Solomon, A. B. Watson, “Cinematica: a system for calibrated, Macintosh-driven displays from within Mathematica,” Behav. Res. Methods Instrum. Comput. 28, 607–610 (1996).
[CrossRef] [PubMed]

Biol. Cybern. (3)

M. R. 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]

T. M. Caelli, B. Julesz, E. Gilbert, “On perceptual analysers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).
[CrossRef] [PubMed]

CVGIP: Graph. Models Image Process. (1)

E. Barth, T. Caelli, C. Zetzsche, “Image encoding, labelling and reconstruction from differential geometry,” CVGIP: Graph. Models Image Process. 55, 428–446 (1993).

Hum. Neurobiol. (1)

T. M. Caelli, M. Hübner, I. Rentschler, “On the discrimination of micropatterns and textures,” Hum. Neurobiol. 5, 129–136 (1986).
[PubMed]

IEEE Trans. Image Process (1)

G. Krieger, C. Zetzsche, “Nonlinear image operators for the evaluation of local intrinsic dimensionality,” Special issue on Nonlinear Image Processing, IEEE Trans. Image Process. 5, 1026–1042 (1996).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

A. C. Bovik, M. Clark, W. S. Geisler, “Multi-channel texture analysis using localized spatial filters,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 55–73 (1990).
[CrossRef]

IEEE Trans. Semicond. Manuf. (1)

T. M. Caelli, “An adaptive computational model for texture segmentation,” IEEE Trans. Semicond. Manuf. 18, 9–17 (1988).

Invest. Ophthalmol. Visual Sci. (1)

E. Barth, G. Krieger, I. Rentschler, B. Treutwein, “Receptor-horizontal cell interactions may induce endstopping,” Invest. Ophthalmol. Visual Sci. 37 (Suppl.), 1056 (1996).

J. Opt. Soc. Am. A (6)

Nature (5)

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

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

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

I. Rentschler, B. Treutwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature 313, 308–310 (1985).
[CrossRef] [PubMed]

A. Dobbins, S. W. Zucker, M. S. Cynader, “Endstopped neurons in the visual cortex as a substrate for calculating curvature,” Nature 329, 438–441 (1987).
[CrossRef] [PubMed]

Pattern Recogn. Lett. (1)

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

Percept. Psychophys. (2)

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]

B. S. Rubenstein, D. Sagi, “Preattentive texture segmentation: the role of line terminations, size, and filter wavelength,” Percept. Psychophys. 58, 489–509 (1996).
[CrossRef] [PubMed]

Perception (7)

E. Barth, C. Zetzsche, I. Rentschler, “End-stopping may yield textons,” Perception 24 (Suppl.), 19 (1995).

C. Zetzsche, W. Schönecker, “Orientation selective filters lead to entropy reduction in the processing of natural images,” Perception 16, 229 (1987).

U. Kriegeskotten-Thiede, C. Zetzsche, “Local amplitude of filter outputs predicts the influence of micropattern spacing, orientation, and elongation on texture discrimination,” Perception 17, 398 (1988).

C. Zetzsche, “Statistical properties of the representation of natural images at different levels in the visual system,” Perception 17, 359 (1988).

G. Krieger, C. Zetzsche, E. Barth, “2D-detectors in biological vision: Volterra–Wiener kernels for end-stopped, dot-responsive, and motion-specific cells,” Perception 22 (Suppl.), 143 (1993).

C. Zetzsche, E. Barth, “Detection of intrinsic signal dimensionality in images and optic flow fields,” Perception 20, 71 (1991).

C. Zetzsche, B. Wegmann, “Coding properties of local amplitude and phase of two-dimensional filter outputs,” Perception 17, 396 (1988).

Philos. Trans. R. Soc. London Ser. B (1)

B. Julesz, “Spatial nonlinearities in the instantaneous perception of textures with identical power spectra,” Philos. Trans. R. Soc. London Ser. B 290, 83–94 (1980).
[CrossRef]

Proc. R. Soc. London Ser. B (1)

H. C. Nothdurft, “Texton segregation by associated differences in global and local luminance distribution,” Proc. R. Soc. London Ser. B 239, 295–320 (1990).
[CrossRef]

Review Mod. Phys. (1)

B. Julesz, “Early vision and focal attention,” Review Mod. Phys. 63, 735–772 (1991).
[CrossRef]

Sci. Am. (1)

B. Julesz, “Experiments in the visual perception of texture,” Sci. Am. 232, 34–43 (1975).
[CrossRef] [PubMed]

Spatial Vis. (1)

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

Vision Res. (7)

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

N. Graham, J. Beck, A. Sutter, “Nonlinear processes in spatial-frequency channel models of perceived texture segregation: effects of sign and amount of contrast,” Vision Res. 32, 719–743 (1992).
[CrossRef] [PubMed]

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

F. Heitger, L. Rosenthaler, R. von der Heydt, E. Peterhans, O. Kübler, “Simulation of neural contour mechanisms: from simple to end-stopped cells,” Vision Res. 32, 63–981 (1992).
[CrossRef]

C. Zetzsche, E. Barth, “Fundamental limits of linear filters in the visual processing of two-dimensional signals,” Vision Res. 30, 1111–1117 (1990).
[CrossRef] [PubMed]

J. Elder, S. Zucker, “The effect of contour closure on the rapid discrimination of two-dimensional shapes,” Vision Res. 33, 981–991 (1993).
[CrossRef] [PubMed]

J. Elder, S. Zucker, “A measure of closure,” Vision Res. 34, 3361–3369 (1994).
[CrossRef] [PubMed]

Other (10)

D. S. Simmons, D. H. Foster, “Segmenting textures of curved-line elements,” in Artificial and Biological Vision Systems, G. A. Orban, H.-H. Nagel, eds. (Springer-Verlag, Berlin, 1992), pp. 324–349.

E. Barth, C. Zetzsche, “Endstopped operators based on iterated nonlinear center-surround inhibition,” in Human Vision and Electronic Imaging III, B. Rogowitz, ed., Proc. SPIE3299, pp. 41–53 (1998).

E. Barth, M. Ferraro, C. Zetzsche, I. Rentschler, “Computational models for the topological selectivity in early and primitive vision systems,” OSA Annual Meeting, Vol. 16 of 1993 OSA Technical Digest Series (Optical Society of America, Washington, D.C., 1993), p. 186.

K. Koffka, Principles of Gestalt Psychology (Harcourt, Brace, New York, 1935).

C. Zetzsche, E. Barth, “Image surface predicates and the neural encoding of two-dimensional signal variation,” in Human Vision and Electronic Imaging: Models, Methods, and Applications, B. Rogowitz, ed., Proc. SPIE1249, 160–177 (1990).

C. Zetzsche, E. Barth, B. Wegmann, “The importance of intrinsically two-dimensional image features in biological vision and picture coding,” in Digital Images and Human Vision, A. Watson, ed. (MIT Press, Cambridge, Mass., 1993), pp. 109–138.

G. Krieger, C. Zetzsche, E. Barth, “Nonlinear image operators for the detection of local intrinsic dimensionality,” in Proceedings of the IEEE Workshop Nonlinear Signal and Image Processing (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1995), pp. 182–185.

A. Papoulis, The Fourier Integral and its Applications (McGraw-Hill, New York, 1962).

J. R. Bergen, “Theories of visual texture perception,” in Vision and Visual Disfunction, D. Regan, ed. (Macmillan, New York, 1991), Vol. 10B, pp. 114–134.

D. Wermser, C.-E. Liedtke, “Texture analysis using a model of the visual system,” in Proceedings of the Sixth International Conference on Pattern Recognition (Institute of Electrical and Electronics Engineers, Piscataway, N.J., 1982), pp. 1078–1080.

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