If depth perception works because the brain checks the difference in the position of the object between the two eyes and concludes how far away it is, how can we still see depth when one eye is closed?
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You really can’t. Your brain does its best to extrapolates what it computes as depth with one eye closed, but the brain could be easily fooled. Someone who is blind in one eye will have significant depth perception problems.
Because that isn’t the only piece of information your brain uses. It basically collates a bunch of different pieces of information:
1. Your eye is always moving slightly and when your eye looks in different directions, it sees different things based upon the relative position of objects in your 3D environment.
2. Over the course of your life you have lots of experience with seeing various objects and your brain develops an expectation of their size. So something that your brain believes should be large but looks small will be interpreted as being further away, and something that your brain believes should be small but looks large will be interpreted as being closer.
3. The parallax created with two eyes can be replicated simply by moving. How things change relative to other objects as you move laterally, and how their size appears to change as you move back and forth, gives your brain information with which to construct a perception of depth.
We can’t. Your brain uses memories/experience to fill the gaps basically.
If you close one eye and then see a new situation you never saw with both eyes you will have a hard time estimating distances.
Your brain tries its best but you really can’t.
Close one eye and get someone to throw a tennis ball to you. Chances are you’ll miss it even if you’re normally good at catching. The reason is because you can no longer properly judge distances accurately enough to accomplish the task.
Approximation and pattern recognition. People who have had one eye permanently damaged don’t see depth any further than what the pattern recognition allows. “Blurrier and smaller = further”, “clearer and bigger = closer”.
But more than once have I seen my friend with a damaged eye approximate a distance wrong, on something whose size he didn’t know for sure.
Because of perspective assumptions.
Your brain assumes a lot of things every second, it’s how most optical illusions work — by assuming things based on context, which is faster and more often then not safer than waiting for more information.
In this case it’s also an”illusion” but more basic and it works the same way that a two dimensional picture with perspective creates “depth” even though it’s literally flat.
Your brain knows things are particular sizes, but perspective lines and lack of depth of focus tell your brain that things are near or far.
Additionally, your eyes are moving like crazy even though you don’t realize it, the movement of one eye can help triangulate a better perspective than just standing still since things at a distance “move” say a different rates than closer things (in addition to any movement of your head or body)
Things like color, shadows, and the relative sizes of objects also help the brain determine how far away something is! Even in video games where both eyes get the same image, your brain can usually figure out depth by a combination of these factors and others. Our brains out wired to assume that things are 3D and figure out how to interpret them using every hint available.
I have one good eye and one lazy bastard.
Most things are fine because I know the size and can easily estimate distance that’s good enough. Things like catching a fast baseball is damn near impossible though. It moves too fast for me to compensate.
Your brain uses whatever it’s given. With two eyes it can triangulate to work out the distance of the object you’re looking at.
If you only have one eye, but you’re moving your head, it can do something similar (half a second ago we looked at the object from *this* angle, and now we’re looking at it from a slightly different angle, and we can compare the two to get a good idea of distance)
If you only have one eye, and your head isn’t moving, your brain can still try to guess based on other cues. Maybe you know how big the object is, and you can use that to get a good estimate of how far away it is, for example. Or it might use the way light falls on the object to provide some sort of estimate. You’ll still have *some* depth perception, but it’ll be less accurate.
What you’re referring to, inferring depth from the disparity between images in the two eyes, is called *stereopsis*. It is only one of many cues that your brain uses to infer depth – albeit a powerful one. [This wikipedia article](https://en.wikipedia.org/wiki/Depth_perception) has a nice overview. Notice all the things listed under “Monocular cues”. *Monocular* as in “requiring only one (*mono*) eye (*oculus*)”. These cues all remain when one eye is closed or disabled. They are also the cues that allow you to interpret 2-D images in three dimensions. Even though you need stereopsis to have the full experience of depth, you can still watch a 2-D movie (or image) without it just looking like a bunch of flat shapes.
For the same reason, it is possible to get a stronger experience of depth from a 2-D video, by closing one eye and sitting close to the screen (to remove conflicting depth cues from your environment). It doesn’t always work because there are often some subtler conflicts in depth information too (e.g. your eye can tell that it is focused a certain distance away on the flat plane of the screen), but especially in scenes with a lot of (camera) motion, the pictorial depth cues can be strong enough to override the conflicts and really make you experience depth.
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