Stereogram Follow-Up: Divergent or Cross-Eyed? [Archive]

arcticpenguin

5th February 2003, 05:55 AM

In my field we deal with this all the time. Divergent view is the standard for publication. Some of the real oldtimers seem to prefer cross-eyed. In the lab we use graphics workstations that circumvent the question, such as 'CrystalEyes' stereo with the special liquid crystal goggles. These feed a separate image to each eye without requiring eye tricks. These technologies require a CRT monitor because current flat panels do not have the necessary refresh rates.

Sharp has announced that it will commercialize a stereo flat panel monitor using a "parallax barrier" within a couple years. I haven't tried it out yet.
http://sharp-world.com/corporate/news/020927.html

davidhorman

5th February 2003, 07:40 AM

The big problem with all these things, though, is that they don't look right the moment you move your head. Someone somewhere was working on a very simple system involving lenses...

What you do is make a "sheet" of lenses and mount it in front of your camera. What you end up with a 2d array of images of your object, each taken from a slightly different angle by virtue of the grid of lenses. The great thing is, to view the image in all it's 3d glory, you just view it through the same sheet of lenses.

David

arcticpenguin

5th February 2003, 08:15 AM

Originally posted by davidhorman
The big problem with all these things, though, is that they don't look right the moment you move your head. Someone somewhere was working on a very simple system involving lenses...

What you do is make a "sheet" of lenses and mount it in front of your camera. What you end up with a 2d array of images of your object, each taken from a slightly different angle by virtue of the grid of lenses. The great thing is, to view the image in all it's 3d glory, you just view it through the same sheet of lenses.

David
Your description failed to convey the idea to me. Can you find a link?

davidhorman

5th February 2003, 01:52 PM

Your description failed to convey the idea to me. Can you find a link?

A quick Google was no use, but I'll give it another try.

The lenses you place in front of the camera were, IIRC, hemispheres pressed out of a flat sheet:

ooooo
ooooo
ooooo
ooooo

Through each one, you'd see a small version of the object beyond (sort of a fly's eye view). So you record that, while moving the object or whatever.

When it comes to playback, you put the grid in front of the monitor (assuming it's dimensions match the grid). What happens, more-or-less (and again, IIRC), is that each lens magnifies the small image behind it so only one pixel is really visible. The different positions of your two eyes means they see different pixels.

That's the best I can do. The example I saw had at most 100 lenses on it, so it was low resolution, but you could see the effect (they moved the camera side-to-side).

David

arcticpenguin

5th February 2003, 02:25 PM

That sounds similar to the "parallax barrier" that Sharp is working on. It is basically a sheet of plastic with prismatic ridges cut into it. I think it is like the "3-D" baseball cards I remember from my youth.

Plutarck

5th February 2003, 06:03 PM

I just try to "unfocus" and blur my vision, and that's what worked for me. Didn't really cross them or look elsewhere - maybe that's what you mean by divergence. Dunno.

I didn't do them much because, well, they hurt your head. Too much downside for too little payoff.

rwald

5th February 2003, 06:05 PM

The divergant method is the "unfocusing" method. The cross-eyed method is if you focus on a point closer than the actual image. I can do both, but find unfocusing/divergance easier.

Plutarck

5th February 2003, 06:11 PM

Originally posted by rwald
The divergant method is the "unfocusing" method. The cross-eyed method is if you focus on a point closer than the actual image. I can do both, but find unfocusing/divergance easier.

Ah, then in that case I shall vote accordingly!

Tez

5th February 2003, 06:32 PM

Speaking of party tricks.

I noticed if I do the "divergent" method then my pupils dilate. I assume this is true of anyone who knows how to do it. Interestingly, this is all that you can really see happening when you do it in front of a mirror - its not like your eyes move noticably apart or anything.

Anyway, its kind of fun, given the right drunken circles, to claim you have control over ALL involunatry muscle movements. This one is trivial to demonstrate to everyone (except in a very well lit bar, in which case what the heck are you doing there). This gets everyone on your side, because its inconceiveable to most people that you have concious control over your pupil size.

You then go on to flippantly mention you have control over your heartbeat. In fact, its not so difficult to do (when I was a sportsfreak I wore a pulse rate monitor about 6 hours per day, and learned to do it by careful breathing). However - once again given the right drunken circumstances - the power of suggestion is so strong that you dont even have to do it properly or probably at all - the person checking your pulse will pretty much believe that your heart rate is doing what you say.

Luceiia

5th February 2003, 06:33 PM

When I taught physical geology in college the images were always divergent. When rummaging around in antique stores the photo sets are always divergent. When looking at calendars with computer generated 3-d stereo images they are always divergent. I've never seen nor heard of (until this thread) cross-eyed stereo images.

I'm not in a mood to strain my brain trying to remember mostly-forgotten optics knowledge to try to ascertain whether cross-eyed stereo imaging is possible, but the skeptic in me is highly doubtful.

As a side note, I taught all of my students how to view them both with and without the aid of lenses. I'd approximate 10% were unable to get the hang of doing it without lenses while the rest had little or no problems at all.

Luceiia
Is chocolate an aphrodisiac? You have to find that one out for yourself!

a_unique_person

5th February 2003, 06:52 PM

Originally posted by Plutarck
I just try to "unfocus" and blur my vision, and that's what worked for me. Didn't really cross them or look elsewhere - maybe that's what you mean by divergence. Dunno.

I didn't do them much because, well, they hurt your head. Too much downside for too little payoff.

ditto. i am thinking of starting up a class action for people who have had their eye sight and brain permanently damaged from trying to look at these damm things.

rwald

5th February 2003, 07:21 PM

Both the divergant and cross-eyed methods of viewing 3D stereographs work. Personally, I find the cross-eyed method more stressful and tireing, and I still need to put my finger in front of my face for it to work (I tried doing otherwise earlier, but it was frustrating), but I can make both work.

Anyway, to help visualize the difference between the two methods, I've made two images. The first (attached to this post) shows how the divergant method works. The two red dots are where the patter repeats, and the blue dot is the point beyond the image where you focus.

rwald

5th February 2003, 07:23 PM

And this image represents the cross-eyed method. Again, the red dots are the repeating pattern, and the blue dot is where the eyes are focused at. Note that now it's in front of the paper.

BillyJoe

6th February 2003, 02:10 AM

rwald,

Your illustrations also demonstrate why the images are different using the divergence and cross-eyed methods.

With the divergence method, the image is further away and looks larger and is the mirror reverse of the image seen with the cross-eyed method.

I'll let everyone work out the details for themselves.

rwald

6th February 2003, 03:54 AM

Two out of three ain't bad.

Yes, the image is further away and looks larger using the divergent method (personally, I've never noticed the "further away" part, but I understand where it comes from). However, it's not the mirror reverse. I'll go into details if you need me to, but the gist of it is that because of the swapping of left red dot/right red dot, what appears to be a mound in the divergent method will look like a dent in the cross-eyed method (and vice versa). That's why if you use the wrong method on a picture, it looks so unusual; everything that's supposed to pop out is recessed, and vice versa.

BillyJoe

6th February 2003, 04:21 AM

Originally posted by rwald
Two out of three ain't bad.

Yes, the image is further away and looks larger ....However, it's not the mirror reverse.....what appears to be a mound in the divergent method will look like a dent in the cross-eyed method . And that's not a mirror reversed image?

I'm pretty sure that if you give me a mound and a mirror I'd be able to show you a dent in the mirror.

arcticpenguin

6th February 2003, 06:30 AM

Originally posted by BillyJoe
And that's not a mirror reversed image?

No it is not. "mirror-reversed" indicates a flip about the Y axis, switching left and right. What we're talking about here is a shift along the axis of sight, depth perception; which object is in front of the other.

DrMatt

6th February 2003, 07:09 AM

I keep a pair of red-green glasses near my monitor. APOD has some nice views of Saturn etc.

Back in the dark ages, before computers were "user friendly", there was a barrel plotter in the computer center in Oberlin. I wrote mainframe software which would generate wireframe stereograms. At a thrift shop, I bought four make-up compacts just to rip the mirrors out of them. I made an arrangement of wood to hold up the plotted stereograms, with fixed mounting points for two of the mirrors, and a moveable mounting for the other two. It worked--for those people who have depth perception. Talking among my friends, I learned that there is a sizable fraction of people who have normal sight in both eyes but no depth perception at all....

davidhorman

6th February 2003, 07:10 AM

No it is not. "mirror-reversed" indicates a flip about the Y axis

Ah, but mirrors don't reverse what you see around the Y-axis, they reverse it around the Z-axis. It looks left-to-right because you had to turn your head around the Y-axis to see what you were seeing in the mirror...

Confused? So was I, when I first came across the question "why does a mirror flip things left-to-right but not top-to-bottom?"

I'm pretty sure that if you give me a mound and a mirror I'd be able to show you a dent in the mirror.

But I really don't know how you'd do that, BillyJoe...

David

arcticpenguin

6th February 2003, 07:26 AM

Originally posted by davidhorman

Ah, but mirrors don't reverse what you see around the Y-axis, they reverse it around the Z-axis. It looks left-to-right because you had to turn your head around the Y-axis to see what you were seeing in the mirror...

Confused? So was I, when I first came across the question "why does a mirror flip things left-to-right but not top-to-bottom?"

I'm not confused, but you are. Assignment of axes is clearly open to convention. My convention was X and Y being in a plane in front of you, such as the plane of your computer monitor. You were wrong to make assumptions about my coordinates without first learning which convention I was using.

The penguin at his job site:

davidhorman

6th February 2003, 08:31 AM

My convention was X and Y being in a plane in front of you, such as the plane of your computer monitor.

That is what I assumed you meant.

Things in mirrors *look* like they've been reversed around the Y-axis (the uppy-downy one), but only because you've turned your head around the same axis to look at the same object in the mirror.

If you look at an object, then crane your head back until you're looking upside down in the mirror (not recommended) what you see would seem to be flipped upside-down.

David

arcticpenguin

6th February 2003, 08:40 AM

You seem to think you can explain this without taking into account the optical properties of the mirror. If you replace the mirror with a pair of mirrors, properly angled (mirrors are perpendicular to each other, each at 45 degree angle to your line of sight) you will see a non-reversed image.

Tez

6th February 2003, 09:40 AM

Originally posted by davidhorman

That is what I assumed you meant.

Things in mirrors *look* like they've been reversed around the Y-axis (the uppy-downy one), but only because you've turned your head around the same axis to look at the same object in the mirror.

If you look at an object, then crane your head back until you're looking upside down in the mirror (not recommended) what you see would seem to be flipped upside-down.

David

I dont quite get this, but perhaps I'm imagining what you say to do wrong! Surely my "upside down" image will still have an interchanged left hand co-ordinate system with a right hand one (assuming plane mirror!). That is, x cross y = -z instead of +z say. I always thought the resolution to the question "why does a planer mirror flip things left/right and not up/down" to be that in fact it does neither - it flips from a right handed co-ordinate system to a left handed one (the labels are arbitrary of course!).

Hmm - if mirrors were somehow built around electroweak interactions instead of just electromagnetic ones this would no longer be true...

arcticpenguin

6th February 2003, 09:42 AM

Originally posted by Tez

I always thought the resolution to the question "why does a planer mirror flip things left/right and not up/down" to be that in fact it does neither - it flips from a right handed co-ordinate system to a left handed one (the labels are arbitrary of course!).

You can switch between a right- and left-handed coordinate system by flipping about an odd number of axes (i.e. 1 or 3).

Tez

6th February 2003, 10:09 AM

Originally posted by arcticpenguin

You can switch between a right- and left-handed coordinate system by flipping about an odd number of axes (i.e. 1 or 3).

obviously

I think that thinking about it as flipping around axes simply obfuscates things. For example - my mirror might have some kind of asymmetric, convoluted surface. As long as the photons reflect only once, however, I will still observe a flipping of the "handedness" despite there being no obvious co-ordinate system/axes to parametrise this around.

Alternatively one can think that I choose to co-ordinatize my space using some crazy-ass curvilinear co-ordinate system. Since spacetime is an orientable manifold (which is truly an amazing fact of nature I think) I will still, when I compute intrinsic properties of the manifold in the mirror that depend on its orientation, notice that the answers I get are the negative of those computed for outside the mirror.

While I'm here I'll mention something that I thing is a rather nice.

When two people communicate, say 1's and 0's, they need to be able to distinguish the 1 from the 0. Quantum mechanically this is not always possible unless a reference frame has been fixed - e.g. when communicating with electron spins, then I need to know what direction in space youre calling "z" say.

But for some systems this can be done intrinsically without fixing a reference frame - in fact the only two examples I know are (i) when the information is encoded in states which are non-degenerate with respect to the hamiltonian of the universe - such as ground and excited state of a free atom or (ii) when the information is encoded in states that rely on the fact we live in an orientable manifold - left and right circularly polarized photons being an example (horizontal and vertical polarization wont do!).

Recently I and two collegues showed that by using large entangled states one can get around the need for establishing reference frames even for the spin case, and do so with asymptotically no loss. This is rather remarkable - it implies that many things which have always been formulated under an assumption of shared reference frames, such as Bell inequalities, in fact can be performed without the need for this - they can be made covariant, to use a physicists term...

Blue Monk

6th February 2003, 10:21 AM

Originally posted by rwald
You know those 3D images, the ones where you need to either diverge or cross your eyes for the images to become clear? I was wondering which of those two methods is most common. Which manner of viewing Magic Eye images do you find easiest, divergent or cross-eyed?

I'm glad you brought that up because I AM cross-eyed (I have a paralyzed nerve in my right eye since birth) and these things have caused me fits to no end, hehe.

Those 3D images I can usually see quite easy, hehe but what used to drive me crazy is trying to get a 3D effect using those damn glasses.

Since my right eye will not move to the right the center of my field of vision is far to the left. When I look at people I feel like I'm looking straight at them when in fact my head is turned to put them in the center of my field of view. If there is anything to my right I can still see it but my brain shuts off my right eye so I don't see double. It is amazing how the brain comphensates as this is all completely transparent to me.

This is a problem with 3D glasses. To get the effect I have to hold them away from my face and to the left and kind of squint to see the 3D effect.

I recently saw a 3D IMAX film and while everyone else is ohhhing and ahhhhing I'm wiggling around in my seat, holding my glasses in front of me trying like hell to see what is going on, hehe.

And for the record, I prefer the term 'cock-eyed' :)

I always said if looks could kill I'd get innocent bystanders.

Luceiia

6th February 2003, 10:39 AM

Originally posted by rwald
And this image represents the cross-eyed method. Again, the red dots are the repeating pattern, and the blue dot is where the eyes are focused at. Note that now it's in front of the paper.

A pair of 3-d stereo images are not identical. For photos they must be taken by two different cameras separated a fair bit from each other.

Your first drawing (divergent) clearly demonstrate that the left eye sees the left image while the right eye sees the right image. Your second drawing (cross-eyed) clearly demonstrates the eyes/images are seen reversed. The complexities of the optical physics involved continues to be beyond my memory, but I doubt that simply reversing one pair of (divergent) 3-d images will result in a correct 3-d perception being achieved using a cross-eyed view.

Can anyone point me to any cross-eyed images anywhere? Online, bookstore, etc?

Luceiia
Chocolate is, let's face it, far more reliable than a man.

arcticpenguin

6th February 2003, 10:43 AM

Originally posted by Luceiia

A pair of 3-d stereo images are not identical. For photos they must be taken by two different cameras separated a fair bit from each other.

Your first drawing (divergent) clearly demonstrate that the left eye sees the left image while the right eye sees the right image. Your second drawing (cross-eyed) clearly demonstrates the eyes/images are seen reversed. The complexities of the optical physics involved continues to be beyond my memory, but I doubt that simply reversing one pair of (divergent) 3-d images will result in a correct 3-d perception being achieved using a cross-eyed view.

Can anyone point me to any cross-eyed images anywhere? Online, bookstore, etc?

Luceiia
Chocolate is, let's face it, far more reliable than a man.
Reversing the two images should properly convert between cross-eyed and wall-eyed.

Check out this product:
http://www.videredesign.com/products.htm
especially the "MEGA-D Megapixel Digital Stereo Head"

rwald

6th February 2003, 05:09 PM

As far as the whole mirror-image debate: I understand how a mirror really flips things along the Z axis, and I guess that in theory, viewing the image cross-eyed vs. divergent also flips the image along the Z axis. But if a mirror didn't flip everything along the Z axis, everything would look unusual (you would be seeing the back of your head, not the front), and that's not how the optical properties work. With the stereograms, they're built for the Z axis to work in one direction, so fliping the image along the Z axis makes the image work unusually.

For the record, I'm assuming that the XY plane is the plane of the stereogram/mirror, and the Z direction is the direction you're looking in.

BillyJoe

7th February 2003, 03:08 AM

Hey, all of you.....

Stop trying to confuse me with axis flipping!

Simply put, when I compare myself to my image in the mirror, my image in the mirror is reversed front to back. If it wasn't I would be looking at the back of my head as someone already pointed out correctly (rwald :) ). It is certainly not reversed left to right as someone else said incorrectly (articpenguin :( ).

When I look at a MagicEye picture with the cross-eyed method I see an image which is the mirror reverse of the image seen with the divergence method. A mound becomes a ditch (say what you like, David).

Can I have my 3 out of 3 now rwald?

regards,
BillyJoe:)

Tez

7th February 2003, 06:51 AM

So let me throw this in to see how well folks really understand it.

A plane mirror has its focal point at infinity, which is a kind of special case.

If you use an appropriate curved mirror and you stand past the focal point then your image *will* be flipped upside down. Will it also still be "left-right" inverted?

arcticpenguin

7th February 2003, 07:14 AM

Originally posted by BillyJoe

Simply put, when I compare myself to my image in the mirror, my image in the mirror is reversed front to back. If it wasn't I would be looking at the back of my head as someone already pointed out correctly (rwald :) ). It is certainly not reversed left to right as someone else said incorrectly (articpenguin :( ).

Acknowledged. I figured out last night what he was saying.

arcticpenguin

7th February 2003, 07:17 AM

Originally posted by Tez
So let me throw this in to see how well folks really understand it.

A plane mirror has its focal point at infinity, which is a kind of special case.

If you use an appropriate curved mirror and you stand past the focal point then your image *will* be flipped upside down. Will it also still be "left-right" inverted?
Compared to the use of a plane mirror, and assuming (not clearly stated) that your curved mirror is radially symmetric about your line of sight (Z axis) the image you see should be flipped in both X and Y, and thus has the same handedness as what you see with a plane mirror. The image is inverted an odd number of times: in Z, in X and in Y, whereas the plane mirror image was inverted only about Z.

Both cases have inversion about an odd number of axes, and will thus have opposite symmetry to your actual self.

davidhorman

7th February 2003, 07:46 AM

Post deleted - Pengy said it better.

David

rwald

7th February 2003, 01:48 PM

While we all admit that a mirror reverses objects along the Z axis, I think that the term "mirror reversal" is still commonly thought of as "reversal along the Y axis." So, I don't think it's best to call the divergent-to-cross-eyed reversal "mirror reversal." I prefer "reversal along the Z axis."

arcticpenguin

7th February 2003, 02:23 PM

Originally posted by rwald
While we all admit that a mirror reverses objects along the Z axis, I think that the term "mirror reversal" is still commonly thought of as "reversal along the Y axis." So, I don't think it's best to call the divergent-to-cross-eyed reversal "mirror reversal." I prefer "reversal along the Z axis." [/B]
That's because most people compare it to what they would look like if they were standing on the other side of the mirror, not how it compares to where they actually are. I.e. they assume the rotation about the Y axis.

rwald

7th February 2003, 02:39 PM

Again, I know that mirrors really reverse along the Z axis. I'm just saying that if you say, "Image A is a mirror image of image B," most people will think that A is B flipped along the Y axis, not B flipped along the Z axis.

arcticpenguin

7th February 2003, 02:48 PM

Granted.

BillyJoe

8th February 2003, 01:32 AM

Originally posted by rwald
....I think that the term "mirror reversal" is still commonly thought of as "reversal along the Y axis."....Well, rwald, I don't know how commonly thought of as "reversal along the Y axis" "mirror reversal" is but every time we look in the mirror - and, hell, it must be at least several times a day for all of us - we are reversed along the Z axis and that should count for something don't you think.

BTW, rwald, have I got my three out of three. :cool:

regards,
BillyJoe