OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 16, Iss. 7 — Jul. 1, 1999
  • pp: 1554–1565

The atoms of vision: Cartesian or polar?

Christoph Zetzsche, Gerhard Krieger, and Bernhard Wegmann  »View Author Affiliations


JOSA A, Vol. 16, Issue 7, pp. 1554-1565 (1999)
http://dx.doi.org/10.1364/JOSAA.16.001554


View Full Text Article

Acrobat PDF (1027 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

The inherent structure of the encoding in early stages of the visual system is investigated from a combined information-theoretical, psychophysical, and neurophysiological perspective. We argue that the classical modeling in terms of linear spatial filters is equivalent to the assumption of a Cartesian organization of the feature space of early vision. We show that such a linear Cartesian feature space would be suboptimal for the exploitation of the statistical redundancies of natural images since these have a radially separable probability-density function. Therefore a more efficient representation can be obtained by a nonlinear encoding that yields a feature space with polar organization. This prediction of the information-theoretical approach regarding the organization of the feature space of early vision is confirmed by our psychophysical measurements of basic discrimination capabilities for elementary Gabor patches, and the necessary nonlinear operations are shown to be closely related to cortical gain control and to the phase invariance of complex cells. Finally, we point out some striking similarities between the polar representation in visual cortex and basic image-coding strategies pursued in shape-gain vector quantization schemes.

© 1999 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(100.7410) Image processing : Wavelets
(330.0330) Vision, color, and visual optics : Vision, color, and visual optics
(330.4060) Vision, color, and visual optics : Vision modeling
(330.4270) Vision, color, and visual optics : Vision system neurophysiology
(330.5510) Vision, color, and visual optics : Psychophysics

Citation
Christoph Zetzsche, Gerhard Krieger, and Bernhard Wegmann, "The atoms of vision: Cartesian or polar?," J. Opt. Soc. Am. A 16, 1554-1565 (1999)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-16-7-1554


Sort:  Author  |  Year  |  Journal  |  Reset

References

  1. D. H. Hubel and T. N. Wiesel, “Receptive fields of single neurones in the cat’s striate cortex,” J. Physiol. (London) 148, 574–591 (1959).
  2. H. B. Barlow, “Single units and sensation: a neuron doctrine for perceptual psychology,” Perception 1, 371–394 (1972).
  3. B. Julesz and R. Schumer, “Early visual perception,” Annu. Rev. Psychol. 32, 575–627 (1981).
  4. I. Fujita, M. Ito, and M. I. K. Cheng, “Columns for visual features of objects in monkey inferotemporal cortex,” Nature (London) 360, 343–346 (1992).
  5. M. Stryker, “Elements of visual perception,” Nature (London) 360, 301–302 (1992).
  6. J. G. Daugman, “Uncertainty relation for resolution in space, spatial frequency, and orientation optimized by two-dimensional visual cortical filters,” J. Opt. Soc. Am. A 2, 1160–1169 (1985).
  7. I. Daubechies, “The wavelet transform, time frequency localization and signal analysis,” IEEE Trans. Inf. Theory 36, 961–1005 (1990).
  8. R. L. DeValois and K. K. DeValois, Spatial Vision (Oxford U. Press, New York, 1988).
  9. N. Graham, Visual Pattern Analyzers (Oxford U. Press, New York, 1989).
  10. D. J. Field, “Relations between the statistics of natural images and the response properties of cortical cells,” J. Opt. Soc. Am. A 4, 2379–2394 (1987).
  11. C. Zetzsche and W. Schönecker, “Orientation selective filters lead to entropy reduction in the processing of natural images,” Perception 16, 229 (1987).
  12. C. Zetzsche, E. Barth, and 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.
  13. F. Attneave, “Some informational aspects of visual perception,” Psychol. Rev. 61, 183–193 (1954).
  14. H. B. Barlow, “Sensory mechanisms, the reduction of redundancy and intelligence,” in National Physical Laboratory Symposium No. 10 (Her Majesty’s Stationary Office, London, 1959).
  15. H. B. Barlow, “Unsupervised learning,” Neural Comput. 1, 295–311 (1989).
  16. J. J. Atick, “Could information theory provide an ecological theory of sensory processing?” Network 3, 213–251 (1992).
  17. H. Barlow, “What is the computational goal of the neocortex?” in Large-Scale Neuronal Theories of the Brain, C. Koch, ed. (MIT Press, Cambridge, Mass., 1994), pp. 1–22.
  18. M. V. Srinivasan, S. B. Laughlin, and A. Dubs, “Predictive coding: a fresh view of inhibition in the retina,” Proc. R. Soc. London Ser. B 216, 427–459 (1982).
  19. J. H. van Hateren, “Real and optimal neural images in early vision,” Nature (London) 360, 68–69 (1992).
  20. B. Olshausen and D. Field, “Wavelet-like receptive fields emerge from a network that learns sparse codes for natural images,” Nature (London) 381, 607–609 (1996).
  21. C. Zetzsche, E. Barth, and B. Wegmann, “Nonlinear aspects of primary vision: entropy reduction beyond decorrelation,” in SID International Symposium—Digest of Technical Papers, XXIV, J. Morreale, ed. (Society for Information Display, Playa del Ray, Calif., 1993), Vol. XXIV, pp. 933–936.
  22. A. B. Watson, “Efficiency of a model human image code,” J. Opt. Soc. Am. A 4, 2401–2417 (1987).
  23. J. G. Daugman, “Complete discrete 2-d Gabor transforms by neural networks for image analysis and compression,” IEEE Trans. Acoust., Speech, Signal Process. 36, 1169–1179 (1988).
  24. A. Bell and T. Sejnowski, “The ‘independent components’ of natural scenes are edge filters,” Vision Res. 37, 3327–3338 (1997).
  25. J. van Hateren and A. van der Schaaf, “Independent component filters of natural images compared with simple cells in primary visual cortex,” Proc. R. Soc. London Ser. B 265, 359–366 (1998).
  26. R. C. Reininger and J. D. Gibson, “Distributions of the two-dimensional DCT coefficients for images,” IEEE Trans. Commun. C-31, 835–839 (1983).
  27. C. Zetzsche, E. Barth, G. Krieger, and B. Wegmann, “Neural network models and the visual cortex: the missing link between cortical orientation selectivity and the natural environment,” Neurosci. Lett. 228(3), 155–158 (1997).
  28. B. Wegmann and C. Zetzsche, “Visual system based polar quantization of local amplitude and local phase of orientation filter outputs,” in Human Vision and Electronic Imaging: Models, Methods, and Applications, B. Rogowitz, ed. Proc. SPIE 1249, 306–317 (1990).
  29. B. Wegmann and C. Zetzsche, “Statistical dependence between orientation filter outputs used in a human vision based image code,” in Visual Communication and Image Processing, M. Kunt, ed., Proc. SPIE 1360, 909–923 (1990).
  30. D. J. Field and D. J. Tolhurst, “The structure and symmetry of simple-cell receptive field properties in the cat’s visual cortex,” Proc. R. Soc. London Ser. B 228, 379–400 (1986).
  31. A. Gersho and M. Gray, Vector Quantization and Signal Compression (Kluwer Academic, Boston, Mass., 1992).
  32. C. Zetzsche and G. Krieger, “Natural image statistics and the exploitation of intrinsic dimensionality,” submitted to Vision Res.
  33. W. Brown and D. MacAdam, “Visual sensitivities to combined chromaticity and luminance differences,” J. Opt. Soc. Am. 39, 808–834 (1949).
  34. G. E. Legge and J. M. Foley, “Contrast masking in human vision,” J. Opt. Soc. Am. 70, 1458–1471 (1980).
  35. D. C. Burr, “Sensitivity to spatial phase,” Vision Res. 20, 391–396 (1980).
  36. C. Tyler and A. Gorea, “Different encoding mechanisms for phase and contrast,” Vision Res. 26, 1073–1082 (1986).
  37. B. Gouled-Smith and J. Thomas, “Why are some spatial discriminations independent of contrast?” J. Opt. Soc. Am. A 6, 713–724 (1989).
  38. S. Bowne, “Contrast discrimination cannot explain spatial frequency, orientation or temporal frequency discrimination,” Vision Res. 30, 449–461 (1990).
  39. L. Itti, J. Braun, D. K. Lee, and C. Koch, “A model of early visual processing,” in Advances in Neural Information Processing Systems, M. Kearns and S. Solla, eds. (MIT Press, Cambridge, Mass., 1998), Vol. 10, pp. 173–179.
  40. E. H. Adelson and J. R. Bergen, “Spatiotemporal energy models for the perception of motion,” J. Opt. Soc. Am. A 2, 284–299 (1985).
  41. C. Morrone and D. J. Burr, “Feature detection in human vision: a phase dependent energy model,” Proc. R. Soc. London Ser. B 235, 221–245 (1988).
  42. C. Zetzsche and B. Wegmann, “Coding properties of local amplitude and phase of two-dimensional filter outputs,” Perception 17, 396 (1988).
  43. B. Wegmann and C. Zetzsche, “Feature-specific vector quantization of images,” in Special issue on Vector Quantization, IEEE Trans. Image Process. 5, 274–288 (1996).
  44. D. G. Albrecht and D. B. Hamilton, “Striate cortex of monkeys and cat: contrast response functions,” J. Neurophysiol. 48, 217–237 (1982).
  45. D. Albrecht and W. Geisler, “Motion selectivity and the contrast-response function of simple cells in the visual cortex,” Visual Neurosci. 7, 531–546 (1991).
  46. D. Heeger, “Nonlinear model of neural responses in cat visual cortex,” in Computational Models of Visual Processing, M. Landy and J. Movshon, eds. (MIT Press, Cambridge, Mass., 1991), pp. 119–133.
  47. M. Carandini and D. G. Heeger, “Summation and division by neurons in primate visual cortex,” Science 264, 1333–1336 (1994).
  48. G. A. Orban, Neuronal Operations in the Visual Cortex (Springer, Heidelberg, 1984).
  49. R. Vogels, “Population coding of stimulus orientation by striate cortical cells,” Biol. Cybern. 64, 25–31 (1990).
  50. F. W. Campbell and J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. (London) 197, 551–566 (1968).
  51. R. L. DeValois, D. G. Albrecht, and L. G. Thorell, “Spatial frequency selectivity of cells in macaque visual cortex,” Vision Res. 22, 545–559 (1982).
  52. M. J. Sabin and R. M. Gray, “Product code vector quantizers for waveform and voice coding,” IEEE Trans. Acoust., Speech, Signal Process. ASSP-32, 474–488 (1984).
  53. C. Zetzsche, G. Krieger, K. Schill, and B. Treutwein, “Natural image statistics and cortical gain control,” Invest. Ophthalmol. Visual Sci. 39 (Suppl.), S424 (1998).
  54. C. Zetzsche and G. Krieger, “Exploitation of natural scene statistics by orientation selectivity and cortical gain control,” Perception 27 (Suppl.), 154 (1998).
  55. C. Zetzsche and G. Krieger, “Nonlinear neurons and higher-order statistics: new approaches to vision and image processing,” in Human Vision and Electronic Image Processing, B. Rogowitz and T. Papathomas, eds., Proc. SPIE 3644 (1999).
  56. G. Sclar and R. Freeman, “Orientation selectivity in the cat’s striate cortex is invariant with stimulus contrast,” Exp. Brain Res. 46, 457–461 (1982).
  57. W. S. Geisler and D. G. Albrecht, “Bayesian analysis of identification performance in monkey visual cortex: nonlinear mechanisms and stimulus certainty,” Vision Res. 35, 2723–2730 (1995).
  58. R. W. Buccigrossi and E. P. Simoncelli, “Image compression via joint statistical characterization in the wavelet domain,” Tech. Rep. 414 (General Robotics and Active Sensory Perception Laboratory, University of Pennsylvania, Philadelphia, 1997).
  59. E. Simoncelli and O. Schwartz, “Derivation of a cortical normalization model from the statistics of natural images,” Invest. Ophthalmol. Visual Sci. 39 (Suppl.), S424 (1998).
  60. E. P. Simoncelli and O. Schwartz, “Modeling surround suppression in v1 neurons with a statistically-derived normalization model,” in Advances in Neural Information Processing Systems, M. S. Kearns, S. A. Solla, and D. A. Cohn, eds., (MIT Press, Cambridge, Mass., 1999).
  61. B. Picinbono, Random Signals and Systems (Prentice-Hall, Englewood Cliffs, N.J., 1993).
  62. I. Rentschler and B. Treutwein, “Loss of spatial phase relationships in extrafoveal vision,” Nature (London) 313, 308–310 (1985).
  63. P. J. Bennett and M. S. Banks, “The effects of contrast, spatial scale, and orientation on foveal and peripheral phase discrimination,” Vision Res. 31, 1759–1786 (1991).
  64. B. Treutwein, “Adaptive psychophysical procedures: a review,” Vision Res. 35, 2503–2522 (1995).

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited