## Regularized learning framework in the estimation of reflectance spectra from camera responses

JOSA A, Vol. 24, Issue 9, pp. 2673-2683 (2007)

http://dx.doi.org/10.1364/JOSAA.24.002673

Enhanced HTML Acrobat PDF (605 KB)

### Abstract

For digital cameras, device-dependent pixel values describe the camera’s response to the incoming spectrum of light. We convert device-dependent RGB values to device- and illuminant-independent reflectance spectra. Simple regularization methods with widely used polynomial modeling provide an efficient approach for this conversion. We also introduce a more general framework for spectral estimation: regularized least-squares regression in reproducing kernel Hilbert spaces (RKHS). Obtained results show that the regularization framework provides an efficient approach for enhancing the generalization properties of the models.

© 2007 Optical Society of America

**OCIS Codes**

(100.3010) Image processing : Image reconstruction techniques

(100.3190) Image processing : Inverse problems

(330.1710) Vision, color, and visual optics : Color, measurement

**ToC Category:**

Image Processing

**History**

Original Manuscript: September 20, 2006

Revised Manuscript: March 23, 2007

Manuscript Accepted: April 13, 2007

Published: July 30, 2007

**Virtual Issues**

Vol. 2, Iss. 10 *Virtual Journal for Biomedical Optics*

**Citation**

Ville Heikkinen, Tuija Jetsu, Jussi Parkkinen, Markku Hauta-Kasari, Timo Jaaskelainen, and Seong Deok Lee, "Regularized learning framework in the estimation of reflectance spectra from camera responses," J. Opt. Soc. Am. A **24**, 2673-2683 (2007)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-24-9-2673

Sort: Year | Journal | Reset

### References

- M. D. Fairchild, Color Appearance Models (Addison-Wesley, 1998).
- M. J. Vrhel and H. J. Trussel, "Color device calibration: a mathematical formulation," IEEE Trans. Image Process. 8, 1796-1806 (1999). [CrossRef]
- 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]
- 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]
- J. Parkkinen, J. Hallikainen, and T. Jaaskelainen, "Characteristic spectra of Munsell colors," J. Opt. Soc. Am. A 6, 318-322 (1989). [CrossRef]
- D. Connah and J. Y. Hardeberg, "Spectral recovery using polynomial models," Proc. SPIE 5667, pp. 65-75 (2005). [CrossRef]
- P. Stigell, K. Miyata, and M. Hauta-Kasari, "Wiener estimation method in estimation of spectral reflectance from rgb images," Pattern Recogn. Image Anal. 15, 327-329 (2005).
- M. Bertero, T. Poggio, and V. Torre, "Ill-posed problems in early vision," Proc. IEEE 76, 869-889 (1988). [CrossRef]
- Å. Björck, Numerical Methods for Least Squares Problems (SIAM, 1996). [CrossRef]
- J. Y. Hardeberg, Acquisition and Reproduction of Color Images--Colorimetric and Multispectral Approaches (Dissertation.com, 2001).
- G. Hong, M. R. Luo, and P. A. Rhodes, "A study of digital camera colorimetric characterization based on polynomial modeling," Color Res. Appl. 26, 76-84 (2001). [CrossRef]
- A. Neumaier, "Solving ill-conditioned and singular linear systems, a tutorial on regularization," SIAM Rev. 99, 636-666 (1998). [CrossRef]
- 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, (IS&T, 2006), pp. 163-166.
- G. Wahba, Spline Models for Observational Data, Vol. 59 of SIAM CBMS-NSF Regional Conference Series in Applied Mathematics (SIAM, 1990). [CrossRef]
- T. Poggio and F. Girosi, "Networks for approximation and learning," Proc. IEEE 78, 1481-1497 (1990). [CrossRef]
- T. Evgeniou, M. Pontil, and T. Poggio, "Regularization networks and support vector machines," Adv. Comput. Math. 13, 1-50 (2000). [CrossRef]
- B. Schölkopf and A. J. Smola, Learning with Kernels (MIT, 2002).
- F. Girosi, M. Jones, and T. Poggio, "Regularization theory and neural network architectures," Neural Comput. 7, 219-269 (1995). [CrossRef]
- J. Parkkinen, "Subspace methods in two machine vision problems," Ph.D. thesis (University of Kuopio, 1989).
- N. Aronszajn, "Theory of reproducing kernels," Trans. Am. Math. Soc. 68, 337-404 (1950). [CrossRef]
- S. Saitoh, Theory of Reproducing Kernels and Its Applications (Longman, 1988).
- J. Shawe-Taylor and N. Christianini, Kernel Methods for Pattern Analysis (Cambridge U. Press, 2004). [CrossRef]
- V. I. Lebedev, An Introduction to Functional Analysis and Computational Mathematics (Birkhäuser, 1997).
- F. Cucker and S. Smale, "On the mathematical foundations of learning," Bull. Am. Math. Soc. 39, 1-49 (2002). [CrossRef]
- T. Poggio, S. Mukherjee, R. Rifkin, A. Rakhlin, and A. Verri, "B," in Uncertainty in Geometric Computations, J.Winkler and M.Niranjan, eds., (Kluwer, 2002), pp. 131-141. [CrossRef]
- F. Girosi, "An equivalence between sparse approximation and support vector machines," Neural Comput. 10, 1455-1480 (1998). [CrossRef] [PubMed]
- V. Vapnik, Statistical Learning Theory (Wiley, 1998).
- B. Hamers, "Kernel models for large scale applications," Ph.D. thesis (Katholieke Universiteit Leuven, 2004).
- T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference and Prediction (Springer-Verlag, 2001).
- M. R. Luo, G. Cui, and B. Rigg, "The development of the CIE 2000 colour-difference formula," Color Res. Appl. 26, 340-350 (2000). [CrossRef]

## 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.