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Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 9 — Sep. 1, 1999
  • pp: 2112–2123

Spatial-scale contribution to the detection of mirror symmetry in fractal noise

Stéphane J. M. Rainville and Frederick A. A. Kingdom  »View Author Affiliations

JOSA A, Vol. 16, Issue 9, pp. 2112-2123 (1999)

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We investigated how the detection of mirror symmetry depends on the distribution of contrast energy across spatial scales. Stimuli consisted of vertically symmetric noise patterns with fractal power spectra defined by 1/fβ slopes (-2β5). While overall rms contrast remained fixed at 25%, symmetry-detection thresholds were obtained by corrupting the signal with variable amounts of noise with identical spectral characteristics. A first experiment measured thresholds as a function of spectral slope, and performance was found to be substantially facilitated in images with power spectra that characterize natural scenes (1.2β3.2). In a second experiment, symmetry was removed from randomly chosen octave bands and replaced by noise with the same spectral profile. Results revealed that only in images with 1/f2 spectra does performance decrease by constant amounts across all frequency bands. Together, the results imply that symmetry mechanisms extract equal amounts of information from constant-octave frequency bands but lack the ability to whiten stimuli whose spectral slopes differ from those of natural scenes. Results are qualitatively well predicted by a multichannel model that (1) relies on spatial filters with equal-volume point-spread functions and constant-octave frequency bandwidths and (2) restricts the computation of symmetry to spatial regions whose dimensions are proportional to the filters’ spatial scale. These findings are also consistent with the notion that mechanisms that mediate the perception of form exploit the ability of early vision to reduce second-order redundancy in natural scenes.

© 1999 Optical Society of America

OCIS Codes
(330.1800) Vision, color, and visual optics : Vision - contrast sensitivity
(330.4060) Vision, color, and visual optics : Vision modeling
(330.5510) Vision, color, and visual optics : Psychophysics
(330.6100) Vision, color, and visual optics : Spatial discrimination
(330.6110) Vision, color, and visual optics : Spatial filtering
(330.6180) Vision, color, and visual optics : Spectral discrimination

Original Manuscript: November 23, 1998
Revised Manuscript: March 19, 1999
Manuscript Accepted: March 19, 1999
Published: September 1, 1999

Stéphane J. M. Rainville and Frederick A. A. Kingdom, "Spatial-scale contribution to the detection of mirror symmetry in fractal noise," J. Opt. Soc. Am. A 16, 2112-2123 (1999)

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  1. R. L. De Valois, D. G. Albrecht, L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982). [CrossRef] [PubMed]
  2. F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).
  3. B. Julesz, J. Chang, “Symmetry perception and spatial-frequency channels,” Perception 8, 711–718 (1979). [CrossRef] [PubMed]
  4. S. C. Dakin, R. F. Hess, “The spatial mechanisms mediating symmetry perception,” Vision Res. 37, 2915–2930 (1997). [CrossRef]
  5. S. C. Dakin, A. M. Herbert, “The spatial region of integration for visual symmetry detection,” Proc. R. Soc. London, Ser. B 265, 659–664 (1998). [CrossRef]
  6. B. Jenkins, “Component processes in the perception of bilaterally symmetric dot textures,” Percept. Psychophys. 34, 433–440 (1983). [CrossRef] [PubMed]
  7. H. B. Barlow, B. C. Reeves, “The versatility and absolute efficiency of detecting mirror symmetry in random dot displays,” Vision Res. 19, 783–793 (1979). [CrossRef] [PubMed]
  8. S. C. Dakin, R. J. Watt, “Detection of bilateral symmetry using spatial filters,” Spatial Vision 8, 393–413 (1994). [CrossRef] [PubMed]
  9. J. Wagemans, L. Van Gool, V. Swinnen, J. Van Horebeek, “Higher-order structure in regularity detection,” Vision Res. 33, 1067–1088 (1993). [CrossRef] [PubMed]
  10. C. W. Tyler, L. Hardage, R. T. Miller, “Multiple mechanisms for the detection of mirror symmetry,” Spatial Vision 9, 79–100 (1995). [CrossRef] [PubMed]
  11. V. G. Bruce, M. J. Morgan, “Violations of symmetry and repetition in visual patterns,” Perception 4, 239–249 (1975). [CrossRef]
  12. S. J. M. Rainville, F. A. A. Kingdom, “Does oblique structure support the detection of mirror symmetry?” Invest. Ophthalmol. 39, S170 (1998).
  13. S. J. M. Rainville, F. A. A. Kingdom, “From spatial filters to mirror symmetry: new findings and new model,” Perception 27, 58a (1998).
  14. U. Koeppl, “Local orientation versus local position as determinants of perceived symmetry,” Perception 22, 111 (1993).
  15. P. Wenderoth, “The salience of vertical symmetry,” Perception 23, 221–236 (1994). [CrossRef] [PubMed]
  16. J. Wagemans, L. Van Gool, J. Van Horebeek, “Orientation selective channels in symmetry detection: effects of cooperation and attention,” in Channels in the Visual Nervous System: Neurophysiology, Psychophysics and Models, B. E. Blum, ed. (Freund, London, 1991), pp. 425–445.
  17. P. Wenderoth, “The effects of the contrast polarity of dot-pair partners on the detection of bilateral symmetry,” Perception 25, 757–771 (1996). [CrossRef] [PubMed]
  18. L. Zhang, “Symmetry perception in human vision,” Ph.D dissertation (University of Trieste, Trieste, Italy, 1991).
  19. P. Carlin, “On symmetry in visual perception,” Ph.D dissertation (University of Stirling, Stirling, Scotland, 1996).
  20. C. W. Tyler, L. Hardage, “Mirror symmetry detection: predominance of second-order pattern processing throughout the visual field,” in Human Symmetry Perception and Its Computational Analysis, C. W. Tyler, ed. (VSP, Utrecht, The Netherlands, 1996).
  21. S. Oomes, “Human visual perception of spatial structure: symmetry, orientation, and attitude,” Ph.D dissertation (Catholic University of Nijmegen, Nijmegen, The Netherlands, 1998).
  22. D. H. Hubel, T. N. Wiesel, “Receptive fields and functional architecture of monkey striate cortex,” J. Physiol. (London) 195, 215–243 (1968).
  23. F. Labonte, Y. Shapira, P. Cohen, J. Faubert, “A model for global symmetry detection in dense images,” Spatial Vision 9, 33–55 (1995). [CrossRef] [PubMed]
  24. B. Jenkins, “Redundancy in the perception of bilateral symmetry in dot textures,” Percept. Psychophys. 32, 171–177 (1982). [CrossRef] [PubMed]
  25. N. Brady, D. J. Field, “What’s constant in contrast constancy? The effects of scaling on the perceived contrast of bandpass patterns,” Vision Res. 35, 739–756 (1995). [CrossRef] [PubMed]
  26. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–9234 (1987). [CrossRef] [PubMed]
  27. G. J. Burton, I. R. Moorhead, “Color and spatial structure natural scenes,” Appl. Opt. 26, 157–170 (1987). [CrossRef] [PubMed]
  28. D. J. Tolhurst, Y. Tadmor, T. Chao, “Amplitude spectra of natural images,” Ophthal. Physiol. Opt. 12, 229–232 (1992). [CrossRef]
  29. D. L. Ruderman, W. Bialeck, “Statistics of natural images: scaling in the woods,” Phys. Rev. Lett. 73, 814–817 (1994). [CrossRef] [PubMed]
  30. D. J. Field, “Scale-invariance and self-similar ‘wavelet’ transforms: an analysis of natural scenes and mammalian visual systems,” in Wavelets, Fractals, and Fourier Transforms, M. Farge, J. C. R. Hunt, J. C. Vassilicos, eds. (Clarendon, Oxford, 1993), pp. 151–193.
  31. D. J. Field, N. Brady, “Visual sensitivity, blur and the sources of variability in the amplitude spectra of natural scenes,” Vision Res. 37, 3367–3383 (1997). [CrossRef]
  32. J. J. Atick, A. N. Redlich, “Towards a theory of early visual processing,” Neural Comput. 2, 308–320 (1990). [CrossRef]
  33. M. V. Srinivasan, S. B. Laughlin, A. Dubs, “Predictive coding: a fresh view of inhibition in the retina,” Proc. R. Soc. London, Ser. B 216, 427–59 (1982). [CrossRef]
  34. C. Blakemore, F. W. Campbell, “On the existence of neurones in the human vision system selectively sensitive to the orientation and size of retinal images,” J. Physiol. (London) 203, 237–260 (1969).
  35. H. R. Wilson, D. K. McFarlane, G. C. Phillips, “Spatial frequency tuning of orientation selective units estimated by oblique masking,” Vision Res. 23, 873–882 (1983). [CrossRef] [PubMed]
  36. L. Croner, E. Kaplan, “Receptive fields of P and M ganglion cells across the primate retina,” Vision Res. 35, 7–24 (1995). [CrossRef] [PubMed]
  37. D. C. Knill, D. Field, D. Kersten, “Human discrimination of fractal images,” J. Opt. Soc. Am. A 7, 1113–1123 (1990). [CrossRef] [PubMed]
  38. Y. Tadmor, D. J. Tolhurst, “Discrimination of changes in the second-order statistics of natural and synthetic images,” Vision Res. 34, 541–554 (1994). [CrossRef] [PubMed]
  39. D. J. Tolhurst, Y. Tadmor, “Band-limited contrast in natural images explains the detectability of changes in the amplitude spectra,” Vision Res. 37, 3203–3215 (1997). [CrossRef]
  40. D. G. Pelli, “The VideoToolbox software for visual psychophysics: transforming numbers into movies,” Spatial Vision 10, 437–442 (1997). [CrossRef] [PubMed]
  41. A. B. Watson, D. G. Pelli, “QUEST: A Bayesian adaptive psychometric method,” Percept. Psychophys. 33, 113–120 (1983). [CrossRef] [PubMed]
  42. J. D. Victor, M. M. Conte, “The role of high-order phase correlations in texture processing,” Vision Res. 36, 1615–1631 (1996). [CrossRef] [PubMed]
  43. S. J. M. Rainville, F. A. A. Kingdom, “Is motion perception sensitive to local phase structures?” Invest. Ophthalmol. 38, S215 (1997).
  44. N. V. S. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).
  45. N. Graham, J. G. Robson, “Summation of very close spatial frequencies: the importance of spatial probability summation,” Vision Res. 27, 815–826 (1987). [CrossRef]
  46. R. F. J. Quick, “A vector-magniture model of contrast detection,” Kybernetik 16, 65–67 (1974). [CrossRef]
  47. N. A. Macmillan, C. D. Creelman, Detection Theory: A User’s Guide (Cambridge U. Press, Cambridge, 1991).
  48. D. M. Green, J. A. Swets, Signal Detection Theory and Psychophysics (Peninsula, Los Altos, Calif., 1988).

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