Abstract

Underwater spectral imaging is a promising method for mapping, classification and health monitoring of coral reefs and seafloor inhabitants. However, the spectrum of light is distorted during the underwater imaging process due to wavelength-dependent attenuation by the water. This paper presents a model-based method that accurately restores brightness of underwater spectral images captured with narrowband filters. A model is built for narrowband underwater spectral imaging. The model structure is derived from physical principles, representing the absorption, scattering and refraction by water and the optical properties of narrowband filters, lenses and image sensors. The model coefficients are calibrated based on spectral images captured underwater and in air. With the imaging model available, energy loss due to water attenuation is restored for images captured at different underwater distances. An experimental setup is built and experiments are carried out to verify the proposed method. Underwater images captured within an underwater distance of 260 cm are restored and compared with those in air. Results show that the relative restoration error is 3.58% on average for the test images, thus proving the accuracy of the proposed method.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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2016 (1)

C. Liu, W. Liu W, X Lu, W Chen, and J Yang, “Potential of multispectral imaging for real-time determination of colour change and moisture distribution in carrot slices during hot air dehydration,” Food Chem. 195, 110–116 (2016).
[Crossref]

2014 (1)

R. Pettersen, G. Johnsen, P. Bruheim, and T. Andreassen, “Development of hyperspectral imaging as a bio-optical taxonomic tool for pigmented marine organisms,” Organisms Diversity & Evolution 14, 237–246 (2014).
[Crossref]

2013 (2)

M. Mehrubeoglu, M. Y. Teng, and P. V. Zimba, “Resolving mixed algal species in hyperspectral images,” Sensors 14, 1–21 (2013).
[Crossref]

M. Mehrubeoglu, D. K. Smith, S. W. Smith, K. B. Strychar, and L. McLauchlan, “Investigating coral hyperspectral properties across coral species and coral state using hyperspectral imaging,” Proc. SPIE 8870, 88700M (2013).
[Crossref]

2012 (1)

2011 (1)

A. Ibrahim, S. Tominaga, and T. Horiuchi, “Invariant representation for spectral reflectance images and its application,” EURASIP J. Image Vide. 2011, 1–12 (2011).
[Crossref]

2007 (1)

R. Ismail, O. Mutanga, and U. Bob, “Forest health and vitality: the detection and monitoring of pinus patula trees infected by sirex noctilio using digital multispectral imagery,” Southern Hemisphere Forestry Journal 69, 39–47 (2007).
[Crossref]

2006 (3)

Y. H. Ahn and P. Shanmugam, “Detecting the red tide algal blooms from satellite ocean color observations in optically complex Northeast-Asia Coastal waters,” Remote Sens. Environ. 103, 419–437 (2006).
[Crossref]

M. A. Kara, M. Ennahachi, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Detection and classification of the mucosal and vascular patterns (mucosal morphology) in Barrett’s esophagus by using narrow band imaging,” Gastrointest Endosc. 64, 155–166 (2006).
[Crossref] [PubMed]

M. A. Kara, A. Mobammed, F. P. Peters, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Endoscopic video-autofluorescence imaging followed by narrow band imaging for detecting early neoplasia in Barrett’s esophagus,” Gastrointest Endosc. 64, 176–185 (2006).
[Crossref] [PubMed]

2005 (2)

D. R. Mishra, S. Narumalani, D. Rundquist, and M. Lawson, “Characterizing the vertical diffuse attenuation coefficient for downwelling irradiance in coastal waters: Implications for water penetration by high resolution satellite data,” ISPRS Journal of photogrammetry and remote sensing 60, 48–64 (2005).
[Crossref]

C. D. Mobley, L. K. Sundman, C. O. Davis, J. H. Bowles, T. V. Downes, R. A. Leathers, M. J. Montes, W. P. Bissett, D. D. R. Kohler, R. P. Reid, E. M. Louchard, and A. C. R. Gleason, “Interpretation of hyperspectral remote-sensing imagery by spectrum matching and look-up tables,” Appl. Opt. 44, 3576–3592 (2005).
[Crossref] [PubMed]

2004 (1)

P. J. Mumby, J. D. Hedley, J. Chisholm, C. Clark, H. Ripley, and J. Jaubert, “The cover of living and dead corals from airborne remote sensing,” Coral Reefs 23, 171–183 (2004).
[Crossref]

2003 (1)

D. Zawada, “Image processing of underwater multispectral imagery,” IEEE Journal of Oceanic Engineering 28, 583–594 (2003).
[Crossref]

2001 (1)

H. Holden and E. LeDrew, “Effects of the water column on hyperspectral reflectance of submerged coral reef features,” Bulletin of Marine Science 69, 685–699 (2001).

2000 (1)

S. W. Brown, G. P. Eppeldauer, P. George, and R. Keith, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–583 (2000).
[Crossref]

1998 (1)

P. J. Mumby, C. D. Clark, E. P. Green, and A. J. Edwards, “Benefits of water column correction and contextual editing for mapping coral reefs,” International Journal of Remote Sensing 19, 203–210 (1998).
[Crossref]

1994 (1)

P. Launeau, A. R. Cruden, and J. L. Bouchez, “Mineral recognition in digital images of rocks: a new approach using multichannel classification,” Can. Mineral. 32, 919 (1994).

1962 (1)

D. F. Swinehart, “The beer-lambert law,” J. Chem. Educ. 39, 333 (1962).
[Crossref]

Aarrestad, S.

S. Aarrestad, “Use of underwater hyperspectral imagery for geological characterization of the seabed,” Masters thesis (Norwegian University of Science and Technology, 2014).

Åhlén, J.

J. Åhlén, “Colour correction of underwater images using spectral data,” Ph.D. thesis (Acta Universitatis Up-saliensis, 2005).

J. Åhlén, E. Bengtsson, and D. Sundgren, “Evaluation of underwater spectral data for colour correction applications,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing (World Scientific and Engineering Academy and Society, 2006), pp. 321–326.

Ahn, Y. H.

Y. H. Ahn and P. Shanmugam, “Detecting the red tide algal blooms from satellite ocean color observations in optically complex Northeast-Asia Coastal waters,” Remote Sens. Environ. 103, 419–437 (2006).
[Crossref]

Allais, A.

Andreassen, T.

R. Pettersen, G. Johnsen, P. Bruheim, and T. Andreassen, “Development of hyperspectral imaging as a bio-optical taxonomic tool for pigmented marine organisms,” Organisms Diversity & Evolution 14, 237–246 (2014).
[Crossref]

Ardelan, M.

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

Bengtsson, E.

J. Åhlén, E. Bengtsson, and D. Sundgren, “Evaluation of underwater spectral data for colour correction applications,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing (World Scientific and Engineering Academy and Society, 2006), pp. 321–326.

Bergman, J. H. M.

M. A. Kara, M. Ennahachi, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Detection and classification of the mucosal and vascular patterns (mucosal morphology) in Barrett’s esophagus by using narrow band imaging,” Gastrointest Endosc. 64, 155–166 (2006).
[Crossref] [PubMed]

M. A. Kara, A. Mobammed, F. P. Peters, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Endoscopic video-autofluorescence imaging followed by narrow band imaging for detecting early neoplasia in Barrett’s esophagus,” Gastrointest Endosc. 64, 176–185 (2006).
[Crossref] [PubMed]

Bissett, W. P.

Bob, U.

R. Ismail, O. Mutanga, and U. Bob, “Forest health and vitality: the detection and monitoring of pinus patula trees infected by sirex noctilio using digital multispectral imagery,” Southern Hemisphere Forestry Journal 69, 39–47 (2007).
[Crossref]

Boffety, M.

Bongiorno, D. L.

D. L. Bongiorno, M. Bryson, and S. B. Williams, “Dynamic spectral-based underwater colour correction,” in Proceedings of IEEE/MTS OCEANS’13 (IEEE2013), pp. 1–9.

Bouchez, J. L.

P. Launeau, A. R. Cruden, and J. L. Bouchez, “Mineral recognition in digital images of rocks: a new approach using multichannel classification,” Can. Mineral. 32, 919 (1994).

Bowles, J. H.

Brown, S. W.

S. W. Brown, G. P. Eppeldauer, P. George, and R. Keith, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–583 (2000).
[Crossref]

Bruheim, P.

R. Pettersen, G. Johnsen, P. Bruheim, and T. Andreassen, “Development of hyperspectral imaging as a bio-optical taxonomic tool for pigmented marine organisms,” Organisms Diversity & Evolution 14, 237–246 (2014).
[Crossref]

Bryson, M.

D. L. Bongiorno, M. Bryson, and S. B. Williams, “Dynamic spectral-based underwater colour correction,” in Proceedings of IEEE/MTS OCEANS’13 (IEEE2013), pp. 1–9.

M. Bryson, M. Johnson-Roberson, O. Pizarro, and S. B. Williams, “Colour-consistent structure-from-motion models using underwater imagery,” in Robotics: Science and Systems VIII, N. Roy, P. Newman, and S. Srinivasa, eds. (MIT, 2013).

Ceng, Z.

X. Li and Z. Ceng, Geometrical Optics, Aberrations and Optical Design, 2nd ed. (Zhejiang University, 2007).

Chen, P. Y.

H. Y. Yang, P. Y. Chen, C. C. Huang, Y. Z. Zhuang, and Y. H. Shiau, “Low complexity underwater image enhancement based on dark channel prior,” in Proceedings of International Conference on Innovations in Bio-inspired Computing and Applications, (IEEE, 2011), pp. 17–20.

Chen, W

C. Liu, W. Liu W, X Lu, W Chen, and J Yang, “Potential of multispectral imaging for real-time determination of colour change and moisture distribution in carrot slices during hot air dehydration,” Food Chem. 195, 110–116 (2016).
[Crossref]

Chisholm, J.

P. J. Mumby, J. D. Hedley, J. Chisholm, C. Clark, H. Ripley, and J. Jaubert, “The cover of living and dead corals from airborne remote sensing,” Coral Reefs 23, 171–183 (2004).
[Crossref]

Clark, C.

P. J. Mumby, J. D. Hedley, J. Chisholm, C. Clark, H. Ripley, and J. Jaubert, “The cover of living and dead corals from airborne remote sensing,” Coral Reefs 23, 171–183 (2004).
[Crossref]

Clark, C. D.

P. J. Mumby, C. D. Clark, E. P. Green, and A. J. Edwards, “Benefits of water column correction and contextual editing for mapping coral reefs,” International Journal of Remote Sensing 19, 203–210 (1998).
[Crossref]

Cruden, A. R.

P. Launeau, A. R. Cruden, and J. L. Bouchez, “Mineral recognition in digital images of rocks: a new approach using multichannel classification,” Can. Mineral. 32, 919 (1994).

Davis, C. O.

Dierssen, H.

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

Downes, T. V.

Edwards, A. J.

P. J. Mumby, C. D. Clark, E. P. Green, and A. J. Edwards, “Benefits of water column correction and contextual editing for mapping coral reefs,” International Journal of Remote Sensing 19, 203–210 (1998).
[Crossref]

Ennahachi, M.

M. A. Kara, M. Ennahachi, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Detection and classification of the mucosal and vascular patterns (mucosal morphology) in Barrett’s esophagus by using narrow band imaging,” Gastrointest Endosc. 64, 155–166 (2006).
[Crossref] [PubMed]

Eppeldauer, G. P.

S. W. Brown, G. P. Eppeldauer, P. George, and R. Keith, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–583 (2000).
[Crossref]

Fearns, P.

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

Fockens, P.

M. A. Kara, M. Ennahachi, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Detection and classification of the mucosal and vascular patterns (mucosal morphology) in Barrett’s esophagus by using narrow band imaging,” Gastrointest Endosc. 64, 155–166 (2006).
[Crossref] [PubMed]

M. A. Kara, A. Mobammed, F. P. Peters, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Endoscopic video-autofluorescence imaging followed by narrow band imaging for detecting early neoplasia in Barrett’s esophagus,” Gastrointest Endosc. 64, 176–185 (2006).
[Crossref] [PubMed]

Fujii, M.

A. Yamashita, M. Fujii, and T. Kaneko, “Color registration of underwater images for underwater sensing with consideration of light attenuation,” in Proceedings of 2007 IEEE International Conference on Robotics and Automation (IEEE, 2007), pp. 4570–4575.

Galland, F.

George, P.

S. W. Brown, G. P. Eppeldauer, P. George, and R. Keith, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–583 (2000).
[Crossref]

Gleason, A. C. R.

Green, E. P.

P. J. Mumby, C. D. Clark, E. P. Green, and A. J. Edwards, “Benefits of water column correction and contextual editing for mapping coral reefs,” International Journal of Remote Sensing 19, 203–210 (1998).
[Crossref]

Hedley, J. D.

P. J. Mumby, J. D. Hedley, J. Chisholm, C. Clark, H. Ripley, and J. Jaubert, “The cover of living and dead corals from airborne remote sensing,” Coral Reefs 23, 171–183 (2004).
[Crossref]

Holden, H.

H. Holden and E. LeDrew, “Effects of the water column on hyperspectral reflectance of submerged coral reef features,” Bulletin of Marine Science 69, 685–699 (2001).

Horiuchi, T.

A. Ibrahim, S. Tominaga, and T. Horiuchi, “Invariant representation for spectral reflectance images and its application,” EURASIP J. Image Vide. 2011, 1–12 (2011).
[Crossref]

Huang, C. C.

H. Y. Yang, P. Y. Chen, C. C. Huang, Y. Z. Zhuang, and Y. H. Shiau, “Low complexity underwater image enhancement based on dark channel prior,” in Proceedings of International Conference on Innovations in Bio-inspired Computing and Applications, (IEEE, 2011), pp. 17–20.

Ibrahim, A.

A. Ibrahim, S. Tominaga, and T. Horiuchi, “Invariant representation for spectral reflectance images and its application,” EURASIP J. Image Vide. 2011, 1–12 (2011).
[Crossref]

Ismail, R.

R. Ismail, O. Mutanga, and U. Bob, “Forest health and vitality: the detection and monitoring of pinus patula trees infected by sirex noctilio using digital multispectral imagery,” Southern Hemisphere Forestry Journal 69, 39–47 (2007).
[Crossref]

Jaubert, J.

P. J. Mumby, J. D. Hedley, J. Chisholm, C. Clark, H. Ripley, and J. Jaubert, “The cover of living and dead corals from airborne remote sensing,” Coral Reefs 23, 171–183 (2004).
[Crossref]

Johnsen, G.

R. Pettersen, G. Johnsen, P. Bruheim, and T. Andreassen, “Development of hyperspectral imaging as a bio-optical taxonomic tool for pigmented marine organisms,” Organisms Diversity & Evolution 14, 237–246 (2014).
[Crossref]

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

Johnson-Roberson, M.

M. Bryson, M. Johnson-Roberson, O. Pizarro, and S. B. Williams, “Colour-consistent structure-from-motion models using underwater imagery,” in Robotics: Science and Systems VIII, N. Roy, P. Newman, and S. Srinivasa, eds. (MIT, 2013).

Kaeli, J.

J. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” in Proceedings of IEEE/MTS OCEANS’11 (IEEE, 2011), pp. 805–810.

Kaneko, T.

A. Yamashita, M. Fujii, and T. Kaneko, “Color registration of underwater images for underwater sensing with consideration of light attenuation,” in Proceedings of 2007 IEEE International Conference on Robotics and Automation (IEEE, 2007), pp. 4570–4575.

Kara, M. A.

M. A. Kara, A. Mobammed, F. P. Peters, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Endoscopic video-autofluorescence imaging followed by narrow band imaging for detecting early neoplasia in Barrett’s esophagus,” Gastrointest Endosc. 64, 176–185 (2006).
[Crossref] [PubMed]

M. A. Kara, M. Ennahachi, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Detection and classification of the mucosal and vascular patterns (mucosal morphology) in Barrett’s esophagus by using narrow band imaging,” Gastrointest Endosc. 64, 155–166 (2006).
[Crossref] [PubMed]

Keith, R.

S. W. Brown, G. P. Eppeldauer, P. George, and R. Keith, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–583 (2000).
[Crossref]

Kohler, D. D. R.

Kunz, C.

J. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” in Proceedings of IEEE/MTS OCEANS’11 (IEEE, 2011), pp. 805–810.

Launeau, P.

P. Launeau, A. R. Cruden, and J. L. Bouchez, “Mineral recognition in digital images of rocks: a new approach using multichannel classification,” Can. Mineral. 32, 919 (1994).

Lawson, M.

D. R. Mishra, S. Narumalani, D. Rundquist, and M. Lawson, “Characterizing the vertical diffuse attenuation coefficient for downwelling irradiance in coastal waters: Implications for water penetration by high resolution satellite data,” ISPRS Journal of photogrammetry and remote sensing 60, 48–64 (2005).
[Crossref]

Leathers, R. A.

LeDrew, E.

H. Holden and E. LeDrew, “Effects of the water column on hyperspectral reflectance of submerged coral reef features,” Bulletin of Marine Science 69, 685–699 (2001).

Li, X.

X. Li and Z. Ceng, Geometrical Optics, Aberrations and Optical Design, 2nd ed. (Zhejiang University, 2007).

Lin, S.

S. Lin and L. Zhang, “Determining the radiometric response function from a single grayscale image,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 66–73.

Liu, C.

C. Liu, W. Liu W, X Lu, W Chen, and J Yang, “Potential of multispectral imaging for real-time determination of colour change and moisture distribution in carrot slices during hot air dehydration,” Food Chem. 195, 110–116 (2016).
[Crossref]

Liu W, W.

C. Liu, W. Liu W, X Lu, W Chen, and J Yang, “Potential of multispectral imaging for real-time determination of colour change and moisture distribution in carrot slices during hot air dehydration,” Food Chem. 195, 110–116 (2016).
[Crossref]

Louchard, E. M.

Lu, X

C. Liu, W. Liu W, X Lu, W Chen, and J Yang, “Potential of multispectral imaging for real-time determination of colour change and moisture distribution in carrot slices during hot air dehydration,” Food Chem. 195, 110–116 (2016).
[Crossref]

Ludvigsen, M.

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

McLauchlan, L.

M. Mehrubeoglu, D. K. Smith, S. W. Smith, K. B. Strychar, and L. McLauchlan, “Investigating coral hyperspectral properties across coral species and coral state using hyperspectral imaging,” Proc. SPIE 8870, 88700M (2013).
[Crossref]

Mehrubeoglu, M.

M. Mehrubeoglu, M. Y. Teng, and P. V. Zimba, “Resolving mixed algal species in hyperspectral images,” Sensors 14, 1–21 (2013).
[Crossref]

M. Mehrubeoglu, D. K. Smith, S. W. Smith, K. B. Strychar, and L. McLauchlan, “Investigating coral hyperspectral properties across coral species and coral state using hyperspectral imaging,” Proc. SPIE 8870, 88700M (2013).
[Crossref]

Mishra, D. R.

D. R. Mishra, S. Narumalani, D. Rundquist, and M. Lawson, “Characterizing the vertical diffuse attenuation coefficient for downwelling irradiance in coastal waters: Implications for water penetration by high resolution satellite data,” ISPRS Journal of photogrammetry and remote sensing 60, 48–64 (2005).
[Crossref]

Mobammed, A.

M. A. Kara, A. Mobammed, F. P. Peters, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Endoscopic video-autofluorescence imaging followed by narrow band imaging for detecting early neoplasia in Barrett’s esophagus,” Gastrointest Endosc. 64, 176–185 (2006).
[Crossref] [PubMed]

Mobley, C. D.

Moline, M.

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

Montes, M. J.

Mumby, P. J.

P. J. Mumby, J. D. Hedley, J. Chisholm, C. Clark, H. Ripley, and J. Jaubert, “The cover of living and dead corals from airborne remote sensing,” Coral Reefs 23, 171–183 (2004).
[Crossref]

P. J. Mumby, C. D. Clark, E. P. Green, and A. J. Edwards, “Benefits of water column correction and contextual editing for mapping coral reefs,” International Journal of Remote Sensing 19, 203–210 (1998).
[Crossref]

Murphy, C.

J. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” in Proceedings of IEEE/MTS OCEANS’11 (IEEE, 2011), pp. 805–810.

Mutanga, O.

R. Ismail, O. Mutanga, and U. Bob, “Forest health and vitality: the detection and monitoring of pinus patula trees infected by sirex noctilio using digital multispectral imagery,” Southern Hemisphere Forestry Journal 69, 39–47 (2007).
[Crossref]

Narumalani, S.

D. R. Mishra, S. Narumalani, D. Rundquist, and M. Lawson, “Characterizing the vertical diffuse attenuation coefficient for downwelling irradiance in coastal waters: Implications for water penetration by high resolution satellite data,” ISPRS Journal of photogrammetry and remote sensing 60, 48–64 (2005).
[Crossref]

Peters, F. P.

M. A. Kara, A. Mobammed, F. P. Peters, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Endoscopic video-autofluorescence imaging followed by narrow band imaging for detecting early neoplasia in Barrett’s esophagus,” Gastrointest Endosc. 64, 176–185 (2006).
[Crossref] [PubMed]

Pettersen, R.

R. Pettersen, G. Johnsen, P. Bruheim, and T. Andreassen, “Development of hyperspectral imaging as a bio-optical taxonomic tool for pigmented marine organisms,” Organisms Diversity & Evolution 14, 237–246 (2014).
[Crossref]

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

Pizarro, O.

M. Bryson, M. Johnson-Roberson, O. Pizarro, and S. B. Williams, “Colour-consistent structure-from-motion models using underwater imagery,” in Robotics: Science and Systems VIII, N. Roy, P. Newman, and S. Srinivasa, eds. (MIT, 2013).

Reid, R. P.

Ripley, H.

P. J. Mumby, J. D. Hedley, J. Chisholm, C. Clark, H. Ripley, and J. Jaubert, “The cover of living and dead corals from airborne remote sensing,” Coral Reefs 23, 171–183 (2004).
[Crossref]

Rundquist, D.

D. R. Mishra, S. Narumalani, D. Rundquist, and M. Lawson, “Characterizing the vertical diffuse attenuation coefficient for downwelling irradiance in coastal waters: Implications for water penetration by high resolution satellite data,” ISPRS Journal of photogrammetry and remote sensing 60, 48–64 (2005).
[Crossref]

Shanmugam, P.

Y. H. Ahn and P. Shanmugam, “Detecting the red tide algal blooms from satellite ocean color observations in optically complex Northeast-Asia Coastal waters,” Remote Sens. Environ. 103, 419–437 (2006).
[Crossref]

Shiau, Y. H.

H. Y. Yang, P. Y. Chen, C. C. Huang, Y. Z. Zhuang, and Y. H. Shiau, “Low complexity underwater image enhancement based on dark channel prior,” in Proceedings of International Conference on Innovations in Bio-inspired Computing and Applications, (IEEE, 2011), pp. 17–20.

Singh, H.

J. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” in Proceedings of IEEE/MTS OCEANS’11 (IEEE, 2011), pp. 805–810.

Smith, D. K.

M. Mehrubeoglu, D. K. Smith, S. W. Smith, K. B. Strychar, and L. McLauchlan, “Investigating coral hyperspectral properties across coral species and coral state using hyperspectral imaging,” Proc. SPIE 8870, 88700M (2013).
[Crossref]

Smith, S. W.

M. Mehrubeoglu, D. K. Smith, S. W. Smith, K. B. Strychar, and L. McLauchlan, “Investigating coral hyperspectral properties across coral species and coral state using hyperspectral imaging,” Proc. SPIE 8870, 88700M (2013).
[Crossref]

Sreide, F.

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

Strychar, K. B.

M. Mehrubeoglu, D. K. Smith, S. W. Smith, K. B. Strychar, and L. McLauchlan, “Investigating coral hyperspectral properties across coral species and coral state using hyperspectral imaging,” Proc. SPIE 8870, 88700M (2013).
[Crossref]

Sundgren, D.

J. Åhlén, E. Bengtsson, and D. Sundgren, “Evaluation of underwater spectral data for colour correction applications,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing (World Scientific and Engineering Academy and Society, 2006), pp. 321–326.

Sundman, L. K.

Swinehart, D. F.

D. F. Swinehart, “The beer-lambert law,” J. Chem. Educ. 39, 333 (1962).
[Crossref]

ten Kate, F. J. W.

M. A. Kara, A. Mobammed, F. P. Peters, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Endoscopic video-autofluorescence imaging followed by narrow band imaging for detecting early neoplasia in Barrett’s esophagus,” Gastrointest Endosc. 64, 176–185 (2006).
[Crossref] [PubMed]

M. A. Kara, M. Ennahachi, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Detection and classification of the mucosal and vascular patterns (mucosal morphology) in Barrett’s esophagus by using narrow band imaging,” Gastrointest Endosc. 64, 155–166 (2006).
[Crossref] [PubMed]

Teng, M. Y.

M. Mehrubeoglu, M. Y. Teng, and P. V. Zimba, “Resolving mixed algal species in hyperspectral images,” Sensors 14, 1–21 (2013).
[Crossref]

Tominaga, S.

A. Ibrahim, S. Tominaga, and T. Horiuchi, “Invariant representation for spectral reflectance images and its application,” EURASIP J. Image Vide. 2011, 1–12 (2011).
[Crossref]

Volent, Z.

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

Voss, K. J.

A. C. R. Gleason, R. P. Reid, and K. J. Voss, “Automated classification of underwater multispectral imagery for coral reef monitoring,” in Proceedings of IEEE/MTS OCEANS’07 (IEEE, 2007), pp. 1–8.

Williams, S. B.

D. L. Bongiorno, M. Bryson, and S. B. Williams, “Dynamic spectral-based underwater colour correction,” in Proceedings of IEEE/MTS OCEANS’13 (IEEE2013), pp. 1–9.

M. Bryson, M. Johnson-Roberson, O. Pizarro, and S. B. Williams, “Colour-consistent structure-from-motion models using underwater imagery,” in Robotics: Science and Systems VIII, N. Roy, P. Newman, and S. Srinivasa, eds. (MIT, 2013).

Yamashita, A.

A. Yamashita, M. Fujii, and T. Kaneko, “Color registration of underwater images for underwater sensing with consideration of light attenuation,” in Proceedings of 2007 IEEE International Conference on Robotics and Automation (IEEE, 2007), pp. 4570–4575.

Yang, H. Y.

H. Y. Yang, P. Y. Chen, C. C. Huang, Y. Z. Zhuang, and Y. H. Shiau, “Low complexity underwater image enhancement based on dark channel prior,” in Proceedings of International Conference on Innovations in Bio-inspired Computing and Applications, (IEEE, 2011), pp. 17–20.

Yang, J

C. Liu, W. Liu W, X Lu, W Chen, and J Yang, “Potential of multispectral imaging for real-time determination of colour change and moisture distribution in carrot slices during hot air dehydration,” Food Chem. 195, 110–116 (2016).
[Crossref]

Zawada, D.

D. Zawada, “Image processing of underwater multispectral imagery,” IEEE Journal of Oceanic Engineering 28, 583–594 (2003).
[Crossref]

Zhang, L.

S. Lin and L. Zhang, “Determining the radiometric response function from a single grayscale image,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 66–73.

Zhuang, Y. Z.

H. Y. Yang, P. Y. Chen, C. C. Huang, Y. Z. Zhuang, and Y. H. Shiau, “Low complexity underwater image enhancement based on dark channel prior,” in Proceedings of International Conference on Innovations in Bio-inspired Computing and Applications, (IEEE, 2011), pp. 17–20.

Zimba, P. V.

M. Mehrubeoglu, M. Y. Teng, and P. V. Zimba, “Resolving mixed algal species in hyperspectral images,” Sensors 14, 1–21 (2013).
[Crossref]

Appl. Opt. (2)

Bulletin of Marine Science (1)

H. Holden and E. LeDrew, “Effects of the water column on hyperspectral reflectance of submerged coral reef features,” Bulletin of Marine Science 69, 685–699 (2001).

Can. Mineral. (1)

P. Launeau, A. R. Cruden, and J. L. Bouchez, “Mineral recognition in digital images of rocks: a new approach using multichannel classification,” Can. Mineral. 32, 919 (1994).

Coral Reefs (1)

P. J. Mumby, J. D. Hedley, J. Chisholm, C. Clark, H. Ripley, and J. Jaubert, “The cover of living and dead corals from airborne remote sensing,” Coral Reefs 23, 171–183 (2004).
[Crossref]

EURASIP J. Image Vide. (1)

A. Ibrahim, S. Tominaga, and T. Horiuchi, “Invariant representation for spectral reflectance images and its application,” EURASIP J. Image Vide. 2011, 1–12 (2011).
[Crossref]

Food Chem. (1)

C. Liu, W. Liu W, X Lu, W Chen, and J Yang, “Potential of multispectral imaging for real-time determination of colour change and moisture distribution in carrot slices during hot air dehydration,” Food Chem. 195, 110–116 (2016).
[Crossref]

Gastrointest Endosc. (2)

M. A. Kara, M. Ennahachi, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Detection and classification of the mucosal and vascular patterns (mucosal morphology) in Barrett’s esophagus by using narrow band imaging,” Gastrointest Endosc. 64, 155–166 (2006).
[Crossref] [PubMed]

M. A. Kara, A. Mobammed, F. P. Peters, P. Fockens, F. J. W. ten Kate, and J. H. M. Bergman, “Endoscopic video-autofluorescence imaging followed by narrow band imaging for detecting early neoplasia in Barrett’s esophagus,” Gastrointest Endosc. 64, 176–185 (2006).
[Crossref] [PubMed]

IEEE Journal of Oceanic Engineering (1)

D. Zawada, “Image processing of underwater multispectral imagery,” IEEE Journal of Oceanic Engineering 28, 583–594 (2003).
[Crossref]

International Journal of Remote Sensing (1)

P. J. Mumby, C. D. Clark, E. P. Green, and A. J. Edwards, “Benefits of water column correction and contextual editing for mapping coral reefs,” International Journal of Remote Sensing 19, 203–210 (1998).
[Crossref]

ISPRS Journal of photogrammetry and remote sensing (1)

D. R. Mishra, S. Narumalani, D. Rundquist, and M. Lawson, “Characterizing the vertical diffuse attenuation coefficient for downwelling irradiance in coastal waters: Implications for water penetration by high resolution satellite data,” ISPRS Journal of photogrammetry and remote sensing 60, 48–64 (2005).
[Crossref]

J. Chem. Educ. (1)

D. F. Swinehart, “The beer-lambert law,” J. Chem. Educ. 39, 333 (1962).
[Crossref]

Metrologia (1)

S. W. Brown, G. P. Eppeldauer, P. George, and R. Keith, “NIST facility for spectral irradiance and radiance responsivity calibrations with uniform sources,” Metrologia 37, 579–583 (2000).
[Crossref]

Organisms Diversity & Evolution (1)

R. Pettersen, G. Johnsen, P. Bruheim, and T. Andreassen, “Development of hyperspectral imaging as a bio-optical taxonomic tool for pigmented marine organisms,” Organisms Diversity & Evolution 14, 237–246 (2014).
[Crossref]

Proc. SPIE (1)

M. Mehrubeoglu, D. K. Smith, S. W. Smith, K. B. Strychar, and L. McLauchlan, “Investigating coral hyperspectral properties across coral species and coral state using hyperspectral imaging,” Proc. SPIE 8870, 88700M (2013).
[Crossref]

Remote Sens. Environ. (1)

Y. H. Ahn and P. Shanmugam, “Detecting the red tide algal blooms from satellite ocean color observations in optically complex Northeast-Asia Coastal waters,” Remote Sens. Environ. 103, 419–437 (2006).
[Crossref]

Sensors (1)

M. Mehrubeoglu, M. Y. Teng, and P. V. Zimba, “Resolving mixed algal species in hyperspectral images,” Sensors 14, 1–21 (2013).
[Crossref]

Southern Hemisphere Forestry Journal (1)

R. Ismail, O. Mutanga, and U. Bob, “Forest health and vitality: the detection and monitoring of pinus patula trees infected by sirex noctilio using digital multispectral imagery,” Southern Hemisphere Forestry Journal 69, 39–47 (2007).
[Crossref]

Other (14)

A. C. R. Gleason, R. P. Reid, and K. J. Voss, “Automated classification of underwater multispectral imagery for coral reef monitoring,” in Proceedings of IEEE/MTS OCEANS’07 (IEEE, 2007), pp. 1–8.

G. Johnsen, Z. Volent, H. Dierssen, R. Pettersen, M. Ardelan, F. Sreide, P. Fearns, M. Ludvigsen, and M. Moline, “Underwater hyperspectral imagery to create biogeochemical maps of seafloor properties,” in Subsea Optics and Imaging, J. Watson and O. Zielinski, eds. (Woodhead Publishing, 2013), pp. 508–535.
[Crossref]

S. Aarrestad, “Use of underwater hyperspectral imagery for geological characterization of the seabed,” Masters thesis (Norwegian University of Science and Technology, 2014).

H. Y. Yang, P. Y. Chen, C. C. Huang, Y. Z. Zhuang, and Y. H. Shiau, “Low complexity underwater image enhancement based on dark channel prior,” in Proceedings of International Conference on Innovations in Bio-inspired Computing and Applications, (IEEE, 2011), pp. 17–20.

X. Li and Z. Ceng, Geometrical Optics, Aberrations and Optical Design, 2nd ed. (Zhejiang University, 2007).

S. Lin and L. Zhang, “Determining the radiometric response function from a single grayscale image,” in Proceedings of IEEE Computer Society Conference on Computer Vision and Pattern Recognition (IEEE, 2005), pp. 66–73.

A. H. Munsell, “Munsell color system”, http://munsell.com/

Thorlabs, “Optical filters”, http://www.thorlabs.com/

J. Åhlén, E. Bengtsson, and D. Sundgren, “Evaluation of underwater spectral data for colour correction applications,” in Proceedings of the 5th WSEAS International Conference on Circuits, Systems, Electronics, Control & Signal Processing (World Scientific and Engineering Academy and Society, 2006), pp. 321–326.

J. Åhlén, “Colour correction of underwater images using spectral data,” Ph.D. thesis (Acta Universitatis Up-saliensis, 2005).

D. L. Bongiorno, M. Bryson, and S. B. Williams, “Dynamic spectral-based underwater colour correction,” in Proceedings of IEEE/MTS OCEANS’13 (IEEE2013), pp. 1–9.

J. Kaeli, H. Singh, C. Murphy, and C. Kunz, “Improving color correction for underwater image surveys,” in Proceedings of IEEE/MTS OCEANS’11 (IEEE, 2011), pp. 805–810.

M. Bryson, M. Johnson-Roberson, O. Pizarro, and S. B. Williams, “Colour-consistent structure-from-motion models using underwater imagery,” in Robotics: Science and Systems VIII, N. Roy, P. Newman, and S. Srinivasa, eds. (MIT, 2013).

A. Yamashita, M. Fujii, and T. Kaneko, “Color registration of underwater images for underwater sensing with consideration of light attenuation,” in Proceedings of 2007 IEEE International Conference on Robotics and Automation (IEEE, 2007), pp. 4570–4575.

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Figures (12)

Fig. 1
Fig. 1

Illustration of narrowband spectral imaging in air and underwater. The image is enlarged due to refraction of water at the same object distance. The brightness of the image is reduced due to water attenuation as well as enlargement of the image.

Fig. 2
Fig. 2

Refraction at the interfaces between water, glass and air. Due to refraction of water, the object looks as if it were moved closer. Therefore the equivalent object distance zw is defined.

Fig. 3
Fig. 3

The experimental setup consists of a mobile phone, a water tank and a narrowband spectral imaging system as shown in (a) and (b). The mobile phone is placed in a waterproof box, acting as a luminous underwater object. The pattern displayed in the screen of the phone consists of 60 color pieces in 6 rows and 10 columns. The filters in the spectral imaging system are tuned by the rotation filter wheel with the wavelength scanning from 420 nm to 700 nm at an interval of 20 nm. The typical transmission of a filter with a central wavelength of around 460 nm [33] is shown in (c).

Fig. 4
Fig. 4

Response of the spectrometer on the color piece (3,7) on the phone screen. The intensity at wavelengths of 447 nm, 540 nm, and 660 nm is recorded for 3500 scans (i.e., 175 s), showing a stable light output by the phone screen.

Fig. 5
Fig. 5

Linear fitting between the brightness of underwater images and the brightness of air images, for estimation of k(λ,l) and b(λ,l), at wavelengths of 460 nm and 620 nm and underwater distances of 60 cm, 160 cm and 260 cm.

Fig. 6
Fig. 6

Exponential fitting between k(λ,l) and underwater distance l, for the estimation of coefficients α(λ) and β(λ). The RSD of the calibration data set is 3.8% and 3.2% for 460 nm and 620 nm, respectively. For the test distances, RSD is 6.4% for 460 nm and 3.6% for 620 nm.

Fig. 7
Fig. 7

Exponential fitting between b(λ,l) and underwater distance l, for the estimation of coefficients ν(λ), κ(λ) and γ(λ). The RSD of the calibration data set is 6.3% and 2.0% for 460 nm and 620 nm, respectively. For the test distances, RSD is 9.5% for 460 nm and 2.9% for 620 nm.

Fig. 8
Fig. 8

Comparison between raw underwater images, restored underwater images and images in air. Brightness and size of underwater images decrease with underwater distance. By restoration, the brightness of underwater images is improved significantly.

Fig. 9
Fig. 9

Comparison among raw underwater spectrum, restored underwater spectrum and spectrum in air, for color pieces (1,5), (2,2) (3,9) and (4,7). The underwater distance is 240 cm. The restored spectra almost overlap the spectra in air, indicating an accurate compensation of spectral energy loss due to water.

Fig. 10
Fig. 10

Color images are constructed, based on raw underwater spectral images captured at an underwater distance of 240 cm (a), restored underwater spectral images with image size unchanged (b), restored underwater spectral images with image size changed to the same as air image and image brightness scaled accordingly (c), spectral images captured in air at an object distance of 340 cm (d). The improvement by restoration is clearly visible in color images.

Fig. 11
Fig. 11

Dependence of the relative restoration error ε on the underwater distance (a) and wavelength (b). The restoration error is averaged over wavelength for certain distance in (a) and averaged over distance for certain wavelength in (b). The spectrum of the mobile phone screen emitting white light is measured by the fiber spectrometer and depicted in (b), showing abrupt change in the intensity in a wavelength range of [420 nm, 480 nm].

Fig. 12
Fig. 12

Sensitivity of the restoration error for images at 460 nm to variation in the optical properties of water (a) and to the error in underwater distance measurement (b).

Equations (27)

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

x = f z f x , y = f z f y , z = f z f z .
E ( x , y , λ , z ) = π 4 ( D f ) 2 C τ l ( λ ) τ f ( λ ) ( z f z ) 2 G ( z ) L ( x , y , λ ) cos 4 θ ,
cos 2 θ = x 2 + y 2 z 2 .
E ( x , y , λ , z ) = C G ( z ) τ l ( λ ) τ f ( λ ) L ( x , y , λ ) .
I ( i , j , λ c , z ) = a t S i , j λ c + Δ λ 2 λ c Δ λ 1 q ( λ ) E ( x , y , λ ) d λ d x d y = a t S i , j λ c + Δ λ 2 λ c Δ λ 1 q ( λ ) C G ( z ) τ l ( λ ) τ f ( λ ) L ( x , y , λ ) d λ d x d y ,
I ( i , j , λ c , z ) = a t S i , j d x d y A C G ( z ) λ c Δ λ 1 λ c + Δ λ 2 q ( λ ) τ l ( λ ) τ f ( λ ) L ( x , y , λ ) d λ H ( x , y , λ c ) , = A C G ( z ) H ( x , y , λ c ) .
x w = f z w f x , y w = f z w f y , z w = f z w f z w ,
z w = l + l n w + d n g ,
E w ( x w , y w , λ , z w ) = β ( λ ) e α ( λ ) l C G ( z w ) τ l ( λ ) τ f ( λ ) L ( x , y , λ ) + E b ( λ ) e ν ( λ ) l + E s ( λ ) ,
I w ( i w , j w , λ c , z w ) = a t S i , j λ c + Δ λ 2 λ c Δ λ 1 q ( λ ) E w ( x w , y w , λ , z w ) d λ d x d y = A C G ( z w ) λ c Δ λ 1 λ c + Δ λ 2 β ( λ ) e α ( λ ) l τ l ( λ ) τ f ( λ ) L ( x , y , λ ) d λ + A λ c Δ λ 1 λ c + Δ λ 2 E b ( λ ) e ν ( λ ) l d λ + A λ c Δ λ 1 λ c + Δ λ 2 E s ( λ ) d λ ,
α ( λ ) α ( λ c ) , β ( λ ) β ( λ c ) , E b ( λ ) E b ( λ c ) , ν ( λ ) ν ( λ c ) , E s ( λ ) E s ( λ c ) ,
I w ( i w , j w , λ c , z w ) β ( λ ) e α ( λ ) l A C G ( z w ) λ c Δ λ 1 λ c + Δ λ 2 τ l ( λ ) τ f ( λ ) L ( x , y , λ ) d λ + A E b ( λ c ) ( Δ λ 1 + Δ λ 2 ) κ ( λ c ) e ν ( λ c ) l + A E s ( λ c ) ( Δ λ 1 + Δ λ 2 ) γ ( λ c ) = β ( λ c ) e α ( λ c ) l A C G ( z w ) H ( x , y , λ c ) + κ ( λ c ) e ν ( λ c ) l + γ ( λ c ) ,
I w ( i w , j w , λ c , z w ) = G ( z w ) G ( z ) β ( λ c ) e α ( λ c ) l k ( λ c , l ) I ( i , j , λ c , z ) + κ ( λ c ) e ν ( λ c ) l + γ ( λ c ) b ( λ c , l ) .
{ I w ( i w , 1 , j w , 1 , λ 1 , z w , 1 ) = G ( z w , 1 ) G ( z 1 ) k ( λ 1 , l 1 ) I ( i 1 , j 1 , λ 1 , z 1 ) + b ( λ 1 , l 1 ) , I w ( i w , 2 , j w , 2 , λ 1 , z w , 1 ) = G ( z w , 1 ) G ( z 1 ) k ( λ 1 , l 1 ) I ( i 2 , j 2 , λ 1 , z 1 ) + b ( λ 1 , l 1 ) , I w ( i w , N , j w , N , λ 1 , z w , 1 ) = G ( z w , 1 ) G ( z 1 ) k ( λ 1 , l 1 ) I ( i N , j N , λ 1 , z 1 ) + b ( λ 1 , l 1 ) .
[ G w ( z w , 1 ) G ( z 1 ) I ( i 1 , j 1 , λ 1 , z 1 ) 1 G w ( z w , 1 ) G ( z 1 ) I ( i 2 , j 2 , λ 1 , z 1 ) 1 G w ( z w , 1 ) G ( z 1 ) I ( i N , j N , λ 1 , z 1 ) 1 ] D [ k ( λ 1 , l 1 ) b ( λ 1 , l 1 ) ] X = [ I w ( i w , 1 , j w , 1 , λ 1 , z w , 1 ) I w ( i w , 2 , j w , 2 , λ 1 , z w , 1 ) I w ( i w , N , j w , N , λ 1 , z w , 1 ) ] Y ,
X ^ = ( D T D ) 1 D T Y ,
β ( λ 1 ) [ e α ( λ 1 ) l 1 e α ( λ 1 ) l 2 e α ( λ 1 ) l M ] P ( α ) = [ k ( λ 1 , l 1 ) k ( λ 1 , l 2 ) k ( λ 1 , l M ) ] K .
α ^ ( λ 1 ) , β ^ ( λ 1 ) = a r g min α * , β * K β * P ( α * ) 2 2 J ,
κ ( λ 1 ) [ e ν ( λ 1 ) l 1 e ν ( λ 1 ) l 2 e ν ( λ 1 ) l M ] Q ( ν ) + γ ( λ 1 ) = [ b ( λ 1 , l 1 ) b ( λ 1 , l 2 ) b ( λ 1 , l M ) ] B .
ν ^ ( λ 1 ) , κ ^ ( λ 1 ) , γ ^ ( λ 1 ) = a r g min v * , κ * , γ * B γ * κ * Q ( ν * ) 2 2 J ,
I ˜ w ( i w , j w , λ c , z w ) = β ^ 1 ( λ c ) e α ^ ( λ c ) l ( I w ( i w , j w , λ c , z w ) κ ^ ( λ c ) e ν ^ ( λ c ) l γ ^ ( λ c ) ) ,
I e ( i , j , λ c , z ) = | I ( i , j , λ c , z ) G ( z ) G ( z w ) I ˜ w ( i w , j w , λ c , z w ) I ^ ( i , j , λ c , z ) | ,
ε ( i , j , λ c , z ) = I e ( i , j , λ c , z ) I ( i , j , λ c , z ) × 100 % .
Intensity variation = I max ( λ ) I min ( λ ) I m e a n ( λ ) ,
I n = 50 t I 0 255 ,
RSD ( y ^ , y ) = std ( y ^ y ) std ( y ) × 100 % .
I c ( x , y ) = Σ λ = 420 700 I ( x , y , λ ) S c ( λ ) T ( λ ) S m ( λ ) max { Σ λ = 420 700 I ( x , y , λ ) S c ( λ ) T ( λ ) S m ( λ ) } , c ( r , g , b ) ,

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