11/10/2017
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`Calculating Stereo Pairs
`
`Calculating Stereo Pairs
`
`See also, 3D Stereo Rendering Using OpenGL (and GLUT)
`Written by Paul Bourke
`July 1999
`
`Introduction
`The following discusses computer based generation of stereo pairs as used to create a perception of depth. Such
`depth perception can be useful in many fields, for example, scientific visualisation, entertainment, games,
`appreciation of architectural spaces, etc.
`Depth cues
`There are a number of cues that the human visual system uses that result in a perception of depth. Some of these
`are present even in two dimensional images, for example:
`Perspective. Objects get smaller the further away they are.
`
`Sizes of known objects. We expect certain object to be smaller than others. If an elephant and a tea cup
`appear the same size then we expect the elephant to be further away.
`
`Occlusion. An object that blocks another is assumed to be in the foreground.
`
`Lighting, shadows. There a number of subtle cues implied by lighting, the way a curved surface reflects
`light suggests the rate of curvature, shadows are a form of occlusion.
`Relative motion. Objects further away seem to move more slowly than objects in the foreground.
`There are other cues that are not present in 2D images, they are:
`Binocular disparity. This is the difference in the images projected onto the back the eye (and then onto the
`visual cortex) because the eyes are separated horizontally by the interocular distance.
`
`Accommodation. This is the muscle tension needed to change the focal length of the eye lens in order to
`focus at a particular depth.
`
`Convergence. This is the muscle tension required to rotate each eye so that it is facing the focal point.
`While binocular disparity is considered the dominant depth cue in most people, if the other cues are presented
`incorrectly they can have a strong detrimental effect. In order to render a stereo pair one needs to create two
`images, one for each eye in such a way that when independently viewed they will present an acceptable image to
`the visual cortex and it will fuse the images and extract the depth information as it does in normal viewing.
`Stereographics using stereo pairs is one of the major three dimensional display technologies. Stereo pairs create a
`"virtual" three dimensional image, binocular disparity and convergence cues are correct but accommodation cues
`are inconsistent because each eye is looking at a flat image. Note: there are 3D display systems where
`accommodation is not in conflict, these are generally referred to as autostereoscopic because in general they do
`not need additional viewing apparatus. Examples of autostereoscopic systems are displays designed around the
`same principles as lenticular sheets or holograms.
`The case where the object is behind the projection plane is illustrated below. The projection for the left eye is on
`the left and the projection for the right eye is on the right, the distance between the left and right eye projections
`is called the horizontal parallax. Since the projections are on the same side as the respective eyes, it is called a
`positive parallax. Note that the maximum positive parallax occurs when the object is at infinity, at this point the
`horizontal parallax is equal to the interocular distance.
`
`https://web.archive.org/web/20010424172531/http://astronomy.swin.edu.au:80/pbourke/stereographics/stereorender/
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`Calculating Stereo Pairs
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`If an object is located in front of the projection plane then the projection for the left eye is on the right and the
`projection for the right eye is on the left. This is known as negative horizontal parallax. Note that a negative
`horizontal parallax equal to the interocular distance occurs when the object is half way between the projection
`plane and the center of the eyes. As the object moves closer to the viewer the negative horizontal parallax
`increases to infinity.
`
`If an object lies at the center of the projection plane then its projection onto the focal plane is coincident for both
`the left and right eye.
`
`Rendering
`There are a couple of methods of setting up a virtual camera and rendering two stereo pairs, many methods are
`strictly incorrect since they introduce vertical parallax. An example of this is called the "Toe-in" method, while
`incorrect it is still often used because the correct "off axis" method requires features not always supported by
`rendering packages.
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`Toe-in (Incorrect)
`In this projection the camera has a fixed and symmetric aperture, each camera is pointed at a single focal point.
`Images created using the "toe-in" method will still appear stereoscopic but the vertical parallax it introduces will
`cause discomfort. The introduced vertical parallax increases out from the center of the projection plane and is
`more important as the camera aperture increases.
`
`Calculating Stereo Pairs
`
`Off-axis (Correct)
`This is the correct way to create stereo pairs. It introduces no vertical parallax and is therefore creates the less
`stressful stereo pairs. Note that it requires a non symmetric camera frustum, this is supported by some rendering
`packages, in particular, OpenGL.
`
`Objects that lie in front of the projection plane will appear to be in front of the computer screen, objects that are
`behind the projection plane will appear to be "into" the screen. It is generally easier to view stereo pairs of
`objects that recede into the screen, to achieve this one would place the focal point closer to the camera than the
`objects of interest. Note, this doesn't lead to as dramatic an effect as objects that pop out of the screen.
`The degree of the stereo effect depends on both the distance of the camera to the projection plane and the
`separation of the left and right camera. Too large a separation can be hard to resolve and is known as
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`hyperstereo. A good ballpark separation of the cameras is 1/15 of the distance to the projection plane, this is
`generally the maximum separation for comfortable viewing. Another constraint in general practice is to ensure
`the negative parallax (projection plane behind the object) does not exceed the eye separation.
`
`A common measure is the parallax angle defined as P = 2 atan(DX / (2 d)) where DX is the horizontal
`separation of a projected point between the two eyes and d is the distance of the eye from the projection plane.
`For easy fusing by the majority of people, the absolute value of P should not exceed 1.5 degrees for all points in
`the scene. Note P is positive for points behind the scene and negative for points infront of the screen. It is not
`uncommon to restrict the negative value of P to some value closer to zero since negative parallax is more
`difficult to fuse especially when objects cut the boundary of the projection plane.
`
`Viewing
`Most stereo pair techniques require some sort of apparatus to present the appropriate image to each eye and are
`thus not "autostereoscopic". The most common methods in use today are LCD shutter glasses or glasses with
`polarised lens.
`
`The projection of stereo pairs can be categorised as either time parallel where both image are present
`simultaneously, or time multiplexed where images are alternatively drawn.
`
`The examples and the system discussed in this report use time multiplexed display with LCD shutters
`synchronised to the alternating images. The following image shows a "standard" arrangement, the computer has
`a stereo capable video/OpenGL card that has a refresh rate of 120Hz. The stereo pairs are displayed on each
`alternate refresh, 60Hz per image. The emitter (on the top of the monitor) sends a signal that is inphase with the
`monitor and the LCD shutter glasses alternatively switch the lenses transparent and opaque. The net effect is the
`left eye only sees the left stereo pair, the right eye only sees the right stereo pair.
`
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`References
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`
`Using ChromaDepth to Obtain Inexpensive Single-image Stereovision for Scientific Visualisation
`
`Journal of Graphics Tools, ACM, Vol 3 No 3 pp1-9
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`
`Generating images for a time multiplexed stereoscopic computer graphics system.
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`
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`Hodges, L.F. and McAllister, D.F.
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`
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`
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