So how then would stereopsis be explained. We already discussed that, of course it's in the first instance explained by these different views of the left eye and the right eye. But this raises a problem because somehow it means that you must be matching the image points in one eye with the image points in the other eye. As you will see as we go forward here, struggling with the ultimate explanation of stereopsis. That matching of corresponding image points in the two eyes is not simply explained by anything that anyone has been able to come up with so far and we'll go into that in a minute. But first let's understand in a little bit more detail how and why the images of points that are near or further away, project differently onto your two retinas. That difference is called binocular disparity, and let me explain it to you. So these black dots are the point of fixation. These, in both of these right and left panels, are indicating the point that your two eyes are looking at. And that of course means that your center of your fovea, the center of your line of sight, is in alignment with these points. Two eyes are converging on these points. Those points that you are converging on that are generally in you with perception of the same depth are called points on the horopter. The horopter is a fancy Greek word but it simply means all the points that you see as being equidistant in depth from you, the observer, when you're looking at a specific point like the black point in these diagrams. So there are a whole series of points on the horopter that look to you as if they're the same depth. And you can hold a pencil out here, look at it and judge yes there's points here that will be in the same depth as the pin, there are points here that will be in the same depth. That's going to form a plane in space. It's actually a very complex plane, when people have actually studied this psychophysically. But you get the general idea, that there is a plane in space, complex though it may be that defines all the points that you perceive as equidistant from the point of fixation, from the point that you are actually focusing, converging your two eyes on because it's a point of interest to you at that moment. Now what happens when you're focusing on a point on the horopter, like this. And other points are newer or further from the horopter. So again, horopter points perceived as equally distant. So whereas these points in the dotted lines, fall of course, on the center of the fovea. The points that are away from the dotted lines. So this point projects to points on the two retinas p and q here that are away from the foveas. And importantly, they're away in opposite directions. So p in this retinal image and q in this retinal image. Are displaced oppositely. They are both displaced towards the temporal side of the eyeball or the visual field. That means that in seeing these things stereoscopically you somehow have to get points p and q together. To judge that, yeah, this is an object that's nearer than the horopter. And conversely that this is an object further away, because these points, m and n, are, again, going to project differently, disparately to the two retinas, and they're going to do this in the opposite way than near points do. So far points and near points, these points are projecting to m and n, but they are shifted nasalward towards the nose the side of the eyeball or the visual space. And again, you have to get m and m somehow together. You have to get them together if you're going to make a judgement that these points are not only not on the horopter, but they're either nearer or further away than the horopter. And that's not easily imagined how you generate, let's say a computation, which I think is how most people think about it, how you generate an algorithm, that would tell you whether the point is near or further away. Now let's leave that question for a moment because it's a deep question that's unresolved. And turn to an advance in physiology that was made in the 1960s and since with many further studies that defined what are called near and far neurons in the visual cortex. So again going back to our Unit recording with a micro electrode in a cat, or a monkey. An animal with stereoscopic vision. And, I should point out that there are lots of animals that don't have stereoscopic vision. Horses, cows, and so on. Don't have stereoscopic vision, well they have little bit, but they don't have much binocular overlap because they're walleye. Their eyes are basically on the sides of their heads. They have only a tiny sliver of binocular overlap and don't see much of the world in stereo. Why? Because it's to their advantage as animals that are preyed on rather than animals that seek prey. To be able to have a panoramic view of the world greater than we have, 180 degrees is what they have, but a wall-eyed animal has a much greater circumference of visual ability for obvious reasons. But coming back to the issue here, for animals like us, that have good stereoscopic vision, cats, monkeys. The discovery was made with micro-electro recording that there were in the visual cortex, again, this is primary visual cortex, there were near cells that were very active when the point was nearer than the horopter in the animal being recorded from under anesthesia. And there was another group of cells that responded more specifically to things that were further from the horopter. And there was, of course, a group of cells that have been given the name tuned excitatory. For objects, points that are on the horopter or near the horopter. So these three categories, near cells, cells that respond to points on the horopter, and cells that respond to points that are farther away from the horopter. That constituted a big advance in understanding stereoscopic vision because it showed that there really were cells in the visual cortex that responded to disparity, and they responded differently to disparities that were cross disparities and uncrossed disparities. Those are the names given to disparities that are coming from near points and further points respectively from the horopter. So, big advance, but it didn't fully explain what I've already mentioned as the correspondence problem. So let's turn to the correspondence problem and look at that in a little bit more detail.
