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An Empirical Explanation: The Chubb Illusion

On empirical grounds, the apparent brightness difference between differently luminant elements of a target should decrease when imperfect transmittance is likely to have contributed to the light being returned from it.
As shown in this Demonstration, the brightness of any luminant stimulus varies, often quite markedly, as a function of the context in which it is presented. An especially intriguing example of this phenomenon is the illusion described by Chubb and colleagues (1989), in which the differential brightness of patterned elements in a target is reduced when the target is embedded in a pattern that has the same spatial frequency but higher luminance contrast (Figure 1).
Figure 1

Figure 1 / The Chubb effect. A 'target' pattern embedded in a surround in which the same pattern has a higher luminance contrast (A) appears to have less contrast than when the same target is placed in a uniform surround of the same average luminance (B) as the surround in (A). The inset below shows that the contrast between the patterned elements of the two identical targets appears the same when presented without their respective surrounds. (After Lotto and Purves, 2001)

The empirical explanation of the phenomenon illustrated in Figure 1 is as follows (see Lotto and Purves, 2001; Purves and Lotto, 2011 for details). All scenes viewed at the surface of the earth are seen through media that, to a greater or lesser degree, affect the amount of light that reaches the eye from the relevant objects (Figure 2).
Figure 2

Figure 2 / The physical effects of transmittance and their perceptual consequences. A) An imperfectly transmitting medium interposed between object and observer reduces the luminance differences between the spectral returns from surfaces seen through that medium (see text for further explanation). B) Illustration showing how the conditions diagrammed in (A) change the appearance of the relevant surfaces. (After Lotto and Purves, 2001)

Although the relative clarity of the atmosphere minimizes the effects of transmittance in most circumstances, viewing objects at a distance, nearby objects in fog or smog, or through semitransparent liquids or solids (e.g., water or glass) are all frequent and consequential factors in determining the spectral properties of the light that ultimately falls on the retina and initiates perception. If, for example, two target surfaces reflect, respectively, 80% and 30% of the incident light, the return from the more reflective surface in perfectly transmitting conditions will be greater than the return from the less reflective surface by a ratio of 8:3. If, however, the same surfaces are viewed through an imperfectly transmitting medium, this ratio is reduced. Although the interposition of such a medium reduces the amount of light coming from the surfaces in question proportionally, some light is also added to the luminances attributable to the two surfaces in question. The latter effect occurs because the medium also reflects light to the eye. Since this reflected light is added equally to any return from a surface viewed through the medium, the luminance attributable to the less reflective target surface is always increased to a greater degree than the luminance associated with the more reflective surface. As a result, the difference in the luminance of the two target surfaces is reduced, in this example from a ratio of 8:3 in perfect transmittance to about 7:5.
In short, an imperfectly transmitting medium, irrespective of its particular properties, always reduces the luminance differences between differently reflective surfaces seen through the medium. If perceptions are generated empirically, then to the extent that a stimulus is consistent with a contribution of imperfect transmittance, this influence will be incorporated into the perception of the target. As a result, the apparent brightness difference between differently luminant elements of a target should decrease when imperfect transmittance is likely to have contributed to the light being returned from it.
The Chubb stimulus in Figure 1 is empirically consistent with a contribution of transmittance to the target for two reasons. First, the borders between the patterned elements of the surround are continuous with the patterned boundaries in the target; and second, the luminances of the target elements accord with the values that would arise if the pattern of the surround were viewed through an imperfectly transmitting medium. Because a uniform background is relatively ambiguous in these respects, imperfect transmittance is more likely to have contributed to the return from the target. The apparent difference in the brightness of the target elements should increase in any such circumstance, even though the luminance ratios in the stimulus and spatial frequencies of the surround and target remain unchanged.
Thus the Chubb illusion (Demonstration) can, like other illusions of brightness, be understood in wholly empirical terms, in this case with the typical consequences of seeing surfaces through imperfectly transmitting media.

References

Purves D, Lotto RB (2011) Why We See What We Do Redux: A Wholly Empirical Theory of Vision. Sunderland, MA: Sinauer Associates.

Lotto RB, Purves D (2001) An empirical explanation of the Chubb illusion. J Cogn Neur 13:1-9.

Chubb C, Sperling G, Solomon JA (1989) Texture interactions determine perceived contrast. Proc Natl Acad Sci USA 86:9631-9635.