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

TL;DR

This paper investigates how paint colors combine mathematically across different color spaces, finding that a symmetrized linear model in CIEXYZ space best predicts mixed paint colors, with implications for color science.

Contribution

It introduces a multivariate linear regression approach to model paint mixing in various color spaces, highlighting the effectiveness of CIEXYZ space for accurate color prediction.

Findings

Symmetrized linear combination in CIEXYZ space yields best fit.

RGB space provides better mean squared error for predictions.

Linear models can effectively approximate physical paint mixing.

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.