Abstract

This paper describes a set of experimental measurements and theoretical calculations designed to recover both the surface-spectral reflectance function and the illuminant spectral-power distribution from the image data. A multichannel vision system comprising six color channels was created with the use of a monochrome CCD camera and color filters. The spectral sensitivity of each color channel is calibrated, and the dynamic range of the camera is extended for sensing a wide range of intensity levels. Three algorithms and the corresponding results are introduced. First, a method of choosing the appropriate dimension of the linear model dimensions is introduced. Second, the illuminant parameters are estimated from the sensor measurements made at multiple points within separate objects. Third, the sensor responses are corrected for highlight and shading variations. The body reflectance parameters, unique to each surface, are recovered from these corrected values. Experimental results with a small number of test surfaces and a simple illumination geometry demonstrate that the illuminant spectrum and the surface-spectral reflectance functions can be recovered to within typical deviations of 1% and 4%, respectively.

© 1996 Optical Society of America

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References

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  1. B. A. Wandell, Foundations of Vision (Sinauer Associates, Sunderland, Mass., 1995).
  2. D. B. Judd, D. L. MacAdam, G. W. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
    [CrossRef]
  3. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
  4. L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 10, 1673–1683 (1986).
    [CrossRef]
  5. J. P. S. Parkkine, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [CrossRef]
  6. M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).
  7. B. Funt, “Linear model and computational color constancy,” in Proceedings of IS&T/SID Color Imaging Conference (Information Science and Technology, Springfield, Va., 1995), pp. 26–29.
  8. S. A. Shafer, “Using color to separate reflection components,” Color Res. Appl. 10, 210–218 (1985).
    [CrossRef]
  9. G. J. Klinker, S. A. Shafer, T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7–32 (1988).
    [CrossRef]
  10. S. Tominaga, B. A. Wandell, “The standard surface reflectance model and illuminant estimation,” J. Opt. Soc. Am. A 6, 576–584 (1989).
    [CrossRef]
  11. H. C. Lee, “Method for computing the scene-illuminant chromaticity from specular highlights,” J. Opt. Soc. Am. A 3, 1694–1699 (1986).
    [CrossRef] [PubMed]
  12. G. Healey, “Estimating spectral reflectance using highlights,” Image Vision Comput. 9, 333–337 (1991).
    [CrossRef]
  13. M. D’Zmura, P. Lennie, “Mechanisms of color constancy,” J. Opt. Soc. Am. A 3, 1662–1682 (1986).
    [CrossRef]
  14. S. Weisberg, Applied Linear Regression (Wiley, New York, 1980).
  15. M. D. Levine, Vision in Man and Machine (McGraw-Hill, New York, 1985).
  16. S. Tominaga, “Color classification of natural color images,” Color Res. Appl. 17, 230–239 (1992).
    [CrossRef]
  17. S. Tominaga, B. Wandell, “Component estimation of surface spectral reflectance,” J. Opt. Soc. Am. A 7, 312–317 (1990).
    [CrossRef]
  18. S. Tominaga, “Surface identification using the dichromatic reflection model,” IEEE Trans. Pattern Mach. Intell. 13, 658–670 (1991).
    [CrossRef]
  19. S. Tominaga, “Dichromatic reflection models for a variety of materials,” Color Res. Appl. 19, 277–285 (1994).
    [CrossRef]

1994 (2)

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

S. Tominaga, “Dichromatic reflection models for a variety of materials,” Color Res. Appl. 19, 277–285 (1994).
[CrossRef]

1992 (1)

S. Tominaga, “Color classification of natural color images,” Color Res. Appl. 17, 230–239 (1992).
[CrossRef]

1991 (2)

S. Tominaga, “Surface identification using the dichromatic reflection model,” IEEE Trans. Pattern Mach. Intell. 13, 658–670 (1991).
[CrossRef]

G. Healey, “Estimating spectral reflectance using highlights,” Image Vision Comput. 9, 333–337 (1991).
[CrossRef]

1990 (1)

1989 (2)

1988 (1)

G. J. Klinker, S. A. Shafer, T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7–32 (1988).
[CrossRef]

1986 (3)

1985 (1)

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

1964 (2)

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).

D. B. Judd, D. L. MacAdam, G. W. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
[CrossRef]

Cohen, J.

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).

D’Zmura, M.

Funt, B.

B. Funt, “Linear model and computational color constancy,” in Proceedings of IS&T/SID Color Imaging Conference (Information Science and Technology, Springfield, Va., 1995), pp. 26–29.

Gershon, R.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Hallikainen, J.

Healey, G.

G. Healey, “Estimating spectral reflectance using highlights,” Image Vision Comput. 9, 333–337 (1991).
[CrossRef]

Iwan, L. S.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Jaaskelainen, T.

Judd, D. B.

Kanade, T.

G. J. Klinker, S. A. Shafer, T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7–32 (1988).
[CrossRef]

Klinker, G. J.

G. J. Klinker, S. A. Shafer, T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7–32 (1988).
[CrossRef]

Lee, H. C.

Lennie, P.

Levine, M. D.

M. D. Levine, Vision in Man and Machine (McGraw-Hill, New York, 1985).

MacAdam, D. L.

Maloney, L. T.

L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 10, 1673–1683 (1986).
[CrossRef]

Parkkine, J. P. S.

Shafer, S. A.

G. J. Klinker, S. A. Shafer, T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7–32 (1988).
[CrossRef]

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

Tominaga, S.

S. Tominaga, “Dichromatic reflection models for a variety of materials,” Color Res. Appl. 19, 277–285 (1994).
[CrossRef]

S. Tominaga, “Color classification of natural color images,” Color Res. Appl. 17, 230–239 (1992).
[CrossRef]

S. Tominaga, “Surface identification using the dichromatic reflection model,” IEEE Trans. Pattern Mach. Intell. 13, 658–670 (1991).
[CrossRef]

S. Tominaga, B. Wandell, “Component estimation of surface spectral reflectance,” J. Opt. Soc. Am. A 7, 312–317 (1990).
[CrossRef]

S. Tominaga, B. A. Wandell, “The standard surface reflectance model and illuminant estimation,” J. Opt. Soc. Am. A 6, 576–584 (1989).
[CrossRef]

Vrhel, M. J.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Wandell, B.

Wandell, B. A.

Weisberg, S.

S. Weisberg, Applied Linear Regression (Wiley, New York, 1980).

Wyszecki, G. W.

Color Res. Appl. (4)

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

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

S. Tominaga, “Color classification of natural color images,” Color Res. Appl. 17, 230–239 (1992).
[CrossRef]

S. Tominaga, “Dichromatic reflection models for a variety of materials,” Color Res. Appl. 19, 277–285 (1994).
[CrossRef]

IEEE Trans. Pattern Mach. Intell. (1)

S. Tominaga, “Surface identification using the dichromatic reflection model,” IEEE Trans. Pattern Mach. Intell. 13, 658–670 (1991).
[CrossRef]

Image Vision Comput. (1)

G. Healey, “Estimating spectral reflectance using highlights,” Image Vision Comput. 9, 333–337 (1991).
[CrossRef]

Int. J. Comput. Vis. (1)

G. J. Klinker, S. A. Shafer, T. Kanade, “The measurement of highlights in color images,” Int. J. Comput. Vis. 2, 7–32 (1988).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (6)

Psychon. Sci. (1)

J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).

Other (4)

B. Funt, “Linear model and computational color constancy,” in Proceedings of IS&T/SID Color Imaging Conference (Information Science and Technology, Springfield, Va., 1995), pp. 26–29.

S. Weisberg, Applied Linear Regression (Wiley, New York, 1980).

M. D. Levine, Vision in Man and Machine (McGraw-Hill, New York, 1985).

B. A. Wandell, Foundations of Vision (Sinauer Associates, Sunderland, Mass., 1995).

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Figures (21)

Fig. 1
Fig. 1

Camera system for multichannel imaging.

Fig. 2
Fig. 2

Setup for measuring the spectral sensitivity of the monochrome CCD camera.

Fig. 3
Fig. 3

Spectral-sensitivity function measured for the monochrome CCD camera.

Fig. 4
Fig. 4

Spectral-sensitivity functions for the six sensors. R, red; B, blue; G, green; Y, yellow.

Fig. 5
Fig. 5

Intersection of multiple color–signal planes.

Fig. 6
Fig. 6

Coordinate system of ( c e , c e ).

Fig. 7
Fig. 7

First three basis functions for the set of nine illuminant spectra.

Fig. 8
Fig. 8

First five basis functions for the database of reflectance spectra.

Fig. 9
Fig. 9

Histogram of the predicted dimension for the illuminant model of a halogen lamp from the image data.

Fig. 10
Fig. 10

Variations of the estimation error Je(m) and the approximation error Ja(m) as a function of the dimension m for the illuminant spectrum of a halogen lamp. The computations of Je(m) were done with the use of the experimental data in Subsection 5.B.1.

Fig. 11
Fig. 11

Average value of the estimation error Js(m, n) over three surfaces of plastic as a function of m and n.

Fig. 12
Fig. 12

Scene of red, green, and yellow plastic cylinders illuminated with a halogen lamp.

Fig. 13
Fig. 13

Color histogram of the combined image of the plastic cylinders in a three-dimensional subspace.

Fig. 14
Fig. 14

Estimation results of the illuminant spectral-power distribution of a halogen lamp. Squares represent the estimate from the image data, and plus signs represent the direct measurement by a spectro-radiometer.

Fig. 15
Fig. 15

Histogram of the normalized sensor outputs for the image of the plastic cylinders in a three-dimensional subspace.

Fig. 16
Fig. 16

Coordinates of the weighting coefficients ( c e , c e ) for three color regions.

Fig. 17
Fig. 17

Estimation results of the surface-spectral reflectance functions for three surfaces of the plastic cylinders. Diamonds represent the estimated spectral reflectance curves from the image data, plus signs represent the measured spectral reflectance curves, and squares represent the five-dimensional model of the reflectance curves.

Fig. 18
Fig. 18

Scene of red, green, and yellow paper cylinders illuminated with a slide projector.

Fig. 19
Fig. 19

Color histogram of the image of the paper cylinder in a three-dimensional subspace.

Fig. 20
Fig. 20

Estimation results of the illuminant spectral-power distribution of a slide projector. Diamonds, plus signs, and squares represent, respectively, the estimate, the direct measurement, and the three-dimensional model of the measurement.

Fig. 21
Fig. 21

Estimation results of the surface-spectral reflectance functions for three surfaces of the paper cylinders. Squares and plus signs represent, respectively, the estimate and the fivedimensional model of the measured reflectance curves.

Equations (25)

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C ( x , λ ) = α ( x ) S ( λ ) E ( λ ) + β ( x ) E ( λ ) ,
E ( λ ) = i = 1 m ε i E i ( λ ) ,
S ( λ ) = j = 1 n σ j S j ( λ ) ,
ρ k ( x ) = C ( x , λ ) R k ( λ ) d λ , k = 1 , 2 , . . . , 6 .
h 1 = ( E 1 ( λ ) R 1 ( λ ) d λ E 1 ( λ ) R 6 ( λ ) d λ ) , . . . , h m = ( E m ( λ ) R 1 ( λ ) d λ E m ( λ ) R 6 ( λ ) d λ ) .
H = ( h 1 , h 2 , . . . , h m ) .
Λ ε = [ i = 1 m ε 1 E i ( λ ) S 1 ( λ ) R 1 ( λ ) d λ i = 1 m ε 1 E i ( λ ) S n ( λ ) R 1 ( λ ) d λ i = 1 m ε i E i ( λ ) S 1 ( λ ) R 6 ( λ ) d λ i = 1 m ε i E i ( λ ) S n ( λ ) R 6 ( λ ) d λ ] .
ρ ( x ) = α ( x ) Λ ε σ + β ( x ) H ε ,
ρ w = i = 1 m ε i h i + η ,
Null hypothesis : ρ w = i = 1 m 1 ε i h i + η , Alternative hypothesis : ρ w = i = 1 m 1 ε i h i + ε m h m + η .
F = ε ̂ m 2 a ( m , m ) [ J m / ( 6 m ) ] ,
J m = ρ w i = 1 m ε ̂ i h i 2 .
c 1 ( i ) u 1 ( i ) + c 2 ( i ) u 2 ( i ) = c 1 ( j ) u 1 ( j ) + c 2 ( j ) u 2 ( j ) for i j .
[ u 1 ( 1 ) u 2 ( 1 ) u 1 ( 2 ) u 2 ( 2 ) 0 0 . . . 0 0 0 0 u 1 ( 2 ) u 2 ( 2 ) u 1 ( 3 ) u 3 ( 3 ) . . . 0 0 . . . u 1 ( 1 ) u 2 ( 1 ) 0 0 0 0 . . . u 1 ( M ) u 2 ( M ) ] ( c 1 ( 1 ) c 2 ( 1 ) c 1 ( 2 ) c 2 ( 2 ) c 1 ( M ) c 2 ( M ) ) = 0 .
[ M 1 0 u 1 ( 1 ) t u 1 ( 2 ) u 1 ( 1 ) t u 2 ( 2 ) . . . u 1 ( 1 ) t u 1 ( M ) u 1 ( 1 ) t u 2 ( M ) 0 M 1 u 2 ( 1 ) t u 1 ( 2 ) u 2 ( 1 ) t u 2 ( 2 ) . . . u 2 ( 1 ) t u 1 ( M ) u 2 ( 1 ) t u 2 ( M ) u 1 ( 1 ) t u 1 ( 2 ) u 2 ( 1 ) t u 1 ( 2 ) M 1 0 . . . u 1 ( 2 ) t u 1 ( M ) u 1 ( 2 ) t u 2 ( M ) u 1 ( 1 ) t u 2 ( 2 ) u 2 ( 1 ) t u 2 ( 2 ) 0 M 1 . . . u 2 ( 2 ) t u 1 ( M ) u 2 ( 2 ) t u 2 ( M ) . . . u 1 ( 1 ) t u 1 ( M ) u 2 ( 1 ) t u 1 ( M ) u 1 ( 2 ) t u 1 ( M ) u 2 ( 2 ) t u 1 ( M ) . . . M 1 0 u 1 ( 1 ) t u 2 ( M ) u 2 ( 1 ) t u 2 ( M ) u 1 ( 2 ) t u 2 ( M ) u 2 ( 2 ) t u 2 ( M ) . . . 0 M 1 ] .
e = 1 M i = 1 M [ c 1 ( i ) u 1 ( i ) + c 2 ( i ) u 2 ( i ) ] .
ε = H + e .
y ( x ) = ρ ( x ) / e ,
y ( x ) = y ( x ) y ¯ ( x ) y ( x ) y ¯ ( x ) ,
Λ ε σ = c e e + c e e ,
ĉ e = [ max ( c e x ) ] / [ max ( c e x / c e x ) ] , ĉ e = max ( c e x ) .
σ = Λ ε + ( ĉ e e + ĉ e e ) ,
J e ( m ) = E ( λ ) i = 1 m ε ̂ i ( m ) E i ( λ ) 2 .
J a ( m ) = E ( λ ) i = 1 m ε i E i ( λ ) 2 ,
J s ( m , n ) = S ( λ ) i = 1 m σ ̂ i ( m , n ) S i ( λ ) 2 .

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