Optimizing color-matching functions for individual observers using a variation method

The CIE system allows the specification of color matches for a standard obs erver using the color-matching functions (cmfs). However, the cmfs of an in dividual observer are different from those of the CIE within a finite range . This article describes the optimization of the cmfs of an individual obse rver based on metameric pairs using a variation method. This is a so much s implified method for estimating rough and ready cmfs of an individual obser ver in comparison with past experiments. The underlying assumption of the o ptimization is that the optimum cmfs will predict that the integrated cone responses of a metameric pair are equal. The feature of the proposed optimi zation method is that the color difference in a metamer pair can be optimiz ed 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 squa re of modified values in the variation method. The cost function of the var iation method is generalized to consider the perception of color difference s by the human visual system. Experiments using measured metamer spectral d ata demonstrate the validity of the proposed method. In the Supplemental Ma terial (found on the IS&T website at www.imaging.org, for no less than 2 ye ars from the date of publication), theorems and characteristics are present ed and proved to demonstrate the rigid theoretical background supporting th e experimental validity.