So first in this lesson, let's talk about seeing distance with one eye, monocular sense of the world away from us in the so called Z-axis in the X, Y, Z-axis of three dimensional space. So there are a whole variety of cues to the monocular sense of distance, how we judge something to be near or far, arises from a variety of information that we get with one eye. And let's go through some of the more obvious aspects of that. And I think the most familiar one that's apparent to all of us every time we look at anything is perspective. In this scene, all of these balls are the same objects. But it should be evident that if you look at a distant ball, it looks much smaller than one that's nearby. And that phenomenon, the fact that distant things look smaller than nearby things when the object is exactly the same, just has to do with projective geometry. That is, how it is that the images that we talked about on our retinas are created. So projected geometry demand just by the rules of geometry that distant things, if the object is again, the same project onto the retina as a smaller extent, a smaller space, a smaller area on the retina than things that are nearby. That's called perspective. But it's certainly not the only monocular cue that tells us whether something is far away. So when we see something we deem to be the same object, let's say human being, and they project onto the retina as a tiny human being. Well, we obviously judge those people to be further away. That applies to all kinds of objects. It can be confusing. But nonetheless, that's one critical cue to distance a scene and judge monocularly. Another obvious one is occlusion. So occlusion refers to the fact that an object in the foreground covers up an object in the background. So this object is obviously covering a portion, this object and that's called occlusion and again that's a familiar phenomenon that we see all the time. I mean there's hardly a seen you could imagine that doesn't include some aspect of occlusion. And also more subtle aspects of a monocular cues that lead us to a good sense of distance based on, basically our experience. And that's called aerial perspective. So you may have noticed when you've gone to an art museum or just looked at any image in a magazine or whatever it may be, that when things are depicted as being distant, they are made fuzzier and bluer than things that are nearby. And that's simply the recognition on the part of the artist or the illustrator that there's more sky interposed between you and the object when the object is distant and when the object is nearby. Sky is blue, so there's more blue sky between you and a distant object than between you and a nearby object. Incidentally, I mean, the sky is blue you should know this because short wavelengths and the bandwidth of human vision that we've talked about before, the shorter wavelengths, the bluish stimuli, are ones that interact more vigorously with the molecules and particles in the atmosphere. And that's why the sky looks blue and why you're interposing more blue sky and fuzziness when you want to depict an object in the distance. That's called aerial perspective, kind of a fancy term for a pretty simple idea. Another aspect cue to monocular depth is one that I think, again, sounds complicated but it's really very simple. It's called motion parallax and again, you'll see this every time you move around the world, move your head and body in the world. And that is that when you move, let's say you move in this direction, the apparent displacement of the objects is in the opposite direction. And near objects, objects that are nearby are apparently displaced more than objects that are further away. Again, that just has to do with the geometry of projections onto the retina, but it has its own motion parallax. And there's another salient few to monocular depth. There are more subtle cues to monocular depth and I'll just show you one of them, sort of make the point that there are a whole variety of instances a phenomenon that you probably haven't noticed. Or would have to pay much more attention to the way you're looking at the world and judging depth than the more obvious ones that I've just been talking about. So these phenomenon, one is called the specific distance tendency and one the equidistance tendency, and here is an observer. Here is the physical position of the object, in this case at eye level. And here's the perceptual distance of the object. So it's been known for a long time and psychophysicists have studied this repeatedly as have so many of the other things that we have been talking about. That the physical position is judge to be in perception a little bit more distance than the actual position measure with, let's say a laser ray scanner or any other measuring device. That's called the specific distance tendency, and again, I doubt that you've it's very unlikely that you've noticed it but again it's occurring all the time and it's obviously important when you want to do anything looking at the world with one eye. The other phenomenon here is the equidistance tendency, again, the physical object is the blue and the perceived distance of the object is the red position. The subtlety of this phenomenon is that when you are looking at something above eye level, remember this one was at eye level, but when you're looking at something above eye level, the perceptual distance, again, seems to be further than the physical distance. And when you're looking at objects below eye level, the perceptual distance is oddly nearer than the physical distance. These are subtle phenomena and they are a challenge to explain. This one and this one are basically opposites and how are you going to explain that? Well, in all of these cases, like other aspects of visual perception that we have been talking about, not only what we see does not correspond to physical measurements but the implication and it's particularly obvious I think in thinking about these queues to monocular depth, is that we learn these things. So I think it's obvious if we go back to these examples that we didn't come into the world knowing about perspective, we didn't come into the world knowing that a near object occludes an object that's further away. We didn't come into the world knowing you have things that are at a distance are going to be fuzzier and bluer-looking and things that are nearby. We learned all these things and as we learn them, we use them as cues to judge distance. In this more subtle case that presents a more specific challenge to psychophysicist, seems that we also learn these cues. But if you want to say and explain how we do them, you need to go back and get some data as to how we actually experience the world when we look at eye level, when we look above eye level, when we look at objects below eye level. Well, that's not hard to do. We can use our old friend, the laser scanner that we talked about before and easily find out in this kind of analysis of scenes that are reported digitally in an ordinary photograph and compared to the laser range scan image. Which you remember tells us the distance and direction of every point in the scanned scene here, we can get the information that shown in this next graph. This is what's called a Contour plot and it's a distribution of the distances from the image plane from the laser scanner. As a function of elevation whether you're looking at the eye level, above our level, below our level. And on this axis are shown the probabilities of the images that you're going to get in those three different circumstances, color-coded in terms of their distance as a function of the angle at which you are looking at the world. So here is the angle of elevation. This would be eye level at zero and this would be looking up, this would be looking down and you can see that there is a difference. The frequency of occurrence of what you see in terms of the distance of objects when you look at eye level, looking up, looking down, it's not all the same. I mean, if you think about it, you might very well expect that, but that's in fact what you see. And when you make these kinds of graphs, you can predict what one should see. Looking up, looking down, looking at eye level, and the outcome of that, as in the outcome of so many of the other things that we've talked about at this point in the course, is that [COUGH] you can predict very well the phenomenology of the specific distance tendency and the equidistance tendency. These rather subtle things and show that they are also learned. You can predict what we see on the basis of the frequency or occurrence of images that we experience just as we predict aerial perspective, and motion parallax, as well as occlusion. All of those things are also, in a more simple minded way, things that we learn that we could predict if we generated statistical information about those phenomena, as well. About those distances, as well. So let's end the lesson by coming back to this slide of these more obvious cues to depth. The bottom line of all of this is that we seem to have learned these monocular cues to depth. And they're very effective. Let me just remind you if it's not obvious to you that when you close one eye you don't have a particularly hard time judging distances and people with one eye get along quite well. There are even professional athletes who have gotten along reasonably well with one eye. And there are numerous people in the world with their injury have only one eye, or not. They can drive, they can participate in sports, they can do all kinds of things. There's not much they can't do. We'll talk about what they can't do in a minute when we get to binocular vision. But the point is, let's say with one eye using this information that we learned in life, through our experience, is very effective in letting us get along in the world. The big problem that people have with one eye, and you can easily demonstrate this for yourself, that if you close one eye and take a finger, and you see it here, you see it here, you see it here. Here, it disappears with one eye, with two eyes, of course, it doesn't disappear until it circles, or half-circles, the full 180 degrees in the [NOISE] front of the visual space that confronts us. People with one eye can only get to the point where the nose blocks the view to the side of the closed eye.
