White's illusion

White's illusion is a brightness illusion where certain stripes of a black and white grating is partially replaced by a gray rectangle (Fig. 1). Both of the gray bars of A and B are the same color and opacity. The brightness of the gray pieces appear to shift toward the brightness of the top and bottom bordering stripes. This is in apparent opposition to lateral inhibition as it cannot explain this occurrence. This occurs even when the gray patches in the black stripes are bordered by more white than black (and conversely for the gray patches in the white stripes). A similar illusion occurs when the horizontal strips have different colors; this is known as Munker-White's illusion or Munker's illusion.

The amount of each bipolar cell response depends on the amount of the stimulation it receives from the receptor and the amount that this response is decreased by the lateral inhibition it receives from its neighboring cells.

Lateral inhibition cannot explain White's illusion. In Figure 2.1 lateral inhibition sent by black cells A and C should make cell O lighter; in Figure 2.2 lateral inhibition sent by white cells A and C should make cell O darker. It is suggested that brightness induction follows the brightness contrast in the direction of the bar not the surrounding area.

In Figure 2.1 we assume that light dropping on cells B and D generates a response of 100 units. Since the points A and C are darker we assume that only 20 units are generated from these points. Another assumption is that the lateral inhibition sent by each cell is 10% of its response; cells B and D send an inhibition of 10 units each and cells A and C send an inhibition of 2 units each. The inhibition sent by cells A and C is larger since their size is bigger than the size of cells B and D (let's say 2 times). This concludes that cell O receives an inhibition I = 10 + 10 + 2 × 2 + 2 × 2 = 28.

In Figure 2.2 with the same assumptions as above stated, cell O receives an inhibition of I = 10 × 2 + 10 × 2 + 2 + 2 = 44.

Because point O in Figure 2.1 receives an inhibition smaller than the point O in Figure 2.2 the gray cell should be lighter.

White and White (1985) concluded that at a higher spatial frequency the grating of White's illusion could be described by brightness assimilation. They also concluded that at lower spatial frequencies White's illusion is still present.

Blakeslee and McCourt (2004) suggested that patterns whose scales are larger compared to the encoding filters (low spatial frequency are represented with a loss of low frequency information exhibiting brightness contrast); patterns whose scales are smaller compared to encoding filters (high spatial frequency), are represented with a loss of high frequency information exhibiting brightness assimilation.

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