A Matrix Based Approach for Color Transformations in Reflections

Abstract

In this thesis, I demonstrate the feasibility of linear regression with 4 × 4 matrices to perform color transformations, specifically looking at the case of color transformations in reflections. I compare and analyze the power and performance linear regression models based on 3 × 3 and 4 × 4 matrices. I conclude that using 4 × 4 matrices in linear regression is more advantageous in power and performance over using 3 × 3 matrices in linear regressions, as 4 × 4 matrices allow for categorically more transformations by including the possibility of translation. This provides more general affine transformations to a color space, rather than being restricted to passing through the origin. I examine the benefits of allowing for negative elements in color transformation matrices. I also touch on the possible differences in application between filled 4 × 4 matrices and diagonal 4 × 4 matrices, and discuss the limitations inherent to linear regression used in any type of matrix operations.