Abstract

We show that the amplitude spectrum of a texture pattern, regardless of its phase spectrum, can be used to predict whether the pattern will convey the veridical three-dimensional (3-D) shape of the surface on which it lies. Patterns from the Brodatz collection of natural textures were overlaid on a flat surface that was then corrugated in depth and projected in perspective. Perceived ordinal shapes, reconstructed from a series of local relative depth judgments, showed that only about a third of the patterns conveyed veridical shape. The phase structure of each pattern was then randomized. Simulated concavities and convexities were presented for both the Brodatz and the phase-randomized patterns in a global shape identification task. The concordance between the shapes perceived from the Brodatz patterns and their phase-randomized versions was 80–88%, showing that the capacity for a pattern to correctly convey concavities and convexities is independent of phase information and that the amplitude spectrum contains all the information required to determine whether a pattern will convey veridical 3-D shape. A measure of the discrete oriented energy centered on the axis of maximum curvature was successful in identifying textures that convey veridical shape.

© 2001 Optical Society of America

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References

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  1. J. J. Gibson, “The perception of visual surfaces,” Am. J. Psychol. 63, 367–384 (1950).
    [CrossRef] [PubMed]
  2. A. Li, Q. Zaidi, “Perception of three-dimensional shape from texture is based on patterns of oriented energy,” Vision Res. 40, 217–242 (2000).
    [CrossRef] [PubMed]
  3. B. G. Cummings, E. B. Johnston, A. J. Parker, “Effects of different texture cues on curved surfaces viewed stereoscopically,” Vision Res. 33, 827–838 (1993).
    [CrossRef]
  4. J. E. Cutting, R. T. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psychol. 113, 196–216 (1984).
    [CrossRef]
  5. D. C. Knill, “Discrimination of planar surface slant from texture: human and ideal observers compared,” Vision Res. 38, 1683–1711 (1998b).
    [CrossRef]
  6. D. C. Knill, “Surface orientation from texture: ideal observers, generic observers and the information content of texture cues,” Vision Res. 38, 1655–1682 (1998a).
    [CrossRef]
  7. D. C. Knill, “Ideal observer perturbation analysis reveals human strategies for inferring surface orientation from texture,” Vision Res. 38, 2635–2656 (1998c).
    [CrossRef]
  8. J. T. Todd, R. A. Akerstrom, “Perception of three-dimensional form from patterns of optical texture,” J. Exp. Psychol. 113, 221–224 (1987).
  9. K. Sakai, L. H. Finkel, “Characterization of the spatial-frequency spectrum in the perception of shape from texture,” J. Opt. Soc. Am. A 12, 1208–1224 (1993).
    [CrossRef]
  10. A. Li, Q. Zaidi, “Information limitations in perception of shape from texture,” Vision Res. 41, 1519–1534 (2001).
    [CrossRef] [PubMed]
  11. K. A. Stevens, “The visual interpretation of surface contours,” Artif. Intel. 17, 47–73 (1981).
    [CrossRef]
  12. D. C. Knill, “Contour into texture: information content of surface contours and texture flow,” J. Opt. Soc. Am. A 18, 12–35 (2001).
    [CrossRef]
  13. P. Brodatz, Textures: A Photographic Album for Artists and Designers (Dover, New York, 1966).
  14. A. R. Rao, G. L. Lohse, “Towards a texture naming system: identifying relevant dimensions of texture,” Vision Res. 36, 1649–1669 (1996).
    [CrossRef] [PubMed]
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    [CrossRef]
  16. Q. Zaidi, A. Li, “Neural model of shape from texture: developable surfaces,” Invest. Ophthalmol. Visual Sci. 41, S219 (2000).
  17. V. Interrante, “Illustrating surface shape in volume data via principal direction-driven 3D line integral convolution,” presented at the SIGGRAPH conference, Los Angeles, California, August 3–, 1997.
  18. A. Li, Q. Zaidi, “Limitations on shape information provided by texture cues,” Vision Res. (to be published).

2001 (2)

A. Li, Q. Zaidi, “Information limitations in perception of shape from texture,” Vision Res. 41, 1519–1534 (2001).
[CrossRef] [PubMed]

D. C. Knill, “Contour into texture: information content of surface contours and texture flow,” J. Opt. Soc. Am. A 18, 12–35 (2001).
[CrossRef]

2000 (2)

Q. Zaidi, A. Li, “Neural model of shape from texture: developable surfaces,” Invest. Ophthalmol. Visual Sci. 41, S219 (2000).

A. Li, Q. Zaidi, “Perception of three-dimensional shape from texture is based on patterns of oriented energy,” Vision Res. 40, 217–242 (2000).
[CrossRef] [PubMed]

1996 (1)

A. R. Rao, G. L. Lohse, “Towards a texture naming system: identifying relevant dimensions of texture,” Vision Res. 36, 1649–1669 (1996).
[CrossRef] [PubMed]

1993 (2)

B. G. Cummings, E. B. Johnston, A. J. Parker, “Effects of different texture cues on curved surfaces viewed stereoscopically,” Vision Res. 33, 827–838 (1993).
[CrossRef]

K. Sakai, L. H. Finkel, “Characterization of the spatial-frequency spectrum in the perception of shape from texture,” J. Opt. Soc. Am. A 12, 1208–1224 (1993).
[CrossRef]

1987 (1)

J. T. Todd, R. A. Akerstrom, “Perception of three-dimensional form from patterns of optical texture,” J. Exp. Psychol. 113, 221–224 (1987).

1984 (1)

J. E. Cutting, R. T. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psychol. 113, 196–216 (1984).
[CrossRef]

1981 (1)

K. A. Stevens, “The visual interpretation of surface contours,” Artif. Intel. 17, 47–73 (1981).
[CrossRef]

1966 (1)

1950 (1)

J. J. Gibson, “The perception of visual surfaces,” Am. J. Psychol. 63, 367–384 (1950).
[CrossRef] [PubMed]

Akerstrom, R. A.

J. T. Todd, R. A. Akerstrom, “Perception of three-dimensional form from patterns of optical texture,” J. Exp. Psychol. 113, 221–224 (1987).

Brodatz, P.

P. Brodatz, Textures: A Photographic Album for Artists and Designers (Dover, New York, 1966).

Cummings, B. G.

B. G. Cummings, E. B. Johnston, A. J. Parker, “Effects of different texture cues on curved surfaces viewed stereoscopically,” Vision Res. 33, 827–838 (1993).
[CrossRef]

Cutting, J. E.

J. E. Cutting, R. T. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psychol. 113, 196–216 (1984).
[CrossRef]

Finkel, L. H.

Gibson, J. J.

J. J. Gibson, “The perception of visual surfaces,” Am. J. Psychol. 63, 367–384 (1950).
[CrossRef] [PubMed]

Interrante, V.

V. Interrante, “Illustrating surface shape in volume data via principal direction-driven 3D line integral convolution,” presented at the SIGGRAPH conference, Los Angeles, California, August 3–, 1997.

Johnston, E. B.

B. G. Cummings, E. B. Johnston, A. J. Parker, “Effects of different texture cues on curved surfaces viewed stereoscopically,” Vision Res. 33, 827–838 (1993).
[CrossRef]

Knill, D. C.

D. C. Knill, “Contour into texture: information content of surface contours and texture flow,” J. Opt. Soc. Am. A 18, 12–35 (2001).
[CrossRef]

D. C. Knill, “Ideal observer perturbation analysis reveals human strategies for inferring surface orientation from texture,” Vision Res. 38, 2635–2656 (1998c).
[CrossRef]

D. C. Knill, “Discrimination of planar surface slant from texture: human and ideal observers compared,” Vision Res. 38, 1683–1711 (1998b).
[CrossRef]

D. C. Knill, “Surface orientation from texture: ideal observers, generic observers and the information content of texture cues,” Vision Res. 38, 1655–1682 (1998a).
[CrossRef]

Li, A.

A. Li, Q. Zaidi, “Information limitations in perception of shape from texture,” Vision Res. 41, 1519–1534 (2001).
[CrossRef] [PubMed]

Q. Zaidi, A. Li, “Neural model of shape from texture: developable surfaces,” Invest. Ophthalmol. Visual Sci. 41, S219 (2000).

A. Li, Q. Zaidi, “Perception of three-dimensional shape from texture is based on patterns of oriented energy,” Vision Res. 40, 217–242 (2000).
[CrossRef] [PubMed]

A. Li, Q. Zaidi, “Limitations on shape information provided by texture cues,” Vision Res. (to be published).

Lohse, G. L.

A. R. Rao, G. L. Lohse, “Towards a texture naming system: identifying relevant dimensions of texture,” Vision Res. 36, 1649–1669 (1996).
[CrossRef] [PubMed]

Millard, R. T.

J. E. Cutting, R. T. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psychol. 113, 196–216 (1984).
[CrossRef]

Parker, A. J.

B. G. Cummings, E. B. Johnston, A. J. Parker, “Effects of different texture cues on curved surfaces viewed stereoscopically,” Vision Res. 33, 827–838 (1993).
[CrossRef]

Rao, A. R.

A. R. Rao, G. L. Lohse, “Towards a texture naming system: identifying relevant dimensions of texture,” Vision Res. 36, 1649–1669 (1996).
[CrossRef] [PubMed]

Robson, J. G.

Sakai, K.

Stevens, K. A.

K. A. Stevens, “The visual interpretation of surface contours,” Artif. Intel. 17, 47–73 (1981).
[CrossRef]

Todd, J. T.

J. T. Todd, R. A. Akerstrom, “Perception of three-dimensional form from patterns of optical texture,” J. Exp. Psychol. 113, 221–224 (1987).

Zaidi, Q.

A. Li, Q. Zaidi, “Information limitations in perception of shape from texture,” Vision Res. 41, 1519–1534 (2001).
[CrossRef] [PubMed]

Q. Zaidi, A. Li, “Neural model of shape from texture: developable surfaces,” Invest. Ophthalmol. Visual Sci. 41, S219 (2000).

A. Li, Q. Zaidi, “Perception of three-dimensional shape from texture is based on patterns of oriented energy,” Vision Res. 40, 217–242 (2000).
[CrossRef] [PubMed]

A. Li, Q. Zaidi, “Limitations on shape information provided by texture cues,” Vision Res. (to be published).

Am. J. Psychol. (1)

J. J. Gibson, “The perception of visual surfaces,” Am. J. Psychol. 63, 367–384 (1950).
[CrossRef] [PubMed]

Artif. Intel. (1)

K. A. Stevens, “The visual interpretation of surface contours,” Artif. Intel. 17, 47–73 (1981).
[CrossRef]

Invest. Ophthalmol. Visual Sci. (1)

Q. Zaidi, A. Li, “Neural model of shape from texture: developable surfaces,” Invest. Ophthalmol. Visual Sci. 41, S219 (2000).

J. Exp. Psychol. (2)

J. T. Todd, R. A. Akerstrom, “Perception of three-dimensional form from patterns of optical texture,” J. Exp. Psychol. 113, 221–224 (1987).

J. E. Cutting, R. T. Millard, “Three gradients and the perception of flat and curved surfaces,” J. Exp. Psychol. 113, 196–216 (1984).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (2)

Vision Res. (7)

A. R. Rao, G. L. Lohse, “Towards a texture naming system: identifying relevant dimensions of texture,” Vision Res. 36, 1649–1669 (1996).
[CrossRef] [PubMed]

D. C. Knill, “Discrimination of planar surface slant from texture: human and ideal observers compared,” Vision Res. 38, 1683–1711 (1998b).
[CrossRef]

D. C. Knill, “Surface orientation from texture: ideal observers, generic observers and the information content of texture cues,” Vision Res. 38, 1655–1682 (1998a).
[CrossRef]

D. C. Knill, “Ideal observer perturbation analysis reveals human strategies for inferring surface orientation from texture,” Vision Res. 38, 2635–2656 (1998c).
[CrossRef]

A. Li, Q. Zaidi, “Information limitations in perception of shape from texture,” Vision Res. 41, 1519–1534 (2001).
[CrossRef] [PubMed]

A. Li, Q. Zaidi, “Perception of three-dimensional shape from texture is based on patterns of oriented energy,” Vision Res. 40, 217–242 (2000).
[CrossRef] [PubMed]

B. G. Cummings, E. B. Johnston, A. J. Parker, “Effects of different texture cues on curved surfaces viewed stereoscopically,” Vision Res. 33, 827–838 (1993).
[CrossRef]

Other (3)

V. Interrante, “Illustrating surface shape in volume data via principal direction-driven 3D line integral convolution,” presented at the SIGGRAPH conference, Los Angeles, California, August 3–, 1997.

A. Li, Q. Zaidi, “Limitations on shape information provided by texture cues,” Vision Res. (to be published).

P. Brodatz, Textures: A Photographic Album for Artists and Designers (Dover, New York, 1966).

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Figures (10)

Fig. 1
Fig. 1

A, Left: Octotropic plaid pattern drawn on a surface corrugated in depth as a function of horizontal position and projected in perspective with the center of the image at eye height. The pattern consists of eight compound gratings, each oriented 22.5 deg from the next. Each compound grating is the sum of three frequencies at random phases. Right: The amplitude spectrum of the uncorrugated pattern. (0, 0) in spatial frequency lies at the center of the panel, and energy amplitude increases with increasing darkness. B, Pattern of white noise filtered with an elliptical filter oriented along the axis of maximum surface curvature. Patterns that do not convey veridical shape: C, Same complex plaid pattern as in A minus the horizontal compound grating. The pattern contains all the relevant texture gradients and frequency modulations consistent with the corrugated surface. D, Pattern of white noise filtered with an elliptical filter oriented along the axis of minimum curvature. E, Pattern of isotropic broadband noise.

Fig. 2
Fig. 2

Amplitude spectra, corrugated patterns, and data for 56 Brodatz patterns, arranged in groups of four panels per pattern. Amplitude spectra of uncorrugated patterns are shown in the first column, corrugated projected patterns in the next column to the right, and data for two observers in the next two columns to the right (AL on the left and JR on the right). The pattern number is indicated above the two data plots. The dashed vertical line in the plots indicates the central phase of the corrugated patterns shown to the left. The perceived shape is classified according to the best-fitting template (see Fig. 3), which appears in the upper right or upper left corner of each data panel. V, veridical; HR, half-rectified; FR, fully rectified; F, flat; O, other. Patterns that were perceived veridically by both observers are presented first, followed by those perceived veridically by only one observer, and finally by neither observer. (Continues on next six pages.)

Fig. 3
Fig. 3

Template shapes to which individual data were compared. Top, veridical; bottom, nonveridical: half-rectified, fully rectified, and flat.

Fig. 4
Fig. 4

Left: examples of Brodatz patterns corrugated and projected in concavity and convexity phase. From top to bottom, Brodatz pattern numbers are D003, D034, D052, D054, and D068. Right: phase-randomized versions of the patterns in the left column. Patterns have all been normalized to have the same mean luminance.

Fig. 5
Fig. 5

Number of correct responses out of 50 for each pattern plotted for the Brodatz patterns along the abscissa and for the phase-randomized patterns along the ordinate. Data are plotted by simulated curvature in the two columns and by observer in the two rows. Each panel contains 56 points, each corresponding to one of the Brodatz/phase-randomized patterns. The solid vertical and horizontal lines indicate the 35/50 correct response boundaries. Patterns for which observers perceived veridical shape in both the Brodatz and the phase-randomized conditions fall in the square at the upper right of each panel; those for which observers perceived nonveridical shapes in both conditions fall in the square at the lower left of each panel.

Fig. 6
Fig. 6

Discreteness index defined as the ratio of the energy within the critical 6-deg wedge of orientations of the amplitude spectrum (gray) and the surrounding 18-deg wedge (dashed lines).

Fig. 7
Fig. 7

Cumulative distributions for Cmean (top row) and Cmax (bottom row) based on the classifications from Experiment 1. Distributions for observer AL are plotted on the left, for JR on the right. Cmean and Cmax are in units of contrast threshold. For Cmean, the mean energy was computed at each spatial frequency within the slice. The resulting profile was filtered by the human CSF before summing. For Cmax, the maximum energy was computed at each spatial frequency within the slice, before filtering with the human CSF and summing. For patterns that conveyed veridical shape (solid curves) values were accumulated from left to right. For patterns that did not convey veridical shape (dashed curves) values were accumulated from right to left.

Fig. 8
Fig. 8

Cumulative distributions of Cmax and Cmean based on the classifications from Experiment 2. See Fig. 7 for details.

Fig. 9
Fig. 9

Cumulative distributions for Rmax and Rmean for Experiment 1. The maximum or the mean energy at each frequency was weighted by a discreteness index (the ratio of energy in the critical 6-deg wedge to the energy in the larger 18-deg wedge) before being filtered with the human CSF and summed.

Fig. 10
Fig. 10

Cumulative distributions of Rmax and Rmean based on the classifications from Experiment 2. See Fig. 9 for details.

Tables (3)

Tables Icon

Table 1 Number of Patterns Seen Veridically for Simulated Curvatures

Tables Icon

Table 2 Minimum Number of MisclassifiedPatterns

Tables Icon

Table 3 Numbers of Patterns in Each Material Category Conveying Veridical Shape

Equations (10)

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

z=A3D cos(2πf3Dx+ϕ)+d,
α=tan-1d sin ω-y cos ω sin θd cos θ cos ω,
σ=f[d+cos(ω+π/2)cos θ]{cos2 θ[cos2(ω+π/2)(d2+y2)+d2 sin2(ω+π/2)-2yd sin(ω+π/2)cos(ω+π/2)sin θ]}1/2.
μ(f)=mean(Ef, θcrit) * CSFf,
m(f)=max(Ef, θcrit) * CSFf.
Cmean=fμ(f),
Cmax=fm(f).
Df=θcritEf,θθsurEf,θ.
Rmean=fDfμ(f),
Rmax=fDf m(f).

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