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Why pictures look right when viewed from the wrong place

Nature Neuroscience volume 8, pages 1401–1410 (2005)Cite this article

An Erratum to this article was published on 01 December 2005

This article has been updated

Abstract

A picture viewed from its center of projection generates the same retinal image as the original scene, so the viewer perceives the scene correctly. When a picture is viewed from other locations, the retinal image specifies a different scene, but we normally do not notice the changes. We investigated the mechanism underlying this perceptual invariance by studying the perceived shapes of pictured objects viewed from various locations. We also manipulated information about the orientation of the picture surface. When binocular information for surface orientation was available, perceived shape was nearly invariant across a wide range of viewing angles. By varying the projection angle and the position of a stimulus in the picture, we found that invariance is achieved through an estimate of local surface orientation, not from geometric information in the picture. We present a model that explains invariance and other phenomena (such as perceived distortions in wide-angle pictures).

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Figure 1: Demonstration of invariance with oblique viewing.
Figure 2: Perspective projection and pictures.
Figure 3: Stimuli, predictions and results for the first experiment.
Figure 4: Rotating the projection plane.
Figure 5: Stimuli, predictions and results for the second experiment.
Figure 6: Stimuli, predictions and results for the third experiment.
Figure 7: Wide-angle distortions, anamorphic painting and architectural photography.

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Change history

  • 21 November 2005

    On page 1402, the first two sentences of the second full paragraph in the second column were omitted. The paragraph should have begun as follows: “An alternative explanation, the local-slant hypothesis, suggests that location of the CoP is not recovered. Instead, the observed invariance is due to an adjustment of the retinal-image shape based on measurements of the local slant of the picture surface at the point of interest. This hypothesis does not require estimates of the location of or distance to the CoP.” The PDF version of this article was corrected on 21 November 2005. Please see the PDF for details.

Notes

  1. *On page 1402, the first two sentences of the second full paragraph in the second column were omitted. The paragraph should have begun as follows: “An alternative explanation, the local-slant hypothesis, suggests that location of the CoP is not recovered. Instead, the observed invariance is due to an adjustment of the retinal-image shape based on measurements of the local slant of the picture surface at the point of interest. This hypothesis does not require estimates of the location of or distance to the CoP.” The PDF version of this article was corrected on 21 November 2005. Please see the PDF for details.

References

  1. da Vinci, L. The Literary Works of Leonardo da Vinci (ed. Richter, J.P.) (Phaidon, London, 1970).

    Google Scholar 

  2. Olmer, P. Tracés Pratiques (Plon, Paris, 1949).

    Google Scholar 

  3. Kubovy, M. The Psychology of Perspective and Renaissance Art (Cambridge Univ. Press, New York, 1986).

    Google Scholar 

  4. La Gournerie, J.D. Traité de Perspective Linéare Contenant les Tracés pour les Tableaux, Plans et Courbes, les Bas-reliefs et les Décorations Théatrales, avec une Théorie des Effets de Perspective (Dalmont et Dunod, Paris, 1859).

    Google Scholar 

  5. Gombrich, E.H. Art and Illusion (Princeton Univ. Press, Princeton, New Jersey, 1960).

    Google Scholar 

  6. Kingslake, R. Lenses in Photography: The Practical Guide to Optics for Photographers (Case-Hoyt, Garden City, New York, 1951).

    Google Scholar 

  7. Pirenne, M.H. Optics, Painting and Photography (Cambridge Univ. Press, Cambridge, UK, 1970).

    Google Scholar 

  8. Alesse, C. Basic 35mm Photo Guide: For Beginning Photographers (Amherst Media, New York, 1989).

    Google Scholar 

  9. Giancoli, D.C. Physics: Principles with Applications (Prentice Hall, Englewood Cliffs, New Jersey, USA, 2000).

    Google Scholar 

  10. Meister, R. The iso-deformation of images and the criterion for delimitation of the usable areas in cine-auditoriums. J. Soc. Motion Pict. Television Eng. 75, 179–182 (1966).

    Google Scholar 

  11. Zorin, D. & Barr, A.H. Correction of geometric perceptual distortions in pictures. in Proceedings of SIGGRAPH 1995 Vol. 14 (ed. Cook, R.) 257–264 (ACM SIGGRAPH/Addison-Wesley, Boston, 1995).

    Google Scholar 

  12. Caprile, B. & Torre, V. Using vanishing points for camera calibration. Int. J. Comput. Vis. 4, 127–140 (1990).

    Article  Google Scholar 

  13. Agrawala, M., Zorin, D. & Munzner, T. Artistic multiprojection rendering. Proceedings of the 11th Europographics Rendering Workshop 11, 125–136 (2000).

    Google Scholar 

  14. Hagen, M.A. Influence of picture surface and station point on the ability to compensate for oblique view in pictorial perception. Dev. Psychol. 12, 57–63 (1976).

    Article  Google Scholar 

  15. Rosinski, R.R. & Farber, J. Compensation for viewing point in the perception of pictured space. in The Perception of Pictures (ed. Hagen, M.A.) 137–176 (Academic, New York, 1980).

    Google Scholar 

  16. Rogers, S.J. Perceiving pictorial space. in Perception of Space and Motion (eds. Epstein, W. & Rogers, S.J.) 119–163 (Academic, San Diego, 1995).

    Chapter  Google Scholar 

  17. Goldstein, E.B. Spatial layout, orientation relative to the observer, and perceived projection in pictures viewed at an angle. J. Exp. Psychol. Hum. Percept. Perform. 13, 256–266 (1987).

    Article  CAS  PubMed  Google Scholar 

  18. Cutting, J.E. Rigidity in cinema seen from the front row, side aisle. J. Exp. Psychol. Hum. Percept. Perform. 13, 323–334 (1987).

    Article  CAS  PubMed  Google Scholar 

  19. Sedgwick, H.A. The effects of viewpoint on the virtual space of pictures. in Pictorial Communication in Virtual and Real Environments (eds. Ellis, S.R., Kaiser, M.K. & Grunwald, A.C.) 460–479 (Taylor & Francis, London, 1991).

    Google Scholar 

  20. Gershun, A. The light field. J. Math. Phys. 23, 51–151 (1939).

    Article  Google Scholar 

  21. Gibson, J.J. The Perception of the Visual World. Houghton-Mifflin, Boston, (1950).

    Google Scholar 

  22. Gårding, J. Shape from texture for smooth curved surfaces in perspective projection. J. Math. Imaging Vis. 2, 329–352 (1992).

    Article  Google Scholar 

  23. Rosinski, R.R., Mulholland, T., Degelman, D. & Farber, J. Picture perception: An analysis of visual compensation. Percept. Psychophys. 28, 521–526 (1980).

    Article  CAS  PubMed  Google Scholar 

  24. Busey, T.A., Brady, N.P. & Cutting, J.E. Compensation is unnecessary for the perception of faces in slanted pictures. Percept. Psychophys. 48, 1–11 (1990).

    Article  CAS  PubMed  Google Scholar 

  25. Perkins, D.N. Compensating for distortion in viewing pictures obliquely. Percept. Psychophys. 14, 13–18 (1973).

    Article  Google Scholar 

  26. Adams, K.R. Perspective and the viewpoint. Leonardo 5, 209–217 (1972).

    Article  Google Scholar 

  27. Greene, R. Determining the preferred viewpoint in linear perspective. Leonardo 16, 97–102 (1983).

    Article  Google Scholar 

  28. Wallach, H. & Marshall, F.J. Shape constancy in pictorial representation. Percept. Psychophys. 39, 233–235 (1986).

    Article  CAS  PubMed  Google Scholar 

  29. Stevens, K.A. Slant-tilt: The visual encoding of surface orientation. Biol. Cybern. 46, 183–195 (1983).

    Article  CAS  PubMed  Google Scholar 

  30. Koenderink, J.J. & van Doorn, A.J. Pictorial space. in Looking into Pictures: An Interdisciplinary Approach to Pictorial Space (eds. Hecht, H., Schwartz, R. & Atherton) 239–299 (MIT Press, Cambridge, Massachusetts, USA, 2003).

    Google Scholar 

  31. Kersten, D., Mamassian, P. & Yuille, A. Object perception as Bayesian Inference. Annu. Rev. Psychol. 55, 271–304 (2004).

    Article  PubMed  Google Scholar 

  32. Landy, M.S., Maloney, L.T., Johnston, E.B. & Young, M. Measurement and modeling of depth cue combination: In defense of weak fusion. Vision Res. 35, 389–412 (1995).

    Article  CAS  PubMed  Google Scholar 

  33. Knill, D.C. & Saunders, J.A. Do humans optimally integrate stereo and texture information for judgments of surface slant? Vision Res. 43, 2539–2558 (2003).

    Article  PubMed  Google Scholar 

  34. Hillis, J.M., Watt, S.J., Landy, M.S. & Banks, M.S. Slant from texture and disparity cues: optimal cue combination. J. Vis. 4, 967–992 (2004).

    PubMed  Google Scholar 

  35. Burt, P. & Julesz, B. A disparity gradient limit for binocular fusion. Science 208, 615–617 (1980).

    Article  CAS  PubMed  Google Scholar 

  36. Banks, M.S., Gepshtein, S. & Landy, M.S. Why is spatial stereoresolution so low? J. Neurosci. 24, 2077–2089 (2004).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  37. Mamassian, P. Prehension of objects oriented in three-dimensional space. Exp. Brain Res. 114, 235–245 (1997).

    Article  CAS  PubMed  Google Scholar 

  38. Thouless, R.H. Phenomenal regression to the “real” object. Br. J. Psychol. 21, 339–359 (1931).

    Google Scholar 

  39. Epstein, W.P. & Park, J.N. Shape constancy: Functional relationships and theoretical formulations. Psychol. Bull. 60, 265–288 (1963).

    Article  Google Scholar 

  40. Regan, D. & Hamstra, S.J. Shape discrimination and the judgment of perfect symmetry: dissociation of shape from size. Vision Res. 32, 1845–1864 (1992).

    Article  CAS  PubMed  Google Scholar 

  41. Evans, F. & Narayanan, A. Immersive data visualization with the VisionDome. SPIE Visual Data Exploration and Analysis VII (SPIE, San Jose, California, USA, 2000).

    Google Scholar 

  42. Topper, D. On anamorphosis: Setting some things straight. Leonardo 33, 115–124 (2000).

    Article  Google Scholar 

  43. Hillis, J.M. & Banks, M.S. Are corresponding points fixed? Vision Res. 41, 2457–2473 (2001).

    Article  CAS  PubMed  Google Scholar 

  44. Backus, B.T., Banks, M.S., van Ee, R. & Crowell, J.A. Horizontal and vertical disparity, eye position, and stereoscopic slant perception. Vision Res. 39, 1143–1170 (1999).

    Article  CAS  PubMed  Google Scholar 

  45. Wichmann, F.A. & Hill, N.J. The psychometric function: I. Fitting, sampling and goodness-of-fit. Perception and psychophysics. Percept. Psychophys. 63, 1293–1313 (2001).

    Article  CAS  PubMed  Google Scholar 

  46. Wichmann, F.A. & Hill, N.J. The psychometric function: II. Bootstrap-based confidence intervals and sampling. Percept. Psychophys. 63, 1314–1329 (2001).

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

We thank M. Landy, J. Hillis, A. Welchman, R. Fleming, S. Gepshtein and M. Ernst for comments on an earlier draft, and R. Bartholomew for technical assistance. This work was supported by NIH research grant R01-EY014194 (M.S.B.), NIH post-doctoral fellowship F32 EY14514 (D.V.) and by DOE Computational Sciences Graduate Fellowship DE-FG02-97ER25308 (A.R.G.).

Author information

Authors and Affiliations

  1. Vision Science Program, School of Optometry, University of California, Berkeley, 94720, California, USA

    Dhanraj Vishwanath, Ahna R Girshick & Martin S Banks

  2. Department of Psychology & Helen Wills Neuroscience Center, University of California, Berkeley, 94720, California, USA

    Martin S Banks

Authors
  1. Dhanraj Vishwanath
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  2. Ahna R Girshick
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Corresponding author

Correspondence to Dhanraj Vishwanath.

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Supplementary information

Supplementary Fig. 1

Predictions and results for the first experiment for the ovoid task for two additional observers. (PDF 44 kb)

Supplementary Fig. 2

Predictions and results for a control experiment that examined the ability to judge the depicted shape of a slanted plane. (PDF 49 kb)

Supplementary Fig. 3

Predictions and results for the first experiment for the slanted-plane task for observers and conditions not shown in Fig. 3. (PDF 90 kb)

Supplementary Fig. 4

Predictions and results for the second experiment for the ovoid task for two additional observers. (PDF 58 kb)

Supplementary Fig. 5

The predictions and results for the second experiment for observers and conditions not shown in Fig. 5. (PDF 134 kb)

Supplementary Fig. 6

Predictions and results for an experiment, in which we looked further for evidence of pictorial compensation by creating a condition in which neither the surface-compensation nor the local-slant mechanism would be triggered. (PDF 164 kb)

Supplementary Fig. 7

Predictions and results for the third experiment for two additional observers. (PDF 77 kb)

Supplementary Fig. 8

Image files for demonstrations. (PDF 119055 kb)

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Vishwanath, D., Girshick, A. & Banks, M. Why pictures look right when viewed from the wrong place. Nat Neurosci 8, 1401–1410 (2005). https://doi.org/10.1038/nn1553

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