Testing parabolic brightness matching functions across four contrast polarity conditions

It is well established that brightness (perceived luminance) or lightness (perceived reflectance) of a patch is modulated by its surroundings. Such influence can be measured using the disk/annulus paradigm (Wallach, 1948) where the luminance of a match disk is adjusted to match the appearance of a target disk that is surrounded by an annulus. Parabolic Brightness Matching Functions (BMFs) are obtained when a 2nd-order polynomial model is fitted to the average perceptual matches made at varying annulus luminance levels on a log-log scale. Rudd (2010) proposed a model that explains the parabolic BMFs, on which a contrast gain control operates between the outer and inner edges of the annulus to influence the target brightness. The model posits that, when the first-order coefficient (k1) of BMFs is plotted against the second-order coefficient (k2), the resulting plot should be a linear function whose slope depends on the contrast polarity of the target disk to its annulus and the luminance of the target disk. Rudd, Kavcar, and Crognale (2023) showed that this linear relationship does not depend on the annulus luminance or the annulus size but instead depends on the contrast polarity—all in-line with the model predictions. Here, we further tested the model by varying the target disk luminance to four additional levels. The model predicts that the slope of the k1 vs k2 plot should itself vary as a linear function of the target disk luminance, and rate of change will be -1.0 for conditions where match disk is decrement to its background and -0.5 where the disk is increment. Our results confirmed the first prediction (strong, negative relationship) across four contrast polarity conditions, but the specific slope predictions were disconfirmed.