Line-mark discrimination probability for a pair of colors
Source:R/palette_prob_bg.R
line_discrim_prob.RdPredicts the proportion of viewers who would detect the color difference between two line marks, as a function of line thickness, using the model fit by Szafir (2018) for line graphs (see Details).
Usage
line_discrim_prob(hex1, hex2, thickness = seq(0.05, 0.5, by = 0.01))Arguments
- hex1, hex2
two hex color strings, e.g.
"#3B4CC0"and"#B40426"- thickness
numeric vector of line thicknesses in degrees of visual angle. Szafir's tested range was 0.05 to 0.35 degrees; the default spans a bit wider for a smooth curve, but see the validated-range caveat above for values outside that range.
Details
Model: p = m_x(s) * dx, m_x(s) = c_x + k_x / s, per CIELAB axis (L*,
a*, b*), combined across axes as sqrt(sum((dx * m_x(s))^2)) and clipped
to [0, 1]. s is line thickness in degrees of visual angle, dx is the
absolute difference between the two colors along that axis.
Caveats:
White background only. Szafir's stimuli were rendered on plain white; this is a white-background baseline and says nothing about gray or black backgrounds.
Validated range. The regressions were fit using six color-difference steps per axis, all below the detection asymptote, and thickness was tested from 0.05 to 0.35 degrees. Outside that range the model is extrapolating: it is linear in
dxper axis, so nothing stops a raw prediction from exceeding 1 (clipped here, which produces a kink rather than the smooth saturation a real psychometric function would have).Cross-axis combination is untested. Szafir's experiment held "which axis differs" as a between-participants factor, so no participant judged a pair differing on more than one axis at once. The Euclidean combination above is the paper's own proposed generalization for real (multi-axis) color pairs, but it was not directly tested that way.