The Weber fraction and asymmetries in luminance thresholds

Abstract

Presented in this article is a method for the determination of the Weber fraction by analyzing data obtained from color-matching experiments. The method is based on a rigorous analysis of the probability density function derived from discrimination judgments made in the xyY space. Analysis shows the thresholds for luminance increments and decrements are shown to be different and asymmetric and the Weber fraction to depend on the target's level of luminance and chromaticity.

Quantal and non-quantal color matches: failure of Grassmann’s laws at short wavelengths

“…The resultant matching values would violate the quantal theory. Asymmetric discrimination around quantal matches has been reported for both chromaticity and luminance under a variety of experimental conditions [6,16,[32][33][34][35].…”

Theoretical analysis of inter‐observer variability in the determination of luminance thresholds

“…The chromaticity coordinates associated to color center m for the reference observer ) threshold limits according to the statistical procedure developed in Ref. 23.…”

“…For a given a color center m with mean luminance Y 0 st,m , and its corresponding threshold of color-differences, we have computed the upper/lower threshold of luminance Y u st,m /Y l st,m for the reference observer by using the statistical method described in Ref. 23. The confidence level used to obtain the luminance thresholds was 0.16 in accordance with Ref.…”

“…The confidence level used to obtain the luminance thresholds was 0.16 in accordance with Ref. 23. The thresholds derived by these procedures for the reference observer serve us as a starting point in the current investigation.…”

“…These distributions will exactly reproduce the Weber fraction for the reference observer, which has been previously determined by the statistical method described in Ref. 23 , and Y l ␣,m are computed for each one of the set of cmf's available, {x i ␣ ()}. In this way, we can estimate for observers who are not directly involved in the color-matching experiment the values of the Weber fraction, or the degree of luminance mismatch with regard to those associated to the reference observer.…”