 All right, I want to now get to the next problem, which is eye movement. So I talked a little bit about the fact that the eye can move. So in the picture that I drew before, where the eye was facing the screen, that's all very nice. But a lot of trouble is caused by the fact that the eyes can move. And our eyes are moving all the time without us being consciously aware of it. You can command your eyes to move, but when you're not commanding your eyes to move, they're moving a lot anyway. They're moving very often, doing all sorts of things. And I want to classify the different types of eye movements. Before I do that, I will first just explain the different eye muscles, just to start off eye movement. Let's take, imagine the eyeball, and you're looking straight at the eye. Let me just draw an iris, perhaps. So for each eye, there are six different muscles that are able to contract or extend, and that will allow your eye to rotate. The ways that they pull on the eye, there are side ones. There's lateral rectus and medial rectus. So you have two eye muscles for side to side. This enables you to do yaw motions with your eyes. So you can go back and forth like this. Right? Some of these side motions may be necessary for binocular vision, for stereo, when you move the depth or distance of an object that you're focusing on. However, you may also just want to move from side to side both eyes together in a coordinated way. Oh, let's see. Which eye is this lateral? I believe this is the right eye, because lateral should be off the side, and medial should be into the center. So I believe this is the right eye. Put my label in the wrong place there, because I'm not going to be able to put my remaining muscles. So there are also some muscles off on the diagonal, four of them. There's a superior, not going to go too far on these kinds of things. It starts to look like an anatomy class, and we're not going to have to worry about too many Latin names. But inferior oblique down here is superior oblique, down here is inferior rectus. So if the eye is a rigid body, how many degrees of freedom does it have for rotation? Just as a rigid body, before we think about any constraints. Two? Really? As a rigid body, how many degrees of freedom does a rigid body have of rotation? Three. Three degrees of freedom, right? So translation part is three, rotation part is three. So there are actually, technically, three degrees of freedom of rotation. And there are three pairs of muscles that can pull the eye back and forth. So it can achieve three degrees of freedom of rotation. However, you are most familiar with it being two degrees of freedom. It probably seems like two degrees of freedom, because we can look up and down, and we can look side to side. But also, when you're converging, it turns out there's a little bit of role happening. So roughly speaking, there are three degrees of freedom, but they're mostly constrained to a two-dimensional surface of rotation. So it's close to two-dimensional, but you can make arguments for being slightly three-dimensional, let's say, right? So there is kind of a thin band for the third dimension of rotations. So it does have all of this extra bit of freedom, but you cannot do absolutely wild motions. Also, there's very tight coupling between the eye muscles from eye to eye as well. You cannot very easily, or maybe in any way, start having your eyes look in different directions, right? So they're definitely designed to be coordinated. All right. So these two side ones, lateral rectus and medial rectus, are for yawing your eyes back and forth, and for pitching up and down, and a little bit of rolling, these other four muscles are used. Types of eye movements. So eye movement, let me put this one over here, called eye movement muscles. And then I'll say types of eye movement. Types of eye movement. Let me just make a nice 2 by 2 table here. I'll put down some names. And then I will, I'll show you a couple of short videos, and then I will explain these different modes. So here I will call the motions conjugate, and here I will call them disjunctive. So conjugate will mean that both eyes are moving together. For whatever the purpose is of the movement, they're moving together. And disjunctive means that they've, they're executing separate motions somehow. They're not, they're not doing the same motion. And over here for this row, I will have voluntary, which means that you can consciously control it, or involuntary, which means you have little or no ability to control it. So on the conjugate side, we have saccades, and pursuit, sometimes called smooth pursuit. On the disjunctive side, we have convergence, which can be coupled together with the other one that goes here, which is divergence. They're just opposites of the same thing. These are the motions that happen when we're trying to match stereo. Maybe that looks like it should be conjugate because they're trying to come together to make stereo, but geometrically in terms of the transforms that are being applied, these are different transforms, right? They're like mirror images, so. As far as involuntary, we have vestibulocular, vestibulocular, and optokinetic. And one more here, microsaccades. So this is an eye looking at a picture. So these are saccades. The eye is looking around at different places. So you're pointing the fovea at a bunch of different locations. We do this all the time when reading, looking at pictures, looking at people, close up, and you may hardly be aware of the different motions that are occurring here. So that's an example of saccades. And then this is how a smooth pursuit looks when your eye is following a moving target, right? It does look smooth compared to the last one, right? In the last case, the eye seems to be jumping from place to place quickly, trying to fixate. It's like taking a bunch of quick photographs for the first one. This one is more of trying to maintain a stable image on the retina as something is moving. So one, saccades. So they involve rapid, rapid jerks in the motion, right? So these jerks, they last for less than 45 milliseconds. And during that time, they may be as high as 900 degrees per second. So very fast motions are occurring. And as I said that one of the main reasons for doing this, while I showed you the video, I said that it improves visual acuity. It's like you're taking a bunch of high resolution photographs, if you like, for your brain to try to take in the whole picture because you cannot take in a high resolution image with a very high field of view all at once. Our eyes are just not designed like that. You get the feeling that it's like that because your brain is doing some kind of repair work to assemble everything together and give you what feels like a high resolution, high field of view image of the world. But the eye doesn't actually have that based on the way the eye movements occur, the way the fovea is designed, the photoreceptor density, all of these things are coming together now and you don't have that. There's a fascinating thing that happens here which is there's a psychotic masking which is that the brain is actually hiding these jerk intervals from your memory or from your perception. So even though these jerky eye motions are happening, you don't perceive them at all. And even your perception of time is somewhat altered from them. So because of this, you have what's called trans-psychotic memory which is a special case of a very general phenomenon that people know in perceptual psychology. It's an example of what's called perceptual constancy. So what does that mean? You perceive what seems to be a single stationary image when in actuality, when performing saccades, your eye is moving around all over the place. I had a very interesting opportunity. I was at Ludwig Maximilian University in Munich about a month ago and I visited a virtual reality lab there where they had a well-designed eye tracker hooked up to a system that would actuate a camera with very low latency exactly as someone is moving their eyes. So what you could do is you could have someone sit there. They start moving their eyes around doing the normal saccades and then you can look on a screen and see what the camera sees when it's mimicking exactly the motions of the eye during saccades. Doesn't that sound interesting? So when you see these motions, it looks like an absolute mess. The image is changing constantly. There should be all kinds of blurring as it turns very quickly. I found it very difficult to make sense out of the images that come from that. By just having a camera that mimics exactly the motions of the eyes in saccades. We don't perceive that. We're doing saccade motions all the time, but we perceive the world as being stationary. Yet it would be a significant engineering challenge to then take that video from the camera that's moving all over the place and try to stabilize it in the same way. You could do it with IMUs and so forth, but you have a lot of work ahead of you just to stabilize that image. The brain is doing the work already in stabilizing, let's say the time sequence, the video that's coming into our photoreceptors. So I find that very interesting. So that's one of the motions is saccade. I'm going to talk about pursuit next, and then we'll take a break in a bit, and then I'll talk about the remainders after that. So two, smooth pursuit. So in this case, you track a moving visual signal. So I could take this notebook and move it back and forth and my eyes are tracking it using smooth pursuit. Now I might also rotate my head some to help that process out. So you can combine, and very naturally we do combine sometimes head motions with these smooth pursuit motions, but that's going to lead also to the vestibular ocular reflex, which is coming next. But let's just separate them out very carefully. So even if you hold your head still, there's smooth pursuit. So if, for example, you may be watching a tennis match or a football match, you watch the ball go back and forth or, of course, a cricket match. And you watch the ball moving, and your eyes are tracking that, right? Same thing for a car going by on the street. So these motions are significantly slower. They're less than 30 degrees per second. And if you're trying to track something that's faster than that with your eyes, what will happen is that some saccades will get mixed in. So the eye will have to jump ahead to catch up. So sometimes, so I'll say otherwise, saccades are added. Saccades are inserted. The main reason for doing this is to reduce motion blur. So you can, this attempts to give a more stable image on the retina as you're moving. As not you're moving, sorry, as the object that you're tracking or whatever features they are as they're moving to make that appear to be a stable image, to make it look motionless as far as your retina is concerned. Questions about that? Yes. That's very interesting. I think that's correct. Yeah, motion blur being the surroundings. However, if you're tracking it, your fovea is aimed at the object of interest. That's where you're getting the highest visual acuity. And there's attention. Your attention is focusing on that, right? And so yes, but the focus is not, the attention is not there. So it's not a problem. That's a very interesting question, though. Why don't we try that during the break? Why don't we do some smooth tracking experiments and see if you notice some kind of blur? That's another question. Do you even, can you design an experiment where you perceive the blur? So the brain's relying on attention to let's say not worry about that. Another thing that happens, which I didn't get to the stereo part yet, but if I converge my eyes to this bottle, for example, then everywhere else there are double images. It's called Diplopia, right? Do you notice that very often? Not really, but now try it. Put something up there, and then at the periphery you'll notice there's multiple images. It's very obvious once you know to look for it. Don't look directly at it, because then you'll focus on something else, but you'll converge to something else. But if you just converge on something close, and then I see two professor monies there out of the side of my eye, so it works very naturally like that. Anyone else? All right, thanks.