IMAGINE THAT you are looking at a dog that is standing behind a picket fence. You do not see several slices of dog; you see a single dog that is partially hidden by a series of opaque vertical slats. The brain’s ability to join these pieces into a perceptual whole demonstrates a fascinating process known as amodal completion.

It is clear why such a tendency would have evolved. Animals must be able to spot a mate, predator or prey through dense foliage. The retinal image may contain only fragments, but the brain’s visual system links them, reconstructing the object so the animal can recognize what it sees. The process seems effortless to us, but it has turned out to be one of those things that is horrendously difficult to program computers to do. Nor is it clear how neurons in the brain’s visual pathways manage the trick.

In the early 20th century Gestalt psychologists were very interested in this problem. They devised a number of cunningly contrived illusions to investigate how the visual system establishes the continuity of an object and its contours when the object is partially obscured. A striking example of amodal completion is an illusion devised by Italian psychologist Gaetano Kanizsa. In one view, you see a set of “chicken feet” arranged geometrically. But if you merely add a set of opaque diagonal bars, a three-dimensional cube springs into focus seemingly by magic, the chicken feet becoming cube corners.

The astonishing thing is you do not even need to overlay real bars—even illusory ones will do. Here the otherwise inexplicable absence of boundaries terminating the chicken feet leads the brain to automatically infer the presence of opaque bars. So you see an illusory cube occluded by illusory bars!

The term “amodal completion” was coined to distinguish it from modal completion. Modal completion is the brain’s tendency to see the full outline of a nonexistent object, as occurs in Kanizsa’s classic triangle illusion. The brain regards it as highly improbable that some sneaky visual scientist has placed three black disks with pie-shaped wedges cut out of them precisely in this manner, preferring instead to see an opaque white triangle that is partially covering three black disks.

Note, however, that modal and amodal completion can coexist. For example, in the Kanizsa triangle, the brain amodally completes each disk behind the corners of the illusory triangle. Similarly, the illusory bars are modally completed, whereas the cube is amodally completed.

Peter U. Tse, a cognitive psychologist at Dartmouth College, has devised many elegant illusions to explore modal and amodal completion. One of them, shown in figure e, is ambiguous, as are many of our favorite illusions. There is a strong bias to see this figure as a stack of rings (amodally completed) encircling an opaque (modally completed) illusory cylinder. Yet one might have a very different take, seeing no cylinder and instead a column of C-shaped metal arches with the sharp ends facing forward. The bias toward seeing rings occurs because it better reflects the real world, which abounds in 3-D objects that occlude one another. Another of Tse’s illusions, which we fondly call “alien grabbing the last doughnut,” also has both modal and amodal aspects. It looks like a bunch of squiggles until the eye discerns a series of tentacular fingers coiled around a doughnut-shaped tube.

The Transparent Tunnel
You might think amodal completion involves reasoning (“there is a fence in the way, which is why I’m seeing slices of dog”), but in fact it is a perceptual phenomenon requiring no cogitation.

When you notice a wagging tail protruding from under the sofa and recognize that a dog must be attached, that is a logical inference. Whereas if the dog’s head were sticking out from the other side of the sofa, then in an automatic and effortless manner, via amodal completion, you would perceive a whole dog without actually seeing its hidden parts.

Similarly, when you see a person’s two arms forming a cross, there are two possible interpretations. A malicious surgeon may have amputated an arm and pasted the two halves on either side of the intact arm—or one arm may simply be placed perpendicularly in front of the other. Your visual system instantly sees that the latter is true; you do not even consider the former interpretation. Again, this is not because of high-level knowledge about the improbability of amputated arms—note that the brain has the same instantaneous reaction when the cross is made of wood, which could quite easily and bloodlessly have been sawed into pieces.

Borderline cases exist, however, such as the bear you “hallucinate” behind a tree. This drawing seems to show only circles bisected by lines, until the addition of what appear to be claws makes the dot at the top right morph into a nose and the circles into paws. Such examples blur the distinction between seeing and knowing. For instance, if you observe a fast-moving toy train go into a short tunnel and emerge on the other side within a third of a second, you will actually “see” the motion of the train, as if the tunnel were transparent. You have modally completed the motion across the tunnel—a phenomenon first pointed out by Gestalt psychologist Albert Michotte (1881–1965).

If the train is slow, on the other hand, taking a minute or more to traverse the tunnel, you still know that a single train entered and then emerged on the other side, but this time it is a logical inference rather than a visual perception. At speeds of about a second, however, you are in a borderline state between perception and logic, and the question of whether you actually “see” the train’s movement comes perilously close to being a philosophical one.

Elongated Cats
The tendency to anticipate contours is so strong it overrides our knowledge of how the world actually works—as demonstrated, for example, when a cat seems unrealistically stretched around a tree: the brain is responding to continuity, independent of whether it makes sense or not.

Such visual anomalies occur because these rules are evolutionarily ancient and were not designed to handle improbable juxtapositions created by scientists. Programming sophisticated object knowledge into the system would have been too demanding—and unnecessary. Only in myth and fantasy do animals abruptly morph into unaccustomed shapes.

According to hierarchical views of visual processing, the detection of edges in a two-dimensional drawing is a relatively simple process that necessarily precedes the act of constructing high-level 3-D representations. Other figures designed by Tse challenge this conclusion.

The simplest is his lab’s logo. It can be seen either as two flat bird heads (one of them upside down) or as a 3-D black worm wrapped around a white cylinder (the worm is amodally completed by the presence of the cylinder). Unlike the Kanizsa triangle, in which the three disk regions align, implying the existence of edges, in this Tse figure there is no direct continuity of luminous edges or physical contours. And yet the brain perceives the 3-D worm. These illusions suggest that amodal completion is not only a matter of filling in continuous contours. The visual system is cleverer than that. In fact, in another Tse creation, objects complete amodally behind contours without their exact shape even being specified.

Object Lessons
In their pioneering work in the 1960s, neurobiologists David H. Hubel and Torsten N. Wiesel of Harvard University showed that brain cells in the primary visual cortex respond principally to the dark/light edges that convey the contours of an object or creature. Rudiger von der Heydt of Johns Hopkins University has subsequently shown that cells in the secondary visual cortex respond to illusory contours such as those of the Kanizsa triangle.

All of which reminds us that a key goal of vision is to detect objects (not merely contours), using any information that happens to be available. Both modal and amodal completion, and the illusions they inspire, derive from this elementary visual imperative