Brightness of luminance distributions with gradual changes

The perception of gradually changing luminance distributions was investigated. Luminance changed across the radius of a disk by a linear, quadratic, or cubic function with varying magnitudes. Subjects selected matching luminances for the inner and outer edges of each stimulus. The threshold for reporting that the inner and outer matches were different occurred at approximately 20% contrast between those regions. This threshold did not vary with the particular function which described the luminance distribution. Further, as the magnitude of luminance change across the stimulus increased, subjects judged the inner and outer edges to differ more in brightness. Matching luminances also depended upon the background configuration with greater differences perceived across the disk radius when the surround and center dot of the stimulus were of opposite, rather than the same, luminance. These results indicate that models of brightness must consider all luminance changes in the stimulus, not just changes of a particular type such as second differences or changes at a luminance step.