Predicting color matches from luminance matches

Abstract

Color vision and spectral sensitivity vary among individuals with normal color vision; thus, for many applications, it is important to measure and correct for an observer's sensitivity. Full correction would require measuring color and luminance matches and is rarely implemented. However, luminance matches (equiluminance settings) are routinely measured and simple to conduct. We modeled how well an observer's color matches could be approximated by measuring only luminance sensitivity, since both depend on a common set of factors. We show that lens and macular pigment density and $L/M$L/M cone ratios alter equiluminance settings in different ways and can therefore be estimated from the settings. In turn, the density variations can account for a large proportion of the normal variation in color matching. Thus, luminance matches may provide a simple method to at least partially predict an observer's color matches without requiring more complex tasks or equipment.

Figure 1.

Biases in luminance matches, relative to a standard observer, produced by variations in spectral sensitivity. Primaries are spectra peaking at 467, 532, or 630 nm (sd = 5 nm). Variations corresponded to ±2 standard deviations in the lens (sd = 18.7%) or macular (sd = 36.5%) pigment density, or to ±4-fold change in L to M cone ratio.

Figure 2.

Errors in the estimates of the lens and macular pigment density and L/M ratio introduced by errors in the luminance matches (simulated by adding Gaussian noise to the correct matches). Each plot shows the log standard deviation in the errors for estimating the lens (red line, L), macular (green line, M), L/M (blue line, R) factors for a fixed set of primaries and a variable reference wavelength. The primary wavelengths and reference wavelength resulting in the smallest errors are indicated by the bars. a) primary wavelengths optimized for the lowest error. b) the rec. 2020 primaries.

Figure 3.

Simulations of the errors in the estimated lens and macular pigment density resulting from unknown variations in the λ_max and optical density of the cone pigments. The standard deviation of the errors in predicted density of the lens (blue line, L) or macular (red line, M) pigment are plotted as a function of wavelength, again for a) primary wavelengths optimized for the lowest error and b) the rec. 2020 primaries.

Figure 4.

An example of color matches predicted from the luminance matches for a single observer differing from the standard observer by 1 sd in all factors. Shown are a) spectral sensitivity and b) color matching functions of the actual individual (dashed line), the individual approximated only from the lens and macular pigment density (open circles) and the standard observer (solid line). c) Coordinates of the matches in the CIELAB color space, for the full observer (red plus signs), lens and macular only (open circles), and standard observer (solid line). d) absolute errors (delta E) in the predicted matches between the actual vs. standard observer (blue, top bars) or the actual vs. lens and macular approximation (white, bottom bars).

Figure 5.

Average estimated errors (delta E) in the color matches for different reference wavelengths predicted for a random sample of observers based on either the standard observer (blue, top bars) or from the lens and macular estimates (white, bottom bars). The two panels show the errors for the rec. 2020 primaries with narrow (5 nm; panel a) or broader (10 nm; panel b) bandwidths.

Figure 6.

Average estimated errors (delta E) in the color matches to the spectra of the MacBeth Color Checker predicted for a random sample of observers based on either the standard observer (blue, top bars) or from the lens and macular estimates (white, bottom bars). The two panels show the errors for the rec. 2020 primaries with narrow (5 nm; panel a) or broader (10 nm; panel b) bandwidths.