Abstract

We analyze the use of linear models for IR spectral reflectance functions. Linear models have been studied extensively for the visible wavelengths and form the basis of several approaches to estimating surface properties from color images. The IR analysis is performed with measured spectral reflectance functions for 394 samples of natural and man-made materials. The mid-wave (3–5 µm) and long-wave (8–12.5 µm) atmospheric windows of the IR spectrum are considered separately. Since materials tend to have stronger spectral features over the 8–12.5 µm range, linear models for the long-wave IR require more parameters than for the mid-wave IR, in order to obtain the same accuracy. We show that a six-parameter linear model provides an excellent approximation for mid-wave (3–5 µm) reflectance functions and that a nine-parameter linear model provides a satisfactory approximation for long-wave (8–12.5 µm) reflectance functions.

© 1998 Optical Society of America

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References

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  1. G. Vane, R. Green, T. Chrien, H. Enmark, E. Hansen, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sensing Environ. 44, 127–143 (1993).
    [CrossRef]
  2. R. W. Basedow, D. C. Armer, M. E. Anderson, “HYDICE system: implementation and performance,” in Imaging Spectrometry, M. R. Descour, J. M. Mooney, D. L. Perry, L. R. Illing, eds., Proc. SPIE2480, 258–267 (1995).
    [CrossRef]
  3. J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369 (1964).
    [CrossRef]
  4. L. 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]
  5. J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
    [CrossRef]
  6. E. L. Krinov, “Spectral reflectance properties of natural formations,” (National Research Council of Canada, Ottawa, 1947).
  7. D. Nickerson, “Spectrophotometric data for a collection of Munsell samples,” (U.S. Department of Agriculture, Washington, D.C., 1957).
  8. B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9, 2–13 (1987).
    [CrossRef]
  9. D. Marimont, B. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905–1913 (1992).
    [CrossRef] [PubMed]
  10. G. Healey, S. Shafer, L. Wolff, eds., Physics-Based Vision: Principles and Practice, COLOR (Jones and Bartlett, Boston, 1992).
  11. G. Healey, Q.-T. Luong, “Color in computer vision: recent progress,” in Handbook of Pattern Recognition and Computer Vision, C. H. Chen, L. F. Pau, P. S. P. Wang, eds. (World Scientific, River Edge, N.J., 1997).
  12. L. Maloney, B. Wandell, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 1673–1683 (1986).
    [CrossRef] [PubMed]
  13. M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993).
    [CrossRef]
  14. M. D’Zmura, G. Iverson, “Color constancy. II. Results for two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2166–2180 (1993).
    [CrossRef]
  15. G. Healey, D. Slater, “Global color constancy: recognition of objects by use of illumination-invariant properties of color distributions,” J. Opt. Soc. Am. A 11, 3003–3010 (1994).
    [CrossRef]
  16. G. Healey, L. Wang, “Illumination-invariant recognition of texture in color images,” J. Opt. Soc. Am. A 12, 1877–1883 (1995).
    [CrossRef]
  17. D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
    [CrossRef]
  18. G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
    [CrossRef]
  19. S. L. Valley, ed., Handbook of Geophysics and Space Environments, (U.S. Air Force Cambridge Research Lab, Bedford, Mass., 1965).
  20. K. Nassau, The Physics and Chemistry of Color: the Fifteen Causes of Color (Wiley, New York, 1983).
  21. P. Slater, Remote Sensing, Optics and Optical Systems (Addison-Wesley, Reading, Mass., 1980).
  22. R. Siegel, J. Howell, Thermal Radiation Heat Transfer (McGraw-Hill, New York, 1981).
  23. G. R. Hunt, R. L. Vincent, “The behavior of spectral features in the infrared emission from particulate surfaces of various grain sizes,” J. Geophys. Res. 73, 6039–6046 (1968).
    [CrossRef]
  24. M. J. Bartholomew, A. B. Kahle, G. Hoover, “Infrared spectroscopy (2.3–20 µm) for the geological interpretation of remotely-sensed multispectral thermal infrared data,” Int. J. Remote Sens. 10, 529–544 (1989).
    [CrossRef]
  25. G. H. Golub, C. F. van Loan, Matrix Computations, (Johns Hopkins U. Press, Baltimore, Md., 1983).
  26. J. Salisbury, L. Walter, N. Vergo, D. D’Aria. Infrared (2.1–25 µm) Spectra of Minerals, (Johns Hopkins U. Press, Baltimore, Md., 1991).
  27. J. Salisbury, B. Hapke, J. Eastes, “Usefulness of weak bands in mid-infrared remote sensing of particulate planetary surfaces,” J. Geophys. Res. 92, 702–710 (1987).
    [CrossRef]
  28. R. Aines, G. Rossman, “Water in minerals? A peak in the infrared,” J. Geophys. Res. 89, 4059–4071 (1984).
    [CrossRef]
  29. M. Hass, G. Sutherland, “The infra-red spectrum and crystal structure of gypsum,” Proc. R. Soc. London 236, 427–445 (1956).
    [CrossRef]
  30. V. C. Farmer, ed., The Infrared Spectra of Minerals, Monograph 4 (Mineralogical Society, London, 1974).
  31. L. Walter, J. Salisbury, “Spectral characterization of igneous rocks in the 8 to 12 µm region,” J. Geophys. Res. 94, 9203–9213 (1989).
    [CrossRef]
  32. P. A. Estep-Barnes, “Infrared spectroscopy,” in Physical Methods in Determinative Mineralogy, 2nd ed., J. Zussman, ed. (Academic, New York, 1977), pp. 529–603.
  33. J. Thompson, J. Salisbury, “The mid-infrared reflectance of mineral mixtures (7–14 µm),” Remote Sensing Environ. 45, 1–13 (1993).
    [CrossRef]

1996 (2)

D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
[CrossRef]

G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
[CrossRef]

1995 (1)

1994 (1)

1993 (4)

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

M. D’Zmura, G. Iverson, “Color constancy. I. Basic theory of two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2148–2165 (1993).
[CrossRef]

M. D’Zmura, G. Iverson, “Color constancy. II. Results for two-stage linear recovery of spectral descriptions for lights and surfaces,” J. Opt. Soc. Am. A 10, 2166–2180 (1993).
[CrossRef]

J. Thompson, J. Salisbury, “The mid-infrared reflectance of mineral mixtures (7–14 µm),” Remote Sensing Environ. 45, 1–13 (1993).
[CrossRef]

1992 (1)

1989 (3)

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

M. J. Bartholomew, A. B. Kahle, G. Hoover, “Infrared spectroscopy (2.3–20 µm) for the geological interpretation of remotely-sensed multispectral thermal infrared data,” Int. J. Remote Sens. 10, 529–544 (1989).
[CrossRef]

L. Walter, J. Salisbury, “Spectral characterization of igneous rocks in the 8 to 12 µm region,” J. Geophys. Res. 94, 9203–9213 (1989).
[CrossRef]

1987 (2)

J. Salisbury, B. Hapke, J. Eastes, “Usefulness of weak bands in mid-infrared remote sensing of particulate planetary surfaces,” J. Geophys. Res. 92, 702–710 (1987).
[CrossRef]

B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

1986 (2)

1984 (1)

R. Aines, G. Rossman, “Water in minerals? A peak in the infrared,” J. Geophys. Res. 89, 4059–4071 (1984).
[CrossRef]

1968 (1)

G. R. Hunt, R. L. Vincent, “The behavior of spectral features in the infrared emission from particulate surfaces of various grain sizes,” J. Geophys. Res. 73, 6039–6046 (1968).
[CrossRef]

1964 (1)

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

1956 (1)

M. Hass, G. Sutherland, “The infra-red spectrum and crystal structure of gypsum,” Proc. R. Soc. London 236, 427–445 (1956).
[CrossRef]

Aines, R.

R. Aines, G. Rossman, “Water in minerals? A peak in the infrared,” J. Geophys. Res. 89, 4059–4071 (1984).
[CrossRef]

Anderson, M. E.

R. W. Basedow, D. C. Armer, M. E. Anderson, “HYDICE system: implementation and performance,” in Imaging Spectrometry, M. R. Descour, J. M. Mooney, D. L. Perry, L. R. Illing, eds., Proc. SPIE2480, 258–267 (1995).
[CrossRef]

Armer, D. C.

R. W. Basedow, D. C. Armer, M. E. Anderson, “HYDICE system: implementation and performance,” in Imaging Spectrometry, M. R. Descour, J. M. Mooney, D. L. Perry, L. R. Illing, eds., Proc. SPIE2480, 258–267 (1995).
[CrossRef]

Bartholomew, M. J.

M. J. Bartholomew, A. B. Kahle, G. Hoover, “Infrared spectroscopy (2.3–20 µm) for the geological interpretation of remotely-sensed multispectral thermal infrared data,” Int. J. Remote Sens. 10, 529–544 (1989).
[CrossRef]

Basedow, R. W.

R. W. Basedow, D. C. Armer, M. E. Anderson, “HYDICE system: implementation and performance,” in Imaging Spectrometry, M. R. Descour, J. M. Mooney, D. L. Perry, L. R. Illing, eds., Proc. SPIE2480, 258–267 (1995).
[CrossRef]

Chrien, T.

G. Vane, R. Green, T. Chrien, H. Enmark, E. Hansen, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sensing 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 (1964).
[CrossRef]

D’Aria, D.

J. Salisbury, L. Walter, N. Vergo, D. D’Aria. Infrared (2.1–25 µm) Spectra of Minerals, (Johns Hopkins U. Press, Baltimore, Md., 1991).

D’Zmura, M.

Eastes, J.

J. Salisbury, B. Hapke, J. Eastes, “Usefulness of weak bands in mid-infrared remote sensing of particulate planetary surfaces,” J. Geophys. Res. 92, 702–710 (1987).
[CrossRef]

Enmark, H.

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

Estep-Barnes, P. A.

P. A. Estep-Barnes, “Infrared spectroscopy,” in Physical Methods in Determinative Mineralogy, 2nd ed., J. Zussman, ed. (Academic, New York, 1977), pp. 529–603.

Golub, G. H.

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

Green, R.

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

Hallikainen, J.

Hansen, E.

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

Hapke, B.

J. Salisbury, B. Hapke, J. Eastes, “Usefulness of weak bands in mid-infrared remote sensing of particulate planetary surfaces,” J. Geophys. Res. 92, 702–710 (1987).
[CrossRef]

Hass, M.

M. Hass, G. Sutherland, “The infra-red spectrum and crystal structure of gypsum,” Proc. R. Soc. London 236, 427–445 (1956).
[CrossRef]

Healey, G.

D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
[CrossRef]

G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
[CrossRef]

G. Healey, L. Wang, “Illumination-invariant recognition of texture in color images,” J. Opt. Soc. Am. A 12, 1877–1883 (1995).
[CrossRef]

G. Healey, D. Slater, “Global color constancy: recognition of objects by use of illumination-invariant properties of color distributions,” J. Opt. Soc. Am. A 11, 3003–3010 (1994).
[CrossRef]

G. Healey, Q.-T. Luong, “Color in computer vision: recent progress,” in Handbook of Pattern Recognition and Computer Vision, C. H. Chen, L. F. Pau, P. S. P. Wang, eds. (World Scientific, River Edge, N.J., 1997).

Hoover, G.

M. J. Bartholomew, A. B. Kahle, G. Hoover, “Infrared spectroscopy (2.3–20 µm) for the geological interpretation of remotely-sensed multispectral thermal infrared data,” Int. J. Remote Sens. 10, 529–544 (1989).
[CrossRef]

Howell, J.

R. Siegel, J. Howell, Thermal Radiation Heat Transfer (McGraw-Hill, New York, 1981).

Hunt, G. R.

G. R. Hunt, R. L. Vincent, “The behavior of spectral features in the infrared emission from particulate surfaces of various grain sizes,” J. Geophys. Res. 73, 6039–6046 (1968).
[CrossRef]

Iverson, G.

Jaaskelainen, T.

Jain, A.

G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
[CrossRef]

Kahle, A. B.

M. J. Bartholomew, A. B. Kahle, G. Hoover, “Infrared spectroscopy (2.3–20 µm) for the geological interpretation of remotely-sensed multispectral thermal infrared data,” Int. J. Remote Sens. 10, 529–544 (1989).
[CrossRef]

Krinov, E. L.

E. L. Krinov, “Spectral reflectance properties of natural formations,” (National Research Council of Canada, Ottawa, 1947).

Luong, Q.-T.

G. Healey, Q.-T. Luong, “Color in computer vision: recent progress,” in Handbook of Pattern Recognition and Computer Vision, C. H. Chen, L. F. Pau, P. S. P. Wang, eds. (World Scientific, River Edge, N.J., 1997).

Maloney, L.

Marimont, D.

Nassau, K.

K. Nassau, The Physics and Chemistry of Color: the Fifteen Causes of Color (Wiley, New York, 1983).

Nickerson, D.

D. Nickerson, “Spectrophotometric data for a collection of Munsell samples,” (U.S. Department of Agriculture, Washington, D.C., 1957).

Parkkinen, J. P. S.

Porter, W.

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

Rossman, G.

R. Aines, G. Rossman, “Water in minerals? A peak in the infrared,” J. Geophys. Res. 89, 4059–4071 (1984).
[CrossRef]

Salisbury, J.

J. Thompson, J. Salisbury, “The mid-infrared reflectance of mineral mixtures (7–14 µm),” Remote Sensing Environ. 45, 1–13 (1993).
[CrossRef]

L. Walter, J. Salisbury, “Spectral characterization of igneous rocks in the 8 to 12 µm region,” J. Geophys. Res. 94, 9203–9213 (1989).
[CrossRef]

J. Salisbury, B. Hapke, J. Eastes, “Usefulness of weak bands in mid-infrared remote sensing of particulate planetary surfaces,” J. Geophys. Res. 92, 702–710 (1987).
[CrossRef]

J. Salisbury, L. Walter, N. Vergo, D. D’Aria. Infrared (2.1–25 µm) Spectra of Minerals, (Johns Hopkins U. Press, Baltimore, Md., 1991).

Siegel, R.

R. Siegel, J. Howell, Thermal Radiation Heat Transfer (McGraw-Hill, New York, 1981).

Slater, D.

D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
[CrossRef]

G. Healey, D. Slater, “Global color constancy: recognition of objects by use of illumination-invariant properties of color distributions,” J. Opt. Soc. Am. A 11, 3003–3010 (1994).
[CrossRef]

Slater, P.

P. Slater, Remote Sensing, Optics and Optical Systems (Addison-Wesley, Reading, Mass., 1980).

Sutherland, G.

M. Hass, G. Sutherland, “The infra-red spectrum and crystal structure of gypsum,” Proc. R. Soc. London 236, 427–445 (1956).
[CrossRef]

Thompson, J.

J. Thompson, J. Salisbury, “The mid-infrared reflectance of mineral mixtures (7–14 µm),” Remote Sensing Environ. 45, 1–13 (1993).
[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. Chrien, H. Enmark, E. Hansen, W. Porter, “The airborne visible infrared imaging spectrometer,” Remote Sensing Environ. 44, 127–143 (1993).
[CrossRef]

Vergo, N.

J. Salisbury, L. Walter, N. Vergo, D. D’Aria. Infrared (2.1–25 µm) Spectra of Minerals, (Johns Hopkins U. Press, Baltimore, Md., 1991).

Vincent, R. L.

G. R. Hunt, R. L. Vincent, “The behavior of spectral features in the infrared emission from particulate surfaces of various grain sizes,” J. Geophys. Res. 73, 6039–6046 (1968).
[CrossRef]

Walter, L.

L. Walter, J. Salisbury, “Spectral characterization of igneous rocks in the 8 to 12 µm region,” J. Geophys. Res. 94, 9203–9213 (1989).
[CrossRef]

J. Salisbury, L. Walter, N. Vergo, D. D’Aria. Infrared (2.1–25 µm) Spectra of Minerals, (Johns Hopkins U. Press, Baltimore, Md., 1991).

Wandell, B.

Wang, L.

IEEE Trans. Pattern. Anal. Mach. Intell. (3)

B. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern. Anal. Mach. Intell. PAMI-9, 2–13 (1987).
[CrossRef]

D. Slater, G. Healey, “The illumination-invariant recognition of 3D objects using local color invariants,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 206–210 (1996).
[CrossRef]

G. Healey, A. Jain, “Retrieving multispectral satellite images using physics-based invariant representations,” IEEE Trans. Pattern. Anal. Mach. Intell. 18, 842–848 (1996).
[CrossRef]

Int. J. Remote Sens. (1)

M. J. Bartholomew, A. B. Kahle, G. Hoover, “Infrared spectroscopy (2.3–20 µm) for the geological interpretation of remotely-sensed multispectral thermal infrared data,” Int. J. Remote Sens. 10, 529–544 (1989).
[CrossRef]

J. Geophys. Res. (4)

L. Walter, J. Salisbury, “Spectral characterization of igneous rocks in the 8 to 12 µm region,” J. Geophys. Res. 94, 9203–9213 (1989).
[CrossRef]

G. R. Hunt, R. L. Vincent, “The behavior of spectral features in the infrared emission from particulate surfaces of various grain sizes,” J. Geophys. Res. 73, 6039–6046 (1968).
[CrossRef]

J. Salisbury, B. Hapke, J. Eastes, “Usefulness of weak bands in mid-infrared remote sensing of particulate planetary surfaces,” J. Geophys. Res. 92, 702–710 (1987).
[CrossRef]

R. Aines, G. Rossman, “Water in minerals? A peak in the infrared,” J. Geophys. Res. 89, 4059–4071 (1984).
[CrossRef]

J. Opt. Soc. Am. A (8)

Proc. R. Soc. London (1)

M. Hass, G. Sutherland, “The infra-red spectrum and crystal structure of gypsum,” Proc. R. Soc. London 236, 427–445 (1956).
[CrossRef]

Psychon. Sci. (1)

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

Remote Sensing Environ. (2)

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

J. Thompson, J. Salisbury, “The mid-infrared reflectance of mineral mixtures (7–14 µm),” Remote Sensing Environ. 45, 1–13 (1993).
[CrossRef]

Other (13)

P. A. Estep-Barnes, “Infrared spectroscopy,” in Physical Methods in Determinative Mineralogy, 2nd ed., J. Zussman, ed. (Academic, New York, 1977), pp. 529–603.

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

J. Salisbury, L. Walter, N. Vergo, D. D’Aria. Infrared (2.1–25 µm) Spectra of Minerals, (Johns Hopkins U. Press, Baltimore, Md., 1991).

R. W. Basedow, D. C. Armer, M. E. Anderson, “HYDICE system: implementation and performance,” in Imaging Spectrometry, M. R. Descour, J. M. Mooney, D. L. Perry, L. R. Illing, eds., Proc. SPIE2480, 258–267 (1995).
[CrossRef]

V. C. Farmer, ed., The Infrared Spectra of Minerals, Monograph 4 (Mineralogical Society, London, 1974).

E. L. Krinov, “Spectral reflectance properties of natural formations,” (National Research Council of Canada, Ottawa, 1947).

D. Nickerson, “Spectrophotometric data for a collection of Munsell samples,” (U.S. Department of Agriculture, Washington, D.C., 1957).

G. Healey, S. Shafer, L. Wolff, eds., Physics-Based Vision: Principles and Practice, COLOR (Jones and Bartlett, Boston, 1992).

G. Healey, Q.-T. Luong, “Color in computer vision: recent progress,” in Handbook of Pattern Recognition and Computer Vision, C. H. Chen, L. F. Pau, P. S. P. Wang, eds. (World Scientific, River Edge, N.J., 1997).

S. L. Valley, ed., Handbook of Geophysics and Space Environments, (U.S. Air Force Cambridge Research Lab, Bedford, Mass., 1965).

K. Nassau, The Physics and Chemistry of Color: the Fifteen Causes of Color (Wiley, New York, 1983).

P. Slater, Remote Sensing, Optics and Optical Systems (Addison-Wesley, Reading, Mass., 1980).

R. Siegel, J. Howell, Thermal Radiation Heat Transfer (McGraw-Hill, New York, 1981).

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Figures (34)

Fig. 1
Fig. 1

Basis functions (3–5 µm).

Fig. 2
Fig. 2

Average error for all materials for 3–5 µm.

Fig. 3
Fig. 3

Average error for material subsets for 3–5 µm.

Fig. 4
Fig. 4

Ei distributions (3–5 µm).

Fig. 5
Fig. 5

Median fit (2 basis functions).

Fig. 6
Fig. 6

Median fit (3 basis functions).

Fig. 7
Fig. 7

Median fit (4 basis functions).

Fig. 8
Fig. 8

Worst fit (2 basis functions).

Fig. 9
Fig. 9

Worst fit (3 basis functions).

Fig. 10
Fig. 10

Worst fit (4 basis functions).

Fig. 11
Fig. 11

Median fit (5 basis functions).

Fig. 12
Fig. 12

Median fit (6 basis functions).

Fig. 13
Fig. 13

Worst fit (5 basis functions).

Fig. 14
Fig. 14

Worst fit (6 basis functions).

Fig. 15
Fig. 15

Basis functions (8–12.5 µm).

Fig. 16
Fig. 16

Average error for all materials for 8–12.5 µm.

Fig. 17
Fig. 17

Average error for material subsets for 8–12.5 µm.

Fig. 18
Fig. 18

Ei distributions (8-12.5f µm).

Fig. 19
Fig. 19

Median fit (2 basis functions).

Fig. 20
Fig. 20

Median fit (3 basis functions).

Fig. 21
Fig. 21

Median fit (4 basis functions).

Fig. 22
Fig. 22

Median fit (5 basis functions).

Fig. 23
Fig. 23

Worst fit (2 basis functions).

Fig. 24
Fig. 24

Worst fit (3 basis functions).

Fig. 25
Fig. 25

Worst fit (4 basis functions).

Fig. 26
Fig. 26

Worst fit (5 basis functions).

Fig. 27
Fig. 27

Median fit (6 basis functions).

Fig. 28
Fig. 28

Median fit (7 basis functions).

Fig. 29
Fig. 29

Median fit (8 basis functions).

Fig. 30
Fig. 30

Median fit (9 basis functions).

Fig. 31
Fig. 31

Worst fit (6 basis functions).

Fig. 32
Fig. 32

Worst fit (7 basis functions).

Fig. 33
Fig. 33

Worst fit (8 basis functions).

Fig. 34
Fig. 34

Worst fit (9 basis functions).

Tables (2)

Tables Icon

Table 1 Median and Worst Fits (3–5 µm)

Tables Icon

Table 2 Median and Worst Fits (8–12.5 µm)

Equations (4)

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

si(λ)1jnσijSj(λ).
Ei=1kWsi(λk)-1jnσijSj(λk)2.
ET=1iMEi,
1kW[si(λk)]2=1.

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