## Spectral estimation theory: beyond linear but before Bayesian

JOSA A, Vol. 20, Issue 7, pp. 1261-1270 (2003)

http://dx.doi.org/10.1364/JOSAA.20.001261

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### Abstract

Most color-acquisition devices capture spectral signals by acquiring only three samples, critically undersampling the spectral information. We analyze the problem of estimating high-dimensional spectral signals from low-dimensional device responses. We begin with the theory and geometry of linear estimation methods. These methods use linear models to characterize the likely input signals and reduce the number of estimation parameters. Next, we introduce two submanifold estimation methods. These methods are based on the observation that for many data sets the deviation between the signal and the linear estimate is systematic; the methods incorporate knowledge of these systematic deviations to improve upon linear estimation methods. We describe the geometric intuition of these methods and evaluate the submanifold method on hyperspectral image data.

© 2003 Optical Society of America

**OCIS Codes**

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

**Citation**

Jeffrey M. DiCarlo and Brian A. Wandell, "Spectral estimation theory: beyond linear but before Bayesian," J. Opt. Soc. Am. A **20**, 1261-1270 (2003)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-20-7-1261

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### References

- D. B. Judd, D. L. MacAdam, and G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964).
- E. L. Krinov, “Surface reflectance properties of natural formations,” Technical Translation TT-439 (National Research Council of Canada, Ottawa, 1947).
- J. Cohen, “Dependency of the spectral reflectance curves of the Munsell color chips,” Psychonomic Sci. 1, 369–370 (1964).
- G. Buchsbaum, “A spatial processor model for object color perception,” J. Franklin Inst. 310, 1–26 (1980).
- 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).
- B. K. P. Horn, “Exact reproduction of colored images,” Comput. Vision Graph. Image Process. 26, 135–167 (1984).
- F. O. Huck, D. J. Jobson, S. K. Park, S. D. Wall, R. E. Arvidson, W. R. Patterson, and W. D. Benton, “Spectrophotometric color estimates of the Viking Lander sites,” J. Geophys. Res. 82, 4401–4411 (1977).
- D. A. Forsyth, “A novel algorithm for color constancy,” Int. J. Comput. Vision 5, 5–36 (1990).
- D. Brainard and W. Freeman, “Bayesian color constancy,” J. Opt. Soc. Am. A 14, 1393–1411 (1997).
- G. D. Finlayson, P. M. Hubel, and S. Hordley, “Color by cor-relation,” in Proceedings of the Fifth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 6–11.
- K. Barnard, L. Martin, and B. Funt, “Colour by correlation in a three-dimensional colour space,” in Sixth European Conference on Computer Vision (Springer-Verlag, Berlin, 2000), pp. 275–289.
- S. Tominaga, S. Ebuisi, and B. A. Wandell, “Scene illumination classification: brighter is better,” J. Opt. Soc. Am. A 18, 55–64 (2001).
- P. Catrysse, A. E. Gamal, and B. Wandell, “Color architectures for CMOS sensor imaging,” in Sensors, Cameras, and Applications for Digital Photography, N. Sampat and T. Yeh, eds., Proc. SPIE 3650, 26–35 (1999).
- J. Chen and K. Huang, “Adaptive color correction by high-order CMAC neural network,” in Proceedings of the Fifth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 182–186.
- J. M. DiCarlo and B. A. Wandell, “Spectral estimation examples: beyond linear but before Bayesian,” (manuscript in preparation), contact authors for information: dicarlo@white.stanford.edu.
- T. Kailath, A. H. Sayed, and B. Hassibi, Linear Estimation (Prentice-Hall, Englewood Cliffs., N.J., 2000), p. 854.
- B. A. Wandell, “The synthesis and analysis of color images,” IEEE Trans. Pattern Anal. Mach. Intell. PAMI-9, 2–13 (1987).
- M. Vrhel and H. Trussell, “Color correction using principal components,” Color Res. Appl. 17, 328–338 (1992).
- M. S. Drew and B. V. Funt, “Natural metamers,” CVGIP: Image Understand. 56, 139–151 (1992).
- 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 (Chiba, Japan, 1999), pp. 42–49.
- M. Vrhel and J. Trussell, “Color device calibration: a mathematical formulation,” IEEE Trans. Image Process. 8, 1796–1806 (1999).
- B. A. Wandell and J. E. Farrell, “Water into wine: converting scanner RGB to tristimulus XYZ,” in Device-Independent Color Imaging and Imaging Systems Integration, R. J. Motta and H. A. Berberian, eds., Proc. SPIE 1909, 92–100 (1993).
- K. V. Mardia, J. T. Kent, and J. M. Bibby, Multivariate Analysis (Academic, London, 1979).
- R. A. Johnson and D. W. Wichern, Applied Multivariate Statistical Analysis (Prentice-Hall, Upper Saddle River, N.J., 2002).
- M. Vrhel, R. Gershon, and L. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 9, 4–9 (1994).
- G. Wyszecki and W. S. Stiles, Color Science: Concepts andMethods, Quantitative Data and Formulae (Wiley, New York, 1982).
- G. Finlayson and M. Drew, “The maximum ignorance assumption with positivity,” in Proceedings of the Fourth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 1996), pp. 202–205.
- J. A. S. Viggiano, “Minimal-knowledge assumptions in digital still camera characterization. I.: Uniform distribution, Toeplitz correlation,” in Proceedings of the Ninth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 2001), pp. 332–336.
- T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning: Data Mining, Inference, and Prediction (Springer-Verlag, Berlin, 2001).
- J. M. DiCarlo and B. A. Wandell, “Illuminant estimation: beyond the bases,” in Proceedings of the Eighth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 2000), pp. 91–96.
- M. Shi and G. Healey, “Using reflectance models for color scanner calibration,” J. Opt. Soc. Am. A 19, 645–656 (2002).
- N. Tsumura, M. Kawabuchi, H. Haneishi, and Y. Miyake, “Mapping pigmentation in human skin by multi-visible-spectral imaging by inverse optical scattering technqiue,” in Proceedings of the Eighth Color Imaging Conference: Color Science, Systems and Applications (Society for Imaging Science and Technology, Springfield, Va., 2000), pp. 81–84.
- H. Poincaré, “Analysis situs,” J. Ec. Polytech Series 2 1, 1–123 (1895).
- V. I. Arnold, “On teaching mathematics,” http://pauli.uni-muenster.de/~munsteg/arnold.html (1997).
- C. S. McCamy, H. Marcus, and J. G. Davidson, “A color-rendition chart,” J. Appl. Photogr. 48, 777–784 (1976).
- K. Barnard, L. Martin, B. Funt, and A. Coath, “A data set for colour research,” Color Res. Appl. 27, 147–151 (2002).
- D. H. Brainard, Hyperspectral image data, http://color.psych.ucsb.edu//hyperspectral/, 1998.
- J. Hardeberg and F. Schmitt, “Color printer characterization using a computational geometry approach,” in Proceedings of the Fifth Color Imaging Conference (Society for Imaging Science and Technology, Springfield, Va., 1997), pp. 97–99.
- H. R. Kang, Color Technology for Electronic Imaging Devices (SPIE Press, Bellingham, Wash., 1997).
- P. Kubelka and F. Munk, “Ein Beitrag sur Optik der Farbanstrche,” Z. Tech. Phys. 12, 593–601 (1931).
- H. E. J. Neugebauer, “Die theoretischen Grundlagen des Mehrfarbendruckes,” Z. Wiss. Photogr. 36, 73–89 (1937).
- 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 (1991).
- P. Hung, “Colorimetric calibrations in electronic imaging devices using a look-up-table model and interpolations,” J. Electron. Imaging 2, 53–61 (1993).
- A. Ribes and F. Schmit, “Reconstructing spectral reflectances with mixture density networks,” in Proceedings of the CGIV (Poitiers, France, 2002), pp. 486–491.

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