If we think about modern traffic or even the simple-looking task of directing a fork with something to eat into our mouth, it is easy to recognize that three-dimensional perception of our three-dimensional world is essential for humans. Our ears can help in giving us cues for directions, but for guessing a distance, our visual sense is much better.

Our eyes only have two-dimensional retina images and no special third component for depth perception. This requires an interpretation of our physiological cues that leads to useful "perception". Looking at a number of optical illusions, it is easy to see that this interpretation does not always have to be correct.

By combining the retinal images of our two eyes we get some of the best and most convincing information about the three dimensions of our world. Two binocular sources of depth perception are

Disparity and Convergence

The 2.4 inch (6 cm) distance between the two pupils causes us to see two slightly different images of the world. This displacement between the horizontal positions of corresponding images is called binocular disparity. It is probably the most important cue for depth perception, the amount of the displacement depends on the relative distance of the objects from the eye. For example, if you position a finger close to your eyes and look at it alternating with the right and the left eye, it is shifted much more than a distant object. By looking at the world with both eyes, we are not aware of the fact that most of the objects seen stimulate different regions of the two retinas. The objects we are directly looking at project their image onto the two foveae, two objects with the same distance to our eyes also have images on corresponding places on the retinas of the two eyes. But objects with different distances are projected onto different parts of the retinas - the reason is the disparity. If disparity of corresponding images on the two retinas is small enough, the visual system can "melt" them to the perception of a three dimensional object, are the corresponding images distorted too much (for example while squinting), there can really be two different pictures in our perception (also see the picture).

The performance of the visual system is really remarkable: It takes two different retina images, compares them for their horizontal distortion of corresponding parts (disparity) and produces a uniform perception of a three dimensional object. We really interpret the horizontal distortion between the two images as depth in the three dimensional world. This effect is also used in making stereograms - especially autostereograms.

We gather other binocular depth information from convergence, this is the converging of the two axes of the eyes, if we are looking at a (nearby) object. Watching a person when looking from a very far to a very narrow object, the converging movement of the eyes can be seen clearly. The information of the convergence is reported to our brain from the eye muscles, but it can only be used for depth perception up to a distance of about ten feet (three meters), because for more distant objects the difference of the angles becomes too small.

There are a number of other possibilities for us, not dependent on the existence of two different retina images.

Motion Parallax

To make this effect clear, try the following: close one eye and bring both index fingers at different distances into a line with a remote object. Keep your eyes fixed on this object and do not move your fingers. If you now move your head to one side, the images of the index fingers will move at different speeds, while the fixed object itself will remain still. This information is called relative motion parallax. When moving, the relative distances of objects determine the amount and the direction of their relative movement in the retina image.

Even if we close one eye and do not move the head, we can still gather information to enable depth perception.

Pictorial Cues

These kinds of depth perception are also found in pictures (speaking of "ordinary" photography or pictures produced by artists, but not stereograms).

Overlay (Interposition)

Gives us the information that an object blocking part of another object from view is nearer than the partially covered object.

Shadows

Give information on the three dimensional form of objects as well as on the position of a source of light.

Other pictorial cues are easily recognized by optical characteristics:

Relative Size

Is due to the fact that objects of the same size but in varying distances cast different retinal image sizes. This so-called size- distance relation gives us cues about the distance of objects of known absolute or relative size.

Linear Perspective

Is known to most of us from drawing-lessons at school. A consequence of the size-distance relation, perspective is mainly expressed by the fact that lines representing physically parallel structures seem to converge in the distance towards a vanishing point. In painting, this principle was not applied until about 1400; before that only overlay, shadows and relative size were used to create depth effects.

Texture Gradient

Is another image factor depending on the size-distance relation. It is mainly applied to textures (structures) of surfaces. A regular structure, e.g. a tiled floor, appears to show smaller structures with increasing distance.

Finally, two other components of perception are to be mentioned, they mainly depend on our experience:

It has been proved that the brighter of two otherwise identical objects is perceived as nearer. There is no satisfactory physical, geometric or photometric explanation for this effect; however, an interpretation is our experience when working with a source of light (e.g. a torch) in dark environment.

Eventually we know (also in our sub-conscious) that light is reduced and refracted by our atmosphere in greater distance, so that mountains on the horizon appear bluish and out of focus. This factor is called Aerial Perspective.

Coherent Interpretation

As a final remark it is to be pointed out that under normal perception conditions all of these different cues to depth perception lead to a single, coherent, three dimensional interpretation of our environment. We regard the perception of depth as a fact but not the various image factors mentioned above. Our visual system uses the cues of information available rather automatically and without employing our consiousness.

Example 1: Fish
Example 2: Money

Regarding the various examples of stereograms, the reader and viewer should - equipped with this knowledge - clearly recognize that it is often sufficient to use one of the physical-psychological tricks from a natural variety to induce our perception to a certain interpretation of depth.

Literature:

• Philip G. Zimbardo: Psychologie, Springer-Verlag, 5. Auflage 1992
• Coren/Porac/Ward: Sensation and Perception, Academic Press 1979
• Dan Dyckman: Das magische Puzzle, Bastei-Lübbe 1994