WEBVTT 00:00:00.000 --> 00:00:02.448 align:middle line:90% [RUSTLING] 00:00:02.448 --> 00:00:03.909 align:middle line:90% [SQUEAKING] 00:00:03.909 --> 00:00:05.370 align:middle line:90% [CLICKING] 00:00:05.370 --> 00:00:09.760 align:middle line:90% 00:00:09.760 --> 00:00:11.920 align:middle line:84% JOSH MCDERMOTT: Let's talk about depth perception. 00:00:11.920 --> 00:00:17.560 align:middle line:84% So the problem here that we're going to talk about today 00:00:17.560 --> 00:00:20.000 align:middle line:84% is that the input to the visual system 00:00:20.000 --> 00:00:23.240 align:middle line:84% consists of two-dimensional images. 00:00:23.240 --> 00:00:25.960 align:middle line:84% The world is three dimensions, and people 00:00:25.960 --> 00:00:29.760 align:middle line:84% are pretty good at estimating the three dimensional structure. 00:00:29.760 --> 00:00:31.640 align:middle line:84% You can hold the shape in your hand 00:00:31.640 --> 00:00:34.640 align:middle line:84% and visually be able to assess the shape. 00:00:34.640 --> 00:00:37.480 align:middle line:84% You can tell how far things are away from you, and so on and so 00:00:37.480 --> 00:00:37.980 align:middle line:90% forth. 00:00:37.980 --> 00:00:41.080 align:middle line:84% So the extraction of three dimensional structure 00:00:41.080 --> 00:00:44.640 align:middle line:84% from the two-dimensional images that the eyes receive 00:00:44.640 --> 00:00:46.383 align:middle line:84% is important for lots of things-- 00:00:46.383 --> 00:00:48.800 align:middle line:84% for navigating through space, for interacting with objects 00:00:48.800 --> 00:00:49.880 align:middle line:90% and so forth. 00:00:49.880 --> 00:00:51.680 align:middle line:84% And the most reliable source of information 00:00:51.680 --> 00:00:54.320 align:middle line:84% about the three-dimensional structure of the world 00:00:54.320 --> 00:00:56.400 align:middle line:90% is visual, at least for humans. 00:00:56.400 --> 00:01:01.000 align:middle line:84% Some other animals use sonar and other things like that. 00:01:01.000 --> 00:01:03.960 align:middle line:84% All right, so the keys to the solutions-- 00:01:03.960 --> 00:01:06.800 align:middle line:84% one key is the fact that you have two eyes. 00:01:06.800 --> 00:01:10.020 align:middle line:84% And we're not going to talk about that in this lecture. 00:01:10.020 --> 00:01:12.240 align:middle line:90% That'll be for next time. 00:01:12.240 --> 00:01:16.640 align:middle line:84% The other key are assumptions that we make about the world 00:01:16.640 --> 00:01:19.760 align:middle line:84% that we have presumably learned or internalized 00:01:19.760 --> 00:01:22.040 align:middle line:84% over evolutionary development, coupled 00:01:22.040 --> 00:01:24.800 align:middle line:84% with implicit knowledge of the physics 00:01:24.800 --> 00:01:28.605 align:middle line:84% and the geometry of light that comes from objects to the eyes. 00:01:28.605 --> 00:01:30.980 align:middle line:84% And so we're going to talk a lot about depth cues, right? 00:01:30.980 --> 00:01:33.140 align:middle line:84% We've talked about cues previously in the class. 00:01:33.140 --> 00:01:35.940 align:middle line:84% When we talk about a cue, we mean a source of information, 00:01:35.940 --> 00:01:38.720 align:middle line:84% so some aspect of the stimulus that provides information, 00:01:38.720 --> 00:01:43.520 align:middle line:84% in this case, about a variable that we care about, depth. 00:01:43.520 --> 00:01:47.140 align:middle line:84% So there are lots of visual cues to 3D shape and depth. 00:01:47.140 --> 00:01:50.440 align:middle line:84% So stereopsis is the one that is best known, 00:01:50.440 --> 00:01:52.840 align:middle line:84% but you can see three dimensions without it. 00:01:52.840 --> 00:01:57.152 align:middle line:84% So if you just close one eye, the world 00:01:57.152 --> 00:01:58.610 align:middle line:84% doesn't really look that different. 00:01:58.610 --> 00:02:01.210 align:middle line:84% You can still tell that certain things are further away 00:02:01.210 --> 00:02:05.210 align:middle line:84% than others, and you can see the three-dimensional shape 00:02:05.210 --> 00:02:06.650 align:middle line:90% of objects pretty well. 00:02:06.650 --> 00:02:10.350 align:middle line:84% So this is a partial list of cues to depth. 00:02:10.350 --> 00:02:12.290 align:middle line:84% We'll talk about a whole bunch of these-- 00:02:12.290 --> 00:02:15.130 align:middle line:84% shape from shading and drop shadows, linear perspective, 00:02:15.130 --> 00:02:18.930 align:middle line:84% texture gradients, familiar size, height and field, 00:02:18.930 --> 00:02:20.890 align:middle line:90% aerial perspective. 00:02:20.890 --> 00:02:23.310 align:middle line:84% Last time we talked about the kinetic depth effect. 00:02:23.310 --> 00:02:24.630 align:middle line:90% There's also motion parallax. 00:02:24.630 --> 00:02:27.770 align:middle line:84% Those are depth cues for motion-- 00:02:27.770 --> 00:02:30.250 align:middle line:90% occlusion, focal blur. 00:02:30.250 --> 00:02:32.655 align:middle line:84% And this is not an exclusive list. 00:02:32.655 --> 00:02:34.530 align:middle line:84% So the first thing I want to talk about today 00:02:34.530 --> 00:02:35.447 align:middle line:90% is shape from shading. 00:02:35.447 --> 00:02:39.230 align:middle line:84% So we've alluded to shape from shading previously in the class, 00:02:39.230 --> 00:02:42.770 align:middle line:84% and it refers to the fact that variations in luminance 00:02:42.770 --> 00:02:46.010 align:middle line:90% are often interpreted as shape. 00:02:46.010 --> 00:02:48.010 align:middle line:84% And the basis from shape from shading 00:02:48.010 --> 00:02:50.630 align:middle line:84% is that many surfaces are approximately Lambertian. 00:02:50.630 --> 00:02:52.490 align:middle line:84% So we talked about Lambertian reflectance 00:02:52.490 --> 00:02:54.790 align:middle line:84% in the context of lightness perception. 00:02:54.790 --> 00:02:58.330 align:middle line:84% So a surface is Lambertian if the amount of reflected light 00:02:58.330 --> 00:03:01.970 align:middle line:84% is determined by the angle between the incident light ray 00:03:01.970 --> 00:03:03.550 align:middle line:90% and the surface normal vector. 00:03:03.550 --> 00:03:05.050 align:middle line:84% But the surface, otherwise, scatters 00:03:05.050 --> 00:03:06.350 align:middle line:90% like equally in all directions. 00:03:06.350 --> 00:03:09.390 align:middle line:84% And so this is a picture that kind of depicts this. 00:03:09.390 --> 00:03:13.530 align:middle line:84% So the black arrow is the surface normal. 00:03:13.530 --> 00:03:15.610 align:middle line:84% So this is a horizontal surface, so the normal 00:03:15.610 --> 00:03:16.990 align:middle line:90% is perpendicular to that. 00:03:16.990 --> 00:03:19.970 align:middle line:84% The yellow arrow is the direction of the illumination. 00:03:19.970 --> 00:03:24.503 align:middle line:84% And then, the little blue arrows are scattered light rays. 00:03:24.503 --> 00:03:26.170 align:middle line:84% And so what you're supposed to take away 00:03:26.170 --> 00:03:28.850 align:middle line:84% from this is that irrespective of the direction 00:03:28.850 --> 00:03:31.090 align:middle line:84% of the illumination, the light gets scattered equally 00:03:31.090 --> 00:03:32.310 align:middle line:90% in all directions. 00:03:32.310 --> 00:03:35.690 align:middle line:84% But you can see that the light is-- 00:03:35.690 --> 00:03:37.770 align:middle line:84% the most light reflects off the surface 00:03:37.770 --> 00:03:40.030 align:middle line:84% when the illumination is perpendicular to the surface. 00:03:40.030 --> 00:03:41.990 align:middle line:84% And as the illumination becomes more oblique, 00:03:41.990 --> 00:03:43.690 align:middle line:84% there's less light that's scattered. 00:03:43.690 --> 00:03:47.650 align:middle line:84% So this is the characteristic of a Lambertian surface. 00:03:47.650 --> 00:03:51.290 align:middle line:84% All right, and so the basis of shape from shading 00:03:51.290 --> 00:03:54.630 align:middle line:84% is kind of like the opposite of what is shown in this diagram. 00:03:54.630 --> 00:03:56.580 align:middle line:84% So this diagram is showing a situation 00:03:56.580 --> 00:03:58.380 align:middle line:84% where the surface orientation is fixed 00:03:58.380 --> 00:04:00.960 align:middle line:84% and the illumination direction is varied. 00:04:00.960 --> 00:04:02.960 align:middle line:84% And that doesn't happen very often in the world. 00:04:02.960 --> 00:04:05.720 align:middle line:84% So typically, in the world, there will be one light source, 00:04:05.720 --> 00:04:07.660 align:middle line:84% and so the direction of illumination 00:04:07.660 --> 00:04:10.043 align:middle line:84% will be fixed in some particular direction. 00:04:10.043 --> 00:04:11.460 align:middle line:84% But the orientation of the surface 00:04:11.460 --> 00:04:13.620 align:middle line:84% will vary because an object is curved. 00:04:13.620 --> 00:04:16.154 align:middle line:84% And so for a fixed lighting direction, 00:04:16.154 --> 00:04:17.779 align:middle line:84% the amount of reflected light will then 00:04:17.779 --> 00:04:20.459 align:middle line:84% vary with the surface orientation. 00:04:20.459 --> 00:04:22.940 align:middle line:84% And so it follows from that that if you 00:04:22.940 --> 00:04:25.520 align:middle line:84% knew the direction of illumination, 00:04:25.520 --> 00:04:28.900 align:middle line:84% and if you also knew that the intensity changes in the image 00:04:28.900 --> 00:04:33.460 align:middle line:84% were only due to shading, then you could infer shape. 00:04:33.460 --> 00:04:36.820 align:middle line:84% And so there are a bunch of classic demonstrations 00:04:36.820 --> 00:04:40.500 align:middle line:84% that people do seem to do this under many conditions. 00:04:40.500 --> 00:04:45.220 align:middle line:84% So this is a classic stimulus and illusion, if you will, 00:04:45.220 --> 00:04:49.040 align:middle line:84% where the physical stimulus is these circles. 00:04:49.040 --> 00:04:51.500 align:middle line:84% And inside each circle, there's a luminance gradient. 00:04:51.500 --> 00:04:54.500 align:middle line:84% And it just goes from light to dark or from dark to light. 00:04:54.500 --> 00:04:58.020 align:middle line:84% And so when you look at this, most people 00:04:58.020 --> 00:05:04.100 align:middle line:84% will see a set of bumps and a set of craters. 00:05:04.100 --> 00:05:05.420 align:middle line:90% OK. 00:05:05.420 --> 00:05:07.700 align:middle line:84% So does anybody want to hazard a guess 00:05:07.700 --> 00:05:10.420 align:middle line:84% as to why some of the circles look like bumps and others 00:05:10.420 --> 00:05:13.420 align:middle line:90% like craters? 00:05:13.420 --> 00:05:14.420 align:middle line:90% Yeah. 00:05:14.420 --> 00:05:16.420 align:middle line:84% AUDIENCE: Well, because you expect 00:05:16.420 --> 00:05:18.520 align:middle line:84% that the light is coming from above, 00:05:18.520 --> 00:05:23.260 align:middle line:84% so it looks like it would be illuminating [INAUDIBLE] 00:05:23.260 --> 00:05:24.080 align:middle line:90% from above. 00:05:24.080 --> 00:05:25.540 align:middle line:84% Then, it makes sense that there'd 00:05:25.540 --> 00:05:28.665 align:middle line:84% be lightness on top of that, shading on the bottom. 00:05:28.665 --> 00:05:29.540 align:middle line:90% JOSH MCDERMOTT: Yeah. 00:05:29.540 --> 00:05:30.728 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:05:30.728 --> 00:05:32.520 align:middle line:84% JOSH MCDERMOTT: Yeah, that's exactly right. 00:05:32.520 --> 00:05:37.500 align:middle line:84% So the visual system seems to have a prior that 00:05:37.500 --> 00:05:39.480 align:middle line:90% favors illumination from above. 00:05:39.480 --> 00:05:41.220 align:middle line:84% So we very commonly-- by default, 00:05:41.220 --> 00:05:43.540 align:middle line:84% we'll assume that illumination comes from above. 00:05:43.540 --> 00:05:48.100 align:middle line:84% And so if the illumination was coming from below, 00:05:48.100 --> 00:05:51.140 align:middle line:84% then the inferred shape would be the reverse of what it is, 00:05:51.140 --> 00:05:51.640 align:middle line:90% right? 00:05:51.640 --> 00:05:54.182 align:middle line:84% So the things that are bumps would be craters and vice versa. 00:05:54.182 --> 00:05:57.095 align:middle line:90% 00:05:57.095 --> 00:05:59.640 align:middle line:84% So shape from shading is important in art. 00:05:59.640 --> 00:06:02.660 align:middle line:84% So bas-relief is a style of sculpture 00:06:02.660 --> 00:06:05.140 align:middle line:84% that relies exclusively on shape from shading. 00:06:05.140 --> 00:06:09.980 align:middle line:84% So there's some material here, and somebody carves some 3D 00:06:09.980 --> 00:06:13.260 align:middle line:84% structure into it, but then, all of the luminance variation just 00:06:13.260 --> 00:06:14.443 align:middle line:90% comes purely from shape. 00:06:14.443 --> 00:06:16.860 align:middle line:84% So it's illuminated from a particular direction, and then, 00:06:16.860 --> 00:06:19.700 align:middle line:84% you're able to see the 3D structure of the shape from 00:06:19.700 --> 00:06:20.963 align:middle line:90% shading. 00:06:20.963 --> 00:06:22.380 align:middle line:84% You can also see evidence of shape 00:06:22.380 --> 00:06:25.980 align:middle line:84% from shading in lots of real-world photographs. 00:06:25.980 --> 00:06:28.780 align:middle line:84% So this is a photograph of a crater 00:06:28.780 --> 00:06:30.400 align:middle line:90% either on the moon or Mars. 00:06:30.400 --> 00:06:32.140 align:middle line:90% I forget which. 00:06:32.140 --> 00:06:35.340 align:middle line:84% But it doesn't really look like a crater here, right? 00:06:35.340 --> 00:06:39.040 align:middle line:84% So the prior favoring light from above is again at work. 00:06:39.040 --> 00:06:42.660 align:middle line:90% So this is the crater. 00:06:42.660 --> 00:06:44.390 align:middle line:84% So it's just flipped upside down here. 00:06:44.390 --> 00:06:46.140 align:middle line:84% So there's lots of examples of photographs 00:06:46.140 --> 00:06:49.515 align:middle line:84% of things where if they're taken from an orientation where 00:06:49.515 --> 00:06:51.390 align:middle line:84% the illumination is coming from the direction 00:06:51.390 --> 00:06:53.710 align:middle line:84% that you don't expect, they look funny. 00:06:53.710 --> 00:06:56.022 align:middle line:84% This is one that I just saw the other day that's 00:06:56.022 --> 00:06:56.730 align:middle line:90% kind of striking. 00:06:56.730 --> 00:06:59.847 align:middle line:84% So this is a picture of sand dunes. 00:06:59.847 --> 00:07:01.930 align:middle line:84% But it really doesn't look like sand dunes, right? 00:07:01.930 --> 00:07:05.270 align:middle line:84% It looks like a whole bunch of little craters in the surface. 00:07:05.270 --> 00:07:09.190 align:middle line:84% So here's the other orientation, and you can see the correct 3D 00:07:09.190 --> 00:07:12.070 align:middle line:90% structure. 00:07:12.070 --> 00:07:14.790 align:middle line:84% This one-- this is a really pretty awesome demonstration 00:07:14.790 --> 00:07:15.650 align:middle line:90% of the same thing. 00:07:15.650 --> 00:07:24.290 align:middle line:84% So this is a physical thing that was actually engineered. 00:07:24.290 --> 00:07:27.550 align:middle line:84% So there's some 3D shapes that are embossed into this thing. 00:07:27.550 --> 00:07:29.650 align:middle line:84% And then, it's lit from a particular direction. 00:07:29.650 --> 00:07:32.790 align:middle line:84% But it's on this table that can rotate, 00:07:32.790 --> 00:07:35.710 align:middle line:84% and so when you look at it now, it kind of 00:07:35.710 --> 00:07:41.870 align:middle line:84% looks like this is sticking out, and this is sticking out. 00:07:41.870 --> 00:07:46.990 align:middle line:90% But whoa. 00:07:46.990 --> 00:07:48.550 align:middle line:90% Now it flips, right? 00:07:48.550 --> 00:07:51.270 align:middle line:84% OK, it's going to get even cooler. 00:07:51.270 --> 00:07:55.070 align:middle line:84% So now, they're going to pour some liquid 00:07:55.070 --> 00:08:00.450 align:middle line:84% so you can verify which parts are actually the valleys. 00:08:00.450 --> 00:08:01.970 align:middle line:90% OK, watch closely. 00:08:01.970 --> 00:08:12.110 align:middle line:90% 00:08:12.110 --> 00:08:16.470 align:middle line:84% Yeah, so you know that the places where the liquid is 00:08:16.470 --> 00:08:19.090 align:middle line:84% present are kind of indented in the surface, 00:08:19.090 --> 00:08:22.670 align:middle line:84% but your priors on the direction of the illumination 00:08:22.670 --> 00:08:27.190 align:middle line:84% are causing you to misperceive the shape from shading. 00:08:27.190 --> 00:08:29.630 align:middle line:84% So again, a great example of how perception 00:08:29.630 --> 00:08:33.590 align:middle line:84% is kind of encapsulated and sometimes cognitively 00:08:33.590 --> 00:08:34.490 align:middle line:90% impenetrable. 00:08:34.490 --> 00:08:37.510 align:middle line:90% 00:08:37.510 --> 00:08:39.090 align:middle line:84% OK, so that's shape from shading. 00:08:39.090 --> 00:08:43.350 align:middle line:84% So again, key principles of shape from shading, 00:08:43.350 --> 00:08:46.750 align:middle line:84% it works for Lambertian surfaces. 00:08:46.750 --> 00:08:48.950 align:middle line:84% Really, the kind of most straightforward way 00:08:48.950 --> 00:08:52.910 align:middle line:84% to infer shape from shading is to know or assume 00:08:52.910 --> 00:08:54.210 align:middle line:90% a direction of illumination. 00:08:54.210 --> 00:08:56.810 align:middle line:84% Sometimes we assume the wrong direction of illumination, 00:08:56.810 --> 00:08:59.590 align:middle line:84% so you get the shape right, shape wrong. 00:08:59.590 --> 00:09:01.870 align:middle line:84% And critically, you have to also assume 00:09:01.870 --> 00:09:05.070 align:middle line:84% that the intensity variation is due to shape 00:09:05.070 --> 00:09:08.330 align:middle line:90% rather than due to, say, paint. 00:09:08.330 --> 00:09:09.830 align:middle line:90% So in these actual-- 00:09:09.830 --> 00:09:11.070 align:middle line:84% this is actually something you could print out 00:09:11.070 --> 00:09:11.850 align:middle line:90% on a piece of paper. 00:09:11.850 --> 00:09:14.267 align:middle line:84% And so the intensity variation here would be due to paint, 00:09:14.267 --> 00:09:16.670 align:middle line:90% and so you misperceive things. 00:09:16.670 --> 00:09:19.110 align:middle line:84% Now, in the real world, things are actually much more 00:09:19.110 --> 00:09:21.510 align:middle line:84% complicated, because shapes often 00:09:21.510 --> 00:09:23.250 align:middle line:84% do have reflectance variation on it, 00:09:23.250 --> 00:09:24.790 align:middle line:84% and people are actually pretty good. 00:09:24.790 --> 00:09:27.147 align:middle line:84% If you take an object that has reflectance variation, 00:09:27.147 --> 00:09:29.730 align:middle line:84% you're pretty good at actually correctly estimating the shape. 00:09:29.730 --> 00:09:31.647 align:middle line:84% So your visual system has this amazing ability 00:09:31.647 --> 00:09:34.070 align:middle line:84% to actually kind of separately infer 00:09:34.070 --> 00:09:36.350 align:middle line:84% the contributions due to shading and the contribution 00:09:36.350 --> 00:09:37.510 align:middle line:90% due to reflectance. 00:09:37.510 --> 00:09:39.710 align:middle line:84% And that's kind of a little bit beyond the scope of what we're 00:09:39.710 --> 00:09:41.377 align:middle line:84% talking about here and not terribly well 00:09:41.377 --> 00:09:44.750 align:middle line:90% understood but remarkable. 00:09:44.750 --> 00:09:51.720 align:middle line:84% Another very powerful cue to depth is shadows. 00:09:51.720 --> 00:09:56.780 align:middle line:84% So this is just a display that has a few shapes, 00:09:56.780 --> 00:09:59.780 align:middle line:84% and you can see that some are in front of the others. 00:09:59.780 --> 00:10:02.920 align:middle line:84% And you can tell that this occludes this, 00:10:02.920 --> 00:10:04.320 align:middle line:90% and this occludes this. 00:10:04.320 --> 00:10:06.880 align:middle line:84% So there are these occlusion cues present here. 00:10:06.880 --> 00:10:10.000 align:middle line:84% But then, when we add shadows to the display, 00:10:10.000 --> 00:10:13.280 align:middle line:84% these are typically called drop shadows, OK? 00:10:13.280 --> 00:10:15.160 align:middle line:84% You now actually see the objects as being 00:10:15.160 --> 00:10:19.480 align:middle line:90% separated in depth, right? 00:10:19.480 --> 00:10:24.120 align:middle line:84% So shadows are a very powerful cue to depth. 00:10:24.120 --> 00:10:26.760 align:middle line:84% The visual system-- so typically, in the real world, 00:10:26.760 --> 00:10:31.580 align:middle line:84% they are caused by one object occluding the illumination, 00:10:31.580 --> 00:10:33.020 align:middle line:90% so blocking the illumination. 00:10:33.020 --> 00:10:36.897 align:middle line:84% And so the region of shadow is typically dark in the image, OK? 00:10:36.897 --> 00:10:38.480 align:middle line:84% And so the visual system seems to have 00:10:38.480 --> 00:10:40.340 align:middle line:90% internalized that regularity. 00:10:40.340 --> 00:10:44.520 align:middle line:84% Because when you artificially make the shadows lighter rather 00:10:44.520 --> 00:10:48.520 align:middle line:84% than darker, and you can do this in graphics programs, 00:10:48.520 --> 00:10:50.160 align:middle line:84% then you don't get the sense of depth. 00:10:50.160 --> 00:10:53.060 align:middle line:84% And what does this look like to people actually? 00:10:53.060 --> 00:10:56.740 align:middle line:90% 00:10:56.740 --> 00:10:58.240 align:middle line:84% AUDIENCE: It looks like [INAUDIBLE]. 00:10:58.240 --> 00:10:58.820 align:middle line:90% JOSH MCDERMOTT: What's that? 00:10:58.820 --> 00:11:01.380 align:middle line:84% AUDIENCE: It looks like the inverted image, the casting 00:11:01.380 --> 00:11:02.160 align:middle line:90% white shadows. 00:11:02.160 --> 00:11:04.040 align:middle line:84% JOSH MCDERMOTT: Yeah, or spray paint kind of, right? 00:11:04.040 --> 00:11:05.920 align:middle line:84% To me, it looks like somebody took a can of spray paint 00:11:05.920 --> 00:11:06.860 align:middle line:90% and sprayed it. 00:11:06.860 --> 00:11:11.280 align:middle line:84% So again, it really doesn't have the same effect 00:11:11.280 --> 00:11:14.047 align:middle line:84% of just a shadow-- doesn't look like one. 00:11:14.047 --> 00:11:15.880 align:middle line:84% And if you just invert the whole image then, 00:11:15.880 --> 00:11:18.520 align:middle line:84% it also doesn't really produce the sense of depth. 00:11:18.520 --> 00:11:20.740 align:middle line:90% So shadows have to be dark. 00:11:20.740 --> 00:11:25.560 align:middle line:90% 00:11:25.560 --> 00:11:28.080 align:middle line:84% In computer graphics programs, you 00:11:28.080 --> 00:11:32.388 align:middle line:84% can play around with both shape from shading and drop shadows. 00:11:32.388 --> 00:11:34.680 align:middle line:84% And these things, again, they're happening all the time 00:11:34.680 --> 00:11:36.720 align:middle line:84% in the world, and you typically are not-- you just don't even 00:11:36.720 --> 00:11:37.512 align:middle line:90% really notice them. 00:11:37.512 --> 00:11:40.360 align:middle line:84% So this is just a picture of eggs. 00:11:40.360 --> 00:11:43.730 align:middle line:84% And in this case, it's pretty obvious that the eggs are 00:11:43.730 --> 00:11:48.530 align:middle line:84% sitting on a table, because you get these kind of shadows 00:11:48.530 --> 00:11:52.450 align:middle line:84% that suggest that the eggs are sitting on the table 00:11:52.450 --> 00:11:53.408 align:middle line:90% and blocking the light. 00:11:53.408 --> 00:11:55.075 align:middle line:84% If you remove the shadows, the eggs kind 00:11:55.075 --> 00:11:57.510 align:middle line:84% look like they're floating in space in front of the table, 00:11:57.510 --> 00:12:00.010 align:middle line:90% right? 00:12:00.010 --> 00:12:01.430 align:middle line:84% But if you get rid of the shading, 00:12:01.430 --> 00:12:03.390 align:middle line:84% so you just color all the eggs white, 00:12:03.390 --> 00:12:05.290 align:middle line:90% now you lose the 3D shape. 00:12:05.290 --> 00:12:07.370 align:middle line:84% So normally, you look at these eggs 00:12:07.370 --> 00:12:08.910 align:middle line:84% and they all just look white, right? 00:12:08.910 --> 00:12:10.490 align:middle line:84% So it's like your visual system is 00:12:10.490 --> 00:12:13.650 align:middle line:84% kind of separating out the contribution of the shading 00:12:13.650 --> 00:12:15.070 align:middle line:90% from that of the reflectance. 00:12:15.070 --> 00:12:17.790 align:middle line:84% And remember how when we looked at the Retinex algorithm, 00:12:17.790 --> 00:12:20.610 align:middle line:84% when we ran the Retinex algorithm on an actual image, 00:12:20.610 --> 00:12:24.130 align:middle line:84% Retinex would make the mistake of actually interpreting some 00:12:24.130 --> 00:12:25.610 align:middle line:84% of the shading that's due to shape 00:12:25.610 --> 00:12:27.210 align:middle line:90% as being due to illumination. 00:12:27.210 --> 00:12:31.650 align:middle line:84% Because Retinex assumes that all of the gradual variation 00:12:31.650 --> 00:12:35.530 align:middle line:84% in luminance is due to illumination, 00:12:35.530 --> 00:12:38.650 align:middle line:84% which is not a correct model of the world. 00:12:38.650 --> 00:12:42.690 align:middle line:84% So there's lots of luminance variation due to shading. 00:12:42.690 --> 00:12:46.930 align:middle line:84% So the visual system is really sensitive to the relationships 00:12:46.930 --> 00:12:50.490 align:middle line:84% between the positions of shadows and the depth 00:12:50.490 --> 00:12:53.782 align:middle line:84% relationships of objects to the surfaces on which they sit. 00:12:53.782 --> 00:12:56.490 align:middle line:84% So the drop shadows kind of have to align correctly for an object 00:12:56.490 --> 00:12:58.130 align:middle line:90% to sit on a surface. 00:12:58.130 --> 00:12:59.990 align:middle line:84% So you remember, in the very first class, 00:12:59.990 --> 00:13:01.648 align:middle line:84% we showed this demonstration of a ball 00:13:01.648 --> 00:13:03.190 align:middle line:84% that kind of rolls across the screen. 00:13:03.190 --> 00:13:05.107 align:middle line:84% And depending on the trajectory of the shadow, 00:13:05.107 --> 00:13:07.490 align:middle line:84% you see these very different 3D trajectories. 00:13:07.490 --> 00:13:09.190 align:middle line:84% And there's lots of these really cool-- 00:13:09.190 --> 00:13:12.650 align:middle line:84% I kind of collect these images, where just 00:13:12.650 --> 00:13:16.850 align:middle line:84% by accident, the shadow's kind of in the wrong place, at then 00:13:16.850 --> 00:13:20.170 align:middle line:84% it causes things to look like they're levitating. 00:13:20.170 --> 00:13:22.130 align:middle line:84% So this is a situation where I guess 00:13:22.130 --> 00:13:24.735 align:middle line:84% there were a lot of flagpoles on this particular beach, 00:13:24.735 --> 00:13:27.110 align:middle line:84% and there's one that just happens to be casting a shadow. 00:13:27.110 --> 00:13:31.170 align:middle line:84% The person's standing on some platform on the sand, 00:13:31.170 --> 00:13:33.930 align:middle line:84% and the alignment of the shadow and the surface 00:13:33.930 --> 00:13:37.130 align:middle line:84% are such-- are good enough that the person looks 00:13:37.130 --> 00:13:40.610 align:middle line:90% like they're kind of floating. 00:13:40.610 --> 00:13:44.862 align:middle line:84% Here's a situation where there's, I guess, 00:13:44.862 --> 00:13:46.570 align:middle line:84% just some dirt on the ground that kind of 00:13:46.570 --> 00:13:48.130 align:middle line:84% happens to be in approximately the right place 00:13:48.130 --> 00:13:50.690 align:middle line:84% and approximately the right color to plausibly be a shadow 00:13:50.690 --> 00:13:54.970 align:middle line:84% and so causes the trash can to float. 00:13:54.970 --> 00:13:58.570 align:middle line:84% This is a cat with supernatural powers. 00:13:58.570 --> 00:14:01.990 align:middle line:84% Again, same kind of thing, just dark patch in the right-- 00:14:01.990 --> 00:14:04.090 align:middle line:90% in the right place. 00:14:04.090 --> 00:14:06.450 align:middle line:84% You can also get some pretty funny instances 00:14:06.450 --> 00:14:12.330 align:middle line:84% of this involving water, because the shadows will 00:14:12.330 --> 00:14:17.770 align:middle line:84% be cast on the bottom of the ocean in this particular case 00:14:17.770 --> 00:14:23.770 align:middle line:84% and can cause the boat to seem like it's floating. 00:14:23.770 --> 00:14:26.050 align:middle line:84% This is another one that I came across, 00:14:26.050 --> 00:14:30.970 align:middle line:84% where the particular angle of the sun 00:14:30.970 --> 00:14:33.170 align:middle line:84% causes the shadow to be in a place 00:14:33.170 --> 00:14:37.877 align:middle line:84% where you can see the train is floating. 00:14:37.877 --> 00:14:39.460 align:middle line:84% So you start looking for these things, 00:14:39.460 --> 00:14:42.540 align:middle line:84% and you see them all over the place. 00:14:42.540 --> 00:14:47.620 align:middle line:84% So shadows are caused by the geometric relationship 00:14:47.620 --> 00:14:51.870 align:middle line:84% between an object and a light source. 00:14:51.870 --> 00:14:55.800 align:middle line:84% And so when you're using the shadow to infer depth, 00:14:55.800 --> 00:14:59.707 align:middle line:84% you're kind of implicitly taking advantage of that relationship. 00:14:59.707 --> 00:15:01.540 align:middle line:84% So the visual system has, like, internalized 00:15:01.540 --> 00:15:04.740 align:middle line:84% something about the relationship between light sources 00:15:04.740 --> 00:15:08.340 align:middle line:90% and objects and shadows. 00:15:08.340 --> 00:15:10.380 align:middle line:84% So you might imagine that what happens 00:15:10.380 --> 00:15:13.337 align:middle line:84% is you actually are building or you're inferring, like, 00:15:13.337 --> 00:15:15.420 align:middle line:84% an entire scene layout in your head, where there's 00:15:15.420 --> 00:15:18.500 align:middle line:84% a light source in a particular place and shadows 00:15:18.500 --> 00:15:20.080 align:middle line:84% that are cast relative to objects. 00:15:20.080 --> 00:15:23.180 align:middle line:84% And that doesn't actually seem to be what is happening. 00:15:23.180 --> 00:15:27.460 align:middle line:84% So this is kind of an interesting demonstration, where 00:15:27.460 --> 00:15:31.900 align:middle line:84% you get pretty good depth from the shadows in the top two 00:15:31.900 --> 00:15:34.580 align:middle line:90% circles of circles. 00:15:34.580 --> 00:15:37.300 align:middle line:84% Logically, that display doesn't really 00:15:37.300 --> 00:15:40.380 align:middle line:84% make sense, because you can tell from the direction 00:15:40.380 --> 00:15:43.440 align:middle line:84% of the shadows relative to the objects that in this case, 00:15:43.440 --> 00:15:45.680 align:middle line:84% the light is coming from the upper left. 00:15:45.680 --> 00:15:47.420 align:middle line:84% In this case, the light must be coming 00:15:47.420 --> 00:15:50.360 align:middle line:84% from the bottom left for the shadows to be where they are. 00:15:50.360 --> 00:15:53.420 align:middle line:84% And so you couldn't really actually generate an image 00:15:53.420 --> 00:15:56.900 align:middle line:84% like this without some really contrived setup 00:15:56.900 --> 00:16:02.180 align:middle line:84% with two sources of light that were only 00:16:02.180 --> 00:16:04.240 align:middle line:90% cast on part of the scene. 00:16:04.240 --> 00:16:07.020 align:middle line:84% But it doesn't seem to bother you. 00:16:07.020 --> 00:16:09.220 align:middle line:84% On the other hand, down here, where 00:16:09.220 --> 00:16:10.980 align:middle line:84% the positioning of the shadows has kind of 00:16:10.980 --> 00:16:14.020 align:middle line:84% been randomized locally, that really 00:16:14.020 --> 00:16:17.380 align:middle line:84% seems to kill the sense of depth for the most part. 00:16:17.380 --> 00:16:21.580 align:middle line:84% So there's some degree of local consistency 00:16:21.580 --> 00:16:24.040 align:middle line:84% that is really required for this to happen, 00:16:24.040 --> 00:16:25.540 align:middle line:84% but it doesn't seem like you're kind 00:16:25.540 --> 00:16:28.340 align:middle line:90% of modeling the global scene. 00:16:28.340 --> 00:16:31.900 align:middle line:84% And this is like-- we've seen some other hints of this 00:16:31.900 --> 00:16:32.920 align:middle line:90% so far in the class. 00:16:32.920 --> 00:16:35.570 align:middle line:84% Remember when we were talking about lightness illusions, 00:16:35.570 --> 00:16:38.310 align:middle line:84% we saw evidence that people weren't really modeling 00:16:38.310 --> 00:16:40.630 align:middle line:84% a full kind of global version of the scene? 00:16:40.630 --> 00:16:43.210 align:middle line:84% There's more local, kind of mid-level stuff going on. 00:16:43.210 --> 00:16:46.190 align:middle line:90% 00:16:46.190 --> 00:16:47.690 align:middle line:90% Any questions about shadows? 00:16:47.690 --> 00:16:52.950 align:middle line:90% 00:16:52.950 --> 00:16:56.510 align:middle line:84% So another regularity that influences depth 00:16:56.510 --> 00:17:01.390 align:middle line:84% is the geometry of the geometrical relationships 00:17:01.390 --> 00:17:03.750 align:middle line:84% between where objects are in the world 00:17:03.750 --> 00:17:06.050 align:middle line:84% and where they project on the retina. 00:17:06.050 --> 00:17:09.958 align:middle line:84% And so very often, we're standing on a ground plane, 00:17:09.958 --> 00:17:11.750 align:middle line:84% and so things that are further away from us 00:17:11.750 --> 00:17:13.891 align:middle line:90% tend to be on the ground plane. 00:17:13.891 --> 00:17:15.349 align:middle line:84% And so things that are further away 00:17:15.349 --> 00:17:17.470 align:middle line:84% tend to be higher in the visual field. 00:17:17.470 --> 00:17:19.369 align:middle line:84% And so you can get these effects like this. 00:17:19.369 --> 00:17:22.890 align:middle line:84% And also, as things move are further away, 00:17:22.890 --> 00:17:24.650 align:middle line:84% they also tend to project smaller images. 00:17:24.650 --> 00:17:27.550 align:middle line:84% And so you can get these effects. 00:17:27.550 --> 00:17:30.670 align:middle line:84% So the one on the left gives like a pretty compelling sense 00:17:30.670 --> 00:17:32.670 align:middle line:84% that the surface is receding in depth, 00:17:32.670 --> 00:17:35.710 align:middle line:84% because the objects get smaller as they go up 00:17:35.710 --> 00:17:36.870 align:middle line:90% in the visual field. 00:17:36.870 --> 00:17:39.370 align:middle line:84% That's more or less what would happen in a typical situation 00:17:39.370 --> 00:17:40.550 align:middle line:90% in the world. 00:17:40.550 --> 00:17:44.990 align:middle line:84% The one on the right has much-- has a much weaker effect, 00:17:44.990 --> 00:17:47.870 align:middle line:84% because it violates that geometric regularity that 00:17:47.870 --> 00:17:51.470 align:middle line:84% is typical of what you would observe in the world. 00:17:51.470 --> 00:17:54.150 align:middle line:84% So again, the common theme here is the visual system 00:17:54.150 --> 00:17:58.550 align:middle line:84% has internalized the regularities of the world 00:17:58.550 --> 00:18:01.950 align:middle line:84% and uses those to solve this ill-posed problem of depth 00:18:01.950 --> 00:18:03.270 align:middle line:90% perception. 00:18:03.270 --> 00:18:07.810 align:middle line:84% So this is an example-- it's kind of an example of a texture 00:18:07.810 --> 00:18:09.310 align:middle line:84% gradient, in the sense that you have 00:18:09.310 --> 00:18:11.430 align:middle line:90% all these repeated elements. 00:18:11.430 --> 00:18:14.170 align:middle line:84% And the texture changes in some systematic way 00:18:14.170 --> 00:18:16.790 align:middle line:84% that's kind of consistent with something receding in depth. 00:18:16.790 --> 00:18:20.110 align:middle line:84% And those are actually super common. 00:18:20.110 --> 00:18:23.590 align:middle line:84% And this is a case where an artist decided 00:18:23.590 --> 00:18:25.130 align:middle line:90% to trick the visual system. 00:18:25.130 --> 00:18:27.590 align:middle line:84% So this is a funny pattern that got painted 00:18:27.590 --> 00:18:31.110 align:middle line:90% on a perfectly flat floor. 00:18:31.110 --> 00:18:35.650 align:middle line:84% But instead of interpreting this as what it is, 00:18:35.650 --> 00:18:42.230 align:middle line:84% which is a flat floor that's got a weird, warped texture on it, 00:18:42.230 --> 00:18:46.230 align:middle line:84% you infer a situation where the depth is 00:18:46.230 --> 00:18:49.550 align:middle line:84% kind of-- where the shape of the floor is kind of curved, 00:18:49.550 --> 00:18:52.013 align:middle line:84% and the texture is uniform and just pasted 00:18:52.013 --> 00:18:52.930 align:middle line:90% on the curved surface. 00:18:52.930 --> 00:18:54.680 align:middle line:84% So, of course, the inference is ill posed. 00:18:54.680 --> 00:18:57.510 align:middle line:84% And so you've got to have priors to constrain the inference. 00:18:57.510 --> 00:18:59.760 align:middle line:84% In this case, the prior's that the texture is uniform, 00:18:59.760 --> 00:19:01.190 align:middle line:84% because textures in the world tend 00:19:01.190 --> 00:19:05.453 align:middle line:84% to be uniform rather than having the weird kind of modeled shape. 00:19:05.453 --> 00:19:06.870 align:middle line:84% Here's another pretty cool example 00:19:06.870 --> 00:19:08.050 align:middle line:90% of the same kind of thing. 00:19:08.050 --> 00:19:14.125 align:middle line:90% 00:19:14.125 --> 00:19:16.750 align:middle line:84% All right, so texture gradients are another really powerful cue 00:19:16.750 --> 00:19:18.430 align:middle line:90% to depth. 00:19:18.430 --> 00:19:22.390 align:middle line:84% OK, another very important thing that 00:19:22.390 --> 00:19:25.930 align:middle line:84% is related to depth perception is what's called Emmert's Law. 00:19:25.930 --> 00:19:30.240 align:middle line:84% So Emmert's Law describes the relationship 00:19:30.240 --> 00:19:34.520 align:middle line:84% between the size that we perceive things to be, 00:19:34.520 --> 00:19:38.040 align:middle line:84% the distance that we perceive them to be away from us, 00:19:38.040 --> 00:19:42.370 align:middle line:84% and the visual angle that they subtend. 00:19:42.370 --> 00:19:46.240 align:middle line:84% So the idea is shown here, which is that you can have 00:19:46.240 --> 00:19:48.340 align:middle line:90% two objects of different sizes. 00:19:48.340 --> 00:19:51.080 align:middle line:84% And if the big one is further away, 00:19:51.080 --> 00:19:53.000 align:middle line:84% it will subtend the same visual angle 00:19:53.000 --> 00:19:55.200 align:middle line:90% as a small one that's closer. 00:19:55.200 --> 00:20:00.600 align:middle line:84% So there's this relationship between visual angle, 00:20:00.600 --> 00:20:02.660 align:middle line:84% inferred distance, and inferred size, 00:20:02.660 --> 00:20:04.120 align:middle line:84% because in the actual world, there 00:20:04.120 --> 00:20:07.120 align:middle line:84% would be a relationship between visual angle, distance, 00:20:07.120 --> 00:20:08.560 align:middle line:90% and size. 00:20:08.560 --> 00:20:12.820 align:middle line:84% And so there's lots of these instances where either you 00:20:12.820 --> 00:20:16.380 align:middle line:84% know how big something is, because it's a familiar object, 00:20:16.380 --> 00:20:19.920 align:middle line:84% and so you use that to infer how far away it is, 00:20:19.920 --> 00:20:22.260 align:middle line:84% or you know how far away something is, 00:20:22.260 --> 00:20:23.850 align:middle line:84% and you use that to infer the size. 00:20:23.850 --> 00:20:26.100 align:middle line:84% And so we're going to do an experiment to verify this. 00:20:26.100 --> 00:20:28.560 align:middle line:84% And so this experiment is going to involve staring at one 00:20:28.560 --> 00:20:30.400 align:middle line:90% of the lights in the ceiling. 00:20:30.400 --> 00:20:34.220 align:middle line:84% So you're going to do this for, I think, about 30 seconds. 00:20:34.220 --> 00:20:37.740 align:middle line:84% So get kind of close to a light and look up at it. 00:20:37.740 --> 00:20:39.840 align:middle line:84% And the purpose of doing this is we're 00:20:39.840 --> 00:20:43.320 align:middle line:84% going to burn a temporary afterimage into your eyes. 00:20:43.320 --> 00:20:46.680 align:middle line:84% And the reason that we're doing that 00:20:46.680 --> 00:20:52.140 align:middle line:84% is that when you generate an afterimage in the eye, right, 00:20:52.140 --> 00:20:55.020 align:middle line:84% that's covering some fixed portion of your retina. 00:20:55.020 --> 00:20:58.120 align:middle line:84% So it corresponds to a particular kind of visual angle 00:20:58.120 --> 00:21:00.180 align:middle line:84% that would normally project onto the retina. 00:21:00.180 --> 00:21:03.280 align:middle line:84% So the idea is that after you stare at this thing, 00:21:03.280 --> 00:21:04.780 align:middle line:84% you're going to get this afterimage. 00:21:04.780 --> 00:21:08.440 align:middle line:84% It's going to have a fixed extent on your retina. 00:21:08.440 --> 00:21:10.300 align:middle line:84% So now what we're going to do-- all right, 00:21:10.300 --> 00:21:12.133 align:middle line:84% hopefully, you got a pretty good afterimage. 00:21:12.133 --> 00:21:15.880 align:middle line:84% So now, I want you to look at your hand, OK? 00:21:15.880 --> 00:21:16.380 align:middle line:90% All right. 00:21:16.380 --> 00:21:18.220 align:middle line:84% So that's going to be some particular size. 00:21:18.220 --> 00:21:23.800 align:middle line:84% Now, take your hand down and look at the wall, OK? 00:21:23.800 --> 00:21:25.460 align:middle line:84% And the thing should look a lot bigger. 00:21:25.460 --> 00:21:27.918 align:middle line:84% You might have to keep blinking to get the afterimage image 00:21:27.918 --> 00:21:29.400 align:middle line:90% to restore itself. 00:21:29.400 --> 00:21:31.120 align:middle line:84% All right, so what we just did is 00:21:31.120 --> 00:21:34.800 align:middle line:84% we generated a stimulus of a fixed extent on the retina. 00:21:34.800 --> 00:21:36.460 align:middle line:90% But you can cause it. 00:21:36.460 --> 00:21:38.500 align:middle line:84% So now, I'm like looking at it on the back wall, 00:21:38.500 --> 00:21:39.250 align:middle line:90% and it's enormous. 00:21:39.250 --> 00:21:41.627 align:middle line:84% So you can cause it to look different sizes 00:21:41.627 --> 00:21:43.460 align:middle line:84% by looking at things at different distances. 00:21:43.460 --> 00:21:47.200 align:middle line:84% And so it seems to be the case that the visual system assumes 00:21:47.200 --> 00:21:49.960 align:middle line:84% that that retinal stimulation is due to something 00:21:49.960 --> 00:21:52.460 align:middle line:84% that happened at the surface that you're looking at. 00:21:52.460 --> 00:21:56.195 align:middle line:84% And so you look at something that's close, 00:21:56.195 --> 00:21:57.820 align:middle line:84% and you assume that the thing is small. 00:21:57.820 --> 00:21:59.695 align:middle line:84% If you look at something that's further away, 00:21:59.695 --> 00:22:00.780 align:middle line:90% you infer that it's large. 00:22:00.780 --> 00:22:01.280 align:middle line:90% Yeah. 00:22:01.280 --> 00:22:04.560 align:middle line:84% AUDIENCE: Why does blinking cause it [INAUDIBLE]? 00:22:04.560 --> 00:22:12.000 align:middle line:84% JOSH MCDERMOTT: Oh, it's just-- it's refreshing the adaptation. 00:22:12.000 --> 00:22:13.960 align:middle line:84% Yeah, so you're kind of temporarily bleaching 00:22:13.960 --> 00:22:16.320 align:middle line:84% the photoreceptors, and I think probably 00:22:16.320 --> 00:22:18.000 align:middle line:84% what's happening is that there may 00:22:18.000 --> 00:22:21.760 align:middle line:84% be some downstream adaptation that you then kind of reset 00:22:21.760 --> 00:22:23.360 align:middle line:90% with the blinking. 00:22:23.360 --> 00:22:24.480 align:middle line:90% Yeah. 00:22:24.480 --> 00:22:27.850 align:middle line:84% So you're just making the afterimage visible again. 00:22:27.850 --> 00:22:30.770 align:middle line:84% I don't know the exact mechanism, actually. 00:22:30.770 --> 00:22:35.130 align:middle line:84% OK, so Emmert's Law-- so the relationship 00:22:35.130 --> 00:22:37.950 align:middle line:84% between how big things look and how far away they seem. 00:22:37.950 --> 00:22:41.450 align:middle line:84% So this is-- that's one example of this, 00:22:41.450 --> 00:22:45.010 align:middle line:84% and it's a pretty good party trick. 00:22:45.010 --> 00:22:47.710 align:middle line:84% And you see Emmert's Law in lots of different settings. 00:22:47.710 --> 00:22:50.290 align:middle line:84% So here, this is a situation where 00:22:50.290 --> 00:22:52.510 align:middle line:84% the big balls look a lot closer than the small balls. 00:22:52.510 --> 00:22:56.530 align:middle line:84% So this is a case where people-- the visual system seems 00:22:56.530 --> 00:23:00.170 align:middle line:84% content to assume that the objects are all the same size, 00:23:00.170 --> 00:23:04.010 align:middle line:84% and thus the changes in size are attributed 00:23:04.010 --> 00:23:05.910 align:middle line:90% to differences in distance. 00:23:05.910 --> 00:23:10.250 align:middle line:90% 00:23:10.250 --> 00:23:15.690 align:middle line:84% Here's a situation where you know the relative size 00:23:15.690 --> 00:23:17.450 align:middle line:90% of these body parts. 00:23:17.450 --> 00:23:19.930 align:middle line:84% You know the hands are of a certain size 00:23:19.930 --> 00:23:21.850 align:middle line:90% relative to somebody's face. 00:23:21.850 --> 00:23:24.930 align:middle line:84% And so the fact that the hand is bigger in the one on the left 00:23:24.930 --> 00:23:27.290 align:middle line:84% leads you to conclude that it's a lot closer. 00:23:27.290 --> 00:23:29.770 align:middle line:84% So again, hand looks closer, and this all kind of 00:23:29.770 --> 00:23:31.375 align:middle line:90% happens implicitly. 00:23:31.375 --> 00:23:32.750 align:middle line:84% And so again, if you look around, 00:23:32.750 --> 00:23:35.050 align:middle line:84% you can find funny instances where of plays 00:23:35.050 --> 00:23:37.810 align:middle line:90% some tricks on perception. 00:23:37.810 --> 00:23:41.690 align:middle line:84% This is kind of an interesting photo 00:23:41.690 --> 00:23:47.370 align:middle line:84% that I came across, where the girl in the middle kind of looks 00:23:47.370 --> 00:23:49.030 align:middle line:90% like she's floating. 00:23:49.030 --> 00:23:54.943 align:middle line:90% 00:23:54.943 --> 00:23:56.610 align:middle line:84% And so I think the reality is that she's 00:23:56.610 --> 00:23:58.350 align:middle line:84% a lot taller than her brothers, right, 00:23:58.350 --> 00:24:01.017 align:middle line:84% but your visual system seems to assume that these things are all 00:24:01.017 --> 00:24:07.090 align:middle line:84% probably the same size, and thus that the girl has 00:24:07.090 --> 00:24:09.270 align:middle line:84% to be closer than she actually is, 00:24:09.270 --> 00:24:13.310 align:middle line:84% which means she's floating in the air or something like that. 00:24:13.310 --> 00:24:19.090 align:middle line:90% 00:24:19.090 --> 00:24:23.340 align:middle line:84% Here, we've got some really big pigeons, OK? 00:24:23.340 --> 00:24:24.960 align:middle line:84% So this is a kind of a funny photo. 00:24:24.960 --> 00:24:27.840 align:middle line:84% Can anybody tell what's going on here? 00:24:27.840 --> 00:24:28.340 align:middle line:90% Yeah. 00:24:28.340 --> 00:24:29.740 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:24:29.740 --> 00:24:32.760 align:middle line:84% JOSH MCDERMOTT: Yeah, but you don't notice the ledge at first, 00:24:32.760 --> 00:24:33.260 align:middle line:90% right? 00:24:33.260 --> 00:24:35.840 align:middle line:84% So it sort of looks like they're right next to the car. 00:24:35.840 --> 00:24:39.660 align:middle line:84% So if you assume that the cars and the birds 00:24:39.660 --> 00:24:42.412 align:middle line:84% are at the same distance, then they're 00:24:42.412 --> 00:24:44.620 align:middle line:84% about the same size on the right, which means they're 00:24:44.620 --> 00:24:45.912 align:middle line:90% about the same size physically. 00:24:45.912 --> 00:24:48.880 align:middle line:90% So you've got giant pigeons. 00:24:48.880 --> 00:24:49.880 align:middle line:90% All right, Emmert's Law. 00:24:49.880 --> 00:24:52.460 align:middle line:84% Any questions about Emmert's Law? 00:24:52.460 --> 00:24:57.360 align:middle line:84% So in some cases, the size is unambiguous, 00:24:57.360 --> 00:24:59.043 align:middle line:84% and thus, that kind of determines 00:24:59.043 --> 00:24:59.960 align:middle line:90% the apparent distance. 00:24:59.960 --> 00:25:01.920 align:middle line:84% In some cases, the distance is less ambiguous, 00:25:01.920 --> 00:25:04.780 align:middle line:84% and that will determine the size. 00:25:04.780 --> 00:25:06.885 align:middle line:90% Yeah. 00:25:06.885 --> 00:25:10.860 align:middle line:84% AUDIENCE: [INAUDIBLE] there has been no large sign [INAUDIBLE] 00:25:10.860 --> 00:25:15.140 align:middle line:84% it's like why do we perceive the pigeions as large [INAUDIBLE] 00:25:15.140 --> 00:25:17.780 align:middle line:90% and not small cars? 00:25:17.780 --> 00:25:20.547 align:middle line:84% JOSH MCDERMOTT: Yeah, I think it's a good question. 00:25:20.547 --> 00:25:22.880 align:middle line:84% Yeah, I don't know the answer to that, and I'm not sure. 00:25:22.880 --> 00:25:25.580 align:middle line:84% I'm not sure that it's completely known. 00:25:25.580 --> 00:25:28.620 align:middle line:84% And, I mean, you might imagine, well, most of us 00:25:28.620 --> 00:25:30.620 align:middle line:84% have a lot of experience with toy cars, 00:25:30.620 --> 00:25:32.880 align:middle line:84% so you might think that it could be the opposite. 00:25:32.880 --> 00:25:37.060 align:middle line:90% 00:25:37.060 --> 00:25:39.620 align:middle line:90% Yeah. 00:25:39.620 --> 00:25:43.020 align:middle line:84% Yeah, no, I think the absolute size of these things 00:25:43.020 --> 00:25:46.420 align:middle line:84% is-- it's interesting that you anchor with the car rather 00:25:46.420 --> 00:25:47.800 align:middle line:90% than the pigeon. 00:25:47.800 --> 00:25:48.300 align:middle line:90% Yeah. 00:25:48.300 --> 00:25:52.580 align:middle line:90% 00:25:52.580 --> 00:25:55.700 align:middle line:84% OK, another cue to depth is aerial perspective. 00:25:55.700 --> 00:25:58.420 align:middle line:84% So in general, things that are further away 00:25:58.420 --> 00:26:02.080 align:middle line:84% are more blurry, because as light travels through the air, 00:26:02.080 --> 00:26:04.740 align:middle line:84% it gets kind of-- it gets scattered. 00:26:04.740 --> 00:26:07.260 align:middle line:84% And things also tend to look a little bit more bluish. 00:26:07.260 --> 00:26:09.800 align:middle line:84% And so you can see this oftentimes in photographs. 00:26:09.800 --> 00:26:13.500 align:middle line:84% This is a photograph of a beautiful landscape. 00:26:13.500 --> 00:26:15.420 align:middle line:84% And the stuff that's further away 00:26:15.420 --> 00:26:20.300 align:middle line:84% is lower contrast, blurrier, and a little bit bluer. 00:26:20.300 --> 00:26:23.900 align:middle line:84% So again, it's like a regularity of the way 00:26:23.900 --> 00:26:28.340 align:middle line:84% that optics works that we seem to have learned. 00:26:28.340 --> 00:26:32.420 align:middle line:84% Another really important depth cue is linear perspective. 00:26:32.420 --> 00:26:36.940 align:middle line:84% So linear perspective is due to the fact 00:26:36.940 --> 00:26:40.460 align:middle line:84% that lines that are parallel in the world 00:26:40.460 --> 00:26:43.340 align:middle line:84% will generally converge in the image, 00:26:43.340 --> 00:26:45.860 align:middle line:84% unless they lie in a plane that's 00:26:45.860 --> 00:26:47.660 align:middle line:90% parallel to the image plane. 00:26:47.660 --> 00:26:51.180 align:middle line:84% So if you have lines that are in a plane that's parallel 00:26:51.180 --> 00:26:53.960 align:middle line:84% to the image plane, those will remain parallel in the image. 00:26:53.960 --> 00:26:58.300 align:middle line:84% But if they're not in the image, they will converge. 00:26:58.300 --> 00:27:01.260 align:middle line:84% And so you can see in this particular case, 00:27:01.260 --> 00:27:04.040 align:middle line:84% this line and this line are a good example of that, 00:27:04.040 --> 00:27:06.940 align:middle line:90% or that and that. 00:27:06.940 --> 00:27:09.788 align:middle line:84% OK, so the question is, like, now how 00:27:09.788 --> 00:27:12.080 align:middle line:84% do we know that lines are parallel in the world, right? 00:27:12.080 --> 00:27:15.480 align:middle line:84% In principle, these lines might not be parallel in the world, 00:27:15.480 --> 00:27:18.350 align:middle line:84% and that's-- does anybody have an idea? 00:27:18.350 --> 00:27:20.610 align:middle line:84% Why are lines parallel in the world? 00:27:20.610 --> 00:27:34.150 align:middle line:90% 00:27:34.150 --> 00:27:35.930 align:middle line:84% What would cause things to be parallel? 00:27:35.930 --> 00:27:39.322 align:middle line:90% 00:27:39.322 --> 00:27:40.030 align:middle line:90% AUDIENCE: Humans? 00:27:40.030 --> 00:27:41.430 align:middle line:90% JOSH MCDERMOTT: Humans, yeah. 00:27:41.430 --> 00:27:43.010 align:middle line:90% I think that's one possibility. 00:27:43.010 --> 00:27:43.510 align:middle line:90% Yeah. 00:27:43.510 --> 00:27:46.150 align:middle line:90% Maybe also gravity. 00:27:46.150 --> 00:27:50.130 align:middle line:84% But people like to construct rectangles, 00:27:50.130 --> 00:27:54.750 align:middle line:84% so there's a lot of things in human-constructed environments 00:27:54.750 --> 00:27:58.476 align:middle line:90% that tend to be parallel. 00:27:58.476 --> 00:28:06.550 align:middle line:84% And so this is a classic illusion where 00:28:06.550 --> 00:28:09.110 align:middle line:84% depth from both linear perspective 00:28:09.110 --> 00:28:11.610 align:middle line:84% and from texture-- so again, we've got linear perspective, 00:28:11.610 --> 00:28:15.190 align:middle line:84% so these lines kind of are converging, 00:28:15.190 --> 00:28:17.490 align:middle line:84% makes it look like that's a lot further away than this. 00:28:17.490 --> 00:28:19.030 align:middle line:90% There's a texture gradient. 00:28:19.030 --> 00:28:24.270 align:middle line:84% And what's cool about this is that it 00:28:24.270 --> 00:28:26.950 align:middle line:84% looks like there's a really big monster chasing a smaller 00:28:26.950 --> 00:28:27.530 align:middle line:90% monster. 00:28:27.530 --> 00:28:30.510 align:middle line:84% But, in fact, the two monsters are exactly 00:28:30.510 --> 00:28:33.590 align:middle line:90% the same size in the image. 00:28:33.590 --> 00:28:35.870 align:middle line:90% So this is, again, Emmert's Law. 00:28:35.870 --> 00:28:37.790 align:middle line:84% So you've got the same visual angle 00:28:37.790 --> 00:28:41.430 align:middle line:84% being subtended by this monster and that monster. 00:28:41.430 --> 00:28:43.350 align:middle line:84% The depth cues indicate that this one 00:28:43.350 --> 00:28:45.410 align:middle line:90% is further away than this one. 00:28:45.410 --> 00:28:47.150 align:middle line:84% So Emmert's Law tells you that this 00:28:47.150 --> 00:28:50.050 align:middle line:84% has got to be proportionally bigger than this one. 00:28:50.050 --> 00:28:56.350 align:middle line:90% 00:28:56.350 --> 00:28:59.910 align:middle line:84% Here's another kind of cool example. 00:28:59.910 --> 00:29:07.270 align:middle line:84% So we've got two cigarettes, and they're 00:29:07.270 --> 00:29:14.070 align:middle line:84% positioned on a drawing that is making use of linear perspective 00:29:14.070 --> 00:29:21.385 align:middle line:84% to cause this to look like it's closer to you than this. 00:29:21.385 --> 00:29:24.140 align:middle line:84% The two cigarettes are physically the same size, 00:29:24.140 --> 00:29:26.840 align:middle line:84% and thus, they're lying on a table, 00:29:26.840 --> 00:29:32.280 align:middle line:84% so they're the same size on the retina. 00:29:32.280 --> 00:29:34.300 align:middle line:84% But they look very different, right? 00:29:34.300 --> 00:29:37.960 align:middle line:90% 00:29:37.960 --> 00:29:42.560 align:middle line:84% This is a thing that I just saw that's kind of interesting. 00:29:42.560 --> 00:29:44.310 align:middle line:90% So check this out. 00:29:44.310 --> 00:29:46.060 align:middle line:84% See if you can figure out what's going on. 00:29:46.060 --> 00:29:48.600 align:middle line:90% 00:29:48.600 --> 00:29:54.780 align:middle line:84% So this is an artist who's drawing this thing. 00:29:54.780 --> 00:29:56.420 align:middle line:90% It's going to look pretty 3D. 00:29:56.420 --> 00:30:05.480 align:middle line:90% 00:30:05.480 --> 00:30:06.620 align:middle line:90% Now, he's going to jump. 00:30:06.620 --> 00:30:19.880 align:middle line:90% 00:30:19.880 --> 00:30:25.480 align:middle line:84% Notice that the artist has changed in size, all right? 00:30:25.480 --> 00:30:29.600 align:middle line:90% 00:30:29.600 --> 00:30:32.500 align:middle line:84% So it looks like this person is changing in size. 00:30:32.500 --> 00:30:37.640 align:middle line:84% Anybody want to try to explain why the person looks 00:30:37.640 --> 00:30:42.920 align:middle line:84% kind of small here, and bigger here, and very big there? 00:30:42.920 --> 00:30:43.420 align:middle line:90% Yeah. 00:30:43.420 --> 00:30:45.740 align:middle line:84% AUDIENCE: He's getting physically close to the camera, 00:30:45.740 --> 00:30:48.120 align:middle line:84% but you don't think he is because he's-- 00:30:48.120 --> 00:30:49.800 align:middle line:84% like, he's just turning [INAUDIBLE]. 00:30:49.800 --> 00:30:50.680 align:middle line:90% JOSH MCDERMOTT: Yeah. 00:30:50.680 --> 00:30:51.180 align:middle line:90% Yeah. 00:30:51.180 --> 00:30:54.320 align:middle line:84% So in reality, this person is jumping horizontally 00:30:54.320 --> 00:30:55.500 align:middle line:90% by a pretty big distance. 00:30:55.500 --> 00:30:59.080 align:middle line:84% So the distance to the camera is changing. 00:30:59.080 --> 00:31:01.720 align:middle line:84% You are misperceiving this person 00:31:01.720 --> 00:31:04.800 align:middle line:84% as actually kind of jumping up and down vertically, right? 00:31:04.800 --> 00:31:09.780 align:middle line:84% And if you assume that the distance is remaining constant, 00:31:09.780 --> 00:31:12.400 align:middle line:84% then the person's got to be changing in size. 00:31:12.400 --> 00:31:14.440 align:middle line:84% So in this case, the depth cues here 00:31:14.440 --> 00:31:16.880 align:middle line:84% are so powerful that they overcome 00:31:16.880 --> 00:31:18.640 align:middle line:84% the presumably strong prior you have 00:31:18.640 --> 00:31:21.460 align:middle line:90% that people stay the same size. 00:31:21.460 --> 00:31:21.960 align:middle line:90% Yeah. 00:31:21.960 --> 00:31:25.560 align:middle line:90% 00:31:25.560 --> 00:31:27.060 align:middle line:90% OK, all right. 00:31:27.060 --> 00:31:32.080 align:middle line:84% So another point I want you to take away from this is that we 00:31:32.080 --> 00:31:34.240 align:middle line:90% see in 3D, right? 00:31:34.240 --> 00:31:37.400 align:middle line:84% So what you perceive is your inference 00:31:37.400 --> 00:31:39.400 align:middle line:84% of the three-dimensional structure of the world. 00:31:39.400 --> 00:31:43.560 align:middle line:84% Now, that is derived from these two-dimensional retinal inputs. 00:31:43.560 --> 00:31:46.880 align:middle line:84% And it's very difficult for you to actually counteract 00:31:46.880 --> 00:31:49.240 align:middle line:84% the visual systems recovery of 3D shape. 00:31:49.240 --> 00:31:51.320 align:middle line:84% So this is a classic demonstration 00:31:51.320 --> 00:31:53.520 align:middle line:84% that was constructed by Roger Shepard, who's 00:31:53.520 --> 00:31:56.000 align:middle line:84% a cognitive psychologist, who also kind of was 00:31:56.000 --> 00:31:56.940 align:middle line:90% an amateur artist. 00:31:56.940 --> 00:31:59.640 align:middle line:84% And so he published a book of these illusions 00:31:59.640 --> 00:32:00.900 align:middle line:90% that he came up with. 00:32:00.900 --> 00:32:02.960 align:middle line:84% And this is probably the most famous. 00:32:02.960 --> 00:32:08.760 align:middle line:84% And so the illusion here is that the parallelograms here and here 00:32:08.760 --> 00:32:12.610 align:middle line:90% are physically the same shape-- 00:32:12.610 --> 00:32:16.028 align:middle line:84% the same size, same shape in the image. 00:32:16.028 --> 00:32:17.070 align:middle line:90% You're shaking your head. 00:32:17.070 --> 00:32:17.850 align:middle line:90% You don't believe me, right? 00:32:17.850 --> 00:32:19.142 align:middle line:90% Yeah, it doesn't look possible. 00:32:19.142 --> 00:32:23.770 align:middle line:84% OK, so here's one way to think about-- to see this. 00:32:23.770 --> 00:32:28.570 align:middle line:84% So this is the image kind of rotated and overlaid. 00:32:28.570 --> 00:32:31.250 align:middle line:84% You can see that they're actually the same. 00:32:31.250 --> 00:32:36.130 align:middle line:90% Here's another animation. 00:32:36.130 --> 00:32:38.530 align:middle line:90% OK. 00:32:38.530 --> 00:32:40.010 align:middle line:90% Yeah. 00:32:40.010 --> 00:32:44.650 align:middle line:84% But it's really kind of hard to believe. 00:32:44.650 --> 00:32:47.010 align:middle line:84% And so the idea is that these two different shapes 00:32:47.010 --> 00:32:52.462 align:middle line:84% in the image look like kind of different shapes 00:32:52.462 --> 00:32:55.170 align:middle line:84% in the world, because the tables are kind of oriented differently 00:32:55.170 --> 00:32:57.290 align:middle line:90% and angled differently. 00:32:57.290 --> 00:33:00.850 align:middle line:84% And you infer these-- so you're inferring these different 3D 00:33:00.850 --> 00:33:03.650 align:middle line:84% shapes in the world, and it's really impossible to access 00:33:03.650 --> 00:33:05.390 align:middle line:90% the 2D shapes in the image. 00:33:05.390 --> 00:33:06.610 align:middle line:90% Yeah. 00:33:06.610 --> 00:33:09.710 align:middle line:84% AUDIENCE: Maybe this is another illusion in that the image, 00:33:09.710 --> 00:33:14.090 align:middle line:84% but is it relevant that the parallelogram 00:33:14.090 --> 00:33:17.770 align:middle line:90% seems slightly askew? 00:33:17.770 --> 00:33:21.810 align:middle line:84% The bottom of the table or of the long table 00:33:21.810 --> 00:33:26.330 align:middle line:84% doesn't look parallel to the top of the long table to me. 00:33:26.330 --> 00:33:28.250 align:middle line:84% JOSH MCDERMOTT: Yeah, it doesn't to me either, 00:33:28.250 --> 00:33:31.410 align:middle line:84% but this one doesn't quite look exactly rectangular either. 00:33:31.410 --> 00:33:31.910 align:middle line:90% Yeah. 00:33:31.910 --> 00:33:32.992 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:33:32.992 --> 00:33:34.950 align:middle line:84% JOSH MCDERMOTT: I don't think that's important. 00:33:34.950 --> 00:33:37.790 align:middle line:84% I think this is just-- that's just another version. 00:33:37.790 --> 00:33:41.250 align:middle line:84% I think in the original version, they actually-- 00:33:41.250 --> 00:33:43.490 align:middle line:90% they look pretty well matched. 00:33:43.490 --> 00:33:46.810 align:middle line:90% 00:33:46.810 --> 00:33:50.550 align:middle line:84% Yeah, but the point is that-- so this distance in the image-- 00:33:50.550 --> 00:33:52.870 align:middle line:84% this is the same as this distance in the image. 00:33:52.870 --> 00:33:55.250 align:middle line:84% But when you look at it, it looks 00:33:55.250 --> 00:33:57.730 align:middle line:84% like it's a much greater distance because 00:33:57.730 --> 00:34:00.870 align:middle line:84% of the foreshortening effect of projective geometry. 00:34:00.870 --> 00:34:04.810 align:middle line:84% So you have this thing that's getting projected onto an image, 00:34:04.810 --> 00:34:07.450 align:middle line:84% and you're inferring the three-dimensional shape 00:34:07.450 --> 00:34:10.969 align:middle line:84% in the world overcoming that projected process 00:34:10.969 --> 00:34:13.110 align:middle line:90% or inverting it correctly. 00:34:13.110 --> 00:34:15.969 align:middle line:90% 00:34:15.969 --> 00:34:18.350 align:middle line:84% OK, so that's kind of an important theme. 00:34:18.350 --> 00:34:21.409 align:middle line:84% And then, the thing that we'll end with here 00:34:21.409 --> 00:34:23.949 align:middle line:84% is this issue of ambiguity and bistability. 00:34:23.949 --> 00:34:27.969 align:middle line:84% So one of the amazing things about perception and vision 00:34:27.969 --> 00:34:30.143 align:middle line:84% in particular is that we're constantly solving 00:34:30.143 --> 00:34:31.310 align:middle line:90% these little posed problems. 00:34:31.310 --> 00:34:32.929 align:middle line:84% So three-dimensional interpretation 00:34:32.929 --> 00:34:35.108 align:middle line:84% in the world in particular is always ambiguous, 00:34:35.108 --> 00:34:37.150 align:middle line:84% especially if you look at the world with one eye. 00:34:37.150 --> 00:34:39.570 align:middle line:84% So there's lots of different possible three-dimensional 00:34:39.570 --> 00:34:42.429 align:middle line:84% structures that are consistent with the image that you observe. 00:34:42.429 --> 00:34:45.690 align:middle line:84% But usually, we see the one interpretation 00:34:45.690 --> 00:34:48.630 align:middle line:84% that is apparently deemed most likely by our visual system. 00:34:48.630 --> 00:34:51.929 align:middle line:84% So vision is typically quite stable. 00:34:51.929 --> 00:34:54.929 align:middle line:84% But sometimes, especially in these more impoverished displays 00:34:54.929 --> 00:34:57.913 align:middle line:84% that we often make use of in perceptual science, 00:34:57.913 --> 00:34:59.330 align:middle line:84% there are multiple interpretations 00:34:59.330 --> 00:35:01.470 align:middle line:84% that are equally likely, and the percept is bistable. 00:35:01.470 --> 00:35:02.950 align:middle line:84% So this is called the Necker cube. 00:35:02.950 --> 00:35:04.350 align:middle line:90% It's like a wireframe cube. 00:35:04.350 --> 00:35:06.628 align:middle line:84% So if you just look at this one on the left, 00:35:06.628 --> 00:35:08.920 align:middle line:84% you'll be able to see it in two different orientations. 00:35:08.920 --> 00:35:14.800 align:middle line:84% So one orientation is that this square is out in front. 00:35:14.800 --> 00:35:18.420 align:middle line:84% The other orientation is that this square is out in front. 00:35:18.420 --> 00:35:20.960 align:middle line:84% And those are both consistent with the image, 00:35:20.960 --> 00:35:22.700 align:middle line:84% and if you look at it, your percept 00:35:22.700 --> 00:35:27.560 align:middle line:84% will kind of flip from one to another, maybe every five or ten 00:35:27.560 --> 00:35:29.000 align:middle line:90% seconds or something like that. 00:35:29.000 --> 00:35:31.940 align:middle line:84% OK, raise your hands if you've seen it flip. 00:35:31.940 --> 00:35:35.320 align:middle line:90% OK, almost everybody. 00:35:35.320 --> 00:35:35.820 align:middle line:90% Yeah. 00:35:35.820 --> 00:35:40.140 align:middle line:90% 00:35:40.140 --> 00:35:45.340 align:middle line:84% And so there are lots of famous examples like this. 00:35:45.340 --> 00:35:49.180 align:middle line:84% So this is kind of combining two famous illusions. 00:35:49.180 --> 00:35:51.220 align:middle line:84% In this particular case, the face 00:35:51.220 --> 00:35:57.100 align:middle line:84% can be seen as an older woman from the side 00:35:57.100 --> 00:36:00.980 align:middle line:84% or a younger woman kind of from the back. 00:36:00.980 --> 00:36:04.920 align:middle line:84% And this person is holding their hands up in a silhouette, 00:36:04.920 --> 00:36:06.620 align:middle line:84% and that's the duck-rabbit illusion. 00:36:06.620 --> 00:36:08.380 align:middle line:84% You can see it as a duck or as a rabbit. 00:36:08.380 --> 00:36:13.660 align:middle line:84% OK, so this is a cartoon that I saw recently. 00:36:13.660 --> 00:36:16.660 align:middle line:84% So the bartender says, can I see your ID? 00:36:16.660 --> 00:36:18.220 align:middle line:90% Wait, never mind. 00:36:18.220 --> 00:36:20.680 align:middle line:84% Wait, yeah, I need to see your ID. 00:36:20.680 --> 00:36:23.940 align:middle line:84% Wait, no-- constantly switching between these interpretations 00:36:23.940 --> 00:36:26.660 align:middle line:84% of someone who's underage and someone who's over age. 00:36:26.660 --> 00:36:29.253 align:middle line:90% 00:36:29.253 --> 00:36:31.920 align:middle line:84% And so this bistability, we had a question about this last time. 00:36:31.920 --> 00:36:33.720 align:middle line:84% Bistability is super interesting, 00:36:33.720 --> 00:36:38.580 align:middle line:84% the fact that you don't get stuck in one interpretation. 00:36:38.580 --> 00:36:45.220 align:middle line:84% And one idea is that this is a situation where the posterior-- 00:36:45.220 --> 00:36:50.420 align:middle line:84% so the probability of the world, given the stimulus, 00:36:50.420 --> 00:36:51.360 align:middle line:90% is multimodal. 00:36:51.360 --> 00:36:53.380 align:middle line:84% So there's multiple interpretations 00:36:53.380 --> 00:36:57.580 align:middle line:84% that are both probable, and maybe your visual system 00:36:57.580 --> 00:37:01.100 align:middle line:84% is sampling from the posterior so that you sometimes see one 00:37:01.100 --> 00:37:03.910 align:middle line:90% thing, sometimes see another. 00:37:03.910 --> 00:37:06.830 align:middle line:84% Maybe it relates to adaptation and what happens 00:37:06.830 --> 00:37:10.390 align:middle line:84% is you see one thing, and so some neurons kind of adapt. 00:37:10.390 --> 00:37:12.270 align:middle line:84% And then, the other interpretation kind 00:37:12.270 --> 00:37:14.390 align:middle line:84% of ends up getting favored in some way-- 00:37:14.390 --> 00:37:17.570 align:middle line:84% could be potentially due to implementation constraints. 00:37:17.570 --> 00:37:21.730 align:middle line:84% We don't really know, but it's fairly prominent. 00:37:21.730 --> 00:37:27.190 align:middle line:84% And then, these are some other examples of bistable things, 00:37:27.190 --> 00:37:31.110 align:middle line:84% analogous to the duck-rabbit illusion. 00:37:31.110 --> 00:37:33.150 align:middle line:90% All right, let's end there. 00:37:33.150 --> 00:37:37.190 align:middle line:84% So next time, we'll resume talking about monocular depth 00:37:37.190 --> 00:37:37.690 align:middle line:90% cues. 00:37:37.690 --> 00:37:39.310 align:middle line:84% And then, we'll get into stereopsis, 00:37:39.310 --> 00:37:44.220 align:middle line:84% how you derive depth information from having two eyes. 00:37:44.220 --> 00:38:03.000 align:middle line:90%