Abstract

We show that surface spectral reflectance can be separated from illumination effects in visible through near-infrared (350 nm–1740 nm) hyperspectral data by using only the information in a single radiance spectrum. The separation method exploits the fact that reflectance and illumination spectra typically lie in distinct subspaces. We present a comparison of a linear and a nonlinear algorithm for the separation. These algorithms compute an estimate of the spectral reflectance up to a scaling factor. In addition, we present an iterative method that is used to determine the starting point for the nonlinear algorithm. We also develop a method for selecting the dimension of the reflectance and illumination subspaces that is appropriate for material identification applications. The accuracy of the separation methods is quantified by application to noisy visible through near-infrared spectral data with a database of 107 materials and 3000 illumination spectra. The utility of the separation method for material identification is demonstrated with the same database. The results show that accurate reflectance recovery and material identification is possible by use of visible through near-infrared spectral data over the outdoor environmental conditions represented in this data set.

© 2004 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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    [CrossRef] [PubMed]
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  14. G. T. Winch, M. C. Boshoff, C. J. Kok, A. G. DuToit, “Spectroradiometric and colorimetric characteristics of daylight in the Southern Hemisphere: Pretoria, South Africa,” J. Opt. Soc. Am. 56, 456–464 (1966).
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  15. G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
    [CrossRef]
  16. J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: Theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
    [CrossRef]
  17. L. T. Maloney, B. A. Wandell, “Color constancy: a method for recovering spectral reflectance,” J. Opt. Soc. Am. A 3, 29–33 (1986).
    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
  20. G. Healey, L. Benites, “Linear models for spectral reflectance functions over the mid-wave and long-wave infrared,” J. Opt. Soc. Am. A 15, 2216–2227 (1998).
    [CrossRef]
  21. G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983).
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    [CrossRef]
  23. D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 11, 431–441 (1963).
    [CrossRef]
  24. J. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice Hall, Englewood Cliffs, N.J., 1983).
  25. F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” presented at the First European Conference on Colour in Graphics, Imaging and Vision, Poitiers, France, April 2–5, 2002.
  26. These data are available at http://speclab.cr.usgs.gov/ .
  27. R. W. Basedow, W. S. Aldrich, J. E. Colwel, W. D. Kinder, “HYDICE system performance: an update,” in Hyperspectral Remote Sensing and Applications, S. Shen, ed., Proc. SPIE2821, 76–84 (1996).
    [CrossRef]

2002 (1)

R. Lenz, “Two-stage principal component analysis of color,” IEEE Trans. Image Process. 10, 630–635 (2002).
[CrossRef]

1998 (3)

1997 (1)

1994 (1)

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

1993 (1)

G. Vane, R. Green, T. Chrein, H. Enmark, E. Hanson, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sens. Environ. 44, 127–143 (1993).
[CrossRef]

1992 (3)

M. S. Drew, B. V. Funt, “Natural metamers,” Comput. Vis. Image Underst. 15, 139–151 (1992).
[CrossRef]

L. Marimont, B. A. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
[CrossRef] [PubMed]

M. J. Vrhel, H. J. Trussell, “Color correction using principal component analysis,” Color Res. Appl. 17, 328–338 (1992).
[CrossRef]

1991 (1)

S. Goward, B. Markham, D. Dye, W. Dolaney, J. Yang, “Normalized difference vegetation index measurements from the Advanced Very High Resolution Radiometer,” Remote Sens. Environ. 35, 257–277 (1991).
[CrossRef]

1990 (1)

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: Theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

1989 (1)

1986 (2)

1980 (1)

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

1978 (1)

1966 (1)

1965 (1)

1964 (2)

1963 (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Aldrich, W. S.

R. W. Basedow, W. S. Aldrich, J. E. Colwel, W. D. Kinder, “HYDICE system performance: an update,” in Hyperspectral Remote Sensing and Applications, S. Shen, ed., Proc. SPIE2821, 76–84 (1996).
[CrossRef]

Basedow, R. W.

R. W. Basedow, W. S. Aldrich, J. E. Colwel, W. D. Kinder, “HYDICE system performance: an update,” in Hyperspectral Remote Sensing and Applications, S. Shen, ed., Proc. SPIE2821, 76–84 (1996).
[CrossRef]

Benites, L.

Berns, R. S.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” presented at the First European Conference on Colour in Graphics, Imaging and Vision, Poitiers, France, April 2–5, 2002.

Boshoff, M. C.

Buchsbaum, G.

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

Chrein, T.

G. Vane, R. Green, T. Chrein, H. Enmark, E. Hanson, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sens. Environ. 44, 127–143 (1993).
[CrossRef]

Cohen, J.

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

Colwel, J. E.

R. W. Basedow, W. S. Aldrich, J. E. Colwel, W. D. Kinder, “HYDICE system performance: an update,” in Hyperspectral Remote Sensing and Applications, S. Shen, ed., Proc. SPIE2821, 76–84 (1996).
[CrossRef]

Das, S. R.

Dennis, J.

J. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice Hall, Englewood Cliffs, N.J., 1983).

Dixon, E. R.

Dolaney, W.

S. Goward, B. Markham, D. Dye, W. Dolaney, J. Yang, “Normalized difference vegetation index measurements from the Advanced Very High Resolution Radiometer,” Remote Sens. Environ. 35, 257–277 (1991).
[CrossRef]

Drew, M. S.

M. S. Drew, B. V. Funt, “Natural metamers,” Comput. Vis. Image Underst. 15, 139–151 (1992).
[CrossRef]

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: Theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

DuToit, A. G.

Dye, D.

S. Goward, B. Markham, D. Dye, W. Dolaney, J. Yang, “Normalized difference vegetation index measurements from the Advanced Very High Resolution Radiometer,” Remote Sens. Environ. 35, 257–277 (1991).
[CrossRef]

Enmark, H.

G. Vane, R. Green, T. Chrein, H. Enmark, E. Hanson, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sens. Environ. 44, 127–143 (1993).
[CrossRef]

Funt, B. V.

M. S. Drew, B. V. Funt, “Natural metamers,” Comput. Vis. Image Underst. 15, 139–151 (1992).
[CrossRef]

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: Theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

Garci´a-Beltrán, A.

Gershon, R.

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

Golub, G. H.

G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983).

Goward, S.

S. Goward, B. Markham, D. Dye, W. Dolaney, J. Yang, “Normalized difference vegetation index measurements from the Advanced Very High Resolution Radiometer,” Remote Sens. Environ. 35, 257–277 (1991).
[CrossRef]

Green, R.

G. Vane, R. Green, T. Chrein, H. Enmark, E. Hanson, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sens. Environ. 44, 127–143 (1993).
[CrossRef]

Hallikainen, J.

Hanson, E.

G. Vane, R. Green, T. Chrein, H. Enmark, E. Hanson, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sens. Environ. 44, 127–143 (1993).
[CrossRef]

Healey, G.

Hernández-Andrés, J.

Ho, J.

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: Theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

Imai, F. H.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” presented at the First European Conference on Colour in Graphics, Imaging and Vision, Poitiers, France, April 2–5, 2002.

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.

Kinder, W. D.

R. W. Basedow, W. S. Aldrich, J. E. Colwel, W. D. Kinder, “HYDICE system performance: an update,” in Hyperspectral Remote Sensing and Applications, S. Shen, ed., Proc. SPIE2821, 76–84 (1996).
[CrossRef]

Kok, C. J.

Lenz, R.

R. Lenz, “Two-stage principal component analysis of color,” IEEE Trans. Image Process. 10, 630–635 (2002).
[CrossRef]

MacAdam, D. L.

Maloney, L. T.

Marimont, L.

Markham, B.

S. Goward, B. Markham, D. Dye, W. Dolaney, J. Yang, “Normalized difference vegetation index measurements from the Advanced Very High Resolution Radiometer,” Remote Sens. Environ. 35, 257–277 (1991).
[CrossRef]

Marquardt, D. W.

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Nieves, J. L.

Parkkinen, J. P. S.

Porter, W.

G. Vane, R. Green, T. Chrein, H. Enmark, E. Hanson, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sens. Environ. 44, 127–143 (1993).
[CrossRef]

Romero, J.

Rosen, M. R.

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” presented at the First European Conference on Colour in Graphics, Imaging and Vision, Poitiers, France, April 2–5, 2002.

Sastri, V. D. P.

Schnabel, R. B.

J. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice Hall, Englewood Cliffs, N.J., 1983).

Slater, D.

Trussell, H. J.

M. J. Vrhel, H. J. Trussell, “Color correction using principal component analysis,” Color Res. Appl. 17, 328–338 (1992).
[CrossRef]

van Loan, C. F.

G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983).

Vane, G.

G. Vane, R. Green, T. Chrein, H. Enmark, E. Hanson, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sens. Environ. 44, 127–143 (1993).
[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).

M. J. Vrhel, H. J. Trussell, “Color correction using principal component analysis,” Color Res. Appl. 17, 328–338 (1992).
[CrossRef]

Wandell, B. A.

Winch, G. T.

Wyszecki, G.

Yang, J.

S. Goward, B. Markham, D. Dye, W. Dolaney, J. Yang, “Normalized difference vegetation index measurements from the Advanced Very High Resolution Radiometer,” Remote Sens. Environ. 35, 257–277 (1991).
[CrossRef]

Appl. Opt. (1)

Color Res. Appl. (2)

M. J. Vrhel, H. J. Trussell, “Color correction using principal component analysis,” Color Res. Appl. 17, 328–338 (1992).
[CrossRef]

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

Comput. Vis. Image Underst. (1)

M. S. Drew, B. V. Funt, “Natural metamers,” Comput. Vis. Image Underst. 15, 139–151 (1992).
[CrossRef]

IEEE Trans. Image Process. (1)

R. Lenz, “Two-stage principal component analysis of color,” IEEE Trans. Image Process. 10, 630–635 (2002).
[CrossRef]

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

J. Ho, B. V. Funt, M. S. Drew, “Separating a color signal into illumination and surface reflectance components: Theory and applications,” IEEE Trans. Pattern Anal. Mach. Intell. 12, 966–977 (1990).
[CrossRef]

J. Franklin Inst. (1)

G. Buchsbaum, “A spatial processor model for object colour perception,” J. Franklin Inst. 310, 1–26 (1980).
[CrossRef]

J. Opt. Soc. Am. (4)

J. Opt. Soc. Am. A (7)

Psychon. Sci. (1)

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

Remote Sens. Environ. (2)

G. Vane, R. Green, T. Chrein, H. Enmark, E. Hanson, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sens. Environ. 44, 127–143 (1993).
[CrossRef]

S. Goward, B. Markham, D. Dye, W. Dolaney, J. Yang, “Normalized difference vegetation index measurements from the Advanced Very High Resolution Radiometer,” Remote Sens. Environ. 35, 257–277 (1991).
[CrossRef]

SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. (1)

D. W. Marquardt, “An algorithm for least-squares estimation of nonlinear parameters,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math. 11, 431–441 (1963).
[CrossRef]

Other (5)

J. Dennis, R. B. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations (Prentice Hall, Englewood Cliffs, N.J., 1983).

F. H. Imai, M. R. Rosen, R. S. Berns, “Comparative study of metrics for spectral match quality,” presented at the First European Conference on Colour in Graphics, Imaging and Vision, Poitiers, France, April 2–5, 2002.

These data are available at http://speclab.cr.usgs.gov/ .

R. W. Basedow, W. S. Aldrich, J. E. Colwel, W. D. Kinder, “HYDICE system performance: an update,” in Hyperspectral Remote Sensing and Applications, S. Shen, ed., Proc. SPIE2821, 76–84 (1996).
[CrossRef]

G. H. Golub, C. F. van Loan, Matrix Computations (Johns Hopkins U. Press, Baltimore, Md., 1983).

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Figures (15)

Fig. 1
Fig. 1

Fraction of the reflectance vector approximations that are not classified correctly as a function of the number of reflectance basis vectors k.

Fig. 2
Fig. 2

Function Φ(Πi, Πi-1) used to select illumination space dimensionality.

Fig. 3
Fig. 3

Interpolated reflectance vectors of ammonioalunite and ammonium chloride in the reflectance set.

Fig. 4
Fig. 4

ARMSE as a function of number of reflectance basis vectors.

Fig. 5
Fig. 5

Interpolated illumination vectors corresponding to two different measurements taken in Boulder, Colorado.

Fig. 6
Fig. 6

ARMSE as a function of number of illumination basis vectors.

Fig. 7
Fig. 7

Actual reflectance function for ammonium chloride and its estimates after the second and fourth iterations. The reflectance and illumination increment vectors used were [3, 3, 3, 2] and [1, 1, 0, 0], respectively.

Fig. 8
Fig. 8

Plot of root-mean-square error of the estimate versus number of iterations for ammonium chloride. The reflectance and illumination increment vectors used were [3, 3, 3, 2] and [1, 1, 0, 0], respectively.

Fig. 9
Fig. 9

Reflectance function and its estimates for ammonioalunite.

Fig. 10
Fig. 10

Illumination function and its estimates.

Fig. 11
Fig. 11

Reflectance function and its estimates for ammonium chloride.

Fig. 12
Fig. 12

Illumination function and its estimates.

Fig. 13
Fig. 13

Plot of ARMSE versus number of reflectance basis vectors. The number of illumination basis vectors used was 2.

Fig. 14
Fig. 14

Plot of ARMSE versus number of illumination basis vectors. The number of reflectance basis vectors used was 11.

Fig. 15
Fig. 15

Plot of ARMSE versus number of illumination and reflectance basis vectors.

Tables (2)

Tables Icon

Table 2 Proportion of Variance Accounted for as a Function of Number of Basis Vectors

Equations (28)

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

E(λ)i=1miEi(λ),
S(λ)j=1nσjSj(λ),
I(λ)=E(λ)S(λ)i=1mj=1niσjEi(λ)Sj(λ).
I(λ)k=1mnakPk(λ).
IPA,
I-PA2.
1S(λ)j=1n^1σ^jSj(λ),
σ1E(λ)i=1mσ^1^iEi(λ),
Aˆ=(1σ1,, 1σn, 2σ1,, 2σn,, mσ1,, mσn)T.
Ipar(λ; b)=i=1mj=1niσjPk(λ),
χ2(b)=I(λ)-Ipar(λ; b)2.
Sˆ(λ)=j=1nσ^jSj(λ),
Eˆ(λ)=i=1m^iEi(λ),
b*=[1*,, m**, σ1*,, σn**],
Em(λ)=i=1miEi(λ),
Sn(λ)=j=1nσjSj(λ),
ΔEm(λ)=E(λ)-Em(λ),
ΔSn(λ)=S(λ)-Sn(λ).
I(λ)=E(λ)S(λ)
=Em(λ)Sn(λ)+Em(λ)ΔSn(λ)+ΔEm(λ)Sn(λ)+ΔEm(λ)ΔSn(λ)
i=1mj=1niσjPk(λ).
sik(λ)-si(λ)=minsik(λ)-sj(λ),j=1, 2,, N.
Πi={Ei(λ)S1(λ), Ei(λ)S2(λ),, Ei(λ)Sn(λ)},
i=1, 2,, M.
Φ(v, Π)=1-Ev,
Φ(Πi, Πi-1)=1nvΠiΦ(v, Πi-1),
Φ(Πi, Πi-1)<T,i=1, 2,, j,
σ2=mI+c,

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