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Comment by roryokane | Hacker News Reader

It is very interesting to me that you need to multiply the distance-to-wall by the cosine of the angle to transform the image from fisheye to normal. It makes me wonder, why is it that our eye in real life sees straight lines as straight, the way this demo renders the image?

To illustrate the question, see https://en.wikipedia.org/wiki/File:Panotools5618.jpg – why do we see the world as in the bottom image instead of in the top one? After all, our eye really is at different distances from different parts of a straight wall, so it sounds logical that we would see the fisheye effect describe in the article. Is the rectilinearity of the image we see caused by the shape of the lens in our eye, or by post-processing in our brain?

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> It makes me wonder, why is it that our eye in real life sees straight lines as straight, the way this demo renders the image?

Your eye doesn't see it as straight, your brain does. Your eye doesn't actually gather a single coherent image, in fact. It's constantly moving[1], bringing the higher-precision fovea at the center of your retina to bear on interesting parts of the scene.

Your brain then accumulates all of that data into a single coherent "image" which is what you consciously perceive. This is why, for example, you are unaware of the blind spot caused by your optic nerve obstructing your retina[2].

A straight line in the world isn't projected onto a straight line on your eye: after all, the back of your eye is curved. (Even if it was, so what, it's not like your rods and cones are aligned in a nice neat grid.) It's just that you've learned that a line of stimulus curved just so across your visual field corresponds to a straight line in 3D space.

[1]: http://en.wikipedia.org/wiki/Saccade [2]: http://en.wikipedia.org/wiki/Blind_spot_(vision)

Wow, the blind-spot test on that Wikipedia page just blew my mind.

There were situations in traffic when I was driving a car and simply did not see cyclists or pedestrians coming. At the time I was aware that one of my eyes were obstructed by the rear-view mirror on the windshield, but that did not explain why I did not see them coming with the other eye.

I wonder why are people not alerted about this when taking the test for the drivers license.

Blind spots are crazy. Your brain will continue some patterns and straight lines right through the blind spot, so it doesn't look blank. http://www.swarthmore.edu/SocSci/fdurgin1/publications/Blind...

I was trying to crack exactly the same problem a decade ago - I was very frustrated by "classical" perspective distortions (such as looking up and down at a very tall pole, you notice in 3D projection the projected width at a given height changes depending on the pitch angle, which is counter-intuitive as your eye doesn't do that). I searched for answers, read Denis Zorin's disertation from Caltech, various different camera models etc. After one talk with a neurosurgeon he mentioned that those "perspective distortions" are perceived often by patients after a brain surgery and as the brain heals the normal undistorted picture begins to emerge. I am still curious if there is a more realistic mathematic formula that would allow us to have exactly the same perspective projection in 3D graphics as we have with our eyes. Anyone knows any recent research on this subject?

this is the perspective projection that we have with our eyes: spherical projection. detail here: http://www.treeshark.com/treeblog/?p=301

At any given moment we're only looking at a very small slice of that larger spherical panorama. Our brains are constantly constructing a coherent 3d model, with the help of various schematic constraints, such as expectations about straight lines being straight.

We perceive straight lines. but that's not what we see. But the curvature is usually so slight that it is very difficult to see.

You need a curved display. A 240 degree sphere segment stretching all around you will allow you to display a fully realistic-looking perspective, as long as the viewer's head is exactly in the centre. Or a head-mounted display like the Oculus could accomplish the same thing.

I would hazard a guess that it's a result of the brain interpreting the electrical impulses before providing the "image" that we "see."

It does a lot of pre-processing, so to speak -- which is why we get such awesome illusions as the Poggendorff illusion [0], tricks like the Pulfrich effect [1], etc.

I don't know enough about the mechanics of how light enters and is interpreted by the eye, but I wouldn't be surprised at ALL if we "should" be seeing more like a fisheye lens but our brain is saying no, no, those lines are straight, based on the countless other stimuli it's receiving.

[0] http://dragon.uml.edu/psych/poggendo.html

[1] http://en.wikipedia.org/wiki/Pulfrich_effect

The brain adjusts the images after learning about the physical world using other senses. If you start wearing glasses turning everything upside down the brain adapts within days.

https://en.wikipedia.org/wiki/Perceptual_adaptation#Experime...

I've always figured the latter explanation - that the picture from our eyes is distorted like that, but the brain corrects the image (it also doesn't hurt that we have two eyes, where as cameras typically don't; I wonder if multi-lens cameras are also subject to that fisheye effect?).

I think it's simpler than some of explanations here. You're not rendering onto the curved eye, you're rendering onto a flat monitor. If you imagine the game view as a window, a straight line outside always projects toward your eye onto a straight line on the window.

Similarly, I used to wonder why an image constructed with 3-point perspective [1] looks perfectly normal, while one with 4-point perspective [2] does not.

[1] http://www.craftsy.com/blog/wp-content/uploads/2013/07/cropp... [2] http://www.termespheres.com/images/perspective/fourpointpers...

> It makes me wonder, why is it that our eye in real life sees straight lines as straight, the way this demo renders the image?

Not always. Next time the Sun and the Moon happen to be in view at the same time, look at the dividing line X on the Moon between the parts illuminated and in shadow. Then draw a straight line Y from the Moon to the Sun.

Common sense tells us that the two lines are perpendicular, but often this is not the case. I don't understand it completely myself, but it is something to do with us residing on a curved surface.

> After all, our eye really is at different distances from different parts of a straight wall, so it sounds logical that we would see the fisheye effect describe in the article.

It's not the distance to the points in the scene that determine where they appear in a perspective projection, it's the angle. For any single point on the screen/retina/projective plane, it can actually correspond to any distance from the camera/eye (i.e., a ray of possible points).

A dumb question/explanation, but wouldn't that be because the screen/viewing pane is flat, while your eye is a ball?

Another way to visualize that calculation, is to see it as if it's adding a curved lens on top of the viewing pane.

I have no idea what I'm talking about, though.

Sometimes after getting new glasses, I would see the world this way until my eyes adjusted.

Its gotta be the shape of our eye, for the same reason the effect works in a mechanical DSLR camera, where light is only refracted through the lens.

> for the same reason the effect works in a mechanical DSLR camera

The sensor on the back of a camera is a flat plane, which is why (with most lenses) you get an image where straight lines appear straight. The sensor on the back of your eye (the retina) is curved.

straight lines are straight in a photograph because of precision manufactured optics shaped specifically to achieve that effect, to reduce "chromatic aberrations" and "barrel distortion".

Would it not be because the retina is curved?

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