Abstract

A detailed investigation has been made of the unusual characteristics of the angular distribution of surface scattering from velvet in the visual region. We present a novel method in which samples of velvet fabric are wrapped around a right-circular cylinder so that reemitted radiance can be measured by a digital CCD camera. This setup makes it relatively simple to acquire a large set of bidirectional reflection distribution function (BRDF) samples. The study reveals that, apart from the grazing specular lobe and an anisotropic backscattering peak near 50°, the overall BRDF’s are rather uniform across the whole angular span of observation. Attempts are made to relate these scattering characteristics to the physical and the geometrical structure of velvet.

© 1998 Optical Society of America

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References

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  1. S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
    [CrossRef]
  2. J. H. Lambert, Photometria Sive de Mensura et Gradibus Luminus, Colorum et Umbrae (Eberhard Kleet, Augsburg, 1760.
  3. K. E. Torrance, E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
    [CrossRef]
  4. R. S. Hunter, The Measurement of Appearance (Wiley, New York, 1975).
  5. D. B. Judd, G. Wyszecki, Color in Business, Science, and Industry, 3rd ed. (Wiley, New York, 1975).
  6. W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Material (Academic, New York, 1979).
  7. S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
    [CrossRef]
  8. S. K. Nayar, M. Oren, “Visual appearance of matte surfaces,” Science 267, 1153–1156 (1995).
    [CrossRef] [PubMed]
  9. M. Oren, S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Computer Vision 14, 227–251 (1995).
    [CrossRef]
  10. K. J. Dana, S. K. Nayar, B. van Ginneken, J. J. Koenderink, “Reflectance and texture of real-world surfaces: summary report,” Tech. Rep. CUCS-046-96 (Columbia University, New York, 1996).
  11. H. Holbein the Younger, Sir Thomas More, panel, 749 mm × 603 mm, 1528.
  12. A. Dürer, Madonna with the Monkey, engraving, 191 mm × 124 mm, 1498.
  13. J. J. Koenderink, A. J. van Doorn, M. Stavridi, “Bidirectional reflection distribution function expressed in terms of surface scattering modes,” in European Conference on Computer Vision, B. Buxton, R. Cipolla, eds. (Springer-Verlag, Berlin, 1996), pp. 28–39.
  14. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (1977).
  15. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989).

1995 (2)

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

M. Oren, S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Computer Vision 14, 227–251 (1995).
[CrossRef]

1991 (1)

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

1985 (1)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

1977 (1)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (1977).

1967 (1)

K. E. Torrance, E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
[CrossRef]

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989).

Dana, K. J.

K. J. Dana, S. K. Nayar, B. van Ginneken, J. J. Koenderink, “Reflectance and texture of real-world surfaces: summary report,” Tech. Rep. CUCS-046-96 (Columbia University, New York, 1996).

Dürer, A.

A. Dürer, Madonna with the Monkey, engraving, 191 mm × 124 mm, 1498.

Egan, W. G.

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Material (Academic, New York, 1979).

Hilgeman, T. W.

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Material (Academic, New York, 1979).

Holbein the Younger, H.

H. Holbein the Younger, Sir Thomas More, panel, 749 mm × 603 mm, 1528.

Hsia, J. J.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (1977).

Hunter, R. S.

R. S. Hunter, The Measurement of Appearance (Wiley, New York, 1975).

Ikeuchi, K.

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

Judd, D. B.

D. B. Judd, G. Wyszecki, Color in Business, Science, and Industry, 3rd ed. (Wiley, New York, 1975).

Kanade, T.

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

Koenderink, J. J.

J. J. Koenderink, A. J. van Doorn, M. Stavridi, “Bidirectional reflection distribution function expressed in terms of surface scattering modes,” in European Conference on Computer Vision, B. Buxton, R. Cipolla, eds. (Springer-Verlag, Berlin, 1996), pp. 28–39.

K. J. Dana, S. K. Nayar, B. van Ginneken, J. J. Koenderink, “Reflectance and texture of real-world surfaces: summary report,” Tech. Rep. CUCS-046-96 (Columbia University, New York, 1996).

Lambert, J. H.

J. H. Lambert, Photometria Sive de Mensura et Gradibus Luminus, Colorum et Umbrae (Eberhard Kleet, Augsburg, 1760.

Nayar, S. K.

M. Oren, S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Computer Vision 14, 227–251 (1995).
[CrossRef]

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

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

K. J. Dana, S. K. Nayar, B. van Ginneken, J. J. Koenderink, “Reflectance and texture of real-world surfaces: summary report,” Tech. Rep. CUCS-046-96 (Columbia University, New York, 1996).

Nicodemus, F. E.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (1977).

Oren, M.

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

M. Oren, S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Computer Vision 14, 227–251 (1995).
[CrossRef]

Richmond, J. C.

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (1977).

Shafer, S. A.

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

Sparrow, E. M.

K. E. Torrance, E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
[CrossRef]

Stavridi, M.

J. J. Koenderink, A. J. van Doorn, M. Stavridi, “Bidirectional reflection distribution function expressed in terms of surface scattering modes,” in European Conference on Computer Vision, B. Buxton, R. Cipolla, eds. (Springer-Verlag, Berlin, 1996), pp. 28–39.

Torrance, K. E.

K. E. Torrance, E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
[CrossRef]

van Doorn, A. J.

J. J. Koenderink, A. J. van Doorn, M. Stavridi, “Bidirectional reflection distribution function expressed in terms of surface scattering modes,” in European Conference on Computer Vision, B. Buxton, R. Cipolla, eds. (Springer-Verlag, Berlin, 1996), pp. 28–39.

van Ginneken, B.

K. J. Dana, S. K. Nayar, B. van Ginneken, J. J. Koenderink, “Reflectance and texture of real-world surfaces: summary report,” Tech. Rep. CUCS-046-96 (Columbia University, New York, 1996).

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989).

Wyszecki, G.

D. B. Judd, G. Wyszecki, Color in Business, Science, and Industry, 3rd ed. (Wiley, New York, 1975).

Color Res. Appl. (1)

S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
[CrossRef]

IEEE Trans. Pattern Anal. Mach. Intell. (1)

S. K. Nayar, K. Ikeuchi, T. Kanade, “Surface reflection: physical and geometrical perspectives,” IEEE Trans. Pattern Anal. Mach. Intell. 13, 611–634 (1991).
[CrossRef]

Int. J. Computer Vision (1)

M. Oren, S. K. Nayar, “Generalization of the Lambertian model and implications for machine vision,” Int. J. Computer Vision 14, 227–251 (1995).
[CrossRef]

J. Opt. Soc. Am. (1)

K. E. Torrance, E. M. Sparrow, “Theory for off-specular reflection from roughened surfaces,” J. Opt. Soc. Am. 57, 1105–1114 (1967).
[CrossRef]

Natl. Bur. Stand. (U.S.) Monogr. (1)

F. E. Nicodemus, J. C. Richmond, J. J. Hsia, “Geometrical considerations and nomenclature for reflectance,” Natl. Bur. Stand. (U.S.) Monogr. 160 (1977).

Science (1)

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

Other (9)

J. H. Lambert, Photometria Sive de Mensura et Gradibus Luminus, Colorum et Umbrae (Eberhard Kleet, Augsburg, 1760.

R. S. Hunter, The Measurement of Appearance (Wiley, New York, 1975).

D. B. Judd, G. Wyszecki, Color in Business, Science, and Industry, 3rd ed. (Wiley, New York, 1975).

W. G. Egan, T. W. Hilgeman, Optical Properties of Inhomogeneous Material (Academic, New York, 1979).

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1989).

K. J. Dana, S. K. Nayar, B. van Ginneken, J. J. Koenderink, “Reflectance and texture of real-world surfaces: summary report,” Tech. Rep. CUCS-046-96 (Columbia University, New York, 1996).

H. Holbein the Younger, Sir Thomas More, panel, 749 mm × 603 mm, 1528.

A. Dürer, Madonna with the Monkey, engraving, 191 mm × 124 mm, 1498.

J. J. Koenderink, A. J. van Doorn, M. Stavridi, “Bidirectional reflection distribution function expressed in terms of surface scattering modes,” in European Conference on Computer Vision, B. Buxton, R. Cipolla, eds. (Springer-Verlag, Berlin, 1996), pp. 28–39.

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Figures (13)

Fig. 1
Fig. 1

Left, detail of Holbein’s portrait, Sir Thomas More. The glossy brightness along the edges of semicircular and thin folds of the subject’s sleeves implies a velvet garment. Right, detail of Dürer’s engraving, Madonna with the Monkey. The left arm of the Madonna is countershaded from the sleeve to suggest rich velvet.

Fig. 2
Fig. 2

Sketch of apparatus used to measure radiance of cylindrical velvet surface (top view). The velvet samples are wrapped around a cylinder and irradiated by a wide, uniform, and parallel beam incident from specified angles aimed at the center of the cylinder, and the scattered light is detected by a digital camera located at a preselected angle. Proportions are not drawn to scale.

Fig. 3
Fig. 3

Specifications of two polar coordinate systems. The origin of one coordinate system coincides with the center of the cylinder. The parameter γ denotes the angle of the point of interest on the cylindrical surface, measured clockwise from 0°. The camera detects the scattered beam at a fixed angle of 90°. The parameter θ specifies the angle between scattered and incident beams. The other polar coordinate system is a local one for every point of interest on the cylindrical surface. The specification is framed in rectangles. The angle of incidence θ i and the viewing angle θ r are measured from 0°, the local surface normal. The angles to the left of the normal are marked as negative; the ones to the right, as positive. The relation between the two coordinate systems is θ i = θ + 90° - γ and θ r = 90° - γ.

Fig. 4
Fig. 4

Planar illustration of slanting fibers on four velvet strips. (a) Three-dimensional view of the orientation of four strips on the velvet fabric. The fabric is laid on the XY plane of a three-dimensional coordinate system; strip 1 lies along the Y axis, strip 2 lies 45° counterclockwise from strip 1, strip 3 lies along the X axis, and strip 4 lies 45° counterclockwise from strip 3. (b) The velvet fabric is woven in rows of fiber bundles, which are illustrated by short-dashed strings on solid lines. The bundles are slanted at a common angle, 40°, from the Z axis clockwise toward the -X axis on the XZ plane. (c) Top view of the orientation of four strips on the velvet fabric; dashed lines, rows of velvet fiber bundles. The projection of slant angle onto this top-view plane is indicated by an upward-pointing arrow. Boldface arrows point to the sides of strips that are viewed sideways when the line of sight coincides with the fabric surface. (d) Side view of slanting fibers on four strips. The fibers in strips 2–4 are slanted to the right, strip 3 having the largest slant.

Fig. 5
Fig. 5

Image of four velvet strips wrapped around a cylinder. Strips are placed in reverse order from top to bottom, starting with strip 4. The angle between irradiating and scattering beams is 65°. The left side of the image shows a sharp boundary between the illuminated velvet and the dark background. The right shows a gradual decline in reflected intensity from illuminated velvet to complete shadow. The gradual decline is caused mainly by shadowing and occlusion between adjacent woven fiber rows.

Fig. 6
Fig. 6

Measured BRDF. For each of four strips, BRDF is given as a function of θ r , and angle θ i as a curve parameter, in the order of increasing values from -80° to 70°.

Fig. 7
Fig. 7

Planar illustration of backscattering along velvet fibers. Dashed lines, the slanting fibers on velvet fabric. The irradiating light falls along the same inclination of velvet fiber, depicted by a thick downward-pointing arrow. The light scattered along the paths of several exit angles is drawn as upward-pointing arrows; the thickness of the lines is proportional to their scattered intensities. When the scattered light exits along the same path, it has had little interaction with fibers. Consequently its radiance is barely absorbed, and it appears to have the highest scattered intensity.

Fig. 8
Fig. 8

Two color radiance ratios plotted against viewing angles θ r to show the changes in the spectral composition in the scattered light, with the angles of incidence θ i , from -80° to -50°, as the curve parameters. One ratio is the value of the red radiance to that of the blue; the other is the value of the red radiance to that of the green. Note that in the solid curves, where θ i = -80°, the radiance at the specular direction, θ r = 80°, has a red-to-blue ratio of 1.91 and a red-to-green ratio of 1.04. Apparently the scattered light retains the numerical relation among colors of the irradiance, which has an RGB ratio of 2:2:1.

Fig. 9
Fig. 9

Sketch of apparatus used to detect scattering from velvet fiber tips. A piece of red velvet is folded between a white-light source and a microscope objective. A green laser light is incident upon the fiber tips. The scattered radiance is detected by the CCD camera. Proportions are not drawn to scale.

Fig. 10
Fig. 10

Microscopic image of green laser light scattered from the fiber tips of red velvet. The image is captured under a green color filter, so what appears bright is very green in a color picture. The fibers all point straight up; the interface between fiber tips and air is readily visible. The light scattered from the tips is seen as shiny dots, some rather sharp and some smeared.

Fig. 11
Fig. 11

Top, scatter plot of measured and predicted BRDF values: 4224 measurement values plotted as a function of the corresponding estimated value; the straight line represents a perfect fit. Bottom, plot of normalized residual errors, which we normalized by dividing by the maximum value of measured BRDF for the velvet sample; these errors are displayed in order of increasing viewing angle.

Fig. 12
Fig. 12

Four graphs, each displaying the BRDF as a function of viewing angles θ r . The graphs are chosen from different strips and different angles of incidence. Solid curves, the measured BRDF; dashed curves, the fitted values.

Fig. 13
Fig. 13

Contour plots of surface scattering modes obtained from the fitted linear combination of 20 basis functions. Upper row, surface scattering modes of the backscattering peak about 50° in strip 3. Radiance changes along the vertical direction signify the scattering characteristics of strip 3. Lower row, surface scattering modes of the specular maximum at large angles in strip 2. Radiance changes along the diagonal direction slanting to the right signify the scattering characteristics of strip 2. Left column, (a1) and (b1), scattering mode from a linear combination of all 20 basis functions. The elliptical peak in (a1) displays the backscattering peak centered about 50°. In (b1) the light spot at the end of the diagonal bar of strip 2 shows the specular maximum at large angles. Middle column, (a2) and (b2), scattering mode from a linear combination of eight basis functions of orders 0, 1, and 2. Right column, (a3) and (b3), scattering mode from a linear combination of 12 basis functions from orders 3 and 4.

Equations (7)

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

θ i = θ + 90 ° - γ ,
θ r = 90 ° - γ .
K n l θ ,   ϕ = Θ n l θ G l ϕ ,
Θ n l θ = n + 1 2 π   R n l 2 sin θ 2 ,
G l ϕ = cos l ϕ for   l 0 sin | l | ϕ for   l < 0 ,
R n ± l ρ = s = 0 n - l / 2 - 1 s × n - s ! s ! n + l / 2 - s ! n - l / 2 - s !   ρ n - 2 s .
f θ i ,   ϕ i ,   θ r ,   ϕ r = nln l   a nln l K n l θ i ,   ϕ i K n l θ r ,   ϕ r + K n l θ i ,   ϕ i K n l θ r ,   ϕ r ,

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