OSA's Digital Library

Virtual Journal for Biomedical Optics

Virtual Journal for Biomedical Optics


  • Editor: Gregory W. Faris
  • Vol. 3, Iss. 12 — Dec. 1, 2008

Evaluation and unification of some methods for estimating reflectance spectra from RGB images

Ville Heikkinen, Reiner Lenz, Tuija Jetsu, Jussi Parkkinen, Markku Hauta-Kasari, and Timo Jääskeläinen  »View Author Affiliations

JOSA A, Vol. 25, Issue 10, pp. 2444-2458 (2008)

View Full Text Article

Enhanced HTML    Acrobat PDF (514 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



The problem of estimating spectral reflectances from the responses of a digital camera has received considerable attention recently. This problem can be cast as a regularized regression problem or as a statistical inversion problem. We discuss some previously suggested estimation methods based on critically undersampled RGB measurements and describe some relations between them. We concentrate mainly on those models that are using a priori information in the form of high-resolution measurements. We use the “kernel machine” framework in our evaluations and concentrate on the use of multiple illuminations and on the investigation of the performance of global and locally adapted estimation methods. We also introduce a nonlinear transformation of reflectance values to ensure that the estimated reflection spectra fulfill physically motivated boundary conditions. The reported experimental results are derived from measured and simulated camera responses from the Munsell Matte, NCS, and Pantone data sets.

© 2008 Optical Society of America

OCIS Codes
(100.3010) Image processing : Image reconstruction techniques
(100.3190) Image processing : Inverse problems
(150.0150) Machine vision : Machine vision
(330.1710) Vision, color, and visual optics : Color, measurement

ToC Category:
Image Processing

Original Manuscript: February 12, 2008
Revised Manuscript: May 29, 2008
Manuscript Accepted: July 18, 2008
Published: September 11, 2008

Virtual Issues
Vol. 3, Iss. 12 Virtual Journal for Biomedical Optics

Ville Heikkinen, Reiner Lenz, Tuija Jetsu, Jussi Parkkinen, Markku Hauta-Kasari, and Timo Jääskeläinen, "Evaluation and unification of some methods for estimating reflectance spectra from RGB images," J. Opt. Soc. Am. A 25, 2444-2458 (2008)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. F. H. Imai and R. S. Berns, “Spectral estimation using trichromatic digital cameras,” in Proceedings of the International Symposium on Multispectral Imaging and Color Reproduction for Digital Archives (Society for Imaging Science and Technology, Society of Multispectral Imaging of Japan, 1999), pp. 42-49.
  2. J.-I. Park, M.-H. Lee, M. D. Grossberg, and S. K. Nayar, “Multispectral imaging using multiplexed illumination,” in ICCV 2007, Eleventh IEEE International Conference on Computer Vision (IEEE, 2007), pp. 14-21.
  3. J. M. Dicarlo, F. Xiao, and B. A. Wandell, “Illuminating illumination,” in The 9th Color Imaging Conference: Color Science and Engineering: Systems, Technologies, Applications (The Society for Imaging Science and Technology, Society of Multispectral Imaging of Japan, 2001), pp. 27-34.
  4. W. Menke, Geophysical Data Analysis: Discrete Inverse Theory (Academic, 1989).
  5. J. B. Cohen and W. E. Kappauf, “Metameric color stimuli, fundamental metamers and Wyszecki's metameric blacks,” Am. J. Psychol. 95, 537-564 (1982). [CrossRef] [PubMed]
  6. J. B. Cohen and W. E. Kappauf, “Color mixture and fundamental metamers: theory, algebra, geometry, application,” Am. J. Psychol. 98, 171-259 (1985). [CrossRef]
  7. P. G. Herzog, D. Knipp, H. Stiebig, and F. König, “Colorimetric characterization of novel multiple channel sensors for imaging and metrology,” J. Electron. Imaging 8, 342-353 (1999). [CrossRef]
  8. W. K. Pratt and C. E. Mancill, “Spectral estimation techniques for the spectral calibration of color image scanner,” Appl. Opt. 15, 73-75 (1976). [CrossRef] [PubMed]
  9. L. T. Maloney and B. A. Wandell, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 29-33 (1986). [CrossRef] [PubMed]
  10. F. Ayala, J. F. Echávarri, and P. Renet, “Use of three tristimulus values from surface reflectance spectra to calculate the principal components for reconstructing these spectra by using only three eigenvectors,” J. Opt. Soc. Am. A 23, 2020-2026 (2006). [CrossRef]
  11. H. Haneishi, T. Hasegawa, A. Hosoi, Y. Yokoyama, N. Tsumura, and Y. Miyake, “System design for accurately estimating the reflectance spectra of art paintings,” Appl. Opt. 39, 6621-6632 (2000). [CrossRef]
  12. Å. Björck, Numerical Methods for Least Squares Problems (SIAM, 1996). [CrossRef]
  13. J. Hernández-Andrés, J. Romero, A. Garca-Beltran, and J. L. Nieves, “Testing linear models on spectral daylight measurements,” Appl. Opt. 37, 971-977 (1998). [CrossRef]
  14. M. A. López-Álvarez, J. Hernández-Andrés, E. M. Valero, and J. Romero, “Selecting algorithms, sensors, and linear bases for optimum spectral recovery of skylight,” J. Opt. Soc. Am. A 24, 942-956 (2007). [CrossRef]
  15. L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673-1683 (1986). [CrossRef] [PubMed]
  16. J. Parkkinen, J. Hallikainen, and T. Jääskeläinen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318-322 (1989). [CrossRef]
  17. D. R. Connah and J. Y. Hardeberg, “Spectral recovery using polynomial models,” Proc. SPIE 5667, 65-75 (2005). [CrossRef]
  18. J. Y. Hardeberg, Acquisition and Reproduction of Color Images--Colorimetric and Multispectral Approaches (Dissertation.com, 2001).
  19. 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]
  20. T. Jetsu, V. Heikkinen, J. Parkkinen, M. Hauta-Kasari, B. Martinkauppi, S. D. Lee, H. W. Ok, and C. Y. Kim, “Color calibration of digital camera using polynomial transformation,” in CGIV, Third European Conference on Color in Graphics, Imaging and Vision (Society for Imaging Science and Technology, 2006), pp. 163-166.
  21. V. Heikkinen, T. Jetsu, J. Parkkinen, M. Hauta-Kasari, Timo Jääaskeläinen, and S. D. Lee, “Regularized learning framework in estimation of reflectance spectra from camera responses,” J. Opt. Soc. Am. A 24, 2673-2683 (2007). [CrossRef]
  22. V. Vapnik, Statistical Learning Theory (Wiley, 1998).
  23. B. Schölkopf and A. J. Smola, Learning With Kernels (MIT, 2002).
  24. G. Wahba, Spline Models for Observational Data, Vol. 59 of SIAM CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM, 1990). [CrossRef]
  25. T. Poggio and F. Girosi, “Networks for approximation and learning,” Proc. IEEE 78, 1481-1497 (1990). [CrossRef]
  26. J. M. Dicarlo and B. A. Wandell, “Spectral estimation theory: beyond linear but before Bayesian,” J. Opt. Soc. Am. A 20, 1261-1270 (2003). [CrossRef]
  27. T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction (Springer-Verlag, 2001).
  28. H.-L. Shen and J. H. Xin, “Spectral characterization of a color scanner by adaptive estimation,” J. Opt. Soc. Am. A 21, 1125-1130 (2004). [CrossRef]
  29. H.-L. Shen and J. H. Xin, “Spectral characterization of a color scanner based on optimized adaptive estimation,” J. Opt. Soc. Am. A 23, 1566-1569 (2006). [CrossRef]
  30. Y. Murakami, T. Obi, M. Yamaguchi, and N. Ohyama, “Nonlinear estimation of spectral reflectance on Gaussian mixture distribution for color image reproduction,” Appl. Opt. 41, 4840-4847 (2002). [CrossRef] [PubMed]
  31. O. Kohonen, J. Parkkinen, and T. Jääskeläinen, “Databases for spectral color science,” Color Res. Appl. 31, 381-388 (2006). [CrossRef]
  32. P. L. Vora and H. J. Trussell, “Measures of goodness of a set of color scanning filters,” J. Opt. Soc. Am. A 10, 1499-1508 (1993). [CrossRef]
  33. G. H. Golub and C. F. Van Loan, Matrix Computations (Johns Hopkins U. Press, 1996).
  34. M. Solli, M. Andersson, R. Lenz, and B. Kruse, “Color measurements with a consumer digital camera using spectral estimation techniques,” in Proceedings of 14th Scandinavian Conference on Image Analysis, Vol. 3540 ofLecture Notes in Computer science (Springer, 2005), pp. 110-114.
  35. N. Shimano, K. Terai, and M. Hironaga, “Recovery of spectral reflectances of objects being imaged by multispectral cameras,” J. Opt. Soc. Am. A 24, 3211-3219 (2007). [CrossRef]
  36. N. Shimano, “Recovery of spectral reflectances of objects being imaged without prior knowledge,” IEEE Trans. Image Process. 15, 1848-1856 (2006). [CrossRef] [PubMed]
  37. N. Ohta and A. R. Robertson, Colorimetry: Fundamentals and Applications, The Wiley-IS&T Series in Imaging Science and Technology (Wiley, 2005). [CrossRef]
  38. 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]
  39. Y. Murakami, K. Letomi, M. Yamaguchi, and N. Ohyama, “Maximum a posteriori estimation of spectral reflectance from color image and multipoint spectral measurements,” Appl. Opt. 46, 7068-7082 (2007). [CrossRef] [PubMed]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited