Mixing Paint: An analysis of color value transformations in multiple coordinate spaces using multivariate linear regression

TL;DR

This work investigates how color mixtures transform across coordinate spaces when painting with subtractive pigments. It applies multivariate linear regression to predict resulting colors from input pigment combinations and compares fits across RGB, CIEXYZ, and other color spaces using $R^2$ and $MSE$ as metrics. A key finding is that a geometrically symmetrized linear combination of colors in CIEXYZ space yields the highest coefficient of determination $R^2$, while the same mapping in RGB space achieves a lower mean squared error $MSE$. These results illustrate that the choice of color space materially affects predictive quality, with CIEXYZ offering better explained variance and RGB providing more precise value predictions under $MSE$, highlighting trade-offs in color-matching applications.

Abstract

I explore the mathematical transformation that occurs in color coordinate space when physically mixing paints of two different colors. I tested 120 pairs of 16 paint colors and used a linear regression to find the most accurate combination of input parameters, both in RGB space and several other color spaces. I found that the fit with the strongest coefficient of determination was a geometrically symmetrized linear combination of the colors in CIEXYZ space, while this same mapping in RGB space returns a better mean squared error.

Figures (1)

• Figure 1: A comparison of additive (RGB) and subtractive (CMY) color spaces. The overlap of two circles indicate the combinations of the colors involved. In these cases, the primary colors of one model are the secondary colors of another. Image taken from Canon.