Transparently Obvious

How the brain sees through the perceptual hurdles of tinted glass, shadows and all things transparent

OUR ABILITY to perceive visual scenes effortlessly depends on intelligent deployment of built-in knowledge about the external world. The key word here is “intelligent,” which raises the questions: Just how smart is the visual system? What is its IQ? For example, does the visual system know the laws of phy­sics? Does it use inductive logic only (as many suspect), or can it perform deduc­tions as well? How does it deal with paradoxes, conflicts or incomplete information? How adaptable is it?

Some insight into perceptual intelligence comes from the study of transparency, a phenomenon explored by Gestalt psychologist Fabio Metelli. He first drew attention to the fact that com­pelling illusions of transparency can be produced by using relatively simple displays.

The word “transparency” is used loosely. Sometimes it refers to seeing an object, such as a sunglass lens, and the objects visible through that object, and sometimes it means seeing something through frosted glass, known as translucency. In this column we will restrict ourselves to the former, because the physical and perceptual laws pertaining to it are simpler.

Physics of Transparency
First let us consider the physics of transparency. If you put a rectangular neutral-density filter, such as dark glasses, on a sheet of white paper, the filter allows only a certain proportion of light through—say, 50 percent. Put another way, if the paper has a brightness, or luminance, of 100 candelas  (cd) per square meter, the portion covered by the filter will have a luminance of 50 cd. If you then add a second such filter so that it partially overlaps the first, the overlapping region will receive 50 percent of the original 50 percent of the light—that is, 25 percent. The relation is always multiplicative.

So much for physics. What about perception? If, as in a, you simply have a dark square in the middle of a light square (with the former being 50 cd and the latter 100 cd), the inner square could be either a filter that cuts light by 50 percent or a darker square that reflects only 50 percent as much of the incident light as does the surrounding background. Without additional information, there is no way the visual system could know which condition exists; because the latter case is far more common in nature, that is what you will always see.

But now consider two rectangles that form a cross with an overlapping region in the middle. In this case it is not inconceivable—and, indeed, it is more probable—that this configu­ration really does consist of two overlapping rectangular pieces of filters rather than five blocks arranged to form a cross. But if it is the former, then the luminance ratios must be such that the central square (the overlapping region) should be darker than the other squares and, of course, darker than the background. In particular, the central square’s luminance should be a multiplicative function in terms of a percentage of the two filters. If the nonoverlapping regions of the two rectangles are, for instance, 66 and 50 percent of the background, respectively, then the inner rectangle should be 50 percent of that 66 percent—or roughly 33 percent (that is, 33 cd assuming the white paper is 100 cd).

Now the question is: Does the visual system have tacit “knowledge” of all these factors? We can find out by using a series of displays (b, c, d) in which the background and rectangles are of a fixed luminance (such as 100 and 50 cd, respectively) while the luminance of the inner square alone changes. In terms of the luminance that would exist with physical transparency, the inner square is set to be too dark (b), appropriately dark (c) or too light (d). If you look at these figures without knowing anything about physics, you see the rectangles as transparent in c but not in b or in d. It is almost as if your visual system knows what you do not know (or did not know until you read this column).

This article was originally published with the title "Illusions: Transparently Obvious."

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