Estimating individual cone fundamentals from their color-matching functions

Abstract

Estimation of individual spectral cone fundamentals from color matching functions is a classical and longstanding problem in color science. In this paper we propose a novel method to carry out this estimation based on a linear optimization technique, employing an assumption of a priori knowledge of the retinal absorptance functions. The result is an estimation of the combined lenticular and macular filtration for an individual, along with the nine coefficients in the linear combination that relates their color matching functions to their estimated spectral cone fundamentals. We test the method on the individual Stiles and Burch color matching functions and derive cone fundamental estimations for different viewing fields and matching experiment repetition. We obtain cone fundamental estimations that are remarkably similar to those available in literature. This suggests that the method yields results that are close to the true fundamentals.

Demonstration of a Human Color Vision Mimic in the Infrared

“…The first step in the development of the CIE-IR chart is the selection of three IR optical filters, which are analogous to the three photopigments contained within the cone receptors in the human eye. , In order to provide discrimination between different chemicals, these optical filters must have significant spectral overlap with the vibrational absorption bands of the chemicals of interest. Such filters may be selected by any number of means; ,, in this study, a simulated annealing optimization approach was employed.…”

“…To implement this technique, a weighting matrix is generated and applied to the filter functions F L , F M , and F S . It is known through the Grassmann Laws that two color-matching functions are linearly related to one another by 3 × 3 matrix multiplication. , Therefore, we define the color-matching functions x̅ , y̅ , and z̅ as a matrix multiplication between the filter functions and a 3 × 3 weighting matrix, M , such that where For the weighting matrix, M , the individual components, b 1 – b 9 , are randomly assigned during the optimization routine, which is described in detail in the Optimization Routine section. These weighted color-matching functions, x̅ , y̅ , and z̅ , then replace the filter functions F L , F M , and F S in eq to define the tristimulus coordinates X , Y , and Z and the resulting x – y coordinates (eq ) for all data.…”

“…It is known through the Grassmann Laws that two colormatching functions are linearly related to one another by 3 × 3 matrix multiplication. 14,29 Therefore, we define the colormatching functions x ̅ , y ̅ , and z ̅ as a matrix multiplication between the filter functions and a 3 × 3 weighting matrix, M, such that…”

“…The output of the three primary light sources was recorded for each test color, thus defining the x̅ , y̅ , and z̅ functions. These functions do not directly represent the biological cone receptors’ color responses; however, they have been shown to be a weighted linear transform of the spectral profile of the cone receptors. , …”

“…These functions do not directly represent the biological cone receptors' color responses; however, they have been shown to be a weighted linear transform of the spectral profile of the cone receptors. 14,15 Using these three wavelength dependent functions, x ̅ , y ̅ , and z ̅ , tristimulus values X, Y, and Z are defined for any given incident light source. These tristimulus values are determined by multiplying the integrated spectral power distribution of an incident light source by the x ̅ , y ̅ , and z ̅ functions.…”