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An Empirical Explanation: Craik-O'Brien-Cornsweet Effect

The common denominator of the Cornsweet stimulus and the simultaneous brightness contrast stimulus is simply what the equiluminant 'targets' in the two luminance profiles have typically turned out to be.
According to a wholly empirical way of understanding the relationship between luminance and brightness, whenever a given stimulus is consistent with the experience of equiluminant targets signifying differently reflective objects, the brightnesses of the returns should appear different. If this idea is correct, then the same perceptual effect elicited by the stimulus profile in this Demonstration should be generated by any stimulus in which regions with the same luminance would have typically turned out to be differently reflective objects in different amounts of light. Another challenge to this way of considering vision is the so called Cornsweet edge.
In this Demonstration, the two equiluminant territories adjoining an opposing pair of luminance gradients that meet along a linear boundary appear differently bright. This stimulus, called the Cornsweet edge, belongs to a larger class referred to as Craik-O'Brien- Cornsweet edges, after the several psychologists who devised such stimuli (Figure 1). Although this illusion has also been rationalized in terms of lateral interactions among neurons in the input stages of the visual system, the region that appears brighter in this Demonstration actually borders the gradient of higher average luminance, whereas the region that appears darker is next to the gradient of lower average luminance, a profile that is in this respect opposite the arrangement of luminances in standard simultaneous brightness contrast stimuli (see Demonstration).
Figure 1

Figure 1 / The Cornsweet edge effect. A) Diagram of the spinning disk used by Cornsweet to demonstrate that when two equiluminant regions are separated by an edge comprising a pair of oppositely disposed luminance gradients, the adjoining territories are 'filled-in' by different lightness/brightness values. B) Standard presentation of the Cornsweet stimulus, shown here as a blowup of a portion of the rotating disk (for the sake of simplicity, the edge in the blowup has been straightened). C) Comparison of the photometric and perceptual profiles of the stimulus in (B). Despite the equal luminances of the territories adjoining the two gradients, the territory (1) to the left of the dark gradient (2) looks darker than the territory (4) to the right of the light gradient (3). D) This effect is abolished by covering up the opposing luminance gradients, as indicated here. (After Purves et al., 1999)

Despite these apparent differences, the effects elicited by both types of stimuli can be understood in the same statistical terms (Purves et al., 1999). The common denominator of the Cornsweet stimulus in thisDemonstration and the simultaneous brightness contrast stimulus in this Demonstration is simply what the equiluminant 'targets' in the two luminance profiles have typically signified with respect to successful behavior. The empirical reason for the perception elicited the Cornsweet stimulus in this Demonstration is that the surfaces bordering the gradients will sometimes have been generated by similarly reflective surfaces under the same illuminant; however, the same stimulus will often have been generated by differently reflective surfaces under different intensities of illumination (Figure 2).
These possible sources influence the reflex response to the stimulus according to their relative frequencies of occurrence, with the result that the two equiluminant regions adjoining the Cornsweet edge look different, the territory adjoining the light gradient appearing brighter than the territory adjoining the dark gradient.
Figure 2

Figure 2 / Possible sources of the Cornsweet stimulus. The luminance gradients in the standard Cornsweet stimulus (or anyplace else) could arise from gradual changes in surface reflectance adjacent to territories having the same reflectance properties and observed under the same illuminant (top panel), or from gradual changes in illumination of two surfaces that have different reflectance properties and are under different illuminants (bottom panel), or any combination of these possibilities. (Although the illuminated side of the darker cube and the shadowed side of the lighter one in the bottom panel look differently bright, they are actually equiluminant; the perceptual effects under discussion here can't be avoided, even in a didactic illustration like this). The statistical significance of these different possible sources of the Cornsweet stimulus is that equiluminant territories adjoining gradients of reflectance will typically have been similarly reflective surfaces under the same illuminant, whereas territories adjoining gradients of illumination will typically have been differently reflective surfaces under different amounts of illumination. (After Purves et al., 1999)

Consistent with this explanation, the effect can be increased - or decreased - by altering the relative probabilities of the possible sources of the stimulus (Figure 3 and Figure 4), as in the simultaneous brightness stimulus illustrated in this Demonstration. In both cases, the target that appears brighter is the one more consistent with the experience of a more reflective surface in relatively less light, whereas the target that appears less bright is more consistent with a less reflective surface in relatively more light. In this Demonstration the variety of information in the stimulus is all consistent with the adjoining territories being differently reflective surfaces in different illuminants, making the Cornsweet effect especially powerful.
Figure 3

Figure 3 / Diminishing the Cornsweet effect by information that increases the probability that the Cornsweet gradients signify variations in reflectance. Panel (A) shows the standard stimulus presented such that the equiluminant territories adjoining the gradients now extend around the Cornsweet stimulus as such (see dotted outline in [B]). In this case, observers see the territories adjoining the Cornsweet edge as having about the same brightness. Panel (C) shows a perspective view to indicate the source that is made more likely by this presentation of the stimulus (i.e., a flat surface with the territories adjoining the Cornsweet edge receiving the same amount of illumination). (After Purves et al., 1999)

Figure 4

Figure 4 / Enhancing the Cornsweet effect by information that increases the probability that the Cornsweet gradients signify variations in illumination. A) The stimulus here is presented in perspective, i.e., the way an object extending away from the observer would appear as a result of the 3-D to 2-D transformation required by projection onto the retina. The addition of perspective enhances the difference in brightness between the two territories compared to the standard presentation. Inset shows the source of the stimulus that is made more likely by this presentation. As in all the other manipulations shown here, the addition of perspective only alters the probability distribution of the possible stimulus sources, since the two territories could still lie in the same plane if their shapes implied a diminution of size with distance only coincidentally. B and C) Given that illumination usually comes from above, a similar enhancement occurs when the Cornsweet stimulus is rotated so that the dark gradient is above the light gradient, as in (B). Conversely, placing the stimulus in the opposite configuration makes it more likely that the source is similarly reflective surfaces under the same illuminant. As a result, the Cornsweet effect in (C) is diminished in comparison with the effect in (B), even though the physical structure of the stimuli are identical. (After Purves et al., 1999)

References

Cornsweet T (1970) Visual Perception. New York: Academic Press.

Purves D, Lotto RB (2004) The Cornsweet effect. Encyclopedia of Neuroscience, 3rd edition Elsevier Science Publishing Co.

Purves D, Shimpi A, Lotto RB (1999) An empirical explanation of the Cornsweet effect. J Neurosci 19:8542-8551.