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Volume: 45 | Article ID: art00009
Optimizing Color-Matching Functions for Individual Observers Using a Variation Method
  DOI :  10.2352/J.ImagingSci.Technol.2001.45.5.art00009  Published OnlineSeptember 2001

The CIE system allows the specification of color matches for a standard observer using the color-matching functions (cmfs). However, the cmfs of an individual observer are different from those of the CIE within a finite range. This article describes the optimization of the cmfs of an individual observer based on metameric pairs using a variation method. This is a so much simplified method for estimating rough and ready cmfs of an individual observer in comparison with past experiments. The underlying assumption of the optimization is that the optimum cmfs will predict that the integrated cone responses of a metameric pair are equal. The feature of the proposed optimization method is that the color difference in a metamer pair can be optimized to 0 at a boundary condition in the variation method, and the smoothness of the modified cmfs results from the cost function of the least mean square of modified values in the variation method. The cost function of the variation method is generalized to consider the perception of color differences by the human visual system. Experiments using measured metamer spectral data demonstrate the validity of the proposed method. In the Supplemental Material (found on the IS&T website at <ext-link ext-link-type="uri" xlink:href=""></ext-link>, for no less than 2 years from the date of publication), theorems and characteristics are presented and proved to demonstrate the rigid theoretical background supporting the experimental validity.

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Nobuhito Matsushiro, Noboru Ohta, Mark Q. Shaw, M. D. Fairchild, "Optimizing Color-Matching Functions for Individual Observers Using a Variation Methodin Journal of Imaging Science and Technology,  2001,  pp 472 - 480,

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