Abstract

The average spectral power distribution of a set of measured daylight spectra, Eav(λ), is used for preliminary screening to select optimal sensor sets for daylight recovery. Spectra quite different from Eav(λ) are applied to the screened sets to obtain minimum total spectral error, which is closely related to recovery metrics but not to the coefficient of error. All basis functions should be utilized to make these two errors equal, to predict precisely the best sensor set, and to extend a set of few sensors to a set of many sensors. These are not acquirable by an exhaustive full search method.

© 2008 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. 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]
  2. Z. Pan, G. Healey, and D. Slater, “Global spectral irradiance variability and material discrimination at Boulder, Colorado,” J. Opt. Soc. Am. A 20, 513-521 (2003).
    [CrossRef]
  3. J. Romero, A. García-Beltrán, and J. Hernández-Andrés, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007-1014 (1997).
    [CrossRef]
  4. D. Judd, D. MacAdam, and G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031-1040 (1964).
    [CrossRef]
  5. 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]
  6. D. H. Marimont and B. A. Wandell, “Linear models of surface and illuminant spectra,” J. Opt. Soc. Am. A 9, 1905-1913(1992).
    [CrossRef] [PubMed]
  7. N. Shimano, “Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise,” Opt. Eng. 45, 013201(2006).
    [CrossRef]
  8. V. Cheung, S. Westland, C. Li, J. Hardeberg, and D. Connah, “Characterization of trichromatic color cameras by using a new multispectral imaging technique,” J. Opt. Soc. Am. A 22, 1231-1240 (2005).
    [CrossRef]
  9. J. L. Nieves, E. M. Valero, S. M. C. Nascimento, J. Hernández-Andrés, and J. Romero, “Multispectral synthesis of daylight using a commercial digital CCD camera,” Appl. Opt. 44, 5696-5703 (2005).
    [CrossRef] [PubMed]
  10. J. Hernández-Andrés, J. L. Nieves, E. M. Valero, and J. Romero, “Spectral-daylight recovery by use of only a few sensors,” J. Opt. Soc. Am. A 21, 13-23 (2004).
    [CrossRef]
  11. M. A. López-Álvarez, J. Hernández-Andrés, J. Romero, and R. L. Lee, Jr., “Designing a practical system for spectral imaging of skylight,” Appl. Opt. 44, 5688-5695 (2005).
    [CrossRef] [PubMed]
  12. A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, 1984).
  13. Collected CCD SPDs via http://140.118.121.195/.
  14. SENTECH, “CCD,” http://www.apisc.com/camera_sentech.htm.
  15. Micromedia, “CMOS,” http://www.micromedia.com.tw/tw/index.php.
  16. YGYES, “filter,” http://www.ygyes.com/en/product.html.
  17. FRAMOS, “LU110”, http://www.framos.de/www.dir/en/produkte/kameras.
  18. DVCCO, “CCD_ICX428,” http://www.dvcco.com/dvc-710_series.html.

2006 (1)

N. Shimano, “Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise,” Opt. Eng. 45, 013201(2006).
[CrossRef]

2005 (3)

2004 (1)

2003 (1)

1998 (2)

1997 (1)

1992 (1)

1964 (1)

Benites, L.

Cheung, V.

Connah, D.

García-Beltrán, A.

Hardeberg, J.

Healey, G.

Hernández-Andrés, J.

Judd, D.

Lee, R. L.

Li, C.

López-Álvarez, M. A.

MacAdam, D.

Marimont, D. H.

Nascimento, S. M. C.

Nieves, J. L.

Pan, Z.

Papoulis, A.

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, 1984).

Romero, J.

Shimano, N.

N. Shimano, “Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise,” Opt. Eng. 45, 013201(2006).
[CrossRef]

Slater, D.

Valero, E. M.

Wandell, B. A.

Westland, S.

Wyszecki, G.

Appl. Opt. (3)

J. Opt. Soc. Am. (1)

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

Opt. Eng. (1)

N. Shimano, “Optimization of spectral sensitivities with Gaussian distribution functions for a color image acquisition device in the presence of noise,” Opt. Eng. 45, 013201(2006).
[CrossRef]

Other (7)

A. Papoulis, Probability, Random Variables, and Stochastic Processes, 2nd ed. (McGraw-Hill, 1984).

Collected CCD SPDs via http://140.118.121.195/.

SENTECH, “CCD,” http://www.apisc.com/camera_sentech.htm.

Micromedia, “CMOS,” http://www.micromedia.com.tw/tw/index.php.

YGYES, “filter,” http://www.ygyes.com/en/product.html.

FRAMOS, “LU110”, http://www.framos.de/www.dir/en/produkte/kameras.

DVCCO, “CCD_ICX428,” http://www.dvcco.com/dvc-710_series.html.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (5)

Fig. 1
Fig. 1

Six basis functions for daylight recovery.

Fig. 2
Fig. 2

Three SPDs of dawn, noon, dusk, not in the training set, reconstructed by the six basis functions.

Fig. 3
Fig. 3

Histogram of δ av for 5005 sensor sets obtained by selecting 6 sensors from 15 proper sensors.

Fig. 4
Fig. 4

Six spectral responsivity functions of the best six-sensor set, number 25.

Fig. 5
Fig. 5

Spectral error of the top 1000 sensor combinations chosen by a full search method.

Tables (8)

Tables Icon

Table 1 Daylight Recovery Metrics of Different Daylight Spectra

Tables Icon

Table 2 Best 10 Sensor Sets Selected Relative to ε or ε ^ from 93 Candidates a

Tables Icon

Table 3 Metrics of Ten Best Sensor Sets with Six Sensors: Recovery Indices a

Tables Icon

Table 4 Top Ten Sensor Sets Obtained by a Full Search Method and by the Proposed Method Are the Same a

Tables Icon

Table 5 Deviations in the Response Value of E av ( λ ) for Sensor Set 25 under Different Noise Levels a

Tables Icon

Table 6 Rankings of the Ten Best Sensor Sets Changed under Different Noise Levels a

Tables Icon

Table 7 Recovery Metrics and Sensor Numbers of Optimal Three- to Six-Sensor Sets a

Tables Icon

Table 8 Recovery Metrics and Sensor Numbers of Optimal Three- to Six-Sensor Sets a

Equations (31)

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

E i ( λ ) = j = 1 k c i j * e j ( λ ) ,
c i j * = vis E i ( λ ) e j ( λ ) d λ .
( L M )
s 1 ( λ ) = s 1 ( λ ) , e 1 ( λ ) e 1 ( λ ) + s 1 ( λ ) , e 2 ( λ ) e 2 ( λ ) + s 1 ( λ ) , e k ( λ ) e k ( λ ) + r 1 ( λ ) s M ( λ ) = s M ( λ ) , e 1 ( λ ) e 1 ( λ ) + s M ( λ ) , e 2 ( λ ) e 2 ( λ ) + s M ( λ ) , e k ( λ ) e k ( λ ) + r M ( λ ) ,
[ s 1 ( λ ) s M ( λ ) ] = [ T ] [ e 1 ( λ ) e k ( λ ) ] + [ P ] [ e k + 1 ( λ ) e 61 ( λ ) ] ,
t i j = s i ( λ ) e j ( λ ) d λ , j = 1 , , k , p i j = s i ( λ ) e j + k ( λ ) d λ , j = 1 , , 61 k ,
Y i = [ s 1 ( λ ) E i ( λ ) d λ s M ( λ ) E i ( λ ) d λ ] = [ T ] [ c 1 * c k * ] + [ P ] [ c k + 1 * c 61 * ] = [ T ] c i * + [ P ] f i * .
Y i w = [ ( s 1 ( λ ) + n 1 ( λ ) ) E i ( λ ) d λ ( s M ( λ ) + n M ( λ ) ) E i ( λ ) d λ ] = { [ T ] + [ T w ] } [ c 1 * c k * ] + { [ P ] + [ P w ] } [ c k + 1 * c 61 * ] = { [ T ] + [ T w ] } c i * + { [ P ] + [ P w ] } f i * ,
t i j w = n i ( λ ) e j ( λ ) d λ , j = 1 , , k , p i j w = n i ( λ ) e j + k ( λ ) d λ , j = 1 , , 61 k ,
Δ Y i = [ T w ] c i * [ P w ] f i * .
Δ Y i = [ T w ] c i * .
Y av = [ Y 1 , av Y M , av ] = [ s 1 ( λ ) E av ( λ ) d λ s M ( λ ) E av ( λ ) d λ ] = [ T ] c av * + [ P ] f av * ,
[ T av ] + Y av c av * = c av c av * = δ av ,
[ E av ( 1 ) E av ( 61 ) ] [ E i ( 1 ) E i ( 61 ) ] = [ d i ( 1 ) d i ( 61 ) ] = d i .
E av = [ E av ( 1 ) E av ( 61 ) ] = { [ e 1 ( 1 ) e k ( 1 ) e 1 ( 61 ) e k ( 61 ) ] c av * + [ e k + 1 ( 1 ) e 61 ( 1 ) e k + 1 ( 61 ) e 61 ( 1 ) ] f av * } = [ U ] c av * + [ V ] f av * ,
E i = [ E i ( 1 ) E i ( 61 ) ] = [ U ] c i * + [ V ] f i * .
d i = [ U ] ( c av * c i * ) + [ V ] ( f av * f i * )
[ U ] ( c av * c i * ) = d i [ V ] ( f av * f i * ) .
[ U ] + { d i Δ i } ( c av * c i * ) = δ d .
c i * = c av * + δ d [ U ] + ( d i Δ i ) ,
c i = c av + [ T av ] + [ T av ] δ d [ T av ] + [ T av ] [ U ] + { d i Δ i } .
c i = c av * + δ av [ T av ] + [ T av ] [ U ] + ( d i Δ i ) + [ T av ] + [ T av ] δ d .
c i c i * = δ av { [ T av ] + [ T av ] [ U ] + ( d i Δ i ) [ U ] + ( d i Δ i ) } + { [ T av ] + [ T av ] I } δ d
c i c i * = δ av { [ T av ] + [ T av ] I } [ U ] + ( d i Δ i ) + { [ T av ] + [ T av ] I } δ d .
c i c i * = δ av { [ T av ] + [ T av ] I } [ U ] + ( d i Δ i ) ,
1 N i = 1 N c i c i * = 1 N i = 1 N δ av { [ T av ] + [ T av ] I } [ U ] + ( d i Δ i ) = ε .
( 30 6 )
( 30 6 )
( 15 6 )
( 30 6 ) = 593775
( 15 3 ) = 455

Metrics