Orthostereoscopy on your computer

Contents for Stereoscopic Perceived Depth (Roundness)

Stretch and Squeeze: 1

Orthostereoscopy ][ Frame magnification ]

Roundness

Conclusions and Comments on Roundness

Measured stereoscopic depth

Equations for perceived depth: S&S: 2

John Hart's equation for roundness

Stereo Base introduction

Stereo base equations

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Orthostereoscopic means the 3D image looks the same shape, size, perspective and depth as in the real world. (Tautomorphic.)

Orthoplastic means objects have the correct shape when viewed stereoscopically, but the size is wrong. Roundness is correct.

Hyperplastic: too much roundness or depth.

Hypoplastic: not enough depth. Flat pictures.

Stereo on a computer can be made orthoplastic. But hardly anybody bothers about orthostereoscopic, except fanatics like me and I only do it on rare occasions, for fun.

Dedicated stereo cameras produce orthostereoscopic scenes, if they are viewed in a suitable stereoscope:

The camera lenses are the same distance apart as the viewer's eyes

The picture is not magnified (e.g. stereoscopic 35mm slides).

The stereoscope lenses have the same focal length as the camera lenses, so the angle of view seen in the stereoscope is the same as the angle seen by the camera.

If the picture is magnified (as a print for example) then the stereoscope focal length must be increased to:
(camera focal length) x (frame magnification),
so that the angle of view of camera and stereoscope is still the same.

When the image is viewed on a computer, it is difficult to get an orthostereoscopic image.

Usually the photographer gives up and concentrates instead on making a satisfying depth impression in his picture, not caring too much if it reproduces reality or not. Orthoplastic is nice, but not essential.

1. Average adult inter-ocular distance is 65mm, but mine is 68mm, and so an orthostereoscopic picture made for me is not going to suit everybody.

2. Your computer or movie screen can be all sorts of sizes and not match mine, so the magnificaiton of the image may be wrong.

3. You may be sitting at any distance from the screen and not at the distance set up during photography. Then the field of view, magnification and stereoscopic perceived depth will be wrong.

4. The angle of view produced by the camera lens will not be the same as the angle of view people in a cinema have of the screen, except for just one person who is sitting in the orthostereoscopic seat.

Makers of binocular head mounted displays (HMD) need the graphics to match the real world and for them orthostereoscopy is an essential consideration. They must consider field of view of the display, varying inter-ocular distance of the observers and magnification, just as photographers must. In addition there are distortions from the convex lenses which are required to make the image seem to sit at the correct distance and in focus. Usually the true image is very small in an HMD and strong magnification is needed, plus a wide image field (typically 40 degrees). The image needs to be distorted to conteract the geometric distortion of the lenses.

Orthostereoscopic when viewed from 1080mm

The anaglyph below is as close as I can get to orthostereoscopic, but only at 1080mm viewing distance from the computer screen.

Distance to the nearest object during photography was 1080mm. If your eyes are not 1080mm away from your computer monitor, the image cannot be orthostereoscopic.

Stereo base (distance between the two cameras) was 65mm, which is the average human inter-ocular distance. Already this picture is not quite orthostereoscopic for my 68mm eye separation.

Magnification of the foreground is one, but only on my 22 inch computer screen running at 1680x1050 pixels. The aneroid altimeter is 80 mm diameter. Since perspective makes it look oval when viewed without the anaglyph glasses, check the maximum, transverse diameter. If it is not 80mm, there is a magnification problem with orthostereoscopy on your computer.

Only an object in the stereo window, at the level of the screen, is going to have normal size (magnification of 1). Objects further back must be smaller, by perspective.

In an orthostereoscopic image, perspective size reduction and stereoscopic depth fade out with distance, while keeping "in normal step" with each other. Perspective makes size reduce in proportion to distance. Stereoscopic depth reduces in proportion to the square of the distance. So keeping 3D and perspective in "normal step" is a bit of a mathematical conundrum, which our brains are able to handle subconsciously, if they have been trained since birth with normal stereoscopic vision. But our conscious thinking of linear versus inverse square, dating from high school maths, often becomes confused!

Stereoscopic vision is said to show us difference in distance, but not the actual distance. Our two eyes do not act like a range-finder. If they did, cross-eye stereoscopic free vision would fail.

There is a theory that distance is deduced from the perceived size of familiar objects and the way they shrink when further away, by perspective. The size and perspective mechanism means people with just one eye still know how far way things are. Other monocular clues also help, especially occlusion and motion disparity.

Blind children who have their vision restored (congenital cataract surgery, for example) are initially confused about distance, because they have not learned how big familiar objects are and how they seem to enlarge when approached. Adults who lose one eye, from injury or surgery, have difficulty with close work such as sewing. A well-known problem is trying to pour fluid into a glass. They usually learn to find the glass by touching the lip of the jug onto it, before tipping, otherwise there is fluid all over the table. "Don't let grandpa pour the wine."

After monocular clues have made the magnification-based decision about distance, stereoscopic vision shows small differences in depth. Especially close by, within arm's reach. Stereo vision works well for fine movements of our fingers. Stereoscopic vision is good for picking up that whisky glass. Or pushing through dense forest, without tripping or getting poked in the eye by twigs. Three dimensional impressions are a skill learned as a small infant, crawling into the world, finding things by touch, manipulating them with fingers (and often tasting them). Infants learn how touch, proprioception, vision, size, 3D shape, colour, and texture are multiple different properties of each thing.

D = 1

Orthostereoscopic from 2 meters

1. The next stereoscopic image was taken from 2,000mm
2. The stereo base was again 65mm
3. Magnification on the screen is again 1 (natural size at the level of the barometer).

   Subtended angle: i/V arc tan(65/2000) = 1.86 degrees, or 0.0325 Radians arc tan(68/2000) = 1.95 degrees, or 0.034 Radians Note: (1/30 = 0.034) This orthostereoscopic example for 2 meters fits closely to the familiar n/30 rule for stereo base. arc tan(1/30) = 1.9 degrees. Also notice that for our purposes, angles measured in Degrees are better replaced with Radians. The angles are small and Radians can be calculated without any reference to trig tables.

• The 3D image is orthostereoscopic (real size and shape) only when you are sitting 2 meters from the screen.
• Sit too close and the barometer looks oval, while the squares are flattened
• Sit at 2 meters and the barometer looks round.
• Beyond 2 meters, the barometer is oval again, but the major axis is running from back to front and not transversely. It looks stretched from how it was when viewed from near-by.

Notice how the perspective is different from the first image of the chess board. Front squares are closer and so look bigger than distant squares, but the size difference from front to back is less in this 2 meter image than on the 1.08 meter picture.

The difference in perspective of the squares and roundness of the barometer can be seen, if you are critical, even without putting on the anaglyph goggles. But in 3D the difference is obvious, while in 2D you have to think about it.

When viewed from less than 2 meters, the stereo depth (roundness) is too flat and the perspective is too small. Only at 2 meters are roundness and perspective both correct - if your eyes are 65mm apart.

D = 1

The aim was to turn the computer screen into a "window on the world." Photographing through an actual window to set up this orthostereoscopic concept of virtual reality was suggested to me by Jay Gharavi of Ventura, California (jaysdesk). The problem was finding a small enough window.

The stereo pair were photographed 1 meter away from the window, with a mildly wide-angle lens: 35mm focal length in 35mm equivalent camera terms. The digital camera was far smaller than full frame 35mm, which is how the picture has such a huge depth of field.

The stereo base between the two cameras was 65mm, which is the average inter-ocular distance for a male adult.

The window and beyond is orthostereoscopic only when viewed from 1 meter.

The image magnification has been set to get the window at natural size on my computer screen, but if you do not have the same size pixels on your screen, it will not be quite right. Even on my 22 inch monitor, the window is too big to fit and I have to pan around slightly.

The disparity of the most distant points in the stereoscopic scene has to be 65mm (this distant part is nearly lost in the glare of the sky around the setting sun, top right.) Disparity can be measured on an anaglyph as the distance between the red and cyan images of the same point (homologous points).

Objects at infinity on an orthostereoscopic picture are separated by 65mm
(or by whatever stereo base you choose, when taking the stereo pair to suit your own eyes.)

When we view a distant point at stereoscopic infinity, the optical axes of our eyes are parallel. Distant disparity equal to the inter-ocular distance (65mm) becomes another property of an orthostereoscopic image.

A Fuji W3 stereo camera has the lenses 75mm apart. If the magnification of a window 1 meter away is set to equal true size on the computer, also 1 meter away, to get correct stereo depth the picture should be taken from:
1 meter x 75 / 65 = 1.15 meter.
When the window is magnified to natural size on the screen, the most distant points will have a disparity of 75mm. You cannot set up a stereo pair with distant disparity greater than the inter-ocular distance and expect the general public to enjoy the experience. That is why a W3 does not quite take orthostereoscopic pictures, but photographers have learned not to care about that.

65mm disparity when viewing infinity is usual for adult males. Optical axes of eyes are parallel whenever we look into the distance. However, on a computer screen, many people cannot fuse a stereo image using parallel eyes when the distant disparity is 65mm. Only experts can fuse 75mm disparity.

The normal brain mechanism is to match eye convergence with focus and it takes experience to overcome that linkage. It seems the difficulty for the inexperienced is focusing on a screen 1 meter away, when their eyes are diverged to parallel, instead of converged onto the screen. Wearing 1 diopter reading glasses makes your eyes focus on 1 meter. That should overcome the focus/convergence mismatch for the distant parts of the scene, but difficulty may return when viewers look at the window frame through the reading glasses. Practice overcomes the focus/convergence problem and experienced stereo photographers have no difficulty.

Stereo pictures designed to be seen by the general public on a television cannot be made with uncrossed disparity (positive disparity into screen space) exceeding 2%, or 1/50 of the screen width. This is the standard for 3D TV laid down by Sky television. On my 22 inch, 16:10 computer monitor that works out as:
465 / 50 = 9.3mm,
which is a lot less than the 65mm disparity in the big picture above and is still exceeded on the small version below. Crossed disparity (negative disparity) can be 1%, giving a total disparity of 3% (1/33).

That means the old 1/30 rule, advocated for years by amateur stereo photographers, can only be used on television if floating windows are employed. Many modern stereographers agree with this, saying floating windows should be used all the time.
For brief moments, Sky allows 4% positive and 2.5% negative disparity, but brief moments do not occur in still photography and those limits only apply to moving pictures in 3D.

65mm disparity is usual in movies, which are seen on a large screen more than 20 meters away. At that distance, disparity and focus are nearly in tune with each other. You can always fuse a big disparity by moving back from the image, but then the perceived depth is exaggerated by stretch.

Of course, if the picture is smaller, the infinity disparity is also smaller, but then it is no longer orthostereoscopic. It is, however, orthoplastic when viewed from 1 meter (stereoscopic depth is in proportion to width, except that both are too small).

John Wattie photography. Click to comment on Flickr.

D = 2.2. The picture is 1/3 size and so the disparity is also reduced to a third.

Howick Historical Village.
Many of the 2D photographs on that site are by the author.

The window is in a restored, 19th century, tiny, wooden, school house. (Dame School.) The glass is old and not perfectly flat. It acts like a wavy lens, distorting the distant building, which is a blacksmith's shop. The 2 left panels are not distorting and must have been replaced with modern glass.When I was a child, all house windows distorted like this and plate glass was only seen in shop windows or other expensive installations.

The distortion is different for each eye, since they are looking through different parts of the rippled glass, and that will add to the difficulty of fusing the image. Experienced stereoscopists may not have difficulty fusing mild distortion like this, but even an experienced worker (Louis Carlsson) protested about this picture.

That is why orthostereoscopy is not worth the effort, except for your private use.

Photomatix

The dynamic range is very high, looking from a dark room into the bright sky around the setting sun. Usually that is impossible for anaglyph manufacture, or even for getting a photograph at all.

The secret is HDR: High Dynamic Range digital photography. Three pictures are taken with 2 stops difference in exposure between them:

1. Over-exposed,
2. Standard exposure,
3. Under exposed.

They are then fused in a computer program, in this case Photomatix. The image you see comes from 6 separate exposures (3, plus another 3 for the other eye.)

Big screen

On a computer screen, we can only see small, close objects orthostereoscopically.

But big movie screens also have problems in showing a realistic "window on the world."

The above images projected onto a large screen would not be orthostereoscopic, unless the magnification was zoomed out until the barometer was 80mm across and you stood 1 meter from the screen. That would be impossible, unless you owned the movie theatre. Roundness at the movies can be orthoplastic but not orthostereoscopic.

Orthostereoscopy on a movie screen, 20 meters away, would be great for showing a large hall at full size. Scenery could be orthostereoscopic, as long as the nearest object in the scene was exactly 20 meters away, the camera lenses had the same angle of coverage as the screen subtends 20 meters away and a 65mm stereo base-line was used. The furthest object would need to be aligned on the screen with a 65mm or less deviation between homologous infinity points.

So, you are not going to see orthostereo at the movies, even if you sit in the one seat the 3D image has been set up for. That seat is called the ortho-stereoscopic seat.

Most movies are not shot for orthostereoscopy - why bother when only one member of the audience can see it that way? Even worse, when you use a 65mm base on movie cameras, the stereo disparity for distant objects on a big movie screen becomes so big the audience has to diverge their eyes. That is painful or impossible for most people and is forbidden in modern 3D movies. Excess disparity can be overcome by bringing the stereo window forwards, off the screen, into the movie theatre (floating window technique), but then orthostereoscopy is definitely lost.

The best seat in the movies is certainly in the centre line of the screen, but how far back depends on how the movie was photographed and may even change during the program. Do not sit close to the screen: the 3D will be flat and the deviation of distant objects may well be uncomfortable. Sit centrally, at the back and you will see the 3D well, but it may well be exaggerated, with excessive depth. Many people prefer too much depth, saying there is little point paying extra for 3D movies unless you see lots of depth.

Stereoscopic projection is too dim. There is a set of filters on the projector and another set worn by the audience, both reducing light. The light is "chopped up" as the frames change, introducing a black phase, which reduces over-all brightness. Modern 3D movies are going to very high frame rates to ensure movement is smooth and there is no flicker, so the duty cycle will always be reduced. Lower brightness means lower resolution and dimmer colours. The colour shifts from normal reds to dominant blues (Purkinje shift). Brighter lights to overcome this mean more heat and burnt-out bulbs. 2D movies can run at 48 candelas per meter squared but 3D movies drop to 10c/m2 behind the glasses. Lasers would be good in the projectors, but there is no white light laser yet.

The screen has to be metallic, or the polarisation will be scrambled. A metallic screen introduces a central hot spot. People in the center line get a bright image, those at the sides of the theatre see a dimmer version and the deterioration begins just 3 seats from the centre line. Dolby and Xpan D systems do not need a silver screen and the sweet spot problem is reduced.

Orthostereoscopy seat: formula

V = MF

V = the correct Viewing distance to sit from the screen (projection, TV or computer) to see an orthostereoscopic image.
M = Frame Magnification
F = Focal length of the camera lens

(Quoted from Lenny Lipton)

Magnification

Frame magnification

(Width of the screen) / (Width of the frame)

or, same thing:- (screen height) / (frame height)

This definition comes from photography, where the frame is the film frame, or the size of the gate in the camera. A 35mm film frame is 24 x 36mm.

Object magnification

(Object size in the final image) / (Real size of the object)

The aneroid barometer in the above images has an object magnification of one, at least it does on my computer screen. The real diameter and the image diameter are both 80mm.

Object magnification =
(Magnification in the camera) x
(35mm correction factor) x
(Frame magnification)

35mm correction factor

For 35mm "full size sensor" digital cameras, the 35mm correction factor is 1.

For 4/3 format digital cameras (Olympus, Panasonic) the sensor is half the 35mm size and the 35mm correction factor is 2.

Small digital cameras have all sorts of 35mm correction factors, but the factor is quoted in the instruction manual. The true lens focal lengths are also in the manual, but are usually forgotten because they are only referred to as their 35mm equivalents. When you buy the camera you only hear about 35mm equivalent lenses in the shop.

Macro lens

A macro lens can have its magnification set from a scale on the lens as you wind it out. This is magnification in the camera, not the final magnification you see on the computer or a paper print. At a magnification of 1, the image on the sensor is the same size as the object. If you are using a small sensor, only part of that image fits on the sensor, as compared with a "full frame camera."

So, if 1:1 magnification is set on the macro lens,
magnification coming out of the camera = 1 x (35mm correction factor)

In the 4/3 system (Olympus, Panasonic), where the sensor is half size, magnification with a macro lens is twice that of a true 35mm camera, once the image is set up on your computer for viewing. This has important consequences in digital macro stereo-photography.

When you are on this web site, only enter 35mm equivalent focal lengths into the equations.

Aspect ratio

For 35mm film, the frame is 36mm x 24mm.
The aspect ratio is 36/24 = 3:2 = 1.5

A "full frame" digital camera, has a 24mm frame height, but the aspect ratio is often 4:3 or 1.33. This is the same aspect as "old" computer and TV screens and is/was a standard video ratio.

HDTV and many modern digital cameras use 16:9 or 1.78

Modern computer screens are 16:10 or 1.6, although increasingly lap-top screens are 16:9.

Stereoscopic images are often cropped from the sides in order to set the stereo window, and the only "constant" becomes the frame height.

Perspective invariance

For this web site, I have chosen the 35mm standard frame size for all mathematical formulae. Digital cameras usually have smaller frames, but they give the same perspective and stereo disparity as a 35mm camera, if the tiny image sensor is multiplied by a ratio to bring it up to 24mm vertical height. This is allowable because cameras have a property called perspective invariance. That means perspective does not change with different size cameras, as long as the angle of view in the cameras is the same.

If a camera size and its lens focal length are scaled up or down to match the size of a 35mm film frame it is called 35mm equivalent. All digital cameras you buy are quoted in terms of 35mm equivalent. They will give enlarged images (say post-card size, for example) with the same perspective as the equivalent 35mm camera does. The images are often better, because small cameras have a bigger depth of field than 35mm cameras and the post-cards produced look sharper. But the perspective on the post cards looks the same as from a 35mm film camera, by perspective invariance.