Two psychophysical responses to surface or self-luminous stimuli are hypothesized. A response to the luminance of the stimulus (α) and a response to the luminance difference between the stimulus and its surround (β) are both considered to be power functions. Lightness or brightness is taken to be an additive or subtractive combination of these two responses (α±Kβ) depending on whether the surround is darker or brighter than the stimulus, respectively. This model is shown to produce a quantitatively adequate explanation of Takasaki’s data on crispening. An attempt is made to use this formulation to fit scaling data from previous magnitude-estimation and partitioning studies of lightness and brightness in which different results have been obtained from different backgrounds. Data from matching experiments that involve different backgrounds for the comparison and standard stimuli are also analyzed by means of the same formulation. The model is compared with the Adams–Cobb–Judd formulation of background effect on lightness, the Takasaki empirical formula for crispening, and Stevens’s power-law formulation for brightness and lightness.
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