Abstract

The mathematical framework for studies of texture perception is discussed. Textures correspond to statistical ensembles, whereas images are spatially finite samples of a texture. The main ideas underlying the use of visual textures in experimental and theoretical analyses of preattentive vision are summarized, with an emphasis on the distinction between texture ensembles and images. The Julesz conjecture [ Perception 2, 391 ( 1973)] is that preattentive discrimination of textures is possible only for textures that have different second-order correlation statistics. Recently Yellot [ J. Opt. Soc. Am. A 10, 777 ( 1993)] claimed that the triple correlation uniqueness (TCU) theorem, a mathematical result that every monochromatic image of finite size is uniquely determined (up to translation) by its third-order statistics, makes higher-order variants of the Julesz conjecture trivial. However, the TCU theorem applies to individual images, and not to texture ensembles, and thus is of limited relevance to the study of texture perception.

© 1994 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Yellott, “Implications of triple correlation uniqueness for texture statistics and the Julesz conjecture,” J. Opt. Soc. Am. A 10, 777–793 (1993).
  2. B. Julesz, E. N. Gilbert, L. A. Shepp, H. L. Frisch, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).
  3. T. Caelli, B. Julesz, “On perceptual analyzers underlying visual texture discrimination. Part I,” Biol. Cybern. 28, 167–175 (1978).
  4. T. Caelli, B. Julesz, E. N. Gilbert, “On perceptual analyzers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).
  5. J. D. Victor, S. Brodie, “Discriminable textures with identical Buffon needle statistics,” Biol. Cybern. 31, 231–234 (1978).
  6. 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 Press, Cambridge, Mass., 1991), pp. 201–230.
  7. B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137–149 (1978).
  8. E. N. Gilbert, “Random colorings of a lattice on squares in the plane,” SIAM J. Alg. Discr. Meth. 1, 152–159 (1980).
  9. J. A. Movshon, E. H. Adelson, M. S. Gizzi, W. T. Newsome, “The analysis of moving visual patterns,” in Pattern Recognition Mechanisms, Exp. Brain Res. Suppl.11, C. Chagas, R. Gattass, C. Gross, eds. (Springer-Verlag, Berlin, 1985), pp. 117–151.
  10. T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).
  11. P. Z. Marmarelis, V. Z. Marmarelis, Analysis of Physiological Systems: The White-Noise Approach (Plenum, New York, 1978).
  12. J. D. Victor, “Complex visual textures as a tool for studying the VEP,” Vision Res. 25, 1811–1827 (1985).
  13. J. D. Victor, V. Zemon, “The human visual evoked potential: analysis of components due to elementary and complex aspects of form,” Vision Res. 25, 1829–1844 (1985).
  14. J. D. Victor, M. M. Conte, “Cortical interactions in texture processing: scale and dynamics,” Vis. Neurosci. 2, 297–313 (1989).
  15. J. D. Victor, M. M. Conte, “Spatial organization of nonlinear interactions in form perception,” Vision Res. 31, 1457–1488 (1991).
  16. A. Gagalowitz, “A new method for texture fields synthesis: some applications to the study of human vision,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3, 520–523 (1981).
  17. B. Julesz, “Early vision and focal attention,” Rev. Mod. Phys. 63, 735–772 (1991).

1993 (1)

1991 (2)

J. D. Victor, M. M. Conte, “Spatial organization of nonlinear interactions in form perception,” Vision Res. 31, 1457–1488 (1991).

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

1989 (1)

J. D. Victor, M. M. Conte, “Cortical interactions in texture processing: scale and dynamics,” Vis. Neurosci. 2, 297–313 (1989).

1985 (3)

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).

J. D. Victor, “Complex visual textures as a tool for studying the VEP,” Vision Res. 25, 1811–1827 (1985).

J. D. Victor, V. Zemon, “The human visual evoked potential: analysis of components due to elementary and complex aspects of form,” Vision Res. 25, 1829–1844 (1985).

1981 (1)

A. Gagalowitz, “A new method for texture fields synthesis: some applications to the study of human vision,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3, 520–523 (1981).

1980 (1)

E. N. Gilbert, “Random colorings of a lattice on squares in the plane,” SIAM J. Alg. Discr. Meth. 1, 152–159 (1980).

1978 (4)

T. Caelli, B. Julesz, “On perceptual analyzers underlying visual texture discrimination. Part I,” Biol. Cybern. 28, 167–175 (1978).

T. Caelli, B. Julesz, E. N. Gilbert, “On perceptual analyzers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).

J. D. Victor, S. Brodie, “Discriminable textures with identical Buffon needle statistics,” Biol. Cybern. 31, 231–234 (1978).

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137–149 (1978).

1973 (1)

B. Julesz, E. N. Gilbert, L. A. Shepp, H. L. Frisch, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).

Adelson, E. H.

J. A. Movshon, E. H. Adelson, M. S. Gizzi, W. T. Newsome, “The analysis of moving visual patterns,” in Pattern Recognition Mechanisms, Exp. Brain Res. Suppl.11, C. Chagas, R. Gattass, C. Gross, eds. (Springer-Verlag, Berlin, 1985), pp. 117–151.

Brodie, S.

J. D. Victor, S. Brodie, “Discriminable textures with identical Buffon needle statistics,” Biol. Cybern. 31, 231–234 (1978).

Caelli, T.

T. Caelli, B. Julesz, “On perceptual analyzers underlying visual texture discrimination. Part I,” Biol. Cybern. 28, 167–175 (1978).

T. Caelli, B. Julesz, E. N. Gilbert, “On perceptual analyzers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).

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 Press, Cambridge, Mass., 1991), pp. 201–230.

Conte, M. M.

J. D. Victor, M. M. Conte, “Spatial organization of nonlinear interactions in form perception,” Vision Res. 31, 1457–1488 (1991).

J. D. Victor, M. M. Conte, “Cortical interactions in texture processing: scale and dynamics,” Vis. Neurosci. 2, 297–313 (1989).

Frisch, H. L.

B. Julesz, E. N. Gilbert, L. A. Shepp, H. L. Frisch, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).

Gagalowitz, A.

A. Gagalowitz, “A new method for texture fields synthesis: some applications to the study of human vision,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3, 520–523 (1981).

Gilbert, E. N.

E. N. Gilbert, “Random colorings of a lattice on squares in the plane,” SIAM J. Alg. Discr. Meth. 1, 152–159 (1980).

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137–149 (1978).

T. Caelli, B. Julesz, E. N. Gilbert, “On perceptual analyzers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).

B. Julesz, E. N. Gilbert, L. A. Shepp, H. L. Frisch, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).

Gizzi, M. S.

J. A. Movshon, E. H. Adelson, M. S. Gizzi, W. T. Newsome, “The analysis of moving visual patterns,” in Pattern Recognition Mechanisms, Exp. Brain Res. Suppl.11, C. Chagas, R. Gattass, C. Gross, eds. (Springer-Verlag, Berlin, 1985), pp. 117–151.

Julesz, B.

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

T. Caelli, B. Julesz, E. N. Gilbert, “On perceptual analyzers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).

T. Caelli, B. Julesz, “On perceptual analyzers underlying visual texture discrimination. Part I,” Biol. Cybern. 28, 167–175 (1978).

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137–149 (1978).

B. Julesz, E. N. Gilbert, L. A. Shepp, H. L. Frisch, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).

Koch, C.

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).

Landy, M. S.

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 Press, Cambridge, Mass., 1991), pp. 201–230.

Marmarelis, P. Z.

P. Z. Marmarelis, V. Z. Marmarelis, Analysis of Physiological Systems: The White-Noise Approach (Plenum, New York, 1978).

Marmarelis, V. Z.

P. Z. Marmarelis, V. Z. Marmarelis, Analysis of Physiological Systems: The White-Noise Approach (Plenum, New York, 1978).

Movshon, J. A.

J. A. Movshon, E. H. Adelson, M. S. Gizzi, W. T. Newsome, “The analysis of moving visual patterns,” in Pattern Recognition Mechanisms, Exp. Brain Res. Suppl.11, C. Chagas, R. Gattass, C. Gross, eds. (Springer-Verlag, Berlin, 1985), pp. 117–151.

Newsome, W. T.

J. A. Movshon, E. H. Adelson, M. S. Gizzi, W. T. Newsome, “The analysis of moving visual patterns,” in Pattern Recognition Mechanisms, Exp. Brain Res. Suppl.11, C. Chagas, R. Gattass, C. Gross, eds. (Springer-Verlag, Berlin, 1985), pp. 117–151.

Poggio, T.

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).

Shepp, L. A.

B. Julesz, E. N. Gilbert, L. A. Shepp, H. L. Frisch, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).

Torre, V.

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).

Victor, J. D.

J. D. Victor, M. M. Conte, “Spatial organization of nonlinear interactions in form perception,” Vision Res. 31, 1457–1488 (1991).

J. D. Victor, M. M. Conte, “Cortical interactions in texture processing: scale and dynamics,” Vis. Neurosci. 2, 297–313 (1989).

J. D. Victor, “Complex visual textures as a tool for studying the VEP,” Vision Res. 25, 1811–1827 (1985).

J. D. Victor, V. Zemon, “The human visual evoked potential: analysis of components due to elementary and complex aspects of form,” Vision Res. 25, 1829–1844 (1985).

J. D. Victor, S. Brodie, “Discriminable textures with identical Buffon needle statistics,” Biol. Cybern. 31, 231–234 (1978).

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137–149 (1978).

Yellott, J.

Zemon, V.

J. D. Victor, V. Zemon, “The human visual evoked potential: analysis of components due to elementary and complex aspects of form,” Vision Res. 25, 1829–1844 (1985).

Biol. Cybern. (4)

T. Caelli, B. Julesz, “On perceptual analyzers underlying visual texture discrimination. Part I,” Biol. Cybern. 28, 167–175 (1978).

T. Caelli, B. Julesz, E. N. Gilbert, “On perceptual analyzers underlying visual texture discrimination. Part II,” Biol. Cybern. 29, 201–214 (1978).

J. D. Victor, S. Brodie, “Discriminable textures with identical Buffon needle statistics,” Biol. Cybern. 31, 231–234 (1978).

B. Julesz, E. N. Gilbert, J. D. Victor, “Visual discrimination of textures with identical third-order statistics,” Biol. Cybern. 31, 137–149 (1978).

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

A. Gagalowitz, “A new method for texture fields synthesis: some applications to the study of human vision,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-3, 520–523 (1981).

J. Opt. Soc. Am. A (1)

Nature (1)

T. Poggio, V. Torre, C. Koch, “Computational vision and regularization theory,” Nature 317, 314–319 (1985).

Perception (1)

B. Julesz, E. N. Gilbert, L. A. Shepp, H. L. Frisch, “Inability of humans to discriminate between visual textures that agree in second-order statistics—revisited,” Perception 2, 391–405 (1973).

Rev. Mod. Phys. (1)

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

SIAM J. Alg. Discr. Meth. (1)

E. N. Gilbert, “Random colorings of a lattice on squares in the plane,” SIAM J. Alg. Discr. Meth. 1, 152–159 (1980).

Vis. Neurosci. (1)

J. D. Victor, M. M. Conte, “Cortical interactions in texture processing: scale and dynamics,” Vis. Neurosci. 2, 297–313 (1989).

Vision Res. (3)

J. D. Victor, M. M. Conte, “Spatial organization of nonlinear interactions in form perception,” Vision Res. 31, 1457–1488 (1991).

J. D. Victor, “Complex visual textures as a tool for studying the VEP,” Vision Res. 25, 1811–1827 (1985).

J. D. Victor, V. Zemon, “The human visual evoked potential: analysis of components due to elementary and complex aspects of form,” Vision Res. 25, 1829–1844 (1985).

Other (3)

P. Z. Marmarelis, V. Z. Marmarelis, Analysis of Physiological Systems: The White-Noise Approach (Plenum, New York, 1978).

J. A. Movshon, E. H. Adelson, M. S. Gizzi, W. T. Newsome, “The analysis of moving visual patterns,” in Pattern Recognition Mechanisms, Exp. Brain Res. Suppl.11, C. Chagas, R. Gattass, C. Gross, eds. (Springer-Verlag, Berlin, 1985), pp. 117–151.

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 Press, Cambridge, Mass., 1991), pp. 201–230.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (1)

Fig. 1
Fig. 1

Demonstration of segregation of two regions with identical statistics.

Metrics