Comparison of methods of parameric correction for evaluating metamerism

Abstract

In practice, most metameric pairs do not achieve colorimetric equality for a set of reference conditions. These parameric pairs are composed of a residual color difference and a metameric difference. Three techniques have been used to correct this residual color difference: an additive correction in L*a*b*, a multiplicative correction in XYZ (recommended by the CIE), and parameric decomposition where the batch's spectrum is adjusted. Parameric decomposition can be viewed as batch correction using three ''colorants'' (process primaries) where the color-mixing model is linear in reflectance. Most often, Cohen and Kappauf's Matrix R technique is used where the primaries are color matching functions. Alternative primaries were derived from a Munsell Book of Color and an automotive paint system using principal component analysis (PCA) and independent component analysis (ICA). 1,152 parameric pairs about 24 color centers were synthesized using the paint system and Kubelka-Munk turbid-media theory. Each parameric pair was corrected to a metameric pair using these methods. Spectral accuracy was evaluated by comparing the corrected spectra to metameric reference spectra calculated using Kubelka-Munk batch correction. The Matrix R technique had the worst spectral accuracy under the reference conditions while both PCA and ICA had similar and reasonable accuracy. The special index of metamerism, change in illuminant, was calculated for each parameric pair using these various correction techniques to achieve colorimetric equality. The Matrix R and CIE-recommended multiplicative techniques were statistically significantly worse than parameric decomposition using Munsell Book of Color PCA and ICA and automotive ICA process primaries.

Image‐based spectral reflectance reconstruction using the matrix R method

“…The first is to replace the tristimulus integration weights used as additive primaries with primaries that better represent complex-subtractive colorants, as demonstrated by Li and Berns. 30 Matrix R is generalized as matrix S, [Eq. (7)], and matrix R method is defined by Eq.…”

“…One is to generate a new transformation matrix, each column of which is a basis vector of a reflectance database, as discussed in Ref. 30. The other approach is to adding some kind of physical constraint.…”

“…These primaries were found to be significantly better than tristimulus integration weights when used to correct paramers computationally that approximated batch correction. 30 Thus, although we do not advocate that matrix R identifies the fundamental, this terminology was adopted in this publication because of its common usage.…”

Metamerism and shade sorting

“…This type of index does not distinguish between test and reference illuminants, but considers only the illuminant pairs. Li and Berns (2007) compared different methods of parameric correction for the evaluation of metamerism. Three techniques have been used to correct this residual colour difference: an additive correction in L * a * b *, a multiplicative correction in XYZ (recommended by the CIE) and parameric decomposition where the batch's spectrum is adjusted.…”

Paramerism and reliable parameric correction

“…2 A variety of methodologies for parameric correction have been developed which are based on spectral or colorimetric adjustment of the pair. Li and Berns 3 investigated the performance of different correction methods for evaluating metamerism and proposed a method using principal component analysis and independent component analysis techniques to derive a set of process primaries applicable for parameric correction. They declared that the Matrix R, additive correction, and multiplicative techniques used for parameric correction usually provide the worst results and hence should not be used.…”