Statistical properties of color matching functions

TL;DR

This paper investigates the statistical properties of color matching functions in human vision, deriving analytical models for variability and correlations based on photon capture noise, and compares these with experimental data.

Contribution

It introduces an analytical framework linking color matching variability to retinal composition and absorption spectra, enhancing understanding of metamerism and color perception.

Findings

Derived analytical expressions for response variability and correlations.

Identified how retinal composition influences color-matching statistics.

Compared theoretical predictions with experimental variability data.

Abstract

In trichromats, color vision entails the projection of an infinite-dimensional space (the one containing all possible electromagnetic power spectra) onto the 3-dimensional space that modulates the activity of the three types of cones. This drastic reduction in dimensionality gives rise to metamerism, that is, the perceptual chromatic equivalence between two different light spectra. The classes of equivalence of metamerism are revealed by color-matching experiments, in which observers adjust the intensity of three monochromatic light beams of three pre-set wavelengths (the primaries) to produce a mixture that is perceptually equal to a given monochromatic target stimulus. Here we use the linear relation between the color matching functions and the absorption probabilities of each type of cone to find particularly useful triplets of primaries. As a second goal, we also derive an analytical description of the trial-to-trial variability and the correlations of color matching functions stemming from Poissonian noise in photon capture. We analyze how the statistical properties of the responses to color-matching experiments vary with the retinal composition and the wavelengths of peak absorption probability, and compare them with experimental data on subject-to-subject variability obtained previously.