Abstract

The spectral properties of outdoor illumination functions can vary significantly, owing to atmospheric conditions and scene geometry. Using a statistical analysis of a comprehensive physical model, we show that the variation in outdoor illumination functions over both the visible range (0.33–0.7 µm) and the visible/near-infrared range (0.4–2.5 µm) can be represented accurately by use of seven-dimensional linear models. The physical model includes solar and scattered radiation as well as the effects of atmospheric gases and aerosols. The modtran 3.5 code was employed for computing radiative transfer aspects of the model. We show that the new model has strong agreement over the visible wavelengths with the empirical study of Judd et al. [J. Opt. Soc. Am. 54, 1031 (1964)]. We also demonstrate the accuracy of the model over the 0.4–2.5-µm spectral range, using measured outdoor illumination functions.

© 1998 Optical Society of America

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References

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    [CrossRef]
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1998

1997

1996

1993

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]

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

D. J. Williams, A. Royer, N. T. O’Neill, S. Achal, G. Weale, “Reflectance extraction from CASI spectra using radiative transfer simulations and a rooftop irradiance collector,” Remote Sensing Environ. 44, 165–178 (1993).

1992

M. D’Zmura, “Color constancy: surface color from changing illumination,” J. Opt. Soc. Am. A 9, 490–493 (1992).
[CrossRef]

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

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

S. A. Clough, M. J. Iacono, J.-L. Moncet, “Line-by-line calculations of atmospheric fluxes and cooling rates: application to water vapor,” J. Geophys. Res. 97, 15,761–15,785 (1992).
[CrossRef]

1990

J. Ho, B. Funt, M. 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]

B. C. Gao, A. F. H. Goetz, “Column atmospheric water vapor and vegetation liquid water retrievals from airborne imaging spectrometer data,” J. Geophys. Res. 95, 3549–3564 (1990).
[CrossRef]

1989

D. Brainard, B. Wandell, W. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

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

1988

R. Gershon, A. Jepson, J. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755–758 (1988).

1986

1980

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

1978

1968

1966

1965

1964

Achal, S.

D. J. Williams, A. Royer, N. T. O’Neill, S. Achal, G. Weale, “Reflectance extraction from CASI spectra using radiative transfer simulations and a rooftop irradiance collector,” Remote Sensing Environ. 44, 165–178 (1993).

Acharya, P. K.

L. S. Bernstein, A. Berk, P. K. Acharya, D. C. Robertson, “Very narrow band model calculations of atmospheric fluxes and cooling rates,” J. Atmos. Sci. 53, 2887–2904 (1996).
[CrossRef]

Alley, R.

J. Conel, R. O. Green, G. Vane, C. Bruegge, R. Alley, “Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere,” in Imaging Spectrometry II, G. Vane, ed., Proc. SPIE834, 140–157 (1987).
[CrossRef]

Anderson, G. P.

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]

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]

Benites, L.

Benner, D. C.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Berk, A.

L. S. Bernstein, A. Berk, P. K. Acharya, D. C. Robertson, “Very narrow band model calculations of atmospheric fluxes and cooling rates,” J. Atmos. Sci. 53, 2887–2904 (1996).
[CrossRef]

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (Geophysics Laboratory, Bedford, Mass., 1989).

Bernstein, L. S.

L. S. Bernstein, A. Berk, P. K. Acharya, D. C. Robertson, “Very narrow band model calculations of atmospheric fluxes and cooling rates,” J. Atmos. Sci. 53, 2887–2904 (1996).
[CrossRef]

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (Geophysics Laboratory, Bedford, Mass., 1989).

Boshoff, M. C.

Brainard, D.

D. Brainard, B. Wandell, W. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

Brown, L. R.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Bruegge, C.

J. Conel, R. O. Green, G. Vane, C. Bruegge, R. Alley, “Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere,” in Imaging Spectrometry II, G. Vane, ed., Proc. SPIE834, 140–157 (1987).
[CrossRef]

Buchsbaum, G.

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

Camy-Peyret, C.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Chrien, T. G.

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

Clough, S. A.

S. A. Clough, M. J. Iacono, J.-L. Moncet, “Line-by-line calculations of atmospheric fluxes and cooling rates: application to water vapor,” J. Geophys. Res. 97, 15,761–15,785 (1992).
[CrossRef]

Cohen, J.

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

Conel, J.

J. Conel, R. O. Green, G. Vane, C. Bruegge, R. Alley, “Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere,” in Imaging Spectrometry II, G. Vane, ed., Proc. SPIE834, 140–157 (1987).
[CrossRef]

Cowan, W.

D. Brainard, B. Wandell, W. Cowan, “Black light: how sensors filter spectral variation of the illuminant,” IEEE Trans. Biomed. Eng. 36, 140–149 (1989).
[CrossRef] [PubMed]

D’Zmura, M.

Das, S. R.

Dixon, E. R.

Drew, M.

J. Ho, B. Funt, M. 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]

Du Toit, A. G.

Enmark, H. T.

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

Flaud, J.-M.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Funt, B.

J. Ho, B. Funt, M. 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]

Gamache, R. R.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Gao, B. C.

B. C. Gao, A. F. H. Goetz, “Column atmospheric water vapor and vegetation liquid water retrievals from airborne imaging spectrometer data,” J. Geophys. Res. 95, 3549–3564 (1990).
[CrossRef]

Garci´a-Beltrán, A.

Gershon, R.

R. Gershon, A. Jepson, J. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755–758 (1988).

Goetz, A. F. H.

B. C. Gao, A. F. H. Goetz, “Column atmospheric water vapor and vegetation liquid water retrievals from airborne imaging spectrometer data,” J. Geophys. Res. 95, 3549–3564 (1990).
[CrossRef]

Goldman, A.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Golub, G. H.

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

Green, R. O.

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

J. Conel, R. O. Green, G. Vane, C. Bruegge, R. Alley, “Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere,” in Imaging Spectrometry II, G. Vane, ed., Proc. SPIE834, 140–157 (1987).
[CrossRef]

Hallikainen, J.

Hansen, E. G.

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

Healey, G.

Hernández-Andrés, J.

Ho, J.

J. Ho, B. Funt, M. 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]

Iacono, M. J.

S. A. Clough, M. J. Iacono, J.-L. Moncet, “Line-by-line calculations of atmospheric fluxes and cooling rates: application to water vapor,” J. Geophys. Res. 97, 15,761–15,785 (1992).
[CrossRef]

Iverson, G.

Jaaskelainen, T.

Jepson, A.

R. Gershon, A. Jepson, J. Tsotsos, “From [R,G,B] to surface reflectance: computing color constant descriptors in images,” Perception 17, 755–758 (1988).

Judd, D. B.

Knuteson, R. O.

Kok, C. J.

MacAdam, D. L.

Malathy Devi, V.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Maloney, L.

Marimont, D.

Massie, S. T.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Moncet, J.-L.

S. A. Clough, M. J. Iacono, J.-L. Moncet, “Line-by-line calculations of atmospheric fluxes and cooling rates: application to water vapor,” J. Geophys. Res. 97, 15,761–15,785 (1992).
[CrossRef]

Nieves, J. L.

O’Neill, N. T.

D. J. Williams, A. Royer, N. T. O’Neill, S. Achal, G. Weale, “Reflectance extraction from CASI spectra using radiative transfer simulations and a rooftop irradiance collector,” Remote Sensing Environ. 44, 165–178 (1993).

Parkkinen, J. P. S.

Perrin, A.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Porter, W. M.

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

Revercomb, H. E.

Richter, R.

R. Richter, “Correction of atmospheric and topographic effects for high spatial resolution satellite imagery,” in Algorithms for Multispectral and Hyperspectral Imagery III, A. Iverson, S. S. Shen, eds., Proc. SPIE3071, 216–224 (1997).
[CrossRef]

Rinsland, C. P.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Robertson, D. C.

L. S. Bernstein, A. Berk, P. K. Acharya, D. C. Robertson, “Very narrow band model calculations of atmospheric fluxes and cooling rates,” J. Atmos. Sci. 53, 2887–2904 (1996).
[CrossRef]

A. Berk, L. S. Bernstein, D. C. Robertson, “modtran: a moderate resolution model for lowtran 7,” (Geophysics Laboratory, Bedford, Mass., 1989).

Romero, J.

Rothman, L. S.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Royer, A.

D. J. Williams, A. Royer, N. T. O’Neill, S. Achal, G. Weale, “Reflectance extraction from CASI spectra using radiative transfer simulations and a rooftop irradiance collector,” Remote Sensing Environ. 44, 165–178 (1993).

Sastri, V. D. P.

Smith, M. A. H.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Tipping, R. H.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Toth, R. A.

L. S. Rothman, R. R. Gamache, R. H. Tipping, C. P. Rinsland, M. A. H. Smith, D. C. Benner, V. Malathy Devi, J.-M. Flaud, C. Camy-Peyret, A. Perrin, A. Goldman, S. T. Massie, L. R. Brown, R. A. Toth, “The hitran molecular database: editions of 1991 and 1992,” J. Quant. Spectrosc. Radiat. Transf. 48, 469–507 (1992).
[CrossRef]

Tsotsos, J.

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J. Conel, R. O. Green, G. Vane, C. Bruegge, R. Alley, “Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere,” in Imaging Spectrometry II, G. Vane, ed., Proc. SPIE834, 140–157 (1987).
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Williams, D. J.

D. J. Williams, A. Royer, N. T. O’Neill, S. Achal, G. Weale, “Reflectance extraction from CASI spectra using radiative transfer simulations and a rooftop irradiance collector,” Remote Sensing Environ. 44, 165–178 (1993).

Winch, G. T.

Wyszecki, G.

Appl. Opt.

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[CrossRef] [PubMed]

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[CrossRef]

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

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J. Conel, R. O. Green, G. Vane, C. Bruegge, R. Alley, “Radiometric spectral characteristics and comparison of ways to compensate for the atmosphere,” in Imaging Spectrometry II, G. Vane, ed., Proc. SPIE834, 140–157 (1987).
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Figures (15)

Fig. 1
Fig. 1

Surface and solar geometry.

Fig. 2
Fig. 2

Ground-spectral-irradiance model.

Fig. 3
Fig. 3

Illumination function with absorption bands.

Fig. 4
Fig. 4

Ground spectral irradiance for two different conditions.

Fig. 5
Fig. 5

Error for linear model (0.33–0.7 µm).

Fig. 6
Fig. 6

Visible basis functions.

Fig. 7
Fig. 7

Fit for Judd mean vector E¯(λ).

Fig. 8
Fig. 8

Fit for Judd vector V1(λ).

Fig. 9
Fig. 9

Fit for Judd vector V2(λ).

Fig. 10
Fig. 10

Fit for Judd vector V3(λ).

Fig. 11
Fig. 11

Fit for Judd vector V4(λ).

Fig. 12
Fig. 12

Error for linear model (0.4–2.5 µm).

Fig. 13
Fig. 13

Visible/near-infrared basis functions.

Fig. 14
Fig. 14

Measured ground spectral irradiance and fit.

Fig. 15
Fig. 15

Measured ground spectral irradiance and fit.

Tables (2)

Tables Icon

Table 1 Range of Atmospheric and Geometric Parameters for Linear Model Computation

Tables Icon

Table 2 First Seven Basis Functions Computed over 0.33–0.7 µm

Equations (5)

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

L(λ)=KTd(θo, ϕo, λ)Eo(λ)cos(θo)+ϕ=02πθ=0π/2Es(θ, ϕ, λ)cos(θ)sin(θ)dθdϕ,
Li(λ)j=1Nσijlj(λ),
Ei=k=1WLi(λk)-j=1Nσijlj(λk)2.
ET=i=1MEi.
X=UΣVT.

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