White's illusion

White's illusion is a brightness illusion. Here, some stripes of a black and white grating are replaced by gray rectangles (see Fig). All gray bars usually have same color and opacity. The brightness of the gray pieces appear to shift toward the brightness of the top and bottom bordering stripes, that is, the gray bars with horizontal black regions on their top and bottom appear darker and those with white regions on their top and bottom appear lighter. But this does not match with what lateral inhibition predicts. This illusion is mostly described for grayscale. A similar illusion occurs for colored patches. This is known as Munker-White's illusion or Munker's illusion.
Lateral inhibition result for White's effect.
The amount of each bipolar cell response depends on the amount of the stimulation it receives from the receptor. Neighboring cells decrease this response. This is called lateral inhibition.
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.
Rules suggested to describe optical illusions such as simultaneous brightness contrast illusion, such as Wallach's ratio rule cannot explain White's illusion. These rules suggest that cell O in figure 2.1 receives less inhibition that cell O in figure 2.2. So, the cell O in figure 2.1 should be lighter than cell O in the other figure. However, the opposite case happens. 
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.
Belongingness.
The belongingness theory has been given as an explanation of White's illusion. Belongingness means that we perceive things depending on its surroundings. According to belongingness theory, the lightness of rectangle A is influenced by the white bars that surround it. Similarly, the rectangle B on the right side is surrounded by the dark bars. So, the lightness of rectangle B is affected by the dark background. As a result, area A which rests on the white background appears darker than area B which rests on the dark background.
Not all scientists accept the belongingness theory. They say that when talking about the background, it is the same as lateral inhibition.