Abstract

An airborne sensor measures the radiance spectrum, which is dependent on the spectral reflectance of the ground material, the orientation of the material surface, and the atmospheric and illumination conditions. We present an algorithm to estimate the surface spectral reflectance, given the sensor radiance spectrum corresponding to a single pixel. The algorithm uses a nonlinear physics-based image formation model. A low-dimensional linear subspace model is used for the reflectance spectra. The solar radiance, sky radiance, and path-scattered radiance are dependent on the environmental conditions and viewing geometry, and this interdependence is considered by using a coupled-subspace model for these spectra. The algorithm uses the Levenberg–Marquardt method to estimate the subspace model parameters. We have applied the algorithm to a large set of synthetic and real data.

© 2007 Optical Society of America

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  1. R. W. Basedow, D. C. Armer, and M. Anderson, "HYDICE system: implementation and performance," Proc. SPIE 2480, 258-267 (1995).
  2. C. G. Simi, S. G. Beaven, E. Winter, C. LaSota, J. Parish, and R. Dixon, "Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms," Proc. SPIE 4049, 218-229 (2000).
  3. G. Vane, R. Green, T. Chrein, H. Enmark, E. Hanson, and W. Porter, "The airborne visible/infrared imaging spectrometer (AVIRIS)," Remote Sens. Environ. 44, 127-143 (1993).
    [CrossRef]
  4. W. Aldrich, M. Kappus, R. Resmini, and P. Mitchell, "HYDICE postflight data processing," Proc. SPIE 2758, 354-363 (1996).
  5. T. Chrien, R. Green, and M. Eastwood, "Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Proc. SPIE 1298, 37-49 (1990).
  6. G. Healey and D. Slater, "Models and methods for automated material identification in hyperspectral imagery acquired under unknown illumination and atmospheric conditions," IEEE Trans. Geosci. Remote Sens. 37, 2706-2717 (1999).
    [CrossRef]
  7. K. Chandra and G. Healey, "Using coupled subspace models for reflectance/illumination separation," Proc. SPIE 5425, 538-548 (2004).
  8. J. Conel, R. O. Green, G. Vane, C. Bruegge, and R. Alley, "Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere," Proc. SPIE 834, 140-157 (1987).
  9. B. C. Gao, K. Heidebrecht, and A. F. H. Goetz, "Derivation of scaled surface reflectances from AVIRIS data," Remote Sens. Environ. 44, 165-178 (1993).
    [CrossRef]
  10. R. O. Green, J. Conel, and D. Roberts, "Estimation of aerosol optical depth, pressure elevation, water vapor, and calculation of apparent surface reflectance from radiance measured by the airborne visible/infrared imaging spectrometer (AVIRIS) using a radiative transfer code," Proc. SPIE 1937, 2-11 (1993).
  11. J. Cohen, "Dependency of the spectral reflectance curves of the Munsell color chips," Psychon. Sci. 1, 369-370 (1964).
  12. L. T. Maloney, "Evaluation of linear models of surface spectral reflectance with small numbers of parameters," J. Opt. Soc. Am. A 3, 1673-1683 (1986).
    [CrossRef] [PubMed]
  13. J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, "Characteristic spectra of Munsell colors," J. Opt. Soc. Am. A 6, 318-322 (1989).
    [CrossRef]
  14. S. R. Das and V. D. P. Sastri, "Spectral distribution and color of tropical daylight," J. Opt. Soc. Am. 55, 319-323 (1965).
    [CrossRef]
  15. E. R. Dixon, "Spectral distribution of Australian daylight," J. Opt. Soc. Am. 68, 437-450 (1978).
    [CrossRef]
  16. J. Hernández-Andrés, J. Romero, A. García-Beltrán, and J. L. Nieves, "Testing linear models on spectral daylight measurements," Appl. Opt. 37, 971-977 (1998).
    [CrossRef]
  17. D. Judd, D. L. MacAdam, and G. Wyszecki, "Spectraldistribution of typical daylight as a function of correlated color temperature," J. Opt. Soc. Am. 54, 1031-1040 (1964).
    [CrossRef]
  18. J. Romero, A. García-Beltrán, and J. Hernández-Andrés, "Linear bases for representation of natural and artificial illuminants," J. Opt. Soc. Am. A 14, 1007-1012 (1997).
    [CrossRef]
  19. G. T. Winch, M. C. Boshoff, C. J. Kok, and A. G. DuToit, "Spectroradiometric and colorimetric characteristics of daylight in the Southern Hemisphere: Pretoria, South Africa," J. Opt. Soc. Am. 56, 456-464 (1966).
    [CrossRef]
  20. L. T. Maloney and B. A. Wandell, "Color constancy: a method for recovering surface spectral reflectance," J. Opt. Soc. Am. A 3, 29-33 (1986).
    [CrossRef] [PubMed]
  21. G. Buchsbaum, "A spatial processor model for object colour perception," J. Franklin Inst. 310, 1-26 (1980).
    [CrossRef]
  22. J. Ho, B. V. Funt, and 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]
  23. L. Marimont and B. A. Wandell, "Linear models of surface and illuminant spectra," J. Opt. Soc. Am. A 9, 1905-1913 (1992).
    [CrossRef] [PubMed]
  24. D. Slater and G. Healey, "Analyzing the spectral dimensionality of outdoor visible and near-infrared illumination functions," J. Opt. Soc. Am. A 15, 2913-2920 (1998).
    [CrossRef]
  25. G. Healey and 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]
  26. J. Schott, Remote Sensing: The Image Chain Approach (Oxford U. Press, 1997).
  27. D. W. Marquardt, "An algorithm for least-squares estimation of nonlinear parameters," J. Soc. Ind. Appl. Math. 11, 431-441 (1963).
    [CrossRef]
  28. K. Chandra and G. Healey, "Estimating visible through near-infrared spectral reflectance from a sensor radiance spectrum," J. Opt. Soc. Am. A 21, 1825-1833 (2004).
    [CrossRef]
  29. The data are available at http://www.usgs.gov/.
  30. A. Berk, L. Bernstein, and D. Robertson, "MODTRAN: a moderate resolution model for LOWTRAN 7," Tech. Rep. GL-TR-89-0122 (Geophysics Laboratory, Bedford, Mass., 1989).
  31. The data are available at http://aviris.jpl.nasa.gov/html/aviris.freedata.html.
  32. F. A. Kruse, J. H. Huntington, and R. O. Green, "Results from the 1995 AVIRIS geology group shoot," in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition: Environmental Research Institute of Michigan (ERIM), (Ann Arbor, 1996), Vol. 1, pp. 211-220.
  33. F. A. Kruse and J. W. Boardman, "Characterization and mapping of kimberlites and related diatremes using hyperspectral remote sensing," in Proceedings of the 2000 IEEE AeroSpace Conference (IEEE, 2000).
    [CrossRef]

2004 (2)

K. Chandra and G. Healey, "Using coupled subspace models for reflectance/illumination separation," Proc. SPIE 5425, 538-548 (2004).

K. Chandra and G. Healey, "Estimating visible through near-infrared spectral reflectance from a sensor radiance spectrum," J. Opt. Soc. Am. A 21, 1825-1833 (2004).
[CrossRef]

2000 (2)

F. A. Kruse and J. W. Boardman, "Characterization and mapping of kimberlites and related diatremes using hyperspectral remote sensing," in Proceedings of the 2000 IEEE AeroSpace Conference (IEEE, 2000).
[CrossRef]

C. G. Simi, S. G. Beaven, E. Winter, C. LaSota, J. Parish, and R. Dixon, "Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms," Proc. SPIE 4049, 218-229 (2000).

1999 (1)

G. Healey and D. Slater, "Models and methods for automated material identification in hyperspectral imagery acquired under unknown illumination and atmospheric conditions," IEEE Trans. Geosci. Remote Sens. 37, 2706-2717 (1999).
[CrossRef]

1998 (3)

1997 (2)

1996 (2)

F. A. Kruse, J. H. Huntington, and R. O. Green, "Results from the 1995 AVIRIS geology group shoot," in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition: Environmental Research Institute of Michigan (ERIM), (Ann Arbor, 1996), Vol. 1, pp. 211-220.

W. Aldrich, M. Kappus, R. Resmini, and P. Mitchell, "HYDICE postflight data processing," Proc. SPIE 2758, 354-363 (1996).

1995 (1)

R. W. Basedow, D. C. Armer, and M. Anderson, "HYDICE system: implementation and performance," Proc. SPIE 2480, 258-267 (1995).

1993 (3)

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

B. C. Gao, K. Heidebrecht, and A. F. H. Goetz, "Derivation of scaled surface reflectances from AVIRIS data," Remote Sens. Environ. 44, 165-178 (1993).
[CrossRef]

R. O. Green, J. Conel, and D. Roberts, "Estimation of aerosol optical depth, pressure elevation, water vapor, and calculation of apparent surface reflectance from radiance measured by the airborne visible/infrared imaging spectrometer (AVIRIS) using a radiative transfer code," Proc. SPIE 1937, 2-11 (1993).

1992 (1)

1990 (2)

J. Ho, B. V. Funt, and 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]

T. Chrien, R. Green, and M. Eastwood, "Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Proc. SPIE 1298, 37-49 (1990).

1989 (2)

J. P. S. Parkkinen, J. Hallikainen, and T. Jaaskelainen, "Characteristic spectra of Munsell colors," J. Opt. Soc. Am. A 6, 318-322 (1989).
[CrossRef]

A. Berk, L. Bernstein, and D. Robertson, "MODTRAN: a moderate resolution model for LOWTRAN 7," Tech. Rep. GL-TR-89-0122 (Geophysics Laboratory, Bedford, Mass., 1989).

1987 (1)

J. Conel, R. O. Green, G. Vane, C. Bruegge, and R. Alley, "Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere," Proc. SPIE 834, 140-157 (1987).

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)

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

D. Judd, D. L. MacAdam, and G. Wyszecki, "Spectraldistribution of typical daylight as a function of correlated color temperature," J. Opt. Soc. Am. 54, 1031-1040 (1964).
[CrossRef]

1963 (1)

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

Aldrich, W.

W. Aldrich, M. Kappus, R. Resmini, and P. Mitchell, "HYDICE postflight data processing," Proc. SPIE 2758, 354-363 (1996).

Alley, R.

J. Conel, R. O. Green, G. Vane, C. Bruegge, and R. Alley, "Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere," Proc. SPIE 834, 140-157 (1987).

Anderson, M.

R. W. Basedow, D. C. Armer, and M. Anderson, "HYDICE system: implementation and performance," Proc. SPIE 2480, 258-267 (1995).

Armer, D. C.

R. W. Basedow, D. C. Armer, and M. Anderson, "HYDICE system: implementation and performance," Proc. SPIE 2480, 258-267 (1995).

Basedow, R. W.

R. W. Basedow, D. C. Armer, and M. Anderson, "HYDICE system: implementation and performance," Proc. SPIE 2480, 258-267 (1995).

Beaven, S. G.

C. G. Simi, S. G. Beaven, E. Winter, C. LaSota, J. Parish, and R. Dixon, "Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms," Proc. SPIE 4049, 218-229 (2000).

Benites, L.

Berk, A.

A. Berk, L. Bernstein, and D. Robertson, "MODTRAN: a moderate resolution model for LOWTRAN 7," Tech. Rep. GL-TR-89-0122 (Geophysics Laboratory, Bedford, Mass., 1989).

Bernstein, L.

A. Berk, L. Bernstein, and D. Robertson, "MODTRAN: a moderate resolution model for LOWTRAN 7," Tech. Rep. GL-TR-89-0122 (Geophysics Laboratory, Bedford, Mass., 1989).

Boardman, J. W.

F. A. Kruse and J. W. Boardman, "Characterization and mapping of kimberlites and related diatremes using hyperspectral remote sensing," in Proceedings of the 2000 IEEE AeroSpace Conference (IEEE, 2000).
[CrossRef]

Boshoff, M. C.

Bruegge, C.

J. Conel, R. O. Green, G. Vane, C. Bruegge, and R. Alley, "Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere," Proc. SPIE 834, 140-157 (1987).

Buchsbaum, G.

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

Chandra, K.

K. Chandra and G. Healey, "Estimating visible through near-infrared spectral reflectance from a sensor radiance spectrum," J. Opt. Soc. Am. A 21, 1825-1833 (2004).
[CrossRef]

K. Chandra and G. Healey, "Using coupled subspace models for reflectance/illumination separation," Proc. SPIE 5425, 538-548 (2004).

Chrein, T.

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

Chrien, T.

T. Chrien, R. Green, and M. Eastwood, "Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Proc. SPIE 1298, 37-49 (1990).

Cohen, J.

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

Conel, J.

R. O. Green, J. Conel, and D. Roberts, "Estimation of aerosol optical depth, pressure elevation, water vapor, and calculation of apparent surface reflectance from radiance measured by the airborne visible/infrared imaging spectrometer (AVIRIS) using a radiative transfer code," Proc. SPIE 1937, 2-11 (1993).

J. Conel, R. O. Green, G. Vane, C. Bruegge, and R. Alley, "Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere," Proc. SPIE 834, 140-157 (1987).

Das, S. R.

Dixon, E. R.

Dixon, R.

C. G. Simi, S. G. Beaven, E. Winter, C. LaSota, J. Parish, and R. Dixon, "Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms," Proc. SPIE 4049, 218-229 (2000).

Drew, M. S.

J. Ho, B. V. Funt, and 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.

Eastwood, M.

T. Chrien, R. Green, and M. Eastwood, "Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Proc. SPIE 1298, 37-49 (1990).

Enmark, H.

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

Funt, B. V.

J. Ho, B. V. Funt, and 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]

Gao, B. C.

B. C. Gao, K. Heidebrecht, and A. F. H. Goetz, "Derivation of scaled surface reflectances from AVIRIS data," Remote Sens. Environ. 44, 165-178 (1993).
[CrossRef]

García-Beltrán, A.

Goetz, A. F. H.

B. C. Gao, K. Heidebrecht, and A. F. H. Goetz, "Derivation of scaled surface reflectances from AVIRIS data," Remote Sens. Environ. 44, 165-178 (1993).
[CrossRef]

Green, R.

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

T. Chrien, R. Green, and M. Eastwood, "Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Proc. SPIE 1298, 37-49 (1990).

Green, R. O.

F. A. Kruse, J. H. Huntington, and R. O. Green, "Results from the 1995 AVIRIS geology group shoot," in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition: Environmental Research Institute of Michigan (ERIM), (Ann Arbor, 1996), Vol. 1, pp. 211-220.

R. O. Green, J. Conel, and D. Roberts, "Estimation of aerosol optical depth, pressure elevation, water vapor, and calculation of apparent surface reflectance from radiance measured by the airborne visible/infrared imaging spectrometer (AVIRIS) using a radiative transfer code," Proc. SPIE 1937, 2-11 (1993).

J. Conel, R. O. Green, G. Vane, C. Bruegge, and R. Alley, "Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere," Proc. SPIE 834, 140-157 (1987).

Hallikainen, J.

Hanson, E.

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

Healey, G.

K. Chandra and G. Healey, "Using coupled subspace models for reflectance/illumination separation," Proc. SPIE 5425, 538-548 (2004).

K. Chandra and G. Healey, "Estimating visible through near-infrared spectral reflectance from a sensor radiance spectrum," J. Opt. Soc. Am. A 21, 1825-1833 (2004).
[CrossRef]

G. Healey and D. Slater, "Models and methods for automated material identification in hyperspectral imagery acquired under unknown illumination and atmospheric conditions," IEEE Trans. Geosci. Remote Sens. 37, 2706-2717 (1999).
[CrossRef]

D. Slater and G. Healey, "Analyzing the spectral dimensionality of outdoor visible and near-infrared illumination functions," J. Opt. Soc. Am. A 15, 2913-2920 (1998).
[CrossRef]

G. Healey and 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]

Heidebrecht, K.

B. C. Gao, K. Heidebrecht, and A. F. H. Goetz, "Derivation of scaled surface reflectances from AVIRIS data," Remote Sens. Environ. 44, 165-178 (1993).
[CrossRef]

Hernández-Andrés, J.

Ho, J.

J. Ho, B. V. Funt, and 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]

Huntington, J. H.

F. A. Kruse, J. H. Huntington, and R. O. Green, "Results from the 1995 AVIRIS geology group shoot," in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition: Environmental Research Institute of Michigan (ERIM), (Ann Arbor, 1996), Vol. 1, pp. 211-220.

Jaaskelainen, T.

Judd, D.

Kappus, M.

W. Aldrich, M. Kappus, R. Resmini, and P. Mitchell, "HYDICE postflight data processing," Proc. SPIE 2758, 354-363 (1996).

Kok, C. J.

Kruse, F. A.

F. A. Kruse and J. W. Boardman, "Characterization and mapping of kimberlites and related diatremes using hyperspectral remote sensing," in Proceedings of the 2000 IEEE AeroSpace Conference (IEEE, 2000).
[CrossRef]

F. A. Kruse, J. H. Huntington, and R. O. Green, "Results from the 1995 AVIRIS geology group shoot," in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition: Environmental Research Institute of Michigan (ERIM), (Ann Arbor, 1996), Vol. 1, pp. 211-220.

LaSota, C.

C. G. Simi, S. G. Beaven, E. Winter, C. LaSota, J. Parish, and R. Dixon, "Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms," Proc. SPIE 4049, 218-229 (2000).

MacAdam, D. L.

Maloney, L. T.

Marimont, L.

Marquardt, D. W.

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

Mitchell, P.

W. Aldrich, M. Kappus, R. Resmini, and P. Mitchell, "HYDICE postflight data processing," Proc. SPIE 2758, 354-363 (1996).

Nieves, J. L.

Parish, J.

C. G. Simi, S. G. Beaven, E. Winter, C. LaSota, J. Parish, and R. Dixon, "Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms," Proc. SPIE 4049, 218-229 (2000).

Parkkinen, J. P. S.

Porter, W.

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

Resmini, R.

W. Aldrich, M. Kappus, R. Resmini, and P. Mitchell, "HYDICE postflight data processing," Proc. SPIE 2758, 354-363 (1996).

Roberts, D.

R. O. Green, J. Conel, and D. Roberts, "Estimation of aerosol optical depth, pressure elevation, water vapor, and calculation of apparent surface reflectance from radiance measured by the airborne visible/infrared imaging spectrometer (AVIRIS) using a radiative transfer code," Proc. SPIE 1937, 2-11 (1993).

Robertson, D.

A. Berk, L. Bernstein, and D. Robertson, "MODTRAN: a moderate resolution model for LOWTRAN 7," Tech. Rep. GL-TR-89-0122 (Geophysics Laboratory, Bedford, Mass., 1989).

Romero, J.

Sastri, V. D. P.

Schott, J.

J. Schott, Remote Sensing: The Image Chain Approach (Oxford U. Press, 1997).

Simi, C. G.

C. G. Simi, S. G. Beaven, E. Winter, C. LaSota, J. Parish, and R. Dixon, "Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms," Proc. SPIE 4049, 218-229 (2000).

Slater, D.

G. Healey and D. Slater, "Models and methods for automated material identification in hyperspectral imagery acquired under unknown illumination and atmospheric conditions," IEEE Trans. Geosci. Remote Sens. 37, 2706-2717 (1999).
[CrossRef]

D. Slater and G. Healey, "Analyzing the spectral dimensionality of outdoor visible and near-infrared illumination functions," J. Opt. Soc. Am. A 15, 2913-2920 (1998).
[CrossRef]

Vane, G.

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

J. Conel, R. O. Green, G. Vane, C. Bruegge, and R. Alley, "Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere," Proc. SPIE 834, 140-157 (1987).

Wandell, B. A.

Winch, G. T.

Winter, E.

C. G. Simi, S. G. Beaven, E. Winter, C. LaSota, J. Parish, and R. Dixon, "Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms," Proc. SPIE 4049, 218-229 (2000).

Wyszecki, G.

Appl. Opt. (1)

IEEE Trans. Geosci. Remote Sens. (1)

G. Healey and D. Slater, "Models and methods for automated material identification in hyperspectral imagery acquired under unknown illumination and atmospheric conditions," IEEE Trans. Geosci. Remote Sens. 37, 2706-2717 (1999).
[CrossRef]

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

J. Ho, B. V. Funt, and 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 (8)

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

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

Psychon. Sci. (1)

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

Remote Sens. Environ. (2)

B. C. Gao, K. Heidebrecht, and A. F. H. Goetz, "Derivation of scaled surface reflectances from AVIRIS data," Remote Sens. Environ. 44, 165-178 (1993).
[CrossRef]

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

Other (13)

W. Aldrich, M. Kappus, R. Resmini, and P. Mitchell, "HYDICE postflight data processing," Proc. SPIE 2758, 354-363 (1996).

T. Chrien, R. Green, and M. Eastwood, "Accuracy of the spectral and radiometric laboratory calibration of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS)," Proc. SPIE 1298, 37-49 (1990).

R. W. Basedow, D. C. Armer, and M. Anderson, "HYDICE system: implementation and performance," Proc. SPIE 2480, 258-267 (1995).

C. G. Simi, S. G. Beaven, E. Winter, C. LaSota, J. Parish, and R. Dixon, "Night vision imaging spectrometer (NVIS) performance parameters and their impact on various detection algorithms," Proc. SPIE 4049, 218-229 (2000).

R. O. Green, J. Conel, and D. Roberts, "Estimation of aerosol optical depth, pressure elevation, water vapor, and calculation of apparent surface reflectance from radiance measured by the airborne visible/infrared imaging spectrometer (AVIRIS) using a radiative transfer code," Proc. SPIE 1937, 2-11 (1993).

K. Chandra and G. Healey, "Using coupled subspace models for reflectance/illumination separation," Proc. SPIE 5425, 538-548 (2004).

J. Conel, R. O. Green, G. Vane, C. Bruegge, and R. Alley, "Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere," Proc. SPIE 834, 140-157 (1987).

The data are available at http://www.usgs.gov/.

A. Berk, L. Bernstein, and D. Robertson, "MODTRAN: a moderate resolution model for LOWTRAN 7," Tech. Rep. GL-TR-89-0122 (Geophysics Laboratory, Bedford, Mass., 1989).

The data are available at http://aviris.jpl.nasa.gov/html/aviris.freedata.html.

F. A. Kruse, J. H. Huntington, and R. O. Green, "Results from the 1995 AVIRIS geology group shoot," in Proceedings of the Second International Airborne Remote Sensing Conference and Exhibition: Environmental Research Institute of Michigan (ERIM), (Ann Arbor, 1996), Vol. 1, pp. 211-220.

F. A. Kruse and J. W. Boardman, "Characterization and mapping of kimberlites and related diatremes using hyperspectral remote sensing," in Proceedings of the 2000 IEEE AeroSpace Conference (IEEE, 2000).
[CrossRef]

J. Schott, Remote Sensing: The Image Chain Approach (Oxford U. Press, 1997).

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Figures (22)

Fig. 1
Fig. 1

Function Φ ( Π i , Π i 1 ) for sensor altitudes 3, 6, and 9 km used to select the coupled-subspace dimensionality.

Fig. 2
Fig. 2

Average RMSE as a function of number of reflectance basis vectors.

Fig. 3
Fig. 3

Average RMSE as a function of number of coupled-subspace basis vectors.

Fig. 4
Fig. 4

Radiance spectrum and its estimate.

Fig. 5
Fig. 5

Reflectance function and its estimate. The reflectance function corresponds to ammonioalunite.

Fig. 6
Fig. 6

E d ( λ ) T u ( λ ) function and its estimate.

Fig. 7
Fig. 7

E s ( λ ) T u ( λ ) function and its estimate.

Fig. 8
Fig. 8

P ( λ ) P est ( λ ) function and its estimate.

Fig. 9
Fig. 9

Plot of average RMSE versus number of reflectance basis vectors. The number of coupled-subspace basis vectors used was two.

Fig. 10
Fig. 10

Plot of average RMSE versus number of coupled-subspace basis vectors. The number of reflectance basis vectors used was 16.

Fig. 11
Fig. 11

Average RMSE as a function of the surface orientation.

Fig. 12
Fig. 12

Reflectance function and its estimates for surface orientations 0° and 72°.

Fig. 13
Fig. 13

DIRSIG image of a desert scene in Nevada.

Fig. 14
Fig. 14

Reflectance function and its estimates using six, nine, and 12 reflectance basis vectors. The reflectance corresponds to desert pavement. Four coupled-subspace vectors were used.

Fig. 15
Fig. 15

Reflectance function and its estimates using six, nine, and 12 reflectance basis vectors. The reflectance corresponds to a painted vehicle. Four coupled-subspace vectors were used.

Fig. 16
Fig. 16

DIRSIG image of an urban scene.

Fig. 17
Fig. 17

Reflectance function and its estimates. The reflectance corresponds to grass. Two coupled-subspace vectors were used.

Fig. 18
Fig. 18

Reflectance function and its estimates. The reflectance corresponds to asphalt. Two coupled-subspace vectors were used.

Fig. 19
Fig. 19

AVIRIS scene (Cuprite, Nevada). Data were collected in 1997.

Fig. 20
Fig. 20

Material map of pixels considered. The pixels considered were spectrally pure. Dark gray, alunite; light gray, kaolinite; black, pixels not considered.

Fig. 21
Fig. 21

Alunite and its estimates.

Fig. 22
Fig. 22

Kaolinite and its estimates.

Tables (4)

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Table 2 Results for the Desert Scene

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Table 3 Results for the Urban Scene

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Table 4 AVIRIS Results

Equations (25)

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I ( λ ) = [ E d ( λ ) cos ( θ ) + K E s ( λ ) ] T u ( λ ) S ( λ ) + P ( λ ) ,
S ( λ ) j = 1 n σ j S j ( λ ) ,
L i = [ E d i ( λ 1 ) T u i ( λ 1 ) , , E d i ( λ W ) T u i ( λ W ) , E s i ( λ 1 ) T u i ( λ 1 ) , , E s i ( λ W ) T u i ( λ W ) , P i ( λ 1 ) , , P i ( λ W ) ] ,
L j = 1 m ϵ j L j ,
E j d ( λ ) = [ L j ( 1 ) , L j ( 2 ) , , L j ( W ) ] ,
E j s ( λ ) = [ L j ( W + 1 ) , L j ( W + 2 ) , , L j ( 2 W ) ] ,
P j ( λ ) = [ L j ( 2 W + 1 ) , L j ( 2 W + 2 ) , , L j ( 3 W ) ] ,
E d ( λ ) T u ( λ ) j = 1 m ϵ j E j d ( λ ) ,
E s ( λ ) T u ( λ ) j = 1 m ϵ j E j s ( λ ) ,
P ( λ ) j = 1 m ϵ j P j ( λ ) .
I ( λ ) I par ( λ , c ) = i = 1 m j = 1 n ϵ i σ j E i d ( λ ) S j ( λ ) cos ( θ ) + K i = 1 m j = 1 n ϵ i σ j E i s ( λ ) S j ( λ ) + i = 1 m ϵ i P i ( λ ) ,
c = [ θ , K , ϵ 1 , ϵ 2 , , ϵ m , σ 1 , σ 2 , , σ n ] .
χ 2 ( c ) = I ( λ ) I par ( λ , c ) 2 ,
S ( λ ) j = 1 n σ ̂ j S j ( λ ) ,
E d ( λ ) T u ( λ ) j = 1 m ϵ ̂ j E j d ( λ ) ,
E s ( λ ) T u ( λ ) j = 1 m ϵ ̂ j E j s ( λ ) ,
P ( λ ) j = 1 m ϵ ̂ j P j ( λ ) ,
Δ S n ( λ ) = S ( λ ) S n ( λ ) ,
Δ E d m ( λ ) = E d ( λ ) T u ( λ ) E d m ( λ ) ,
Δ E s m ( λ ) = E s ( λ ) T u ( λ ) E s m ( λ ) ,
Δ P m ( λ ) = P ( λ ) P m ( λ ) ,
I ( λ ) = { [ E d m ( λ ) + Δ E d m ( λ ) ] cos ( θ ) + K [ E s m ( λ ) + Δ E s m ( λ ) ] } { S n ( λ ) + Δ S n ( λ ) } + P m ( λ ) + Δ P m ( λ ) = E d m ( λ ) S n ( λ ) cos ( θ ) + K E s m ( λ ) S n ( λ ) + P m ( λ ) + ρ ( λ ) ,
E d m ( λ ) S n ( λ ) cos ( θ ) + K E s m ( λ ) S n ( λ ) + P m ( λ ) ,
Π i = [ E i d ( λ ) S 1 ( λ ) , , E i d ( λ ) S n ( λ ) , E i s ( λ ) S 1 ( λ ) , , E i s ( λ ) S n ( λ ) , P i ( λ ) ] ,
I ( λ ) P est ( λ ) = [ E d ( λ ) cos ( θ ) + K E s ( λ ) ] T u ( λ ) S ( λ ) + P ( λ ) P est ( λ ) .

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