Binocular Vis ion and the Perception of Depth CHAPTER 8 8.1 up your thumb at arm's length. focus on a more distant object. You INTRODUCTION Now open that eye and close the will notice two somewhat transpar­ other. Notice that your thumb ap­ ent fingers in front of the distant - pears to move against the back­ object. Alterna tely, focus on th e fin­ Up to now we've been concerned ground as you alternate eyes-each ger, and you can see two images of with m onocular* optics; the cam­ eye sees a slightly different view. the dista nt object. The TRY IT offers eras we considered had one (pOSSi­ Nevertheless, normally you see another example.) bly compound) lens, the properties only one view--somehow your brain Why bother with two images of of vision we described required only combines the two images into one the same scene? These slightly dif­ on e eye, and the optical instru­ view of the world. In Figure 7 .3, we ferent images enable you to gauge m ents we discussed were mostly de­ showed the neural connections that the depth of a three-dimensionaL signed for the use of one eye. We allow this mixing of the signals scene. Among animals, predators now want to acknowledge that we, from your two eyes. Notice that a (such as cats) have their two eyes in like many other animals, have two given side of the brain gets signals front, with overlapping fields of eyes and ask what might be the ad­ from the corresponding pOints of view, to enable them to judge accu­ vantage of this binoculart arrange­ each eye, allowing it to combine rately the distance to their prey. On ment. them into one view of the world. the other hand, animals (such as One advantage of the second eye (There are occasions, however, when is that it provides us with an in­ your brain Isn't able to provide a creasedjield oj view. Close one eye single, smoothly combined, view, FIGURE 8,1 and you immediately notice that and you become aware of the t~o part of the scene previously visible images produced by your two eyes. Edward Hicks' "The Peaceable Kingdom" shows both predators and prey. They are is no longer in your field of view. Hold up a finger in your field of easily distinguis hable by the location of Many animals, such as fish or rab­ view, fairly close to your eyes, and their eyes. bits, have eyes set in oppos ite sides of their heads, each eye providing a separate view of the world. To­ gether, two such eyes, with practi­ ~~~o~rl~inthdr~~~ view, enable the animal to see a sweeping panorama. (The field of view of a rabbit is 360°, allowing it to see all around without turning its hea d , with only 24° overlap be­ tween the two eyes.) However, your two eyes, placed in th e front of your head, have fields of view that overlap considerably. (Your field of view is 208°, with 130° over lap.) Your eyes thus provide slightly d ifferent views of almost the same scene. Close one eye a nd hold 'Greek monos, single, plus Latin oculus, eye. tLatin bini, a pair. 207 CHAPTER B: BINOCULAR VISION AND THE PERCEPTION OF DEPTH 208 rabbits or deer) who are likely to be that provide conflicting visual that while you sleep an artist or someone else's dinner have non­ depth cues. By examining the re­ photographer has made an ex­ overlapping fields of view to give sulting illusions, we can learn tremely realistic picture of the view them the wide angle of view best for about the way the brain processes from your bedroom window and detecting predators (Fig. 8.1). Sim­ the variOUS cues in arriving at its pasted it to the outside of your win­ ilarly, animals that leap about the depth determinations. dow so when you awake you see the branch es of a tree (such as squir­ Let's examine a number of the picture (Fig. 8.2). How can you tell rels and our simian ancestors) techniques by which we visually whether you are looking at such a must be able to gauge the depth of fathom the depths of the world painting or at the actual scene out­ those branches, and correspond­ around us. We'll begin by separat­ side your Window? In the next few ingly h ave two eyes in the front. ing the depth cues that can be used sections, we'll discuss several tech­ Th e brain, as we1J see, uses many in a painting from those normally niques for distinguishing the two cues in its determination of depth. unavailable to the artist. Imagine alternatives. S ome require Signals from two eyes, but others do not. These latter In­ clude the cues that artists rely on FIGURE 8.2 when they convey a feeling of depth TRY IT Rene Magritte, "The Human Condition in two-dimensional pictures. It is I. " How can we visually distinguish FOR SECTIO N 8.1 also possible to playoff one cue between the artist's rendering of the against the other-to create scenes outside world and the world itself? Two eyes provide two views Hold one end of a string against your upper lip and pull the other end straight in front of you. You will see not one but two strings stretching out in front of you and crossing. These correspond to the images from your two eyes, as you can readily confirm by alternately closing each eye. The point at which they cross is the point on the string at which you "aim" your eyes (the point toward which your eyes converge). Try looking at different points of the string, beginning close to you and moving away, and notice how the cross-over point moves away from you as you do this. (Having a friend slide a finger along the string may enhance this effect.) 8.2 -ACCOMMODATION Just as you can measure the dis­ tance to an Object by focusing you r camera on it and noting the lens' position, the amount of accommo­ dation necessary to focus your eye on an Object tells you the object's distance. [f you see an objec l clearly while your eyes are relaxed, you know that it is far from you. [f, however, you must tense your cili­ ary muscles to make the Object come into focus, then the object must be closer. Thus wh en looking out your window at the actual street scene, you would accommodate dif­ ferently for objects at different dis­ 8.4 PARALLAX 209 tances in the scene. The artist, at­ tions of gaze is bigger than if you 8.4 tempting to simulate that scene look at a distant object (Fig. 8.3). PARALLAX with a picture, must decide what is This angle is called the angle of in focus and what is not. Once the convergence of your eyes. (For an artist makes that decision, no object at the normal near pOint. 25 -To gauge depth, you rely much amount of accommodation on your cm, the angle of convergence takes more heavily on the fact that your part will s harpen the focus of an ob­ its maximum value of about 15°. It view is different from different po­ ject painted out of focus. is only 1° for an object about 4 m sitions-the phenomenon of paral­ If you were a cha meleon, you'd from your eyes.) If your brain keeps lax.* With one eye closed, hold you r rely very heavily on th e technique of track of the convergence of your thumb a few centimeters from this accommoda tion to gauge the dis­ eyes, it can determine the distance page, so it blocks your view of the tance to flying insects as you flicked to the object that your eyes are word "parallax." By moving your them w i th your tongue. If you cover vie\ving by uSing the rangefinder head, you can Change your view one eye of a chameleon, he main­ principle (Sec. 4.2D). As you scan a suffiCiently so that you can see the tains his high degree of accuracy in painted picture, your convergence, word. This is possible only because fly-flic king-binocula r vision is not like your accommodation, remains your thumb and the word are at d if­ important here. However, give a unchanged. because all the objects ferent distances from your eye. So, chameleon a pair of glasses that lie in the plane of the picture. How­ your view of different objects change the amount of accommoda­ ever, when you view objects at dif­ changes as you move, according to tion necessary and his tongue flaps ferent depths in an actual scene, their distance from you (Fig. 8.4 ). futilely at the fleeing fly. your convergence changes. No matter how carefully our artist Humans, on the other hand, Like accommodation, conver­ simulates other depth cues, as long make little use of this technique, gence is most effective for determin­ as she confines herself to a flat can­ possibly because our potential meals ing depth in nearby scenes, but you vas, she cannot overcome parallax. are gen rally more than a tongue's make relatively little use of it. That You need only move your head and dislance away. Accommodation as a you make some use of convergence, compare the relative positions of way of determining depth is at best however, can be seen from the TRY the distant scene and the window only useful for close objects.