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Michael E. Rudd, Iris K. Zemach; Contrast, assimilation, and neural edge integration. Journal of Vision 2002;2(7):199. doi: https://doi.org/10.1167/2.7.199.
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A dark disk surrounded by a bright annulus appears darker as the annulus luminance is increased. Mechanistically, this darkness induction could result either from a direct neural computation of the disk/annulus ratio (for example, by a neural mechanism with center-surround antagonism), or from independent induction effects that originate from the inner and outer borders of the annulus. A recent neural filling-in model of darkness induction (Rudd, 2001; Rudd & Arrington, 2001) postulates that darkness inducing signals originating from separate borders combine linearly to influence disk brightness. We extended this model to include both brightness and darkness induction effects. According to the extended model, the inner edge of the surround annulus induces darkness in the disk (contrast) and the outer edge induces brightness in the disk (assimilation). The magnitude of each induction effect is proportional to the log luminance ratio of the border that generates the effect. We tested this theory and found that disk brightness is determined by a linear sum of independent inductions exerted by the inner and outer annulus edges, as predicted. Two disks were presented side-by-side on a flat-panel monitor. Each was surrounded by a higher intensity annulus. The luminance of the right annulus was varied to modulate the brightness of the right disk. The luminance of the left annulus was fixed. The subject adjusted the intensity of the left disk to achieve a brightness match to the right disk. For each of three observers, the response setting of the left disk varied inversely as a power of the right annulus luminance (power law exponents in the range .54 – .83 ). These results represent a substantial failure of both Wallach's ratio rule (Wallach, 1948) and any theory of darkness induction based strictly on local disk border contrast. But the filling-in model gives an exact quantitative account of the data and successfully predicts the log-log slopes (i.e., power law exponents) of the brightness matching curves from a knowledge of the intercepts. The assimilation produced by the outer edge is weakened when the edge is moved farther away from the disk, also consistent with the model. When assimilation is thus weakened, local border contrast dominates and brightness matches follow the ratio rule more closely.
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