Abstract

Our aim is to develop a method for obtaining the reflectance spectra of samples in the near-infrared (NIR) region (800–1000 nm) by using a small number of measurements performed with a conventional CCD camera (multispectral imaging). We experimentally determined the spectral sensitivity of the CCD camera in the NIR range, used a method based on principal component analysis to reconstruct the spectral reflectance of the samples, and analyzed the number and shape of the filters that need to be used to apply this method. Finally we obtained the reflectance spectra of a set of 30 spectral curves by numerical simulation. The small amount of errors in the spectral reconstruction shows the potential of this method for reconstructing spectral reflectances in the NIR range.

© 2003 Optical Society of America

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References

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    [CrossRef]
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  23. M. Wolski, C. A. Bouman, J. P. Allebach, E. Walowit, “Optimization of sensor response functions for colorimetry of reflective and emissive objects,” IEEE Trans. Image Process. 5, 507–517 (1996).
    [CrossRef] [PubMed]
  24. M. J. Vrhel, H. J. Trussell, “Design and realization of optimal color filters for multiilluminant color correction,” J. Electron. Imaging 4, 6–14 (1995).
    [CrossRef]
  25. M. J. Vrhel, H. J. Trussell, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
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  26. G. Sharma, H. J. Trussell, “Figures of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
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2002 (1)

F. M. Martinez-Verdú, J. Pujol, P. Capilla, “Calculation of the color matching functions of digital cameras from their complete spectral sensitivities,” J. Imaging Sci. Technol. 46, 15–25 (2002).

2001 (1)

G. Hong, M. R. Luo, P. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modeling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

2000 (3)

D. Scribner, P. Warren, J. Schuler, “Extending color vision methods to bands beyond the visible,” Mach. Vision Appl. 11, 306–312 (2000).
[CrossRef]

M. D. Mermelstein, K. A. Snail, R. G. Priest, “Spectral and radiometric calibration of midwave and longwave infrared cameras,” Opt. Eng. 39, 347–352 (2000).
[CrossRef]

F. Imai, R. S. Berns, “Comparative analysis of spectral reflectance reconstruction in various spaces using a trichromatic camera system,” J. Imaging Sci. Technol. 44, 280–287 (2000).

1999 (1)

1998 (1)

D. Scribner, P. Warren, J. Schuler, M. Satyshur, M. Kruer, “Infrared color vision: an approach to sensor fusion,” Opt. Photon. News 9, 27–32 (1998).
[CrossRef]

1997 (3)

G. Sharma, H. J. Trussell, “Figures of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
[CrossRef] [PubMed]

P. L. Vora, H. J. Trussell, “Mathematical methods for the design of color scanning filters,” IEEE Trans. Image Process. 6, 312–320 (1997).
[CrossRef] [PubMed]

P. L. Vora, H. J. Trussell, “Mathematical methods for the analysis of color scanning filters,” IEEE Trans. Image Process. 6, 321–327 (1997).
[CrossRef] [PubMed]

1996 (1)

M. Wolski, C. A. Bouman, J. P. Allebach, E. Walowit, “Optimization of sensor response functions for colorimetry of reflective and emissive objects,” IEEE Trans. Image Process. 5, 507–517 (1996).
[CrossRef] [PubMed]

1995 (1)

M. J. Vrhel, H. J. Trussell, “Design and realization of optimal color filters for multiilluminant color correction,” J. Electron. Imaging 4, 6–14 (1995).
[CrossRef]

1994 (2)

M. J. Vrhel, H. J. Trussell, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef] [PubMed]

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

1993 (1)

1992 (1)

M. J. Vrhel, H. J. Trussell, “Color correction using principal components,” Color Res. Appl. 17, 4–9 (1992).
[CrossRef]

1989 (1)

1963 (1)

Allebach, J. P.

M. Wolski, C. A. Bouman, J. P. Allebach, E. Walowit, “Optimization of sensor response functions for colorimetry of reflective and emissive objects,” IEEE Trans. Image Process. 5, 507–517 (1996).
[CrossRef] [PubMed]

Berns, R. S.

F. Imai, R. S. Berns, “Comparative analysis of spectral reflectance reconstruction in various spaces using a trichromatic camera system,” J. Imaging Sci. Technol. 44, 280–287 (2000).

Boscolo, A.

Bouman, C. A.

M. Wolski, C. A. Bouman, J. P. Allebach, E. Walowit, “Optimization of sensor response functions for colorimetry of reflective and emissive objects,” IEEE Trans. Image Process. 5, 507–517 (1996).
[CrossRef] [PubMed]

Bouzada, A.

F. M. Martinez-Verdú, J. Pujol, A. Bouzada, P. Capilla, “Spectroradiometric characterization of the spectral linearity of a conventional digital camera,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts IV, G. B. Beretta, R. Eschbach, eds., Proc. SPIE3648, 279–290 (1999).
[CrossRef]

Brettel, H.

J. Y. Hardeberg, F. Schmitt, H. Brettel, J. Crettez, H. Maı̂tre, “Multispectral image acquisition and simulation of illuminant changes,” in Colour Imaging: Vision and Technology, L. W. MacDonald, M. R. Luo, eds. (Wiley, Chichester, UK, 1999), pp. 145–164.

J. Y. Hardeberg, H. Brettel, F. Schmitt, “Spectral characterization of electronic cameras,” in Electronic Imaging: Processing, Printing and Publishing in Color, J. Bares, ed., Proc. SPIE3409, 100–109 (1998).
[CrossRef]

Burns, D. A.

D. A. Burns, E. W. Ciurczak, Handbook of Near-Infrared Analysis (NIR Publications, Chichester, West Sussex, UK, 1999).

Capilla, P.

F. M. Martinez-Verdú, J. Pujol, P. Capilla, “Calculation of the color matching functions of digital cameras from their complete spectral sensitivities,” J. Imaging Sci. Technol. 46, 15–25 (2002).

F. M. Martinez-Verdú, J. Pujol, A. Bouzada, P. Capilla, “Spectroradiometric characterization of the spectral linearity of a conventional digital camera,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts IV, G. B. Beretta, R. Eschbach, eds., Proc. SPIE3648, 279–290 (1999).
[CrossRef]

Chang, Y.

Ciurczak, E. W.

D. A. Burns, E. W. Ciurczak, Handbook of Near-Infrared Analysis (NIR Publications, Chichester, West Sussex, UK, 1999).

Crettez, J.

J. Y. Hardeberg, F. Schmitt, H. Brettel, J. Crettez, H. Maı̂tre, “Multispectral image acquisition and simulation of illuminant changes,” in Colour Imaging: Vision and Technology, L. W. MacDonald, M. R. Luo, eds. (Wiley, Chichester, UK, 1999), pp. 145–164.

Farrell, J. E.

P. M. Hubel, D. Sherman, J. E. Farrell, “A comparison of methods of sensor spectral sensitivity estimation,” in Proceedings of the Second Color Imaging Conference: Color Science, Systems, and Applications [The Society for Imaging Science and Technology (IST), 7003 Kilworth Lane, Springfield, Va. 22151, 1994], Vol. 48, pp. 45–48 (ISBN: 0-89208-180-5).

Gershon, R.

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

Hackwood, S.

Hardeberg, J. Y.

J. Y. Hardeberg, H. Brettel, F. Schmitt, “Spectral characterization of electronic cameras,” in Electronic Imaging: Processing, Printing and Publishing in Color, J. Bares, ed., Proc. SPIE3409, 100–109 (1998).
[CrossRef]

J. Y. Hardeberg, F. Schmitt, H. Brettel, J. Crettez, H. Maı̂tre, “Multispectral image acquisition and simulation of illuminant changes,” in Colour Imaging: Vision and Technology, L. W. MacDonald, M. R. Luo, eds. (Wiley, Chichester, UK, 1999), pp. 145–164.

Holst, G. C.

G. C. Holst, CCD Arrays, Cameras and Displays (SPIE Press, Bellingham, Wash., 1998).

G. C. Holst, “Solid-state cameras,” in Handbook of Optics, Vol. 3, M. Bass, J. M. Enoch, E. W. Van Stryland, W. L. Wolfe, eds. (McGraw-Hill, New York, 2001), pp. 4.1–4.21.

Hong, G.

G. Hong, M. R. Luo, P. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modeling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

Hubel, P. M.

P. M. Hubel, D. Sherman, J. E. Farrell, “A comparison of methods of sensor spectral sensitivity estimation,” in Proceedings of the Second Color Imaging Conference: Color Science, Systems, and Applications [The Society for Imaging Science and Technology (IST), 7003 Kilworth Lane, Springfield, Va. 22151, 1994], Vol. 48, pp. 45–48 (ISBN: 0-89208-180-5).

Imai, F.

F. Imai, R. S. Berns, “Comparative analysis of spectral reflectance reconstruction in various spaces using a trichromatic camera system,” J. Imaging Sci. Technol. 44, 280–287 (2000).

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).

Ji, W.

L. W. MacDonald, W. Ji, “Color characterization of a high-resolution digital camera,” in Proceedings of the First European Conference on Color in Graphics, Imaging, and Vision (CGIV2002) [Society for Imaging Science and Technology (IST), 7003 Kilworth Lane, Springfield, Va. 22151, 2002], Vol. 1, pp. 433–437 (ISBN 0-89208-239-9).

König, F.

F. König, “Reconstruction of natural spectra from a color sensor using nonlinear estimation methods,” in Proceedings of IST 50th Annual Conference (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 454–458.

Kruer, M.

D. Scribner, P. Warren, J. Schuler, M. Satyshur, M. Kruer, “Infrared color vision: an approach to sensor fusion,” Opt. Photon. News 9, 27–32 (1998).
[CrossRef]

Liang, P.

Luo, M. R.

G. Hong, M. R. Luo, P. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modeling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

MacDonald, L. W.

L. W. MacDonald, W. Ji, “Color characterization of a high-resolution digital camera,” in Proceedings of the First European Conference on Color in Graphics, Imaging, and Vision (CGIV2002) [Society for Imaging Science and Technology (IST), 7003 Kilworth Lane, Springfield, Va. 22151, 2002], Vol. 1, pp. 433–437 (ISBN 0-89208-239-9).

Mai^tre, H.

J. Y. Hardeberg, F. Schmitt, H. Brettel, J. Crettez, H. Maı̂tre, “Multispectral image acquisition and simulation of illuminant changes,” in Colour Imaging: Vision and Technology, L. W. MacDonald, M. R. Luo, eds. (Wiley, Chichester, UK, 1999), pp. 145–164.

Martinez-Verdú, F. M.

F. M. Martinez-Verdú, J. Pujol, P. Capilla, “Calculation of the color matching functions of digital cameras from their complete spectral sensitivities,” J. Imaging Sci. Technol. 46, 15–25 (2002).

F. M. Martinez-Verdú, J. Pujol, A. Bouzada, P. Capilla, “Spectroradiometric characterization of the spectral linearity of a conventional digital camera,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts IV, G. B. Beretta, R. Eschbach, eds., Proc. SPIE3648, 279–290 (1999).
[CrossRef]

Mermelstein, M. D.

M. D. Mermelstein, K. A. Snail, R. G. Priest, “Spectral and radiometric calibration of midwave and longwave infrared cameras,” Opt. Eng. 39, 347–352 (2000).
[CrossRef]

Poletto, L.

Priest, R. G.

M. D. Mermelstein, K. A. Snail, R. G. Priest, “Spectral and radiometric calibration of midwave and longwave infrared cameras,” Opt. Eng. 39, 347–352 (2000).
[CrossRef]

Pujol, J.

F. M. Martinez-Verdú, J. Pujol, P. Capilla, “Calculation of the color matching functions of digital cameras from their complete spectral sensitivities,” J. Imaging Sci. Technol. 46, 15–25 (2002).

F. M. Martinez-Verdú, J. Pujol, A. Bouzada, P. Capilla, “Spectroradiometric characterization of the spectral linearity of a conventional digital camera,” in Color Imaging: Device-Independent Color, Color Hardcopy, and Graphic Arts IV, G. B. Beretta, R. Eschbach, eds., Proc. SPIE3648, 279–290 (1999).
[CrossRef]

Rhodes, P.

G. Hong, M. R. Luo, P. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modeling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

Satyshur, M.

D. Scribner, P. Warren, J. Schuler, M. Satyshur, M. Kruer, “Infrared color vision: an approach to sensor fusion,” Opt. Photon. News 9, 27–32 (1998).
[CrossRef]

Schmitt, F.

J. Y. Hardeberg, F. Schmitt, H. Brettel, J. Crettez, H. Maı̂tre, “Multispectral image acquisition and simulation of illuminant changes,” in Colour Imaging: Vision and Technology, L. W. MacDonald, M. R. Luo, eds. (Wiley, Chichester, UK, 1999), pp. 145–164.

J. Y. Hardeberg, H. Brettel, F. Schmitt, “Spectral characterization of electronic cameras,” in Electronic Imaging: Processing, Printing and Publishing in Color, J. Bares, ed., Proc. SPIE3409, 100–109 (1998).
[CrossRef]

Schuler, J.

D. Scribner, P. Warren, J. Schuler, “Extending color vision methods to bands beyond the visible,” Mach. Vision Appl. 11, 306–312 (2000).
[CrossRef]

D. Scribner, P. Warren, J. Schuler, M. Satyshur, M. Kruer, “Infrared color vision: an approach to sensor fusion,” Opt. Photon. News 9, 27–32 (1998).
[CrossRef]

Scribner, D.

D. Scribner, P. Warren, J. Schuler, “Extending color vision methods to bands beyond the visible,” Mach. Vision Appl. 11, 306–312 (2000).
[CrossRef]

D. Scribner, P. Warren, J. Schuler, M. Satyshur, M. Kruer, “Infrared color vision: an approach to sensor fusion,” Opt. Photon. News 9, 27–32 (1998).
[CrossRef]

Sharma, G.

G. Sharma, H. J. Trussell, “Figures of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
[CrossRef] [PubMed]

Sherman, D.

P. M. Hubel, D. Sherman, J. E. Farrell, “A comparison of methods of sensor spectral sensitivity estimation,” in Proceedings of the Second Color Imaging Conference: Color Science, Systems, and Applications [The Society for Imaging Science and Technology (IST), 7003 Kilworth Lane, Springfield, Va. 22151, 1994], Vol. 48, pp. 45–48 (ISBN: 0-89208-180-5).

Simonds, J. L.

Snail, K. A.

M. D. Mermelstein, K. A. Snail, R. G. Priest, “Spectral and radiometric calibration of midwave and longwave infrared cameras,” Opt. Eng. 39, 347–352 (2000).
[CrossRef]

Tondello, G.

Trussell, H. J.

G. Sharma, H. J. Trussell, “Figures of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
[CrossRef] [PubMed]

P. L. Vora, H. J. Trussell, “Mathematical methods for the analysis of color scanning filters,” IEEE Trans. Image Process. 6, 321–327 (1997).
[CrossRef] [PubMed]

P. L. Vora, H. J. Trussell, “Mathematical methods for the design of color scanning filters,” IEEE Trans. Image Process. 6, 312–320 (1997).
[CrossRef] [PubMed]

M. J. Vrhel, H. J. Trussell, “Design and realization of optimal color filters for multiilluminant color correction,” J. Electron. Imaging 4, 6–14 (1995).
[CrossRef]

M. J. Vrhel, H. J. Trussell, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef] [PubMed]

P. L. Vora, H. J. Trussell, “Measure of goodness of a set of color-scanning filters,” J. Opt. Soc. Am. A 10, 1499–1508 (1993).
[CrossRef]

M. J. Vrhel, H. J. Trussell, “Color correction using principal components,” Color Res. Appl. 17, 4–9 (1992).
[CrossRef]

Vora, P. L.

P. L. Vora, H. J. Trussell, “Mathematical methods for the design of color scanning filters,” IEEE Trans. Image Process. 6, 312–320 (1997).
[CrossRef] [PubMed]

P. L. Vora, H. J. Trussell, “Mathematical methods for the analysis of color scanning filters,” IEEE Trans. Image Process. 6, 321–327 (1997).
[CrossRef] [PubMed]

P. L. Vora, H. J. Trussell, “Measure of goodness of a set of color-scanning filters,” J. Opt. Soc. Am. A 10, 1499–1508 (1993).
[CrossRef]

Vrhel, M. J.

M. J. Vrhel, H. J. Trussell, “Design and realization of optimal color filters for multiilluminant color correction,” J. Electron. Imaging 4, 6–14 (1995).
[CrossRef]

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, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef] [PubMed]

M. J. Vrhel, H. J. Trussell, “Color correction using principal components,” Color Res. Appl. 17, 4–9 (1992).
[CrossRef]

Walowit, E.

M. Wolski, C. A. Bouman, J. P. Allebach, E. Walowit, “Optimization of sensor response functions for colorimetry of reflective and emissive objects,” IEEE Trans. Image Process. 5, 507–517 (1996).
[CrossRef] [PubMed]

Warren, P.

D. Scribner, P. Warren, J. Schuler, “Extending color vision methods to bands beyond the visible,” Mach. Vision Appl. 11, 306–312 (2000).
[CrossRef]

D. Scribner, P. Warren, J. Schuler, M. Satyshur, M. Kruer, “Infrared color vision: an approach to sensor fusion,” Opt. Photon. News 9, 27–32 (1998).
[CrossRef]

Wolski, M.

M. Wolski, C. A. Bouman, J. P. Allebach, E. Walowit, “Optimization of sensor response functions for colorimetry of reflective and emissive objects,” IEEE Trans. Image Process. 5, 507–517 (1996).
[CrossRef] [PubMed]

Appl. Opt. (2)

Color Res. Appl. (3)

G. Hong, M. R. Luo, P. Rhodes, “A study of digital camera colorimetric characterization based on polynomial modeling,” Color Res. Appl. 26, 76–84 (2001).
[CrossRef]

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 components,” Color Res. Appl. 17, 4–9 (1992).
[CrossRef]

IEEE Trans. Image Process. (5)

P. L. Vora, H. J. Trussell, “Mathematical methods for the design of color scanning filters,” IEEE Trans. Image Process. 6, 312–320 (1997).
[CrossRef] [PubMed]

P. L. Vora, H. J. Trussell, “Mathematical methods for the analysis of color scanning filters,” IEEE Trans. Image Process. 6, 321–327 (1997).
[CrossRef] [PubMed]

M. Wolski, C. A. Bouman, J. P. Allebach, E. Walowit, “Optimization of sensor response functions for colorimetry of reflective and emissive objects,” IEEE Trans. Image Process. 5, 507–517 (1996).
[CrossRef] [PubMed]

M. J. Vrhel, H. J. Trussell, “Filter considerations in color correction,” IEEE Trans. Image Process. 3, 147–161 (1994).
[CrossRef] [PubMed]

G. Sharma, H. J. Trussell, “Figures of merit for color scanners,” IEEE Trans. Image Process. 6, 990–1001 (1997).
[CrossRef] [PubMed]

J. Electron. Imaging (1)

M. J. Vrhel, H. J. Trussell, “Design and realization of optimal color filters for multiilluminant color correction,” J. Electron. Imaging 4, 6–14 (1995).
[CrossRef]

J. Imaging Sci. Technol. (2)

F. M. Martinez-Verdú, J. Pujol, P. Capilla, “Calculation of the color matching functions of digital cameras from their complete spectral sensitivities,” J. Imaging Sci. Technol. 46, 15–25 (2002).

F. Imai, R. S. Berns, “Comparative analysis of spectral reflectance reconstruction in various spaces using a trichromatic camera system,” J. Imaging Sci. Technol. 44, 280–287 (2000).

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

Mach. Vision Appl. (1)

D. Scribner, P. Warren, J. Schuler, “Extending color vision methods to bands beyond the visible,” Mach. Vision Appl. 11, 306–312 (2000).
[CrossRef]

Opt. Eng. (1)

M. D. Mermelstein, K. A. Snail, R. G. Priest, “Spectral and radiometric calibration of midwave and longwave infrared cameras,” Opt. Eng. 39, 347–352 (2000).
[CrossRef]

Opt. Photon. News (1)

D. Scribner, P. Warren, J. Schuler, M. Satyshur, M. Kruer, “Infrared color vision: an approach to sensor fusion,” Opt. Photon. News 9, 27–32 (1998).
[CrossRef]

Other (10)

G. C. Holst, CCD Arrays, Cameras and Displays (SPIE Press, Bellingham, Wash., 1998).

G. C. Holst, “Solid-state cameras,” in Handbook of Optics, Vol. 3, M. Bass, J. M. Enoch, E. W. Van Stryland, W. L. Wolfe, eds. (McGraw-Hill, New York, 2001), pp. 4.1–4.21.

D. A. Burns, E. W. Ciurczak, Handbook of Near-Infrared Analysis (NIR Publications, Chichester, West Sussex, UK, 1999).

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[CrossRef]

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Figures (14)

Fig. 1
Fig. 1

Experimental setup for spectral characterization.

Fig. 2
Fig. 2

Complete chain of the multichannel image-acquisition system and the final spectral-reconstruction step.

Fig. 3
Fig. 3

Responsivity of the JAI CV-M10 camera corresponding to λ = 900 nm.

Fig. 4
Fig. 4

Action spectrum of the JAI CV-M10 camera corresponding to λ = 900 nm.

Fig. 5
Fig. 5

Relative action spectrum corresponding to the following normalized outputs: 0.078, 0.1, 0.2, 0.3, 0.5, 0.6, 0.7, and 0.8.

Fig. 6
Fig. 6

Solid curve, dots, experimental relative spectral sensitivity of the JAI CV-M10 camera; dashed line, corresponding standard deviation and relative spectral sensitivity provided by the manufacturer.

Fig. 7
Fig. 7

Spectral reflectance curves of eight representative samples (S1, S2, S3, S4, S5, S6, S7, S8) belonging to the original data matrix: solid circles, theoretical curves; open circles, real curves).

Fig. 8
Fig. 8

Spectral radiance of the halogen lamps used in the simulation.

Fig. 9
Fig. 9

Spectral transmittance of the five optimum filters obtained with the illuminant of color temperature, Tc 1 = 2852 K.

Fig. 10
Fig. 10

Spectral sensitivity of the five optimum channels. The sensitivity includes the spectral response of the JAI CV-M10 camera, the emitted spectral radiance of the illuminant (Tc 1 = 2852 K), and the transmittance of the optimum filters.

Fig. 11
Fig. 11

Mean percentage of reconstruction and RMSE with the corresponding standard deviation for 2, 3, 4, 5, and 6 filters when the illuminant of color temperature, Tc 1 = 2852 K, is used.

Fig. 12
Fig. 12

Percentage of reconstruction and RMSE of the samples that belong to the original data matrix obtained with the illuminant of color temperature, Tc 1 = 2852 K, for 2 and 5 filters.

Fig. 13
Fig. 13

Reconstructions of samples S5 and S8 of the original data matrix with 2 and 5 filters.

Fig. 14
Fig. 14

Mean percentage of reconstruction and RMSE of the samples that belong to the original data matrix obtained for several existing reconstruction methods: LIN, linear interpolation; SPL, spline interpolation; CUB, cubic interpolation; DFT, discrete Fourier-transform approximation; MDST, modified discrete sine transform approximation; MP, Moore-Penrose pseudoinverse; SM, smoothing inverse; WIE, Wiener inverse; NLIN, nonlinear fitting; PCA. The illuminant of color temperature, Tc 1 = 2852 K, and the five optimum filters are used.

Tables (1)

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Table 1 Parameter Δλ of the Filters with the Best Reconstruction and Mean, Standard Deviation, Maximum and Minimum P rec, and RMSE Values for the Studied Cases

Equations (16)

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NOλ=Hλ12bit-1λhcηλKλ,
Hλ=π4Asensor1+mobj2LeλF2 τobjTatmt,
Hλ=1.60578×10-8LeλJ,
NOλ=aλ+bλ1+exp-Hλ-cλdλ.
rλ, Hλ=responseconstant energy, rλ, Hλ=aλ+bλ1+exp-Hλ-cλdλHλ.
aλ, NOλ=constant responseenergy, aλ, NOλ=NOλcλ-dλlnbλNOλ-aλ-1.
zzM+αv1+βv2+γv3+δv4++ξvp, pn,
Xi=λminλmax iλrλτλFiλSλdλ,
Rλ=iλrλSλ.
Xi=λminλmax RλFiλdλ
Xi=RFi.
RRM+αv1+βv2+γv3++ξvp, p<n,
Xi=RFiRMFi+αv1Fi+βv2Fi+γv3Fi++ξvpFi, p<n.
percentage of reconstruction, Prec=1-λminλmaxrexp-rrec2λminλmaxrexp2×100,
and root-mean-square error, RMSE=1Nλλminλmaxrexp-rrec21/2,
Tλ=Tmax exp-0.5λ-λ0Δλ2,

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