Abstract

We investigate the ability of human observers to judge the direction of illumination from image texture. Photographs of 61 real surfaces were used, taken from the Columbia–Utrecht Reflectance and Texture (Curet) database (http://www.cs.columbia.edu/CAVE/curet). All samples were normally viewed but obliquely illuminated, the elevation of the source being 22.5°, 45.0°, or 67.5°. The illumination was with a collimated, parallel beam. Stimuli were presented in random orientation, and observers had to judge both the elevation and the azimuth of the source. Observers judged the azimuth within approximately 15°, except for the fact that they committed random (with approximately 50% probability) sign flips (180° flips). Connected with this finding is the fact that observers judged the illumination to be from above rather than below in the overwhelming majority of cases, despite the fact that each case occurred with equal probability. The elevation of the illumination can be judged to some extent but is not far above chance level. The data are in good agreement with a simple model that bases the estimate of illumination direction on the second-order statistics of local luminance gradients. This locates the locus of the probable mechanism very early in the visual stream.

© 2003 Optical Society of America

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References

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  1. J. D. Foley, A. van Dam, S. K. Feiner, J. F. Hughes, Computer Graphics, Principles and Practice (Addison-Wesley, Reading, Mass., 1990).
  2. J. Gårding, “Direct estimation of shape from texture,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1202–1208 (1993).
    [CrossRef]
  3. M. Oren, S. K. Nayar, “Visual appearance of matte surfaces,” Science 267, 1153–1156 (1995).
    [CrossRef] [PubMed]
  4. J. H. Lambert, Photometria Sive de Mensure de Gradibus Luminis, Colorum et Umbræ (Eberhard Klett, Augsburg, Germany, 1760).
  5. B. K. P. Horn, M. J. Brooks, Shape from Shading (MIT Press, Cambridge, Mass., 1989).
  6. J. J. Gibson, The Perception of the Visual World (Houghton Mifflin, Boston, 1950).
  7. R. Lu, “Ecological optics of materials,” Ph.D. dissertation (Utrecht University, Utrecht, The Netherlands, 2000).
  8. S. C. Pont, J. J. Koenderink, “Bidirectional texture contrast function,” in Proceedings of the European Conference on Computer Vision, Part IV, Vol. 2353 of Lecture Notes in Computer Science, A. Heyden, G. Sparr, M. Nielsen, P. Johansen, eds. (Springer-Verlag, Heidelberg, 2002), pp. 808–822.
  9. T. Leung, J. Malik, “Representing and recognizing the visual appearance of materials using three-dimensional textons,” Int. J. Comput. Vision 43, 29–44 (2001).
    [CrossRef]
  10. Columbia–Utrecht Reflectance and Texture (Curet) database, http://www.cs.columbia.edu/CAVE/curet .
  11. K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 151–157.
  12. K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 18, 1–34 (1999).
    [CrossRef]
  13. M. S. Longuet-Higgins, “The statistical analysis of a random moving surface,” Philos. Trans. R. Soc. London Ser. A 249, 321–364 (1957).
    [CrossRef]
  14. A. Pentland, “On the extraction of shape information from shading,” in Proceedings of the Seventh National Conference on Artificial Intelligence (American Association for Artificial Intelligence Press, Menlo Park, Calif., 1988), pp. 826–830.
  15. V. S. Ramachandran, “Perceiving shape from shading,” Sci. Am. 259(2), 76–83 (1988).
    [CrossRef] [PubMed]
  16. R. G. F. Erens, A. M. L. Kappers, J. J. Koenderink, “Estimating local shape from shading in the presence of global shading,” Percept. Psychophys. 54, 334–342 (1993).
    [CrossRef] [PubMed]
  17. A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).
  18. R. Hess, “Developmental sensory impairment: amblyopia or tarachopia?” Hum. Neurobiol. 1, 1–29 (1982).
  19. A. Gershun, “The light field,” translated by P. Moon, G. Timoshenko, J. Math. Phys. (Cambridge, Mass.)18, 51–151 (1939).
  20. M. D. Spivak, A Comprehensive Introduction to Differential Geometry, 3rd ed. (Publish or Perish, Houston, Tex., 1999), five volumes.
  21. M. V. Berry, J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
    [CrossRef]
  22. J. J. Koenderink, A. J. van Doorn, “Generic neighborhood operators,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 597–605 (1992).
    [CrossRef]

2001 (1)

T. Leung, J. Malik, “Representing and recognizing the visual appearance of materials using three-dimensional textons,” Int. J. Comput. Vision 43, 29–44 (2001).
[CrossRef]

1999 (1)

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 18, 1–34 (1999).
[CrossRef]

1995 (1)

M. Oren, S. K. Nayar, “Visual appearance of matte surfaces,” Science 267, 1153–1156 (1995).
[CrossRef] [PubMed]

1993 (2)

J. Gårding, “Direct estimation of shape from texture,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1202–1208 (1993).
[CrossRef]

R. G. F. Erens, A. M. L. Kappers, J. J. Koenderink, “Estimating local shape from shading in the presence of global shading,” Percept. Psychophys. 54, 334–342 (1993).
[CrossRef] [PubMed]

1992 (1)

J. J. Koenderink, A. J. van Doorn, “Generic neighborhood operators,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 597–605 (1992).
[CrossRef]

1988 (1)

V. S. Ramachandran, “Perceiving shape from shading,” Sci. Am. 259(2), 76–83 (1988).
[CrossRef] [PubMed]

1982 (1)

R. Hess, “Developmental sensory impairment: amblyopia or tarachopia?” Hum. Neurobiol. 1, 1–29 (1982).

1977 (1)

M. V. Berry, J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

1957 (1)

M. S. Longuet-Higgins, “The statistical analysis of a random moving surface,” Philos. Trans. R. Soc. London Ser. A 249, 321–364 (1957).
[CrossRef]

Berry, M. V.

M. V. Berry, J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

Brooks, M. J.

B. K. P. Horn, M. J. Brooks, Shape from Shading (MIT Press, Cambridge, Mass., 1989).

Dana, K. J.

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 18, 1–34 (1999).
[CrossRef]

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 151–157.

Erens, R. G. F.

R. G. F. Erens, A. M. L. Kappers, J. J. Koenderink, “Estimating local shape from shading in the presence of global shading,” Percept. Psychophys. 54, 334–342 (1993).
[CrossRef] [PubMed]

Feiner, S. K.

J. D. Foley, A. van Dam, S. K. Feiner, J. F. Hughes, Computer Graphics, Principles and Practice (Addison-Wesley, Reading, Mass., 1990).

Foley, J. D.

J. D. Foley, A. van Dam, S. K. Feiner, J. F. Hughes, Computer Graphics, Principles and Practice (Addison-Wesley, Reading, Mass., 1990).

Gårding, J.

J. Gårding, “Direct estimation of shape from texture,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1202–1208 (1993).
[CrossRef]

Gershun, A.

A. Gershun, “The light field,” translated by P. Moon, G. Timoshenko, J. Math. Phys. (Cambridge, Mass.)18, 51–151 (1939).

Gibson, J. J.

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

Hannay, J. H.

M. V. Berry, J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

Hess, R.

R. Hess, “Developmental sensory impairment: amblyopia or tarachopia?” Hum. Neurobiol. 1, 1–29 (1982).

Horn, B. K. P.

B. K. P. Horn, M. J. Brooks, Shape from Shading (MIT Press, Cambridge, Mass., 1989).

Hughes, J. F.

J. D. Foley, A. van Dam, S. K. Feiner, J. F. Hughes, Computer Graphics, Principles and Practice (Addison-Wesley, Reading, Mass., 1990).

Kappers, A. M. L.

R. G. F. Erens, A. M. L. Kappers, J. J. Koenderink, “Estimating local shape from shading in the presence of global shading,” Percept. Psychophys. 54, 334–342 (1993).
[CrossRef] [PubMed]

Koenderink, J. J.

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 18, 1–34 (1999).
[CrossRef]

R. G. F. Erens, A. M. L. Kappers, J. J. Koenderink, “Estimating local shape from shading in the presence of global shading,” Percept. Psychophys. 54, 334–342 (1993).
[CrossRef] [PubMed]

J. J. Koenderink, A. J. van Doorn, “Generic neighborhood operators,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 597–605 (1992).
[CrossRef]

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 151–157.

S. C. Pont, J. J. Koenderink, “Bidirectional texture contrast function,” in Proceedings of the European Conference on Computer Vision, Part IV, Vol. 2353 of Lecture Notes in Computer Science, A. Heyden, G. Sparr, M. Nielsen, P. Johansen, eds. (Springer-Verlag, Heidelberg, 2002), pp. 808–822.

Lambert, J. H.

J. H. Lambert, Photometria Sive de Mensure de Gradibus Luminis, Colorum et Umbræ (Eberhard Klett, Augsburg, Germany, 1760).

Leung, T.

T. Leung, J. Malik, “Representing and recognizing the visual appearance of materials using three-dimensional textons,” Int. J. Comput. Vision 43, 29–44 (2001).
[CrossRef]

Longuet-Higgins, M. S.

M. S. Longuet-Higgins, “The statistical analysis of a random moving surface,” Philos. Trans. R. Soc. London Ser. A 249, 321–364 (1957).
[CrossRef]

Lu, R.

R. Lu, “Ecological optics of materials,” Ph.D. dissertation (Utrecht University, Utrecht, The Netherlands, 2000).

Malik, J.

T. Leung, J. Malik, “Representing and recognizing the visual appearance of materials using three-dimensional textons,” Int. J. Comput. Vision 43, 29–44 (2001).
[CrossRef]

Nayar, S. K.

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 18, 1–34 (1999).
[CrossRef]

M. Oren, S. K. Nayar, “Visual appearance of matte surfaces,” Science 267, 1153–1156 (1995).
[CrossRef] [PubMed]

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 151–157.

Oren, M.

M. Oren, S. K. Nayar, “Visual appearance of matte surfaces,” Science 267, 1153–1156 (1995).
[CrossRef] [PubMed]

Papoulis, A.

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).

Pentland, A.

A. Pentland, “On the extraction of shape information from shading,” in Proceedings of the Seventh National Conference on Artificial Intelligence (American Association for Artificial Intelligence Press, Menlo Park, Calif., 1988), pp. 826–830.

Pont, S. C.

S. C. Pont, J. J. Koenderink, “Bidirectional texture contrast function,” in Proceedings of the European Conference on Computer Vision, Part IV, Vol. 2353 of Lecture Notes in Computer Science, A. Heyden, G. Sparr, M. Nielsen, P. Johansen, eds. (Springer-Verlag, Heidelberg, 2002), pp. 808–822.

Ramachandran, V. S.

V. S. Ramachandran, “Perceiving shape from shading,” Sci. Am. 259(2), 76–83 (1988).
[CrossRef] [PubMed]

Spivak, M. D.

M. D. Spivak, A Comprehensive Introduction to Differential Geometry, 3rd ed. (Publish or Perish, Houston, Tex., 1999), five volumes.

van Dam, A.

J. D. Foley, A. van Dam, S. K. Feiner, J. F. Hughes, Computer Graphics, Principles and Practice (Addison-Wesley, Reading, Mass., 1990).

van Doorn, A. J.

J. J. Koenderink, A. J. van Doorn, “Generic neighborhood operators,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 597–605 (1992).
[CrossRef]

van Ginneken, B.

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 18, 1–34 (1999).
[CrossRef]

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 151–157.

ACM (Assoc. Comput. Mach.) Trans. Graphics (1)

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” ACM (Assoc. Comput. Mach.) Trans. Graphics 18, 1–34 (1999).
[CrossRef]

Hum. Neurobiol. (1)

R. Hess, “Developmental sensory impairment: amblyopia or tarachopia?” Hum. Neurobiol. 1, 1–29 (1982).

IEEE Trans. Pattern Anal. Mach. Intell. (2)

J. J. Koenderink, A. J. van Doorn, “Generic neighborhood operators,” IEEE Trans. Pattern Anal. Mach. Intell. 14, 597–605 (1992).
[CrossRef]

J. Gårding, “Direct estimation of shape from texture,” IEEE Trans. Pattern Anal. Mach. Intell. 15, 1202–1208 (1993).
[CrossRef]

Int. J. Comput. Vision (1)

T. Leung, J. Malik, “Representing and recognizing the visual appearance of materials using three-dimensional textons,” Int. J. Comput. Vision 43, 29–44 (2001).
[CrossRef]

J. Phys. A (1)

M. V. Berry, J. H. Hannay, “Umbilic points on Gaussian random surfaces,” J. Phys. A 10, 1809–1821 (1977).
[CrossRef]

Percept. Psychophys. (1)

R. G. F. Erens, A. M. L. Kappers, J. J. Koenderink, “Estimating local shape from shading in the presence of global shading,” Percept. Psychophys. 54, 334–342 (1993).
[CrossRef] [PubMed]

Philos. Trans. R. Soc. London Ser. A (1)

M. S. Longuet-Higgins, “The statistical analysis of a random moving surface,” Philos. Trans. R. Soc. London Ser. A 249, 321–364 (1957).
[CrossRef]

Sci. Am. (1)

V. S. Ramachandran, “Perceiving shape from shading,” Sci. Am. 259(2), 76–83 (1988).
[CrossRef] [PubMed]

Science (1)

M. Oren, S. K. Nayar, “Visual appearance of matte surfaces,” Science 267, 1153–1156 (1995).
[CrossRef] [PubMed]

Other (12)

J. H. Lambert, Photometria Sive de Mensure de Gradibus Luminis, Colorum et Umbræ (Eberhard Klett, Augsburg, Germany, 1760).

B. K. P. Horn, M. J. Brooks, Shape from Shading (MIT Press, Cambridge, Mass., 1989).

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

R. Lu, “Ecological optics of materials,” Ph.D. dissertation (Utrecht University, Utrecht, The Netherlands, 2000).

S. C. Pont, J. J. Koenderink, “Bidirectional texture contrast function,” in Proceedings of the European Conference on Computer Vision, Part IV, Vol. 2353 of Lecture Notes in Computer Science, A. Heyden, G. Sparr, M. Nielsen, P. Johansen, eds. (Springer-Verlag, Heidelberg, 2002), pp. 808–822.

A. Pentland, “On the extraction of shape information from shading,” in Proceedings of the Seventh National Conference on Artificial Intelligence (American Association for Artificial Intelligence Press, Menlo Park, Calif., 1988), pp. 826–830.

Columbia–Utrecht Reflectance and Texture (Curet) database, http://www.cs.columbia.edu/CAVE/curet .

K. J. Dana, B. van Ginneken, S. K. Nayar, J. J. Koenderink, “Reflectance and texture of real-world surfaces,” in Proceedings of IEEE Conference on Computer Vision and Pattern Recognition (Institute of Electrical and Electronics Engineers, New York, 1997), pp. 151–157.

J. D. Foley, A. van Dam, S. K. Feiner, J. F. Hughes, Computer Graphics, Principles and Practice (Addison-Wesley, Reading, Mass., 1990).

A. Papoulis, The Fourier Integral and Its Applications (McGraw-Hill, New York, 1962).

A. Gershun, “The light field,” translated by P. Moon, G. Timoshenko, J. Math. Phys. (Cambridge, Mass.)18, 51–151 (1939).

M. D. Spivak, A Comprehensive Introduction to Differential Geometry, 3rd ed. (Publish or Perish, Houston, Tex., 1999), five volumes.

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Figures (15)

Fig. 1
Fig. 1

Hemispherical depression and hemispherical protrusion, both on a globally planar surface. The surfaces (both plane and modulation) are nearly Lambertian white surfaces. Illumination from an oblique direction and from the normal direction (“head on”) are shown. All views are from the normal direction (the plane frontoparallel). Note that in either case the elevation is easily judged from the cast shadow.

Fig. 2
Fig. 2

In the left column is shown a pair of dipole modulations (first-order derivatives of Gaussians). The same dipoles are repeated in the other columns, though some context has been added.

Fig. 3
Fig. 3

Some of the stimuli used in this experiment. These are all surfaces taken from the daily life environment. The elevation of the source is 45° for all these examples.

Fig. 4
Fig. 4

Stimulus (left) and response panel (right) on the Macintosh desktop. Note that the stimulus appears in a circular cutout on a black background. The observer has (mouse) control over the direction of the virtual light source that determines the rendering in the response panel. The pattern in the response panel serves to indicate both the elevation and the azimuth of the illumination in an intuitive fashion.

Fig. 5
Fig. 5

Raw results for observers I–III. The disks represent a half-space of directions. The normal direction is at the center, and grazing angles are at the perimeter of the disk. Thus distance from the center specifies elevation of the source, and angle specifies azimuth. The small open circle in each scatterplot represents the fiducial direction; all responses from a single session are given in these scatterplots. The three subfigures for each observer are for the three elevations of the incident beam.

Fig. 6
Fig. 6

Histograms of the azimuth judgments for observers I–III.

Fig. 7
Fig. 7

Histograms of the elevation judgments for observers I–III for the fiducial values 22.5°, 45.0°, and 67.5°.

Fig. 8
Fig. 8

Histograms of all azimuth responses for observers I–III. Since the data were fully scrambled, a veridical response would yield a uniform distribution. Instead, there is a very strong preference for “illumination from above” for each observer.

Fig. 9
Fig. 9

Scatterplots of data from observers I and II: (a) azimuth, (b) elevation.

Fig. 10
Fig. 10

“Crumpled paper” sample from the Curet database (top row: all in normal view, illuminated from the right, three different elevations of the source) with power spectra (bottom row). Note that the power spectra are bimodal, the axis being determined by the direction of illumination.

Fig. 11
Fig. 11

A Gaussian protrusion (top left) and indentation (bottom left) in a globally planar surface give rise to “dipole” illuminance perturbations of the globally uniform illuminance of the plane. The examples (center column) assume a beam incident from the right. The dipoles of the hill (center top) and the dimple (center bottom) are of opposite polarity. In the right column are shown the autocorrelation function of these illuminance perturbations (top right) and their spatial power spectrum (bottom right). Both the autocorrelation function and the power spectrum are second-order statistics and thus insensitive to the dipole polarity (same for the hill and the dimple).

Fig. 12
Fig. 12

Four examples from the Curet database (from left to right: “terry cloth,” “orange peel,” “pebbles,” and “crumpled paper”) at various heights of illumination (top to bottom: elevations 67.5°, 45.0°, and 22.5°). Note the changes in luminance and contrast.

Fig. 13
Fig. 13

Scatterplot of the rms contrast against the average luminance for all stimuli used in the experiments. At the right the histogram of rms contrast values and on top the histogram of average luminance values for all stimuli are indicated. There is a predominance of low-contrast stimuli and of darkish stimuli. However, the distribution is evidently correlated in that especially light stimuli with high contrast are totally lacking.

Fig. 14
Fig. 14

Histograms of the average luminance levels for the three elevations of the incident beam.

Fig. 15
Fig. 15

On the left are a number of “edge detectors,” and on the right are a number of “line detectors.” The terms are unfortunate; these are first- and second-order derivatives, respectively, at some particular scale (given by their size). Such units can conceivably exist on many scales, in all directions, and in any position in the visual field. The primary visual cortex appears to represent a fair sampling. The statistics derived here apply immediately to ensembles of such receptive fields.

Equations (11)

Equations on this page are rendered with MathJax. Learn more.

flipped/flipped=30flipped/correct=17correct/flipped=16correct/correct=37.
p+qhxpyqr+shxrys=p+r+q+shxp+ryq+s ρ(0)=(-1)(1/2)(p+r+q+s)mp+r,q+s;
ρ(r)=h(r0)h(r0+r)=dkexp i(kr)E(k).
mu,v=dkkxukyvE(k),
mu,v=Mu+v02πcosu θ sinv θ dθ,
Mp=02πkdk[kpE(k)].
hxx2hxxhxyhxxhyyhxyhxxhxy2hxyhyyhyyhxxhyyhxyhyy2=M48310130001,
hxxx2hxxxhxxyhxxxhxyyhxxxhyyyhxxyhxxxhxxy2hxxyhxyyhxxyhyyyhxyyhxxxhxyyhxxyhxyy2hxyyhyyyhyyyhxxxhyyyhxxyhyyyhxyyhyyy2
=M6165010010110100105.
I(r)=I0{-hx, -hy, 1}(1+hx2+hy2)1/2 {cos θ cos ϕ, cos θ sin ϕ, sin θ}.
S=2+cos 2ϕsin 2ϕsin 2ϕ2-cos 2ϕ.

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