Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Article
  • Published:

Cardinal rules: visual orientation perception reflects knowledge of environmental statistics

Nature Neuroscience volume 14, pages 926–932 (2011)Cite this article

Subjects

Abstract

Humans are good at performing visual tasks, but experimental measurements have revealed substantial biases in the perception of basic visual attributes. An appealing hypothesis is that these biases arise through a process of statistical inference, in which information from noisy measurements is fused with a probabilistic model of the environment. However, such inference is optimal only if the observer's internal model matches the environment. We found this to be the case. We measured performance in an orientation-estimation task and found that orientation judgments were more accurate at cardinal (horizontal and vertical) orientations. Judgments made under conditions of uncertainty were strongly biased toward cardinal orientations. We estimated observers' internal models for orientation and found that they matched the local orientation distribution measured in photographs. In addition, we determined how a neural population could embed probabilistic information responsible for such biases.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Observer model for local two-dimensional orientation estimation.
Figure 2: Derivation of the estimator θ̂(m(θ)).
Figure 3: Stimuli and experimental results.
Figure 4: Example cross-noise comparison.
Figure 5: Recovered priors for subject S1 and mean subject.
Figure 6: Natural image statistics.
Figure 7: Comparison of human observers' priors and environmental distribution for subject S1 (left) and the mean subject (right).
Figure 8: Simulations of neural models with non-uniform encoder and population vector decoder.

Similar content being viewed by others

References

  1. Helmholtz, H. Treatise on Physiological Optics (Thoemmes Press, Bristol, UK, 2000).

  2. El-Bizri, N. A philosophical perspective on Alhazen's optics. Arab. Sci. Philos. 15, 189–218 (2005).

    Article  Google Scholar 

  3. Knill, D.C. & Richards, W. Perception as Bayesian Inference (Cambridge University Press, Cambridge, UK, 1996).

  4. Geisler, W.S., Perry, J.S., Super, B.J. & Gallogly, D.P. Edge co-occurrence in natural images predicts contour grouping performance. Vision Res. 41, 711–724 (2001).

    Article  CAS  Google Scholar 

  5. Simoncelli, E.P. Distributed Analysis and Representation of Visual Motion. PhD thesis, Massachusetts Institute of Technology (1993).

    Google Scholar 

  6. Griffiths, T.L., Kemp, C. & Tenenbaum, J.B. Bayesian models of cognition. in Cambridge Handbook of Computational Psychology (ed. Sun, R.) 59–100 (Cambridge University Press, 2008).

  7. Körding, K.P. & Wolpert, D.M. Bayesian integration in sensorimotor learning. Nature 427, 244–247 (2004).

    Article  Google Scholar 

  8. Tassinari, H., Hudson, T.E. & Landy, M.S. Combining priors and noisy visual cues in a rapid pointing task. J. Neurosci. 26, 10154–10163 (2006).

    Article  CAS  Google Scholar 

  9. Mamassian, P. & Goutcher, R. Prior knowledge on the illumination position. Cognition 81, 1–9 (2001).

    Article  Google Scholar 

  10. Burge, J., Fowlkes, C.C. & Banks, M.S. Natural-scene statistics predict how the figure-ground cue of convexity affects human depth perception. J. Neurosci. 30, 7269–7280 (2010).

    Article  CAS  Google Scholar 

  11. Weiss, Y., Simoncelli, E.P. & Adelson, E.H. Motion illusions as optimal percepts. Nat. Neurosci. 5, 598–604 (2002).

    Article  CAS  Google Scholar 

  12. Brainard, D.H. et al. Bayesian model of human color constancy. J. Vis. 6, 1267–1281 (2006).

    Article  Google Scholar 

  13. Stocker, A.A. & Simoncelli, E.P. Noise characteristics and prior expectations in human visual speed perception. Nat. Neurosci. 9, 578–585 (2006).

    Article  CAS  Google Scholar 

  14. Dakin, S.C. Information limit on the spatial integration of local orientation signals. J. Opt. Soc. Am. A Opt. Image Sci. Vis. 18, 1016–1026 (2001).

    Article  CAS  Google Scholar 

  15. Appelle, S. Perception and discrimination as a function of stimulus orientation: the “oblique effect” in man and animals. Psychol. Bull. 78, 266–278 (1972).

    Article  CAS  Google Scholar 

  16. Landy, M.S., Goutcher, R., Trommershäuser, J. & Mamassian, P. Visual estimation under risk. J. Vis. 7, 1–15 (2007).

    Article  Google Scholar 

  17. Coppola, D.M., Purves, H.R., McCoy, A.N. & Purves, D. The distribution of oriented contours in the real world. Proc. Natl. Acad. Sci. USA 95, 4002–4006 (1998).

    Article  CAS  Google Scholar 

  18. van der Schaaf, A. & van Hateren, J.H. Modelling the power spectra of natural images: statistics and information. Vision Res. 36, 2759–2770 (1996).

    Article  CAS  Google Scholar 

  19. Switkes, E., Mayer, M.J. & Sloan, J.A. Spatial frequency analysis of the visual environment: anisotropy and the carpentered environment hypothesis. Vision Res. 18, 1393–1399 (1978).

    Article  CAS  Google Scholar 

  20. Farid, H. & Simoncelli, E.P. Differentiation of discrete multidimensional signals. IEEE Trans. Image Process. 13, 496–508 (2004).

    Article  Google Scholar 

  21. Campbell, F.W. & Robson, J.G. Application of Fourier analysis to the visibility of gratings. J. Physiol. (Lond.) 197, 551–566 (1968).

    Article  CAS  Google Scholar 

  22. Tomassini, A., Morgan, M.J. & Solomon, J.A. Orientation uncertainty reduces perceived obliquity. Vision Res. 50, 541–547 (2010).

    Article  Google Scholar 

  23. Schwartz, O., Hsu, A. & Dayan, P. Space and time in visual context. Nat. Rev. Neurosci. 8, 522–535 (2007).

    Article  CAS  Google Scholar 

  24. Shadlen, M.N., Britten, K.H., Newsome, W.T. & Movshon, J.A. A computational analysis of the relationship between neuronal and behavioral responses to visual motion. J. Neurosci. 16, 1486–1510 (1996).

    Article  CAS  Google Scholar 

  25. Cohen, E.H. & Zaidi, Q. Fundamental failures of shape constancy resulting from cortical anisotropy. J. Neurosci. 27, 12540–12545 (2007).

    Article  CAS  Google Scholar 

  26. Maloney, L.T. & Mamassian, P. Bayesian decision theory as a model of human visual perception: testing Bayesian transfer. Vis. Neurosci. 26, 147–155 (2009).

    Article  Google Scholar 

  27. Birch, E.E., Gwiazda, J., Bauer, J.A. Jr. Naegele, J. & Held, R. Visual acuity and its meridional variations in children aged 7–60 months. Vision Res. 23, 1019–1024 (1983).

    Article  CAS  Google Scholar 

  28. Timney, B.N. & Muir, D. Orientation anisotropy: incidence and magnitude in Caucasian and Chinese subjects. Science 193, 699–701 (1976).

    Article  CAS  Google Scholar 

  29. Mayer, M.J. Development of anisotropy in late childhood. Vision Res. 17, 703–710 (1977).

    Article  CAS  Google Scholar 

  30. Blakemore, C. & Cooper, G.F. Development of the brain depends on the visual environment. Nature 228, 477–478 (1970).

    Article  CAS  Google Scholar 

  31. Mitchell, D.E., Freeman, R.D., Millodot, M. & Haegerstrom, G. Meridional amblyopia: evidence for modification of the human visual system by early visual experience. Vision Res. 13, 535–558 (1973).

    Article  CAS  Google Scholar 

  32. Orban, G.A., Vandenbussche, E. & Vogels, R. Human orientation discrimination tested with long stimuli. Vision Res. 24, 121–128 (1984).

    Article  CAS  Google Scholar 

  33. Li, B., Peterson, M.R. & Freeman, R.D. The oblique effect: a neural basis in the visual cortex. J. Neurophysiol. 90, 204–217 (2003).

    Article  Google Scholar 

  34. De Valois, R.L., Yund, E.W. & Hepler, N. The orientation and direction selectivity of cells in macaque visual cortex. Vision Res. 22, 531–544 (1982).

    Article  CAS  Google Scholar 

  35. Chapman, B. & Bonhoeffer, T. Overrepresentation of horizontal and vertical orientation preferences in developing ferret area 17. Proc. Natl. Acad. Sci. USA 95, 2609–2614 (1998).

    Article  CAS  Google Scholar 

  36. Furmanski, C.S. & Engel, S.A. An oblique effect in human primary visual cortex. Nat. Neurosci. 3, 535–536 (2000).

    Article  CAS  Google Scholar 

  37. Jazayeri, M. & Movshon, J.A. Optimal representation of sensory information by neural populations. Nat. Neurosci. 9, 690–696 (2006).

    Article  CAS  Google Scholar 

  38. Zhang, K., Ginzburg, I., McNaughton, B.L. & Sejnowski, T.J. Interpreting neuronal population activity by reconstruction: unified framework with application to hippocampal place cells. J. Neurophysiol. 79, 1017–1044 (1998).

    Article  CAS  Google Scholar 

  39. Simoncelli, E.P. Optimal estimation in sensory systems. in The Cognitive Neurosciences IV (ed. Gazzaniga, M.) 525–535 (MIT Press, 2009).

  40. Fischer, B.J. Bayesian estimates from heterogeneous population codes. Int. Jt. Conf. Neural Netw. 1–7 (2010).

  41. Ringach, D.L., Shapley, R.M. & Hawken, M.J. Orientation selectivity in macaque V1: diversity and laminar dependence. J. Neurosci. 22, 5639–5651 (2002).

    Article  CAS  Google Scholar 

  42. Georgopoulos, A.P., Schwartz, A.B. & Kettner, R.E. Neuronal population coding of movement direction. Science 233, 1416–1419 (1986).

    Article  CAS  Google Scholar 

  43. Ma, W.J., Beck, J.M., Latham, P.E. & Pouget, A. Bayesian inference with probabilistic population codes. Nat. Neurosci. 9, 1432–1438 (2006).

    Article  CAS  Google Scholar 

  44. Seung, H.S. & Sompolinsky, H. Simple models for reading neuronal population codes. Proc. Natl. Acad. Sci. USA 90, 10749–10753 (1993).

    Article  CAS  Google Scholar 

  45. Ganguli, D. & Simoncelli, E.P. Implicit encoding of prior probabilities in optimal neural populations. in Advances in Neural Information Processing Systems 23 NIPS. (eds. Williams, C., Lafferty, J., Zemel, R., Shawe-Taylor, J. & Culotta, A). (MIT Press, Cambridge, Massachusetts, 2010).

  46. Green, D.M. & Swets, J.A. Signal Detection Theory and Psychophysics (Wiley, Oxford, UK, 1966).

  47. Stocker, A.A. & Simoncelli, E.P. Visual motion aftereffects arise from a cascade of two isomorphic adaptation mechanisms. J. Vis. 9, 1–14 (2009).

    Article  Google Scholar 

  48. Burt, P. & Adelson, E. The Laplacian pyramid as a compact image code. IEEE Trans. Commun. 31, 532–540 (1983).

    Article  Google Scholar 

  49. Granlund, G.H. & Knutsson, H. Signal Processing for Computer Vision (Kluwer Academic Publishers, Norwell, Massachusetts, 1995).

  50. Swindale, N.V. Orientation tuning curves: empirical description and estimation of parameters. Biol. Cybern. 78, 45–56 (1998).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

We wish to thank D. Ganguli for helpful discussions on image statistics and population coding, T. Saarela for the monitor calibration and N. Solomon for assisting with the experiments. This work was funded by US National Institutes of Health grants EY019451 (A.R.G.) and EY16165 (M.S.L.), and the Howard Hughes Medical Institute (E.P.S.).

Author information

Authors and Affiliations

  1. Department of Psychology, New York University, New York, New York, USA

    Ahna R Girshick, Michael S Landy & Eero P Simoncelli

  2. Center for Neural Science, New York University, New York, New York, USA

    Ahna R Girshick, Michael S Landy & Eero P Simoncelli

  3. Howard Hughes Medical Institute, New York University, New York, New York, USA

    Eero P Simoncelli

  4. Courant Institute for Mathematical Sciences, New York University, New York, New York, USA

    Eero P Simoncelli

Authors
  1. Ahna R Girshick
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael S Landy
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Eero P Simoncelli
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

A.R.G., M.S.L. and E.P.S. contributed to the design of the experiments, design of the analyses and the writing of the manuscript. A.R.G. conducted the experiments and performed the analyses.

Corresponding author

Correspondence to Ahna R Girshick.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary Text and Figures

Supplementary Figures 1–5 (PDF 504 kb)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Girshick, A., Landy, M. & Simoncelli, E. Cardinal rules: visual orientation perception reflects knowledge of environmental statistics. Nat Neurosci 14, 926–932 (2011). https://doi.org/10.1038/nn.2831

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nn.2831

This article is cited by

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing