Statistical properties of 1st- and 2nd-order brightness induction in a disk/annulus paradigm

The brightness of a disk can be strongly affected by the luminance of a surrounding annulus. This effect—brightness induction—can be either positive (assimilation) or negative (contrast) (1st-order effects), and the strength and sign of induction can also vary with the annulus luminance (2nd-order effects). We previously studied brightness induction using disk/annulus stimuli in which the target disk luminance was 18.03 cd/m2, its annulus luminance varied either from 4.54-14.45 cd/m2 or from 22.62-71.60 cd/m2, and the background field was either 0.25 or 180.70 cd/m2 (disk radius 0.70°, annulus width 0.35°). Participants adjusted the luminance of a match disk to match the target in brightness at six levels of annulus luminance. A 2nd-order polynomial regression model was fit to plots of individual subject matches vs annulus luminance. The model coefficients corresponding to 1st- and 2nd-order induction effects were linearly related by a proportionality constant that differed for incremental and decremental targets. Here, we extended our experiments to annulus widths ranging from 0.1-3.6° in 0.7° steps and analyzed average data from three subjects. The linear relationships found earlier between the 1st- and 2nd-order coefficients were confirmed and constant across annulus widths. The patterns of induction effects for specific luminance polarity conditions are complex, but they confirm those seen in earlier research and extend them to a larger annulus width range. For some luminance polarity conditions, assimilation and contrast are observed over different ranges of annulus luminance and size. Complementary research has shown that several types of appearance matches can be made with disk/annulus stimuli. Subjects can match the disks on “brightness,” or on specific perceptual attributes, such as perceived luminance, contrast, or lightness under different assumptions about the illumination. We argue that our parameterized polynomial regression model characterizes the statistical properties of the entire family of allowable matches.