WEBVTT 00:00:00.000 --> 00:00:01.997 align:middle line:90% [SQUEAKING] 00:00:01.997 --> 00:00:03.993 align:middle line:90% [RUSTLING] 00:00:03.993 --> 00:00:05.490 align:middle line:90% [CLICKING] 00:00:05.490 --> 00:00:11.145 align:middle line:90% 00:00:11.145 --> 00:00:12.020 align:middle line:90% PROFESSOR: All right. 00:00:12.020 --> 00:00:17.072 align:middle line:84% So, so far in this class, we've introduced the basic idea 00:00:17.072 --> 00:00:19.280 align:middle line:84% of perception as inferring the structure of the world 00:00:19.280 --> 00:00:20.520 align:middle line:90% from sensory input. 00:00:20.520 --> 00:00:23.320 align:middle line:84% And we spent about the first third of the class talking 00:00:23.320 --> 00:00:25.840 align:middle line:90% about the sense of hearing. 00:00:25.840 --> 00:00:28.680 align:middle line:84% So remember, we started out talking about the ear 00:00:28.680 --> 00:00:31.260 align:middle line:84% and how the ear is this device to measure sound. 00:00:31.260 --> 00:00:32.718 align:middle line:84% So sound is a mechanical vibration. 00:00:32.718 --> 00:00:34.510 align:middle line:84% Your ear turns that into electrical signals 00:00:34.510 --> 00:00:35.760 align:middle line:90% that get sent to your brain. 00:00:35.760 --> 00:00:38.010 align:middle line:84% And then we talked about how the problem of perception 00:00:38.010 --> 00:00:40.480 align:middle line:84% is to take those electrical signals that you're 00:00:40.480 --> 00:00:43.040 align:middle line:84% getting from your ear, and then to infer what's happening out 00:00:43.040 --> 00:00:44.200 align:middle line:90% there in the world. 00:00:44.200 --> 00:00:47.640 align:middle line:84% So the problem of vision is really analogous to that. 00:00:47.640 --> 00:00:49.600 align:middle line:84% And so we're going to begin by talking 00:00:49.600 --> 00:00:52.920 align:middle line:84% about the eye and the retina, which 00:00:52.920 --> 00:00:57.260 align:middle line:84% is the part of your visual system that measures light. 00:00:57.260 --> 00:01:00.010 align:middle line:84% Again, the big picture here is that things in the world 00:01:00.010 --> 00:01:01.890 align:middle line:84% give off clues to their existence. 00:01:01.890 --> 00:01:04.610 align:middle line:84% Your sensory organs detect these clues. 00:01:04.610 --> 00:01:07.250 align:middle line:84% And in vision, the clues come in the form 00:01:07.250 --> 00:01:09.210 align:middle line:84% of photons that reflect off of objects 00:01:09.210 --> 00:01:11.290 align:middle line:90% and are absorbed by your eye. 00:01:11.290 --> 00:01:13.058 align:middle line:84% And the task of perception is to take 00:01:13.058 --> 00:01:14.850 align:middle line:84% input from your sensory receptors and infer 00:01:14.850 --> 00:01:16.390 align:middle line:90% what is out there in the world. 00:01:16.390 --> 00:01:19.470 align:middle line:90% 00:01:19.470 --> 00:01:22.170 align:middle line:90% So vision relies on light. 00:01:22.170 --> 00:01:24.710 align:middle line:84% Remember, light is electromagnetic radiation. 00:01:24.710 --> 00:01:28.010 align:middle line:84% There's a wide range of electromagnetic radiation, 00:01:28.010 --> 00:01:30.370 align:middle line:90% as indicated on this diagram. 00:01:30.370 --> 00:01:34.090 align:middle line:84% And the part of that spectrum that you can see 00:01:34.090 --> 00:01:36.610 align:middle line:84% is a very narrow part where the wavelengths 00:01:36.610 --> 00:01:41.850 align:middle line:84% vary from around 400 nanometers to around 700 nanometers. 00:01:41.850 --> 00:01:45.530 align:middle line:84% And then on either side there's ultraviolet and infrared, 00:01:45.530 --> 00:01:48.050 align:middle line:90% and then lots of other stuff. 00:01:48.050 --> 00:01:48.550 align:middle line:90% All right. 00:01:48.550 --> 00:01:50.930 align:middle line:84% So this is a big picture of your visual system, 00:01:50.930 --> 00:01:52.390 align:middle line:90% sideways view of the brain. 00:01:52.390 --> 00:01:55.330 align:middle line:90% So we've got your eyes here. 00:01:55.330 --> 00:01:58.090 align:middle line:84% Light comes in, forms an image on the back of your eye. 00:01:58.090 --> 00:02:00.750 align:middle line:84% Electrical signals are carried by the optic nerve 00:02:00.750 --> 00:02:04.190 align:middle line:84% to the LGN or lateral geniculate nucleus, which 00:02:04.190 --> 00:02:07.470 align:middle line:84% is the part of the thalamus that carries visual signals, and then 00:02:07.470 --> 00:02:10.789 align:middle line:84% from there, projects to the visual cortex, which 00:02:10.789 --> 00:02:14.350 align:middle line:90% is a large part of your cortex. 00:02:14.350 --> 00:02:17.430 align:middle line:84% All right, so let's take a look at the eye. 00:02:17.430 --> 00:02:20.990 align:middle line:84% So cross-sectional view of the eye. 00:02:20.990 --> 00:02:25.070 align:middle line:90% Light enters via the pupil. 00:02:25.070 --> 00:02:28.470 align:middle line:84% The eye is protected by the cornea, 00:02:28.470 --> 00:02:32.030 align:middle line:84% which is this-- it's a very hard part of the eye. 00:02:32.030 --> 00:02:34.410 align:middle line:84% But light passes through there, passes through the pupil, 00:02:34.410 --> 00:02:36.290 align:middle line:90% which is an aperture. 00:02:36.290 --> 00:02:39.350 align:middle line:84% So the iris can change the size of the pupil 00:02:39.350 --> 00:02:41.732 align:middle line:84% in order to control the amount of light that gets in. 00:02:41.732 --> 00:02:43.190 align:middle line:84% And then you've got the lens, which 00:02:43.190 --> 00:02:47.270 align:middle line:84% focuses light into an image on the back of the eye. 00:02:47.270 --> 00:02:50.890 align:middle line:84% So the back of the eye has a few different structures, 00:02:50.890 --> 00:02:53.370 align:middle line:84% and the most important one is the retina, 00:02:53.370 --> 00:02:55.910 align:middle line:84% which is this layer of cells that does 00:02:55.910 --> 00:02:58.000 align:middle line:90% the transduction for vision. 00:02:58.000 --> 00:03:00.960 align:middle line:84% And then those electrical signals from the retina 00:03:00.960 --> 00:03:04.440 align:middle line:84% are then carried via the optic nerve out of the eye. 00:03:04.440 --> 00:03:08.120 align:middle line:90% This is a slice of the retina. 00:03:08.120 --> 00:03:11.280 align:middle line:84% So you can see that it's this big matrix of cells. 00:03:11.280 --> 00:03:14.560 align:middle line:84% At the back here, we have photoreceptors. 00:03:14.560 --> 00:03:17.320 align:middle line:84% And then there's all these other layers of cells. 00:03:17.320 --> 00:03:19.800 align:middle line:84% You can see the cell bodies in some of these layers, 00:03:19.800 --> 00:03:21.200 align:middle line:84% and then some of the other layers 00:03:21.200 --> 00:03:26.160 align:middle line:84% which are primarily containing axons that connect 00:03:26.160 --> 00:03:28.480 align:middle line:90% different types of cells. 00:03:28.480 --> 00:03:33.818 align:middle line:84% And then the output layer of the retina are the ganglion cells. 00:03:33.818 --> 00:03:35.860 align:middle line:84% Now, one of the curious things about the retina-- 00:03:35.860 --> 00:03:38.000 align:middle line:84% and we'll talk more about this in a moment-- 00:03:38.000 --> 00:03:41.968 align:middle line:84% is that it's kind of set up backwards relative to what 00:03:41.968 --> 00:03:44.260 align:middle line:84% you would think would be a sensible engineering design. 00:03:44.260 --> 00:03:47.000 align:middle line:90% So this is the back of the eye. 00:03:47.000 --> 00:03:53.000 align:middle line:84% And if you look here, the light is coming in like this. 00:03:53.000 --> 00:03:55.640 align:middle line:84% And so naively, you would expect that what you'd want to do 00:03:55.640 --> 00:03:58.237 align:middle line:84% is actually put the photoreceptors here, 00:03:58.237 --> 00:04:00.320 align:middle line:84% and then have all the other processing after that. 00:04:00.320 --> 00:04:02.340 align:middle line:84% The reason being that, well, in order 00:04:02.340 --> 00:04:04.740 align:middle line:84% to get to the photoreceptors, the light 00:04:04.740 --> 00:04:07.500 align:middle line:84% has to pass through all this stuff. 00:04:07.500 --> 00:04:10.160 align:middle line:84% So it's kind of a funny way to actually set the eye up. 00:04:10.160 --> 00:04:13.750 align:middle line:84% As far as we know, it's a fluke of evolution. 00:04:13.750 --> 00:04:15.500 align:middle line:84% And we'll talk more about the consequences 00:04:15.500 --> 00:04:16.542 align:middle line:90% of that in just a second. 00:04:16.542 --> 00:04:18.042 align:middle line:84% But you can see from looking at this 00:04:18.042 --> 00:04:20.260 align:middle line:84% that there's a bunch of different types of cells 00:04:20.260 --> 00:04:22.375 align:middle line:90% within the retina. 00:04:22.375 --> 00:04:24.500 align:middle line:84% And lots of people have devoted their entire career 00:04:24.500 --> 00:04:26.740 align:middle line:84% to understanding these cells, and their connections 00:04:26.740 --> 00:04:27.780 align:middle line:90% and their function. 00:04:27.780 --> 00:04:30.020 align:middle line:84% For the purposes of this class, the main thing 00:04:30.020 --> 00:04:31.700 align:middle line:84% you should be aware of is there's 00:04:31.700 --> 00:04:35.080 align:middle line:90% five main classes of cells. 00:04:35.080 --> 00:04:39.220 align:middle line:84% So there's the photoreceptors, which absorb photons 00:04:39.220 --> 00:04:41.940 align:middle line:90% and generate a voltage. 00:04:41.940 --> 00:04:44.100 align:middle line:84% You've got bipolar cells that get input 00:04:44.100 --> 00:04:48.020 align:middle line:84% from the photoreceptors, as well as horizontal cells. 00:04:48.020 --> 00:04:50.400 align:middle line:84% There's amacrine cells and there's ganglion cells. 00:04:50.400 --> 00:04:54.700 align:middle line:84% So one respect in which these types of cells differ 00:04:54.700 --> 00:04:59.710 align:middle line:84% is that some of the types don't fire action potentials. 00:04:59.710 --> 00:05:03.830 align:middle line:84% They just vary their membrane potential in response to light. 00:05:03.830 --> 00:05:07.870 align:middle line:84% And the main reason we think why that's the case 00:05:07.870 --> 00:05:09.590 align:middle line:84% is that the signals don't actually 00:05:09.590 --> 00:05:10.610 align:middle line:90% have to travel very far. 00:05:10.610 --> 00:05:12.287 align:middle line:84% The connections are primarily local. 00:05:12.287 --> 00:05:13.870 align:middle line:84% And remember, one of the things that's 00:05:13.870 --> 00:05:15.328 align:middle line:84% very useful about action potentials 00:05:15.328 --> 00:05:17.630 align:middle line:84% is it allows you to send electrical signals 00:05:17.630 --> 00:05:19.110 align:middle line:90% over long distances. 00:05:19.110 --> 00:05:21.930 align:middle line:84% So these cell classes in the retina, 00:05:21.930 --> 00:05:25.330 align:middle line:84% they primarily just talk to each other over very local distances. 00:05:25.330 --> 00:05:27.750 align:middle line:84% And so presumably, they don't need spikes. 00:05:27.750 --> 00:05:30.750 align:middle line:84% But the amacrine cells and the ganglion cells fire action 00:05:30.750 --> 00:05:31.250 align:middle line:90% potentials. 00:05:31.250 --> 00:05:33.190 align:middle line:84% The ganglion cells in particular are, 00:05:33.190 --> 00:05:35.570 align:middle line:84% as I said, the primary output cell class of the retina, 00:05:35.570 --> 00:05:39.570 align:middle line:84% and so they have to send signals all the way up to the thalamus. 00:05:39.570 --> 00:05:42.190 align:middle line:90% 00:05:42.190 --> 00:05:47.190 align:middle line:84% So this is a picture that shows those five primary cell types. 00:05:47.190 --> 00:05:49.488 align:middle line:84% So the processing kind of starts with the receptors. 00:05:49.488 --> 00:05:51.030 align:middle line:84% There's two types of receptors, which 00:05:51.030 --> 00:05:54.053 align:middle line:84% we'll talk about in a second, and then culminates 00:05:54.053 --> 00:05:54.970 align:middle line:90% in the ganglion cells. 00:05:54.970 --> 00:05:57.208 align:middle line:84% And as we discussed, the orientation 00:05:57.208 --> 00:05:59.000 align:middle line:84% here is very counterintuitive because light 00:05:59.000 --> 00:06:02.360 align:middle line:84% is coming in this way and has to pass through all this stuff. 00:06:02.360 --> 00:06:03.340 align:middle line:90% Why is that a problem? 00:06:03.340 --> 00:06:05.840 align:middle line:84% Well, you would think that all of these cell bodies 00:06:05.840 --> 00:06:08.120 align:middle line:84% would actually cause the light to scatter 00:06:08.120 --> 00:06:11.100 align:middle line:84% and would decrease the quality of the image. 00:06:11.100 --> 00:06:13.660 align:middle line:90% 00:06:13.660 --> 00:06:15.240 align:middle line:84% And so some evidence for this kind 00:06:15.240 --> 00:06:17.940 align:middle line:90% comes from species comparisons. 00:06:17.940 --> 00:06:22.080 align:middle line:84% So the eye has evolved many, many times. 00:06:22.080 --> 00:06:24.520 align:middle line:84% And so if you look across all the different species that 00:06:24.520 --> 00:06:28.060 align:middle line:84% exist, you can see things that look like eyes in most of them, 00:06:28.060 --> 00:06:31.440 align:middle line:84% but there will be interesting differences and similarities. 00:06:31.440 --> 00:06:35.760 align:middle line:84% So in particular, this feature of the receptor layer 00:06:35.760 --> 00:06:38.600 align:middle line:84% is kind of being oriented backwards is something 00:06:38.600 --> 00:06:41.320 align:middle line:84% that you see in vertebrates, but that you 00:06:41.320 --> 00:06:43.017 align:middle line:90% don't see in cephalopods. 00:06:43.017 --> 00:06:44.600 align:middle line:84% So cephalopods are things like squids, 00:06:44.600 --> 00:06:47.300 align:middle line:90% and octopi and things like that. 00:06:47.300 --> 00:06:50.780 align:middle line:84% And so you see this structure that looks like an eye, 00:06:50.780 --> 00:06:53.080 align:middle line:84% but you can see that in the octopus, 00:06:53.080 --> 00:06:56.300 align:middle line:84% the photoreceptors actually kind come first, 00:06:56.300 --> 00:06:58.820 align:middle line:90% followed by other stuff. 00:06:58.820 --> 00:06:59.320 align:middle line:90% All right? 00:06:59.320 --> 00:07:01.740 align:middle line:84% Whereas in vertebrates, the photoreceptors 00:07:01.740 --> 00:07:05.100 align:middle line:84% are kind of at the back, and then you 00:07:05.100 --> 00:07:09.300 align:middle line:84% have these cell bodies that all the light has to travel through. 00:07:09.300 --> 00:07:11.140 align:middle line:84% And this has actually major consequences 00:07:11.140 --> 00:07:13.540 align:middle line:84% for how the optic nerve exits the eye, which 00:07:13.540 --> 00:07:15.740 align:middle line:90% we'll talk about in a second. 00:07:15.740 --> 00:07:17.473 align:middle line:84% So as far as we can tell, the fact 00:07:17.473 --> 00:07:19.640 align:middle line:84% that the retina is wired up backwards is, as I said, 00:07:19.640 --> 00:07:20.980 align:middle line:90% a fluke of evolution. 00:07:20.980 --> 00:07:24.740 align:middle line:84% It's some kind of local minimum that was found. 00:07:24.740 --> 00:07:28.860 align:middle line:84% And but there are a couple of adaptations 00:07:28.860 --> 00:07:33.080 align:middle line:84% that have been added on to this over the course of evolution, 00:07:33.080 --> 00:07:34.918 align:middle line:84% as far as we can tell, that mitigate 00:07:34.918 --> 00:07:35.960 align:middle line:90% the consequences of this. 00:07:35.960 --> 00:07:40.060 align:middle line:84% And so one of those is that at the fovea, which 00:07:40.060 --> 00:07:43.540 align:middle line:84% is the center of your gaze, and as we will discuss later 00:07:43.540 --> 00:07:45.740 align:middle line:84% in this lecture, the center of your gaze 00:07:45.740 --> 00:07:48.423 align:middle line:84% is where your spatial resolution is highest. 00:07:48.423 --> 00:07:50.340 align:middle line:84% So normally, if you want to look at something, 00:07:50.340 --> 00:07:52.920 align:middle line:84% you direct your fovea to that something. 00:07:52.920 --> 00:07:56.710 align:middle line:84% And then you can get a very high resolution image. 00:07:56.710 --> 00:08:01.690 align:middle line:84% So at the fovea, the cell bodies and the axons are displaced. 00:08:01.690 --> 00:08:04.710 align:middle line:84% And this is presumably to maximize the resolution 00:08:04.710 --> 00:08:08.375 align:middle line:84% in the part of the eye where the sampling is densest 00:08:08.375 --> 00:08:09.750 align:middle line:84% and where you really want to have 00:08:09.750 --> 00:08:12.270 align:middle line:90% really good spatial resolution. 00:08:12.270 --> 00:08:14.030 align:middle line:84% So you can see that the cell bodies here 00:08:14.030 --> 00:08:15.447 align:middle line:84% are moved out of the way, and that 00:08:15.447 --> 00:08:17.630 align:middle line:84% means that the light doesn't really get scattered. 00:08:17.630 --> 00:08:22.588 align:middle line:84% And I guess the idea is that out here, away from the fovea, 00:08:22.588 --> 00:08:24.630 align:middle line:84% the little bit of scattering that kind of happens 00:08:24.630 --> 00:08:26.330 align:middle line:84% from the cell bodies is acceptable. 00:08:26.330 --> 00:08:29.550 align:middle line:84% And also, one of the things that kind of mitigates this issue 00:08:29.550 --> 00:08:31.950 align:middle line:84% is the fact that the cell bodies are pretty translucent. 00:08:31.950 --> 00:08:33.367 align:middle line:84% So it's not like they're absorbing 00:08:33.367 --> 00:08:35.909 align:middle line:90% lots of light themselves. 00:08:35.909 --> 00:08:38.270 align:middle line:84% Now, the other major consequence of the fact 00:08:38.270 --> 00:08:41.570 align:middle line:84% that the retina is hooked up backwards is what's shown here. 00:08:41.570 --> 00:08:44.290 align:middle line:84% So the axons of the ganglion cells, 00:08:44.290 --> 00:08:45.830 align:middle line:84% which form the optic nerve, those 00:08:45.830 --> 00:08:48.290 align:middle line:90% have to exit the eye somewhere. 00:08:48.290 --> 00:08:51.250 align:middle line:84% And the problem is that with this being set up 00:08:51.250 --> 00:08:54.850 align:middle line:84% the way that it is, the place where they exit the eye 00:08:54.850 --> 00:08:58.230 align:middle line:84% is going to be a location where you can't have photoreceptors. 00:08:58.230 --> 00:09:01.030 align:middle line:90% 00:09:01.030 --> 00:09:04.610 align:middle line:84% So this is a picture showing the axons from the ganglion 00:09:04.610 --> 00:09:05.882 align:middle line:90% cell leaving the eye. 00:09:05.882 --> 00:09:07.590 align:middle line:84% So this is a cross-section of the retina. 00:09:07.590 --> 00:09:09.890 align:middle line:84% You can see these different cell layers here. 00:09:09.890 --> 00:09:12.090 align:middle line:84% The photoreceptors would be back here. 00:09:12.090 --> 00:09:14.530 align:middle line:84% The axons all kind of converge and then exit the eye 00:09:14.530 --> 00:09:16.610 align:middle line:90% at this particular location. 00:09:16.610 --> 00:09:19.930 align:middle line:84% So the consequence of this is that there 00:09:19.930 --> 00:09:24.090 align:middle line:84% is a region of the retina where there are no photoreceptors. 00:09:24.090 --> 00:09:26.290 align:middle line:84% And the consequence of that is that there 00:09:26.290 --> 00:09:30.890 align:middle line:84% is a region of visual space when your eye is directed 00:09:30.890 --> 00:09:34.018 align:middle line:84% in a particular place that you can't see, 00:09:34.018 --> 00:09:35.810 align:middle line:84% because you don't have photoreceptors there 00:09:35.810 --> 00:09:37.570 align:middle line:90% to detect the light. 00:09:37.570 --> 00:09:40.510 align:middle line:84% So we can demonstrate this ourselves. 00:09:40.510 --> 00:09:44.330 align:middle line:84% So we're going to do a demonstration of the blind spot 00:09:44.330 --> 00:09:45.690 align:middle line:90% that everybody has. 00:09:45.690 --> 00:09:48.010 align:middle line:84% And in order to see this, you're going 00:09:48.010 --> 00:09:50.030 align:middle line:84% to have to only look with one eye. 00:09:50.030 --> 00:09:52.640 align:middle line:90% 00:09:52.640 --> 00:09:54.940 align:middle line:84% So I want you to close your left eye 00:09:54.940 --> 00:09:58.060 align:middle line:84% and then fixate your left index finger. 00:09:58.060 --> 00:09:59.580 align:middle line:90% So I'm going to do this myself. 00:09:59.580 --> 00:10:00.660 align:middle line:90% All right? 00:10:00.660 --> 00:10:02.540 align:middle line:84% You're then going to place your right index 00:10:02.540 --> 00:10:05.980 align:middle line:84% finger next to the left one, and then slowly 00:10:05.980 --> 00:10:09.100 align:middle line:84% move your right index finger to the right. 00:10:09.100 --> 00:10:15.740 align:middle line:84% So again, close your left eye, and then move that finger away, 00:10:15.740 --> 00:10:18.060 align:middle line:90% and then-- yep, there we go. 00:10:18.060 --> 00:10:21.620 align:middle line:84% So you'll reach this place where you can't see 00:10:21.620 --> 00:10:23.260 align:middle line:90% the tip of your right finger. 00:10:23.260 --> 00:10:26.180 align:middle line:90% 00:10:26.180 --> 00:10:29.208 align:middle line:90% Yeah, it's pretty cool. 00:10:29.208 --> 00:10:31.000 align:middle line:84% So the tip of your finger should disappear. 00:10:31.000 --> 00:10:33.900 align:middle line:84% And this is because it has entered the blind spot 00:10:33.900 --> 00:10:35.820 align:middle line:90% of your right eye. 00:10:35.820 --> 00:10:40.820 align:middle line:84% So hopefully, that works for everybody. 00:10:40.820 --> 00:10:43.783 align:middle line:84% So this is something that's happening all the time. 00:10:43.783 --> 00:10:45.200 align:middle line:84% You're stuck with this blind spot. 00:10:45.200 --> 00:10:48.040 align:middle line:84% The reason that you most you don't notice this, we think, 00:10:48.040 --> 00:10:51.390 align:middle line:84% is partly because the blind spots in the two eyes 00:10:51.390 --> 00:10:54.458 align:middle line:84% are kind of in different parts of the visual field. 00:10:54.458 --> 00:10:56.250 align:middle line:84% So usually, you got both of your eyes open. 00:10:56.250 --> 00:11:01.390 align:middle line:84% And so there's one eye that is detecting most of the stuff 00:11:01.390 --> 00:11:03.670 align:middle line:90% that you can see. 00:11:03.670 --> 00:11:06.430 align:middle line:84% And so you have to do these very careful experiments in order 00:11:06.430 --> 00:11:08.710 align:middle line:90% to be able to detect this. 00:11:08.710 --> 00:11:11.550 align:middle line:84% So again, the blind spot is a consequence, we think, 00:11:11.550 --> 00:11:15.270 align:middle line:84% of the retina kind of being set up backwards. 00:11:15.270 --> 00:11:18.130 align:middle line:84% So let's talk a little bit about the photoreceptors. 00:11:18.130 --> 00:11:22.110 align:middle line:84% So the photoreceptors are cells that contain photo pigments 00:11:22.110 --> 00:11:25.270 align:middle line:84% that absorb photons, and that then produce 00:11:25.270 --> 00:11:26.570 align:middle line:90% a change in membrane potential. 00:11:26.570 --> 00:11:29.870 align:middle line:84% There's two types of photoreceptors, the rods 00:11:29.870 --> 00:11:31.270 align:middle line:90% and the cones. 00:11:31.270 --> 00:11:33.990 align:middle line:84% They're called this because the physical shape of the receptor 00:11:33.990 --> 00:11:37.350 align:middle line:90% is different. 00:11:37.350 --> 00:11:42.590 align:middle line:84% And they're different physiologically in lots of ways. 00:11:42.590 --> 00:11:45.510 align:middle line:84% So one respect in which the rods and the cones differ 00:11:45.510 --> 00:11:48.390 align:middle line:84% is that their density on the retina 00:11:48.390 --> 00:11:52.490 align:middle line:84% varies quite dramatically with what we call eccentricity, 00:11:52.490 --> 00:11:54.050 align:middle line:90% or distance from the fovea. 00:11:54.050 --> 00:11:57.210 align:middle line:84% So this is a graph that shows the photoreceptor 00:11:57.210 --> 00:12:02.370 align:middle line:84% density plotted separately for rods in blue and cones in red. 00:12:02.370 --> 00:12:05.190 align:middle line:84% So zero here corresponds to the fovea. 00:12:05.190 --> 00:12:07.310 align:middle line:90% That's the center of gaze. 00:12:07.310 --> 00:12:10.810 align:middle line:84% And then you can either move out in the nasal direction 00:12:10.810 --> 00:12:14.290 align:middle line:84% towards the nose or the temporal direction. 00:12:14.290 --> 00:12:18.610 align:middle line:84% And what this graph is showing is that at the fovea, 00:12:18.610 --> 00:12:20.750 align:middle line:84% the density of cones is very, very high, 00:12:20.750 --> 00:12:23.570 align:middle line:90% and there's actually no rods. 00:12:23.570 --> 00:12:26.370 align:middle line:84% As you move out of the fovea, the density of the cones 00:12:26.370 --> 00:12:28.250 align:middle line:84% drops quite a lot, and the density 00:12:28.250 --> 00:12:31.490 align:middle line:90% of the rods kind of increases. 00:12:31.490 --> 00:12:39.370 align:middle line:84% And then these are images of the retinal mosaic taken 00:12:39.370 --> 00:12:40.570 align:middle line:90% from these different points. 00:12:40.570 --> 00:12:45.610 align:middle line:84% And so you can see that at the fovea, 00:12:45.610 --> 00:12:47.370 align:middle line:84% you only you see evidence of only having 00:12:47.370 --> 00:12:49.150 align:middle line:90% a single type of receptor. 00:12:49.150 --> 00:12:50.900 align:middle line:84% And then you get out here in the periphery 00:12:50.900 --> 00:12:56.140 align:middle line:84% and you can see that there's two types of receptors. 00:12:56.140 --> 00:12:59.380 align:middle line:84% All right, the other thing that you can see on this diagram 00:12:59.380 --> 00:13:01.040 align:middle line:90% is what's called the optic disk. 00:13:01.040 --> 00:13:03.140 align:middle line:84% So this is the location on the retina where 00:13:03.140 --> 00:13:04.820 align:middle line:90% the optic nerve leaves the eye. 00:13:04.820 --> 00:13:06.860 align:middle line:84% And there, there are no photoreceptors. 00:13:06.860 --> 00:13:09.960 align:middle line:90% 00:13:09.960 --> 00:13:13.460 align:middle line:84% So you're going to hear me talk a lot about eccentricity. 00:13:13.460 --> 00:13:14.720 align:middle line:90% So what is eccentricity? 00:13:14.720 --> 00:13:17.300 align:middle line:84% Again, in vision science, eccentricity 00:13:17.300 --> 00:13:19.600 align:middle line:90% is distance from the fovea. 00:13:19.600 --> 00:13:23.160 align:middle line:84% So we always use the fovea as a reference point. 00:13:23.160 --> 00:13:26.580 align:middle line:84% And then typically, we will measure eccentricity in degrees 00:13:26.580 --> 00:13:29.080 align:middle line:90% of visual angle from the fovea. 00:13:29.080 --> 00:13:32.780 align:middle line:90% 00:13:32.780 --> 00:13:37.780 align:middle line:84% So a good rule of thumb is that one degree of visual angle 00:13:37.780 --> 00:13:44.060 align:middle line:84% is approximately the width of a fingertip at arm's length. 00:13:44.060 --> 00:13:48.880 align:middle line:84% The full moon, which is about the same size as the sun, 00:13:48.880 --> 00:13:51.640 align:middle line:84% when considered as an image on your retina, is about half 00:13:51.640 --> 00:13:57.360 align:middle line:84% of a degree, and the blind spot is about 5 degrees, so pretty 00:13:57.360 --> 00:13:57.860 align:middle line:90% big. 00:13:57.860 --> 00:14:02.500 align:middle line:90% 00:14:02.500 --> 00:14:06.565 align:middle line:84% So there's these big differences in the distribution of receptors 00:14:06.565 --> 00:14:08.440 align:middle line:84% in different parts of the eye, so that's just 00:14:08.440 --> 00:14:10.638 align:middle line:90% an empirical fact. 00:14:10.638 --> 00:14:12.680 align:middle line:84% And there's also big differences in the responses 00:14:12.680 --> 00:14:14.520 align:middle line:84% of the different types of receptors. 00:14:14.520 --> 00:14:18.840 align:middle line:84% And one place that this shows up is in dark adaptation. 00:14:18.840 --> 00:14:22.480 align:middle line:84% And so the big picture here is that the rods 00:14:22.480 --> 00:14:26.920 align:middle line:84% are very sensitive to light and are primarily used in low light 00:14:26.920 --> 00:14:30.040 align:middle line:90% conditions, so at night. 00:14:30.040 --> 00:14:32.560 align:middle line:84% The cones are less sensitive to light 00:14:32.560 --> 00:14:35.200 align:middle line:84% and are mostly active during the day. 00:14:35.200 --> 00:14:38.400 align:middle line:84% So if you go outside on a bright day, 00:14:38.400 --> 00:14:41.960 align:middle line:84% the cones will be active and responsible for your vision, 00:14:41.960 --> 00:14:45.340 align:middle line:84% and the rods won't be doing anything. 00:14:45.340 --> 00:14:48.610 align:middle line:84% And then you go inside to a dark room, 00:14:48.610 --> 00:14:52.290 align:middle line:84% and then the rods will take over. 00:14:52.290 --> 00:14:54.450 align:middle line:84% But this process is not instantaneous, 00:14:54.450 --> 00:14:56.790 align:middle line:84% and it involves a process of dark adaptation. 00:14:56.790 --> 00:15:01.050 align:middle line:84% And that's because both types of receptors adapt, to some extent, 00:15:01.050 --> 00:15:02.570 align:middle line:90% to the ongoing light. 00:15:02.570 --> 00:15:06.810 align:middle line:84% So this is the result of a classic experiment 00:15:06.810 --> 00:15:11.830 align:middle line:84% that measures the detection threshold for light. 00:15:11.830 --> 00:15:15.050 align:middle line:84% So your task is just to say whether a light is present 00:15:15.050 --> 00:15:16.090 align:middle line:90% or not. 00:15:16.090 --> 00:15:19.370 align:middle line:84% You vary the amount of light that's present and figure out 00:15:19.370 --> 00:15:21.650 align:middle line:84% the threshold for telling whether there's 00:15:21.650 --> 00:15:23.150 align:middle line:90% a light that's present or not. 00:15:23.150 --> 00:15:27.210 align:middle line:84% And so that threshold in this experiment 00:15:27.210 --> 00:15:31.290 align:middle line:84% is measured as a function of the amount of time 00:15:31.290 --> 00:15:33.590 align:middle line:84% that you've spent in a dark room. 00:15:33.590 --> 00:15:35.710 align:middle line:84% So the idea is, you're out on the street, 00:15:35.710 --> 00:15:38.690 align:middle line:84% you go into this dark room like a movie theater, 00:15:38.690 --> 00:15:40.950 align:middle line:84% or in this case, this would have been a room in a lab. 00:15:40.950 --> 00:15:42.867 align:middle line:84% And then you measure your detection threshold. 00:15:42.867 --> 00:15:45.010 align:middle line:84% So everybody has had the informal experience 00:15:45.010 --> 00:15:47.500 align:middle line:84% of walking into a movie theater and initially not being 00:15:47.500 --> 00:15:48.560 align:middle line:90% able to see very much. 00:15:48.560 --> 00:15:51.580 align:middle line:84% And then you sit there, and then over time, you 00:15:51.580 --> 00:15:54.160 align:middle line:84% can see the seats around you, and the people around you 00:15:54.160 --> 00:15:55.340 align:middle line:90% and so forth. 00:15:55.340 --> 00:15:57.740 align:middle line:84% So that's the process of dark adaptation. 00:15:57.740 --> 00:15:59.900 align:middle line:84% So something's changing in your visual system 00:15:59.900 --> 00:16:02.440 align:middle line:84% to make it easier to see in low-light conditions. 00:16:02.440 --> 00:16:04.700 align:middle line:84% And part of that are changes that 00:16:04.700 --> 00:16:07.140 align:middle line:84% are happening at the level of the photoreceptor. 00:16:07.140 --> 00:16:10.900 align:middle line:84% Now, if you do this experiment and you measure the threshold 00:16:10.900 --> 00:16:12.660 align:middle line:84% as a function of time, you're going 00:16:12.660 --> 00:16:16.120 align:middle line:84% to get the purple curve that's shown here. 00:16:16.120 --> 00:16:18.380 align:middle line:84% So what happens is that, initially, your threshold 00:16:18.380 --> 00:16:19.500 align:middle line:90% is high. 00:16:19.500 --> 00:16:23.740 align:middle line:84% And then as time goes on, the threshold drops. 00:16:23.740 --> 00:16:28.340 align:middle line:84% And then you get to this point, and it kind of 00:16:28.340 --> 00:16:32.440 align:middle line:84% starts to drop, again, a little more aggressively. 00:16:32.440 --> 00:16:35.020 align:middle line:84% So the curve has got of funny shape. 00:16:35.020 --> 00:16:38.180 align:middle line:84% And we believe-- in fact, there's now lots of evidence-- 00:16:38.180 --> 00:16:41.260 align:middle line:84% that that funny shape comes from the contributions 00:16:41.260 --> 00:16:43.780 align:middle line:84% of two types of photoreceptors, the cones and the rods. 00:16:43.780 --> 00:16:44.280 align:middle line:90% All right? 00:16:44.280 --> 00:16:48.440 align:middle line:84% So as I said initially, in high light levels, 00:16:48.440 --> 00:16:51.840 align:middle line:84% your cones are the ones that are active, 00:16:51.840 --> 00:16:54.600 align:middle line:90% and your rods are saturated. 00:16:54.600 --> 00:16:56.600 align:middle line:84% And so you walk into this dark room, 00:16:56.600 --> 00:16:59.120 align:middle line:84% and the cones are the photoreceptor class 00:16:59.120 --> 00:17:02.720 align:middle line:84% that determines your light sensitivity. 00:17:02.720 --> 00:17:05.440 align:middle line:84% Both types of receptors start adapting, 00:17:05.440 --> 00:17:09.099 align:middle line:84% but the sensitivity of the rods is, for this initial period, 00:17:09.099 --> 00:17:11.140 align:middle line:84% still going to be worse than that of the cones. 00:17:11.140 --> 00:17:13.240 align:middle line:84% So the cones adapt a little bit, but then 00:17:13.240 --> 00:17:17.160 align:middle line:84% they kind of cap out at this level of sensitivity. 00:17:17.160 --> 00:17:18.960 align:middle line:90% That's the best they can do. 00:17:18.960 --> 00:17:22.240 align:middle line:84% So then the rods continue to adapt, 00:17:22.240 --> 00:17:26.400 align:middle line:84% and their sensitivity starts to exceed that of the cones. 00:17:26.400 --> 00:17:28.960 align:middle line:84% And the idea is that your behavioral threshold 00:17:28.960 --> 00:17:32.120 align:middle line:84% will be determined by whichever class of photoreceptors 00:17:32.120 --> 00:17:34.260 align:middle line:84% is more sensitive at that moment in time. 00:17:34.260 --> 00:17:36.460 align:middle line:84% And so here, that'll be the cones, 00:17:36.460 --> 00:17:38.540 align:middle line:84% and then here, that will be the rods. 00:17:38.540 --> 00:17:46.330 align:middle line:90% 00:17:46.330 --> 00:17:46.830 align:middle line:90% All right. 00:17:46.830 --> 00:17:49.757 align:middle line:84% So there are conditions in which you are primarily 00:17:49.757 --> 00:17:52.090 align:middle line:84% dependent on rods and conditions where you are primarily 00:17:52.090 --> 00:17:54.650 align:middle line:90% dependent on cones. 00:17:54.650 --> 00:17:57.290 align:middle line:84% And so-called rod and cone vision 00:17:57.290 --> 00:17:59.310 align:middle line:90% have a number of differences. 00:17:59.310 --> 00:18:03.310 align:middle line:84% So in general, rod vision is more sensitive than cone vision. 00:18:03.310 --> 00:18:04.850 align:middle line:84% So when you're reliant on your rods, 00:18:04.850 --> 00:18:07.290 align:middle line:84% you're better able to detect light. 00:18:07.290 --> 00:18:09.450 align:middle line:84% And so some of this comes from the fact 00:18:09.450 --> 00:18:11.530 align:middle line:84% that individual rod photoreceptors 00:18:11.530 --> 00:18:15.690 align:middle line:84% are more sensitive to light than individual cone photoreceptors. 00:18:15.690 --> 00:18:18.210 align:middle line:84% But part of this also derives from the fact 00:18:18.210 --> 00:18:20.970 align:middle line:84% that there is higher convergence from the rods 00:18:20.970 --> 00:18:22.690 align:middle line:90% to the ganglion cells. 00:18:22.690 --> 00:18:27.770 align:middle line:84% So remember, photoreceptors of transduced light 00:18:27.770 --> 00:18:31.290 align:middle line:84% send their signals to this set of different cells, 00:18:31.290 --> 00:18:33.810 align:middle line:84% culminating in the ganglion cells. 00:18:33.810 --> 00:18:37.470 align:middle line:84% And so with the rods, there's a high degree of convergence. 00:18:37.470 --> 00:18:40.530 align:middle line:84% What that means is that a single ganglion cell will get input 00:18:40.530 --> 00:18:43.890 align:middle line:90% from roughly 120 rods. 00:18:43.890 --> 00:18:46.250 align:middle line:84% So they're pooling signals from a lot of different rods, 00:18:46.250 --> 00:18:48.167 align:middle line:84% and that makes them very sensitive, of course, 00:18:48.167 --> 00:18:51.350 align:middle line:84% at the cost of spatial resolution. 00:18:51.350 --> 00:18:55.030 align:middle line:84% By comparison, the convergence from the cones to the ganglion 00:18:55.030 --> 00:18:57.290 align:middle line:90% cells is much less. 00:18:57.290 --> 00:18:59.083 align:middle line:84% So in the fovea, it's very often 1 to 1. 00:18:59.083 --> 00:19:00.750 align:middle line:84% So a single ganglion cell will get input 00:19:00.750 --> 00:19:02.010 align:middle line:90% from a single photoreceptor. 00:19:02.010 --> 00:19:03.870 align:middle line:84% And again, we believe that's in order 00:19:03.870 --> 00:19:06.830 align:middle line:84% to maximize spatial resolution in conditions where 00:19:06.830 --> 00:19:08.650 align:middle line:90% the light levels are high. 00:19:08.650 --> 00:19:13.190 align:middle line:90% 00:19:13.190 --> 00:19:16.210 align:middle line:84% All right, so rod vision is more sensitive than cone vision, 00:19:16.210 --> 00:19:18.450 align:middle line:84% but this comes at the cost of acuity, like we said. 00:19:18.450 --> 00:19:21.830 align:middle line:84% So rod vision has lower acuity than cone vision. 00:19:21.830 --> 00:19:24.557 align:middle line:84% Some of this is due to the convergence. 00:19:24.557 --> 00:19:26.890 align:middle line:84% And then another difference is that the rods are slower, 00:19:26.890 --> 00:19:28.723 align:middle line:84% so they also have a longer integration time. 00:19:28.723 --> 00:19:31.750 align:middle line:84% And again, this is a trade off between, in this case, 00:19:31.750 --> 00:19:34.430 align:middle line:84% temporal resolution and sensitivity. 00:19:34.430 --> 00:19:37.270 align:middle line:84% So integrating over time maybe increases 00:19:37.270 --> 00:19:40.670 align:middle line:84% the likelihood, the ability to detect some photons 00:19:40.670 --> 00:19:44.920 align:middle line:84% by pooling over time at the cost of being 00:19:44.920 --> 00:19:50.400 align:middle line:84% able to distinguish temporal patterns of stimulation. 00:19:50.400 --> 00:19:53.080 align:middle line:84% Another big difference between rods and cones 00:19:53.080 --> 00:19:56.140 align:middle line:84% is that rods do not support color vision. 00:19:56.140 --> 00:19:59.160 align:middle line:84% And the reason for this is that there's only one type of rod. 00:19:59.160 --> 00:20:02.600 align:middle line:84% By comparison, there are three types of cones, 00:20:02.600 --> 00:20:04.800 align:middle line:84% and the cones thus allow you to distinguish 00:20:04.800 --> 00:20:06.480 align:middle line:90% different wavelengths of light. 00:20:06.480 --> 00:20:08.920 align:middle line:84% So we'll talk a lot about this when 00:20:08.920 --> 00:20:13.455 align:middle line:84% we talk about color vision in a few weeks. 00:20:13.455 --> 00:20:15.080 align:middle line:84% Another big difference is that the rods 00:20:15.080 --> 00:20:17.520 align:middle line:90% are absent from the fovea. 00:20:17.520 --> 00:20:20.960 align:middle line:90% 00:20:20.960 --> 00:20:22.760 align:middle line:84% And this has the consequence of something 00:20:22.760 --> 00:20:25.220 align:middle line:84% called that is known as Arago's phenomena. 00:20:25.220 --> 00:20:28.800 align:middle line:84% So if you're outside on a very dark night, so in conditions 00:20:28.800 --> 00:20:30.520 align:middle line:84% where you're relying on your rods, 00:20:30.520 --> 00:20:32.300 align:middle line:84% and you're looking up at the stars, 00:20:32.300 --> 00:20:36.040 align:middle line:84% if you look directly at a star, you won't be able to see it. 00:20:36.040 --> 00:20:39.120 align:middle line:84% And that's because you're using your rods for vision, 00:20:39.120 --> 00:20:42.130 align:middle line:84% and there are no rods directly in the fovea. 00:20:42.130 --> 00:20:45.050 align:middle line:84% So you'll have to look a little bit away from the star 00:20:45.050 --> 00:20:46.830 align:middle line:90% in order to be able to see it. 00:20:46.830 --> 00:20:51.278 align:middle line:90% 00:20:51.278 --> 00:20:54.130 align:middle line:84% So if you measure sensitivity to light 00:20:54.130 --> 00:20:57.250 align:middle line:84% as a function of wavelength, you'll 00:20:57.250 --> 00:20:58.790 align:middle line:84% see that there are some differences. 00:20:58.790 --> 00:21:01.930 align:middle line:84% And the two words that we're going 00:21:01.930 --> 00:21:04.490 align:middle line:84% to use here to refer to conditions in which you 00:21:04.490 --> 00:21:09.570 align:middle line:84% are reliant on rods and cones are scotopic and photopic. 00:21:09.570 --> 00:21:15.970 align:middle line:84% So scotopic refers to conditions where the light level is low, so 00:21:15.970 --> 00:21:18.410 align:middle line:84% kind of during the night most of the time, 00:21:18.410 --> 00:21:20.290 align:middle line:84% if you're outside at least, and when 00:21:20.290 --> 00:21:22.030 align:middle line:90% you're mostly reliant on rods. 00:21:22.030 --> 00:21:26.290 align:middle line:84% Photopic refers to high light levels, so daytime vision 00:21:26.290 --> 00:21:28.290 align:middle line:90% where you're using your cones. 00:21:28.290 --> 00:21:31.130 align:middle line:90% 00:21:31.130 --> 00:21:34.650 align:middle line:84% So these graphs here show sensitivity 00:21:34.650 --> 00:21:36.110 align:middle line:90% as a function of wavelength. 00:21:36.110 --> 00:21:39.073 align:middle line:84% So sensitivity is 1 over the threshold. 00:21:39.073 --> 00:21:40.490 align:middle line:84% So if you're very, very sensitive, 00:21:40.490 --> 00:21:42.870 align:middle line:84% that means your detection threshold is low. 00:21:42.870 --> 00:21:45.150 align:middle line:84% And so in photopic conditions where 00:21:45.150 --> 00:21:48.790 align:middle line:84% you're reliant on your cones, peak sensitivity 00:21:48.790 --> 00:21:51.470 align:middle line:90% is around 550 nanometers. 00:21:51.470 --> 00:21:54.750 align:middle line:84% Scotopic vision, by comparison, has peak sensitivity 00:21:54.750 --> 00:21:56.990 align:middle line:90% at 505 nanometers. 00:21:56.990 --> 00:21:59.710 align:middle line:84% And you can see that your sensitivity to red light 00:21:59.710 --> 00:22:01.490 align:middle line:90% is basically nonexistent. 00:22:01.490 --> 00:22:06.390 align:middle line:84% So by red light, I mean wavelengths 00:22:06.390 --> 00:22:08.210 align:middle line:84% that are close to around 700 nanometers, 00:22:08.210 --> 00:22:09.810 align:middle line:90% so longer wavelength light. 00:22:09.810 --> 00:22:11.990 align:middle line:84% And we call that red light, because if you 00:22:11.990 --> 00:22:14.830 align:middle line:84% look at that in isolation, all other things being equal, 00:22:14.830 --> 00:22:16.510 align:middle line:90% it'll appear red. 00:22:16.510 --> 00:22:23.050 align:middle line:84% And this is just an empirical fact about the rod sensitivity. 00:22:23.050 --> 00:22:26.698 align:middle line:90% 00:22:26.698 --> 00:22:31.550 align:middle line:84% So as we mentioned, there are three types of cones. 00:22:31.550 --> 00:22:33.430 align:middle line:84% The three types of cones are distinguished 00:22:33.430 --> 00:22:35.470 align:middle line:90% by their spectral sensitivity. 00:22:35.470 --> 00:22:38.410 align:middle line:84% So this is a graph that plots sensitivity, 00:22:38.410 --> 00:22:39.940 align:middle line:90% and it's been normalized here. 00:22:39.940 --> 00:22:42.740 align:middle line:84% So the peak sensitivity is 1 as a function of wavelength. 00:22:42.740 --> 00:22:45.320 align:middle line:84% And there are three curves here, each for the three 00:22:45.320 --> 00:22:47.840 align:middle line:90% types of cone photoreceptors. 00:22:47.840 --> 00:22:50.600 align:middle line:84% And so those will often be referred to as the S cones, 00:22:50.600 --> 00:22:52.220 align:middle line:90% the M cones, and the L cones. 00:22:52.220 --> 00:22:56.080 align:middle line:84% And so S stands for short wavelength, M for medium, 00:22:56.080 --> 00:22:59.000 align:middle line:90% and L for long wavelength. 00:22:59.000 --> 00:23:01.440 align:middle line:84% And so you can see that the S cones have their peak 00:23:01.440 --> 00:23:05.400 align:middle line:84% sensitivity down here at around 450 nanometers. 00:23:05.400 --> 00:23:08.480 align:middle line:84% The M cones, it's around 550, and the L cones, 00:23:08.480 --> 00:23:09.940 align:middle line:90% it's a little bit higher. 00:23:09.940 --> 00:23:13.515 align:middle line:90% 00:23:13.515 --> 00:23:16.820 align:middle line:84% So an important idea around photoreceptors, 00:23:16.820 --> 00:23:19.400 align:middle line:84% which we will return to when we talk about color vision, 00:23:19.400 --> 00:23:23.080 align:middle line:84% is what is called the principle of univariance. 00:23:23.080 --> 00:23:27.200 align:middle line:84% And the idea is that the receptor response 00:23:27.200 --> 00:23:31.200 align:middle line:84% doesn't contain any information about the wavelength of light. 00:23:31.200 --> 00:23:35.320 align:middle line:84% So these curves, they tell you how likely 00:23:35.320 --> 00:23:38.340 align:middle line:84% a receptor is to absorb a photon of a given wavelength. 00:23:38.340 --> 00:23:38.840 align:middle line:90% All right? 00:23:38.840 --> 00:23:41.180 align:middle line:84% And so when your sensitivity is very high, 00:23:41.180 --> 00:23:44.740 align:middle line:84% that effectively means that the photopigment in the receptor 00:23:44.740 --> 00:23:47.600 align:middle line:84% is very likely to absorb that particular wavelength. 00:23:47.600 --> 00:23:53.300 align:middle line:84% And that means that if you are firing some number of photons 00:23:53.300 --> 00:23:56.100 align:middle line:84% per unit time at that photoreceptor, 00:23:56.100 --> 00:23:58.300 align:middle line:84% at this particular wavelength, you're 00:23:58.300 --> 00:24:00.140 align:middle line:84% going to get a large response, whereas 00:24:00.140 --> 00:24:04.100 align:middle line:84% at this particular wavelength, you'll get a lower response. 00:24:04.100 --> 00:24:07.660 align:middle line:84% But the concept here is that the response of the photoreceptor 00:24:07.660 --> 00:24:09.180 align:middle line:90% is a scalar. 00:24:09.180 --> 00:24:12.080 align:middle line:84% It can just vary its membrane potential. 00:24:12.080 --> 00:24:14.660 align:middle line:84% And the effect of the wavelength on the photoreceptor 00:24:14.660 --> 00:24:18.380 align:middle line:84% is just to vary the probability of absorption, which varies 00:24:18.380 --> 00:24:19.840 align:middle line:90% the magnitude of the response. 00:24:19.840 --> 00:24:24.860 align:middle line:84% And the consequence of that is that you 00:24:24.860 --> 00:24:28.600 align:middle line:84% can trade off between wavelength and intensity. 00:24:28.600 --> 00:24:32.260 align:middle line:84% So in other words, I can take a low-intensity light that 00:24:32.260 --> 00:24:35.820 align:middle line:84% is at 450 nanometers and present that to the S cone 00:24:35.820 --> 00:24:39.870 align:middle line:84% and get an identical response than if I have a 425 nanometer 00:24:39.870 --> 00:24:42.270 align:middle line:84% light that is at a higher intensity. 00:24:42.270 --> 00:24:45.678 align:middle line:84% So the consequence of that is that a single photoreceptor 00:24:45.678 --> 00:24:47.470 align:middle line:84% on its own doesn't really directly give you 00:24:47.470 --> 00:24:49.230 align:middle line:84% any information about wavelength. 00:24:49.230 --> 00:24:51.910 align:middle line:84% And that's why you actually need more than one receptor type 00:24:51.910 --> 00:24:53.827 align:middle line:84% if you actually want to be able to distinguish 00:24:53.827 --> 00:24:54.790 align:middle line:90% different wavelengths. 00:24:54.790 --> 00:24:56.450 align:middle line:84% So that's the principle of univariance. 00:24:56.450 --> 00:24:59.550 align:middle line:84% There's just one dimension along which 00:24:59.550 --> 00:25:01.490 align:middle line:84% the response of the receptor varies. 00:25:01.490 --> 00:25:04.350 align:middle line:90% 00:25:04.350 --> 00:25:04.850 align:middle line:90% All right. 00:25:04.850 --> 00:25:07.310 align:middle line:84% So one interesting empirical fact 00:25:07.310 --> 00:25:10.270 align:middle line:84% is that there's a fair amount of individual variation 00:25:10.270 --> 00:25:15.190 align:middle line:84% in the nature of the receptor mosaic on the retina. 00:25:15.190 --> 00:25:20.830 align:middle line:84% So these are pictures that were generated with a method called 00:25:20.830 --> 00:25:25.070 align:middle line:84% adaptive optics, whereby you can look inside someone's eye 00:25:25.070 --> 00:25:27.810 align:middle line:90% and image the cone mosaic. 00:25:27.810 --> 00:25:30.230 align:middle line:84% So this was introduced back in 1999 00:25:30.230 --> 00:25:32.910 align:middle line:90% by David Williams at Rochester. 00:25:32.910 --> 00:25:34.430 align:middle line:84% And these are two different images 00:25:34.430 --> 00:25:38.000 align:middle line:84% of the cone mosaic from two different individuals. 00:25:38.000 --> 00:25:40.600 align:middle line:84% And the point is just that they look kind of different. 00:25:40.600 --> 00:25:43.220 align:middle line:84% The distribution of the receptors is not identical. 00:25:43.220 --> 00:25:46.720 align:middle line:84% And this probably indicates that there 00:25:46.720 --> 00:25:50.560 align:middle line:84% would be individual differences in the nature of color vision. 00:25:50.560 --> 00:25:55.880 align:middle line:84% But exactly what those would be is, I think, not yet clear. 00:25:55.880 --> 00:25:57.640 align:middle line:90% So those are photoreceptors. 00:25:57.640 --> 00:25:59.720 align:middle line:84% The other kind of class of cells that we're 00:25:59.720 --> 00:26:03.180 align:middle line:84% going to talk a fair bit about today are ganglion cells. 00:26:03.180 --> 00:26:06.240 align:middle line:84% So remember, this is the type of cell that provides 00:26:06.240 --> 00:26:08.320 align:middle line:90% the output from the retina. 00:26:08.320 --> 00:26:12.640 align:middle line:84% And there are two main types of ganglion cells 00:26:12.640 --> 00:26:15.120 align:middle line:84% that are defined anatomically, and they're called 00:26:15.120 --> 00:26:17.820 align:middle line:90% midget cells and parasol cells. 00:26:17.820 --> 00:26:20.366 align:middle line:90% 00:26:20.366 --> 00:26:22.720 align:middle line:84% So this is a picture on the bottom 00:26:22.720 --> 00:26:27.660 align:middle line:84% of the dendritic field of each type of ganglion cell, 00:26:27.660 --> 00:26:28.880 align:middle line:90% so an example of each. 00:26:28.880 --> 00:26:32.040 align:middle line:84% So remember, the dendrites in a neuron 00:26:32.040 --> 00:26:34.460 align:middle line:84% are the place where they collect input right. 00:26:34.460 --> 00:26:37.460 align:middle line:90% So axon is the kind of output-- 00:26:37.460 --> 00:26:39.160 align:middle line:84% provides the output of the neuron. 00:26:39.160 --> 00:26:41.500 align:middle line:90% The dendrites collect the input. 00:26:41.500 --> 00:26:43.100 align:middle line:84% And so the dendrites in this case 00:26:43.100 --> 00:26:45.020 align:middle line:84% are distributed over space in order 00:26:45.020 --> 00:26:47.913 align:middle line:84% to get input from photoreceptors that are 00:26:47.913 --> 00:26:49.080 align:middle line:90% at different parts of space. 00:26:49.080 --> 00:26:51.080 align:middle line:84% They're not usually directly connected to photoreceptors. 00:26:51.080 --> 00:26:52.100 align:middle line:84% They're getting input from other types 00:26:52.100 --> 00:26:53.808 align:middle line:84% of cells that are, in turn, getting input 00:26:53.808 --> 00:26:55.000 align:middle line:90% from photoreceptors. 00:26:55.000 --> 00:26:58.140 align:middle line:84% But the spatial distribution reflects 00:26:58.140 --> 00:27:01.220 align:middle line:84% the region of the retinal image from which they're 00:27:01.220 --> 00:27:01.960 align:middle line:90% getting input. 00:27:01.960 --> 00:27:03.660 align:middle line:84% And you can see that the midget cell 00:27:03.660 --> 00:27:06.180 align:middle line:84% has a small dendritic field, indicating 00:27:06.180 --> 00:27:08.140 align:middle line:84% that it is collecting input from a very 00:27:08.140 --> 00:27:09.740 align:middle line:90% small region of the image. 00:27:09.740 --> 00:27:11.940 align:middle line:84% And the parasol cell has a large dendritic field, 00:27:11.940 --> 00:27:13.857 align:middle line:84% indicating it's collecting input from a larger 00:27:13.857 --> 00:27:15.100 align:middle line:90% region of the image. 00:27:15.100 --> 00:27:15.600 align:middle line:90% All right. 00:27:15.600 --> 00:27:18.140 align:middle line:90% 00:27:18.140 --> 00:27:20.940 align:middle line:84% So parasol cells and midget cells 00:27:20.940 --> 00:27:23.600 align:middle line:84% differ in a bunch of their response properties. 00:27:23.600 --> 00:27:25.960 align:middle line:84% So parasol cells are what are called achromatic, 00:27:25.960 --> 00:27:29.980 align:middle line:84% so they tend to respond equally to all wavelengths, 00:27:29.980 --> 00:27:32.860 align:middle line:84% because they pool responses across cones. 00:27:32.860 --> 00:27:35.110 align:middle line:84% They tend to prefer first stimuli that 00:27:35.110 --> 00:27:37.150 align:middle line:90% change a lot over time. 00:27:37.150 --> 00:27:41.190 align:middle line:84% Midget cells are often sensitive to both luminance and color. 00:27:41.190 --> 00:27:44.270 align:middle line:84% That's often because they'll receive input 00:27:44.270 --> 00:27:47.550 align:middle line:84% from particular types of cones, and to be 00:27:47.550 --> 00:27:51.830 align:middle line:84% less sensitive to temperature changes and stimuli. 00:27:51.830 --> 00:27:56.190 align:middle line:84% So these two classes of ganglion cells 00:27:56.190 --> 00:28:00.130 align:middle line:84% project to the lateral geniculate nucleus, or LGN, 00:28:00.130 --> 00:28:02.110 align:middle line:84% which is the part of the thalamus that's 00:28:02.110 --> 00:28:03.630 align:middle line:90% involved in vision. 00:28:03.630 --> 00:28:05.710 align:middle line:84% And the lateral geniculate nucleus 00:28:05.710 --> 00:28:08.447 align:middle line:84% itself contains two main classes of cells. 00:28:08.447 --> 00:28:10.530 align:middle line:84% We now know there are some other classes, as well, 00:28:10.530 --> 00:28:12.710 align:middle line:90% but there's two primary ones. 00:28:12.710 --> 00:28:13.870 align:middle line:90% All right. 00:28:13.870 --> 00:28:15.510 align:middle line:84% And the classes of cells in the LGN 00:28:15.510 --> 00:28:18.910 align:middle line:84% are called parvocellular and magnocellular. 00:28:18.910 --> 00:28:21.637 align:middle line:84% Now, the nomenclature here is quite unfortunate 00:28:21.637 --> 00:28:23.470 align:middle line:84% and makes this a little bit hard to remember 00:28:23.470 --> 00:28:27.630 align:middle line:84% because the parasol cells in the ganglion cell 00:28:27.630 --> 00:28:30.510 align:middle line:84% layer of the retina project to the magnocellular 00:28:30.510 --> 00:28:32.510 align:middle line:90% layers of the LGN. 00:28:32.510 --> 00:28:35.690 align:middle line:84% The midget cells in the retina project to the parvocellular 00:28:35.690 --> 00:28:36.830 align:middle line:90% layers of the LGN. 00:28:36.830 --> 00:28:38.770 align:middle line:84% So it's kind of the opposite of what would 00:28:38.770 --> 00:28:40.350 align:middle line:90% be convenient to remember. 00:28:40.350 --> 00:28:43.225 align:middle line:90% 00:28:43.225 --> 00:28:47.010 align:middle line:84% Now, for both cell types, the size of the dendritic field, 00:28:47.010 --> 00:28:49.730 align:middle line:84% and thus what we call the receptive field, so 00:28:49.730 --> 00:28:53.170 align:middle line:84% the region of space to which the neuron responds, 00:28:53.170 --> 00:28:54.630 align:middle line:90% increases with eccentricity. 00:28:54.630 --> 00:28:56.930 align:middle line:84% Remember, eccentricity is distance from the fovea. 00:28:56.930 --> 00:28:59.310 align:middle line:84% And so this is a diagram that shows this. 00:28:59.310 --> 00:29:04.970 align:middle line:84% So what this is plotting is the receptive field's diameter-- 00:29:04.970 --> 00:29:08.370 align:middle line:84% so it's the region of space to which the neuron responds-- 00:29:08.370 --> 00:29:10.750 align:middle line:84% as a function of retinal eccentricity. 00:29:10.750 --> 00:29:13.970 align:middle line:84% So this is the result of an experiment where you stick 00:29:13.970 --> 00:29:15.110 align:middle line:90% an electrode in the retina. 00:29:15.110 --> 00:29:20.370 align:middle line:84% You're recording the responses of a ganglion cell presenting 00:29:20.370 --> 00:29:22.450 align:middle line:84% light stimuli, and then measuring 00:29:22.450 --> 00:29:26.790 align:middle line:84% the region of the image that evokes a response in the neuron. 00:29:26.790 --> 00:29:30.290 align:middle line:84% And so that's the quantity that's plotted on the y-axis. 00:29:30.290 --> 00:29:32.260 align:middle line:84% And then you do this at different retinal 00:29:32.260 --> 00:29:33.743 align:middle line:90% eccentricities. 00:29:33.743 --> 00:29:35.660 align:middle line:84% And so the point here, there's two main things 00:29:35.660 --> 00:29:39.100 align:middle line:90% that you should note from this. 00:29:39.100 --> 00:29:41.400 align:middle line:84% One is that when you're close to the fovea, 00:29:41.400 --> 00:29:44.140 align:middle line:84% the receptive field size is small. 00:29:44.140 --> 00:29:46.660 align:middle line:84% And that's consistent with this general idea 00:29:46.660 --> 00:29:50.900 align:middle line:84% that the fovea is where you have really high-resolution vision. 00:29:50.900 --> 00:29:54.918 align:middle line:84% So remember, there's lots of cones there. 00:29:54.918 --> 00:29:56.460 align:middle line:84% You keep the receptive field small so 00:29:56.460 --> 00:29:59.660 align:middle line:84% that you can distinguish different fine grained patterns 00:29:59.660 --> 00:30:01.540 align:middle line:90% there. 00:30:01.540 --> 00:30:04.940 align:middle line:84% As you move from the fovea out to the periphery, 00:30:04.940 --> 00:30:08.500 align:middle line:84% so increasing eccentricity, the receptive field size 00:30:08.500 --> 00:30:10.580 align:middle line:90% tends to increase. 00:30:10.580 --> 00:30:13.140 align:middle line:84% But you can also see that the receptive fields, 00:30:13.140 --> 00:30:15.840 align:middle line:90% they fall in these two lines. 00:30:15.840 --> 00:30:19.600 align:middle line:84% And these two lines correspond to the midget cells-- 00:30:19.600 --> 00:30:22.300 align:middle line:84% that's the lower of the two lines-- 00:30:22.300 --> 00:30:23.900 align:middle line:90% and the parasol cell. 00:30:23.900 --> 00:30:25.440 align:middle line:84% That's the upper of the two lines. 00:30:25.440 --> 00:30:28.260 align:middle line:84% So the parasol cells at a given eccentricity 00:30:28.260 --> 00:30:31.400 align:middle line:84% have bigger receptive fields than the midget cells. 00:30:31.400 --> 00:30:35.190 align:middle line:84% But in both cases, the receptive field grows with eccentricity. 00:30:35.190 --> 00:30:38.830 align:middle line:84% And so this phenomenon here, whereby receptive field size 00:30:38.830 --> 00:30:40.410 align:middle line:84% increases with retinal eccentricity, 00:30:40.410 --> 00:30:42.350 align:middle line:84% this is a very general organizing principle 00:30:42.350 --> 00:30:43.910 align:middle line:90% within the visual system. 00:30:43.910 --> 00:30:48.230 align:middle line:84% So receptive fields tend to be small in the fovea 00:30:48.230 --> 00:30:49.770 align:middle line:84% and then larger in the periphery. 00:30:49.770 --> 00:30:53.470 align:middle line:90% 00:30:53.470 --> 00:30:56.550 align:middle line:84% So this is an eye chart that was designed 00:30:56.550 --> 00:30:59.950 align:middle line:84% by Stuart Anstis, a vision scientist, that 00:30:59.950 --> 00:31:03.590 align:middle line:84% is intended to compensate for changes in resolution 00:31:03.590 --> 00:31:04.490 align:middle line:90% with eccentricity. 00:31:04.490 --> 00:31:06.270 align:middle line:84% And so the idea of this eye chart 00:31:06.270 --> 00:31:09.950 align:middle line:84% is that if you look at the center dot, 00:31:09.950 --> 00:31:13.700 align:middle line:84% then all of the letters should be equally recognizable. 00:31:13.700 --> 00:31:15.950 align:middle line:84% And the reason for this is that the size of the letter 00:31:15.950 --> 00:31:18.650 align:middle line:84% has been scaled up with eccentricity. 00:31:18.650 --> 00:31:21.470 align:middle line:84% So the ones that are closer to the fovea, those are smaller. 00:31:21.470 --> 00:31:24.090 align:middle line:84% The ones that are out in the periphery are larger. 00:31:24.090 --> 00:31:26.443 align:middle line:90% So the resolution falls. 00:31:26.443 --> 00:31:28.110 align:middle line:84% So the spatial resolution of your vision 00:31:28.110 --> 00:31:31.730 align:middle line:84% falls in proportion to the distance of your fovea. 00:31:31.730 --> 00:31:35.672 align:middle line:84% And this is some evidence that those phenomena that we're 00:31:35.672 --> 00:31:37.130 align:middle line:84% seeing in receptive fields actually 00:31:37.130 --> 00:31:41.850 align:middle line:84% have consequences for what you can see. 00:31:41.850 --> 00:31:45.250 align:middle line:84% So major organizing principle of the visual system 00:31:45.250 --> 00:31:48.330 align:middle line:84% is the foveal periphery distinction. 00:31:48.330 --> 00:31:51.890 align:middle line:84% And it's an interesting question as to why the visual system is 00:31:51.890 --> 00:31:53.290 align:middle line:90% set up the way that it is. 00:31:53.290 --> 00:31:57.810 align:middle line:84% And so as we have discussed at several earlier points in this 00:31:57.810 --> 00:32:01.370 align:middle line:84% class, one of the ways that we can answer these "why" 00:32:01.370 --> 00:32:05.650 align:middle line:84% questions is by building computational models that are 00:32:05.650 --> 00:32:07.210 align:middle line:84% optimized for different conditions, 00:32:07.210 --> 00:32:10.518 align:middle line:84% and investigating the conditions in which this optimized system 00:32:10.518 --> 00:32:12.810 align:middle line:84% ends up finding some of the same solutions that you see 00:32:12.810 --> 00:32:13.970 align:middle line:90% in biology. 00:32:13.970 --> 00:32:16.090 align:middle line:84% And so there's a paper that I like 00:32:16.090 --> 00:32:18.130 align:middle line:84% a lot that came out a few years ago 00:32:18.130 --> 00:32:21.830 align:middle line:84% that did this for the problem of retinal image sampling. 00:32:21.830 --> 00:32:24.330 align:middle line:84% So the paper is posing this question 00:32:24.330 --> 00:32:29.980 align:middle line:84% of why we have this foveal image sampling strategy. 00:32:29.980 --> 00:32:33.260 align:middle line:84% This is work by Brian Chung, and Eric Weiss and Bruno Olshausen. 00:32:33.260 --> 00:32:38.380 align:middle line:84% So I'll just read this little excerpt from the paper. 00:32:38.380 --> 00:32:42.660 align:middle line:84% So they write, "The human retina contains 1.5 million ganglion 00:32:42.660 --> 00:32:46.020 align:middle line:84% cells, whose axons form the sole output of the retina. 00:32:46.020 --> 00:32:48.975 align:middle line:84% These essentially constitute about 300,000 distinct samples 00:32:48.975 --> 00:32:51.100 align:middle line:84% of the image, due to the multiplicity of cell types 00:32:51.100 --> 00:32:53.960 align:middle line:84% coding different aspects, such as on versus off channels," 00:32:53.960 --> 00:32:56.540 align:middle line:84% which we're going to talk about in a moment. 00:32:56.540 --> 00:33:01.020 align:middle line:84% "If these were packed uniformly at highest resolution, 00:33:01.020 --> 00:33:05.140 align:middle line:84% they would subtend an image area spanning just 5 by 5 degrees. 00:33:05.140 --> 00:33:07.660 align:middle line:84% Thus, we would have high resolution but essentially 00:33:07.660 --> 00:33:09.060 align:middle line:90% tunnel vision. 00:33:09.060 --> 00:33:11.700 align:middle line:84% Alternatively, if they were spread out uniformly over 00:33:11.700 --> 00:33:13.620 align:middle line:84% the entire monocular visual field, 00:33:13.620 --> 00:33:17.840 align:middle line:84% spanning roughly 150 degrees, we would have wide field coverage, 00:33:17.840 --> 00:33:20.660 align:middle line:84% but with very blurry vision, with each sample subtending 00:33:20.660 --> 00:33:23.620 align:middle line:84% a quarter of a degree, which would make even the largest 00:33:23.620 --> 00:33:25.800 align:middle line:84% letters on a Snellen eye chart--" 00:33:25.800 --> 00:33:29.280 align:middle line:84% that's the kind of standard eye chart for diagnosing vision-- 00:33:29.280 --> 00:33:30.800 align:middle line:90% "illegible. 00:33:30.800 --> 00:33:34.360 align:middle line:84% Thus, the primate solution, which is to have a fovea, 00:33:34.360 --> 00:33:37.560 align:middle line:84% makes intuitive sense as a way to achieve the best of both 00:33:37.560 --> 00:33:38.600 align:middle line:90% of these worlds. 00:33:38.600 --> 00:33:41.600 align:middle line:84% However, we are still lacking a quantitative demonstration 00:33:41.600 --> 00:33:43.560 align:middle line:84% that such a sampling strategy emerges 00:33:43.560 --> 00:33:45.440 align:middle line:84% as the optimal design for subserving 00:33:45.440 --> 00:33:49.160 align:middle line:90% some set of visual tasks. 00:33:49.160 --> 00:33:52.160 align:middle line:84% We explore whether what is the optimal retinal sampling 00:33:52.160 --> 00:33:54.780 align:middle line:84% lattice for an overt attentional system, 00:33:54.780 --> 00:33:56.200 align:middle line:84% performing a simple visual search 00:33:56.200 --> 00:33:58.960 align:middle line:84% task requiring the classification of an object. 00:33:58.960 --> 00:34:01.240 align:middle line:84% We propose a learnable retinal sampling lattice 00:34:01.240 --> 00:34:04.920 align:middle line:84% to explore what properties are best suited for this task. 00:34:04.920 --> 00:34:07.680 align:middle line:84% While evolutionary pressure has tuned the retinal configurations 00:34:07.680 --> 00:34:11.199 align:middle line:84% found in the primate retina, we instead utilize gradient descent 00:34:11.199 --> 00:34:15.880 align:middle line:84% optimization for in-silico model by constructing a fully 00:34:15.880 --> 00:34:17.880 align:middle line:84% differentiable, dynamically controllable model 00:34:17.880 --> 00:34:20.460 align:middle line:90% of attention." 00:34:20.460 --> 00:34:22.719 align:middle line:90% So here's the idea. 00:34:22.719 --> 00:34:26.980 align:middle line:84% They've got this system that has a receptor lattice. 00:34:26.980 --> 00:34:28.570 align:middle line:84% So there's some number of receptors 00:34:28.570 --> 00:34:30.130 align:middle line:90% that can sample an image. 00:34:30.130 --> 00:34:34.570 align:middle line:84% And each receptor has a particular position 00:34:34.570 --> 00:34:37.090 align:middle line:90% and a particular width. 00:34:37.090 --> 00:34:41.850 align:middle line:84% So there's this kernel that has these learnable parameters, 00:34:41.850 --> 00:34:43.830 align:middle line:84% and there's a whole bunch of these. 00:34:43.830 --> 00:34:46.170 align:middle line:84% And the idea is that they are going 00:34:46.170 --> 00:34:49.969 align:middle line:84% to optimize the position and width of the receptors 00:34:49.969 --> 00:34:53.909 align:middle line:84% on this retina for a vision task. 00:34:53.909 --> 00:34:57.050 align:middle line:84% And in this case, the vision task 00:34:57.050 --> 00:35:02.450 align:middle line:84% is to find and identify the digit on a cluttered background. 00:35:02.450 --> 00:35:07.910 align:middle line:84% So these are examples of stimuli from this task. 00:35:07.910 --> 00:35:09.670 align:middle line:84% So you can see this one has a four. 00:35:09.670 --> 00:35:10.930 align:middle line:90% This has a one. 00:35:10.930 --> 00:35:12.170 align:middle line:90% There's a nine. 00:35:12.170 --> 00:35:14.810 align:middle line:84% So they're in different places, and there's 00:35:14.810 --> 00:35:20.550 align:middle line:84% some other junk that's kind of added in to make the task hard. 00:35:20.550 --> 00:35:23.330 align:middle line:84% So the system has to solve this problem. 00:35:23.330 --> 00:35:26.110 align:middle line:84% And they're training the system up to solve this problem, 00:35:26.110 --> 00:35:32.860 align:middle line:84% but allowing the system to optimize its receptor lattice. 00:35:32.860 --> 00:35:36.060 align:middle line:84% And they additionally introduced these other constraints 00:35:36.060 --> 00:35:37.220 align:middle line:90% on the problem. 00:35:37.220 --> 00:35:41.780 align:middle line:84% So in one version of the system that they trained up, 00:35:41.780 --> 00:35:44.440 align:middle line:84% the system was allowed to translate its retina, 00:35:44.440 --> 00:35:46.653 align:middle line:84% so essentially, to make eye movements, 00:35:46.653 --> 00:35:48.820 align:middle line:84% to position the receptor lattice at different places 00:35:48.820 --> 00:35:51.440 align:middle line:90% within the image. 00:35:51.440 --> 00:35:53.540 align:middle line:84% And then in another condition, it 00:35:53.540 --> 00:35:55.040 align:middle line:84% was allowed to translate its retina, 00:35:55.040 --> 00:35:57.440 align:middle line:84% but it could also zoom the retinal lattice. 00:35:57.440 --> 00:35:59.900 align:middle line:84% This is like the kind of thing you can do with your phone, 00:35:59.900 --> 00:36:03.070 align:middle line:84% but which the biological visual system doesn't actually do. 00:36:03.070 --> 00:36:04.320 align:middle line:90% We don't have a zoom function. 00:36:04.320 --> 00:36:05.760 align:middle line:90% We can just translate. 00:36:05.760 --> 00:36:08.780 align:middle line:90% 00:36:08.780 --> 00:36:12.180 align:middle line:84% And so what they found was that in the condition where 00:36:12.180 --> 00:36:15.060 align:middle line:84% the retina could be translated around, 00:36:15.060 --> 00:36:18.340 align:middle line:84% eccentricity dependence of the sampling in the retina 00:36:18.340 --> 00:36:20.900 align:middle line:90% emerged as an optimal solution. 00:36:20.900 --> 00:36:26.520 align:middle line:84% So these are showing the settings of the receptor lattice 00:36:26.520 --> 00:36:29.760 align:middle line:84% over different amounts of training, 00:36:29.760 --> 00:36:31.680 align:middle line:84% so optimization for this problem. 00:36:31.680 --> 00:36:33.580 align:middle line:84% So this is like the initialization. 00:36:33.580 --> 00:36:36.440 align:middle line:84% They initialize these things as uniformly spaced. 00:36:36.440 --> 00:36:39.240 align:middle line:84% And then you can see that over the course of the optimization, 00:36:39.240 --> 00:36:42.920 align:middle line:84% what happens is that some of the receptors 00:36:42.920 --> 00:36:47.600 align:middle line:84% get moved kind of close together in this one part of the sampling 00:36:47.600 --> 00:36:50.865 align:middle line:84% lattice, and they also get very small right. 00:36:50.865 --> 00:36:52.240 align:middle line:84% So that's like the system is kind 00:36:52.240 --> 00:36:57.560 align:middle line:84% of evolving this strategy where there's a whole bunch of very 00:36:57.560 --> 00:37:00.200 align:middle line:84% small receptive fields that are packed into one particular part 00:37:00.200 --> 00:37:02.680 align:middle line:90% of the sampling lattice. 00:37:02.680 --> 00:37:05.365 align:middle line:90% 00:37:05.365 --> 00:37:13.280 align:middle line:84% And so they quantified this by plotting the receptive field 00:37:13.280 --> 00:37:17.000 align:middle line:84% size as a function of eccentricity, and so in cases 00:37:17.000 --> 00:37:19.900 align:middle line:84% where the model could translate its retina. 00:37:19.900 --> 00:37:23.400 align:middle line:84% So these are two solutions that it found, and you see this kind 00:37:23.400 --> 00:37:25.370 align:middle line:90% of eccentricity dependence. 00:37:25.370 --> 00:37:29.250 align:middle line:84% Whereas in the alternative problem constraint 00:37:29.250 --> 00:37:32.447 align:middle line:84% of being able to zoom in addition to translate, 00:37:32.447 --> 00:37:34.030 align:middle line:84% the solution they found was different. 00:37:34.030 --> 00:37:36.370 align:middle line:84% There was much less of a fovea, and you 00:37:36.370 --> 00:37:40.670 align:middle line:84% see much less of this eccentricity dependence. 00:37:40.670 --> 00:37:43.730 align:middle line:84% So here are examples of the model actually performing 00:37:43.730 --> 00:37:44.730 align:middle line:90% the task. 00:37:44.730 --> 00:37:48.350 align:middle line:84% So this is one trial of this task, 00:37:48.350 --> 00:37:51.130 align:middle line:84% and it's just showing you where the sampling 00:37:51.130 --> 00:37:55.430 align:middle line:84% lattice is kind of positioned relative to the digit. 00:37:55.430 --> 00:37:58.170 align:middle line:84% And the point is that over time, the sampling lattice 00:37:58.170 --> 00:38:01.370 align:middle line:84% kind of gets moved so that the fovea, in this case, 00:38:01.370 --> 00:38:02.910 align:middle line:84% is kind of centered on the digit, 00:38:02.910 --> 00:38:10.130 align:middle line:84% so that it can optimally or best recognize the digit. 00:38:10.130 --> 00:38:12.450 align:middle line:84% And this bottom row is what happens when the thing can 00:38:12.450 --> 00:38:15.130 align:middle line:90% zoom its retina, as well. 00:38:15.130 --> 00:38:18.410 align:middle line:84% And there you can see this uniform receptor lattice, 00:38:18.410 --> 00:38:24.908 align:middle line:84% and it just kind of shrinks it down to fit onto the digit. 00:38:24.908 --> 00:38:26.450 align:middle line:84% So what do we learn from all of this? 00:38:26.450 --> 00:38:29.950 align:middle line:84% So the inference that you should make here 00:38:29.950 --> 00:38:34.350 align:middle line:84% is that this is evidence that a fovea is a useful way 00:38:34.350 --> 00:38:37.910 align:middle line:84% to attain high resolution vision, given, one, 00:38:37.910 --> 00:38:40.350 align:middle line:84% a limit on the number of samples that can be transmitted 00:38:40.350 --> 00:38:42.030 align:middle line:84% to the brain from the optic nerve, 00:38:42.030 --> 00:38:43.870 align:middle line:84% and number two, the ability to move 00:38:43.870 --> 00:38:47.110 align:middle line:84% the eyes to position the fovea at different locations. 00:38:47.110 --> 00:38:50.270 align:middle line:84% And so it seems that biological vision 00:38:50.270 --> 00:38:54.430 align:middle line:84% has evolved this strategy that's just a good sampling strategy 00:38:54.430 --> 00:38:56.090 align:middle line:90% for being able to solve tasks. 00:38:56.090 --> 00:38:59.450 align:middle line:84% So in other words, you have the ability to move your eyes. 00:38:59.450 --> 00:39:01.950 align:middle line:84% And then in concert with that, the retina 00:39:01.950 --> 00:39:04.597 align:middle line:84% has the receptors packed in this very, very non-uniform way. 00:39:04.597 --> 00:39:06.430 align:middle line:84% So there's this one part of the retina where 00:39:06.430 --> 00:39:07.890 align:middle line:90% you have really good sampling. 00:39:07.890 --> 00:39:10.670 align:middle line:84% And if you want to see stuff, you typically direct your fovea 00:39:10.670 --> 00:39:13.660 align:middle line:90% to that part of the retina. 00:39:13.660 --> 00:39:24.000 align:middle line:90%