Stereoscopic depth rendition

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Stereoscopic depth rendition specifies how the depth of a three-dimensional object is encoded in a stereoscopic reconstruction. It needs attention to ensure a realistic depiction of the three-dimensionality of viewed scenes and is a specific instance of the more general task of 3D rendering of objects in two-dimensional displays.

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Depth in stereograms

A stereogram consists of a pair of two-dimensional frames, one for each eye. Common to both are the widths and heights of objects; their depth is encoded in the differences between right and left eye views. The geometric relationship between an object's third dimension and these position differences is presented below and depends on the location of the stereo-camera lenses and the observer's eyes. Other factors, however, contribute to the depth seen in a stereoscopic view and whether it corresponds to that in the actual object; the act of viewing a stereoscopic display often alters observers' three-dimensional perception. [1]

Stereoscopic reconstruction

The right and left eyes' panels in a stereoscopic reconstruction are created by projection from the principal points of the twin recording camera. The geometrical situation is most clearly understood by analyzing how the screens are generated when a small cubical element of side length dx = dy = dz is photographed from a distance z with a twin camera whose lenses are a distance a apart.

Geometry of screen view of a small cube at a distance z captured by a twin camera with separation a. Right and left eye images are shown superimposed. 3DCube.png
Geometry of screen view of a small cube at a distance z captured by a twin camera with separation a. Right and left eye images are shown superimposed.

In the left eye panel of the stereogram the distance AB is the representation of the front face of the cube, in the right eye panel, there is in addition BC, the representation of the cube's depth, i.e., the intercept on the screen of the rays from the cameras’ principal points to the back of the cube. This interval computes to the first order to . (To simplify the account, the right and left screens are taken to be superimposed, as they would be in a 3D display with LCD goggles.) Hence the depth/width ratio of the cube’s view, as embodied in its representation on the viewing screen, is r = a×dz/z×dx = a/z since dx=dz and depends solely on the distance of the target from the twin lenses and their separation and remains constant with scale or magnification changes. The depth/width ratio of the actual object, of course, is 1.00.

This stereogram with the cube, whose depth/width ratio had been captured with recording parameters ac and zc and embodied in the ratio BC/AB = rc=ac/zc, is now viewed by an observer with interocular separation ao at a distance zo. An overall scale change in BC/AB does not matter, but unless ro = rc, i.e., ao/zo = ac/zc. this no longer represents a cube but rather becomes, for this observer at this distance, a configuration for which

R = rc/ro ...... (1)

i.e., whose depth is R times that of a cube.

Depth rendition defined

A stereogram of intertwining rings. When fused by an observer, perceived depth increases with viewing distance. Anneaux.jpg
A stereogram of intertwining rings. When fused by an observer, perceived depth increases with viewing distance.

The stereoscopic depth rendition r is a measure of the flattening or expansion in depth for a display situation and is equal to the ratio of the angles of depth and width subtended at the eye in the stereogram reconstruction of a small cubical element. A value r > 1 says that what is seen has an expanded depth relative to the actual configuration.

A numerical example will illustrate: a structure is photographed by a stereocamera with interlens separation ac = 25 cm from a distance of 1 m, zc = 100. Hence rc = ac/zc = 0.25 and on the screens the right and left representation of the cube's far edge will be separated by ¼ the distance of the width. This stereogram is now viewed from a distance of 39 cm (the magnification does not matter, only the ratio BC/AB has to have been conserved) by an observer with interocular distance 6.5 cm, i.e., ro = 6.5/39 = 0.167. According to equation (1) for this view the structure has a stereoscopic depth rendition given by R = rc/ro = 0.25/0.167 = 1.5, meaning that the observer is presented with the geometrical situation not of a cube but of a structure 1.5× as deep as it is wide. For this to become a cube ro needs to be 0.25 which occurs for an observation distance zo = 6.5/0.25 = 26 cm.

This example illustrates that a given stereoscopic presentation for a given observer gains in depth/width ratio (expands in depth) with increasing observation distance. Observers, who can fuse the twin images of the rings by voluntarily changing their convergence, can verify this by moving away and towards the viewing screen.

Homeomorphic and heteromorphic rendition

Only when the recording and viewing situations have the same r value, i.e., only when ac/zc = ao/zo will the depth/width ratios of the actual structure and its view be identical. This particular condition has been termed homeomorphic by Moritz von Rohr and was contrasted by him with the heteromorphic one in which the r values of the stereoscopic and actual views differ. [2]

Non-veridical depth: other factors

But homeomorphic rendition with geometrical parameters identical to the original does not assure that an observer's perception of depth in a stereoscopic image is the same as that in the actual three-dimensional structure. An observer judgment of the apparent disposition of objects in space depends on many factors other than the geometrical ones that pertain to the angles subtended by the components at the two eyes. This was well described in the classical study by Wallach and Zuckerman who pointed out that the depth in the view through binoculars seems foreshortened. [3] Scenes appear flattened through field glasses, even non-prismatic ones without artificial extension of the base, which provide merely overall magnification and leave the r value unchanged.

In contrast to the rules, laid out above, for calculating the geometrically defined stereoscopic depth rendition, the perceived depth involves factors — context, previous experience — that are individual and not specifiable with the same degree of generality. Chief among them is the distance at which the configuration appears to the viewer. This is by no means fixed: the subjectivez is only vaguely related to the actual object distance, as is obvious in watching 3D film. Because apparent distance is the main source of judging object size (size or subjective constancy), observers' reports on the perceived depth/width ratio can deviate substantially from calculated values. [4] [5] [6] On the other hand, recent research confirms that the relative depths seen in three-dimensional configurations scale up more or less in proportion to the stereoscopic depth rendition arrived at within the purely geometrical framework. [7]

Related Research Articles

The aspect ratio of a geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side – the ratio of width to height, when the rectangle is oriented as a "landscape".

The focal length of an optical system is a measure of how strongly the system converges or diverges light; it is the inverse of the system's optical power. A positive focal length indicates that a system converges light, while a negative focal length indicates that the system diverges light. A system with a shorter focal length bends the rays more sharply, bringing them to a focus in a shorter distance or diverging them more quickly. For the special case of a thin lens in air, a positive focal length is the distance over which initially collimated (parallel) rays are brought to a focus, or alternatively a negative focal length indicates how far in front of the lens a point source must be located to form a collimated beam. For more general optical systems, the focal length has no intuitive meaning; it is simply the inverse of the system's optical power.

Circle of confusion Blurry region in optics

In optics, a circle of confusion is an optical spot caused by a cone of light rays from a lens not coming to a perfect focus when imaging a point source. It is also known as disk of confusion, circle of indistinctness, blur circle, or blur spot.

Stereoscopy Technique for creating or enhancing the illusion of depth in an image

Stereoscopy is a film (non-digital) technique for creating or enhancing the illusion of depth in an image by means of stereopsis for binocular vision. The word stereoscopy derives from Greek στερεός (stereos), meaning 'firm, solid', and σκοπέω (skopeō), meaning 'to look, to see'. Any stereoscopic image is called a stereogram. Originally, stereogram referred to a pair of stereo images which could be viewed using a stereoscope.

Depth perception Visual ability to perceive the world in three dimensions (3D)

Depth perception is the visual ability to perceive the world in three dimensions (3D) and the distance of an object. Depth sensation is the corresponding term for animals, since although it is known that animals can sense the distance of an object, it is not known whether they "perceive" it in the same subjective way that humans do.

Autostereogram single-image stereogram designed to create the visual illusion of a three-dimensional scene

An autostereogram is a single-image stereogram (SIS), designed to create the visual illusion of a three-dimensional (3D) scene from a two-dimensional image. In order to perceive 3D shapes in these autostereograms, one must overcome the normally automatic coordination between accommodation (focus) and horizontal vergence. The illusion is one of depth perception and involves stereopsis: depth perception arising from the different perspective each eye has of a three-dimensional scene, called binocular parallax.

Magnification process of enlarging something only in appearance, not in physical size

Magnification is the process of enlarging the apparent size, not physical size, of something. This enlargement is quantified by a calculated number also called "magnification". When this number is less than one, it refers to a reduction in size, sometimes called minification or de-magnification.

A stereo display is a display device capable of conveying depth perception to the viewer by means of stereopsis for binocular vision.

A volumetric display device is a graphic display device that forms a visual representation of an object in three physical dimensions, as opposed to the planar image of traditional screens that simulate depth through a number of different visual effects. One definition offered by pioneers in the field is that volumetric displays create 3D imagery via the emission, scattering, or relaying of illumination from well-defined regions in (x,y,z) space.

Random-dot stereogram (RDS) is stereo pair of images of random dots which when viewed with the aid of a stereoscope, or with the eyes focused on a point in front of or behind the images, produces a sensation of depth, with objects appearing to be in front of or behind the display level.

Anaglyph 3D stereoscopic 3D effect

Anaglyph 3D is the stereoscopic 3D effect achieved by means of encoding each eye's image using filters of different colors, typically red and cyan. Anaglyph 3D images contain two differently filtered colored images, one for each eye. When viewed through the "color-coded" "anaglyph glasses", each of the two images reaches the eye it's intended for, revealing an integrated stereoscopic image. The visual cortex of the brain fuses this into the perception of a three-dimensional scene or composition.

Stereopsis is a term that is most often used to refer to the perception of depth and 3-dimensional structure obtained on the basis of visual information deriving from two eyes by individuals with normally developed binocular vision. Because the eyes of humans, and many animals, are located at different lateral positions on the head, binocular vision results in two slightly different images projected to the retinas of the eyes. The differences are mainly in the relative horizontal position of objects in the two images. These positional differences are referred to as horizontal disparities or, more generally, binocular disparities. Disparities are processed in the visual cortex of the brain to yield depth perception. While binocular disparities are naturally present when viewing a real 3-dimensional scene with two eyes, they can also be simulated by artificially presenting two different images separately to each eye using a method called stereoscopy. The perception of depth in such cases is also referred to as "stereoscopic depth".

Autostereoscopy any method of displaying stereoscopic images (adding binocular perception of 3D depth) without the use of special headgear or glasses on the part of the viewer

Autostereoscopy is any method of displaying stereoscopic images without the use of special headgear or glasses on the part of the viewer. Because headgear is not required, it is also called "glasses-free 3D" or "glassesless 3D". There are two broad approaches currently used to accommodate motion parallax and wider viewing angles: eye-tracking, and multiple views so that the display does not need to sense where the viewers' eyes are located.

3D stereo view

A 3D stereo view is the viewing of objects through any stereo pattern.

Computer stereo vision is the extraction of 3D information from digital images, such as those obtained by a CCD camera. By comparing information about a scene from two vantage points, 3D information can be extracted by examining the relative positions of objects in the two panels. This is similar to the biological process Stereopsis. Stereoscopic images are often stored as MPO files. Recently, researchers pushed to develop methods to reduce the storage needed for these files in order to maintain the high quality of the stereo image.

Wiggle stereoscopy

Wiggle stereoscopy is an example of stereoscopy in which left and right images of a stereogram are animated. This technique is also called wiggle 3-D or wobble 3-D, sometimes also Piku-Piku.

Orthoscopy used in optics and vision for the condition of normal, distortion-free view, from "ortho", straight, right, correct, and "scope", seeing.

Stereoscopic acuity, also stereoacuity, is the smallest detectable depth difference that can be seen in binocular vision.

Visual space is the experience of space by an aware observer. It is the subjective counterpart of the space of physical objects. There is a long history in philosophy, and later psychology of writings describing visual space, and its relationship to the space of physical objects. A partial list would include René Descartes, Immanuel Kant, Hermann von Helmholtz, William James, to name just a few.

Hans Wallach American psychologist

Hans Wallach was a German-American experimental psychologist whose research focused on perception and learning. Although he was trained in the Gestalt psychology tradition, much of his later work explored the adaptability of perceptual systems based on the perceiver's experience, whereas most Gestalt theorists emphasized inherent qualities of stimuli and downplayed the role of experience. Wallach's studies of achromatic surface color laid the groundwork for subsequent theories of lightness constancy, and his work on sound localization elucidated the perceptual processing that underlies stereophonic sound. He was a member of the National Academy of Sciences, a Guggenheim Fellow, and recipient of the Howard Crosby Warren Medal of the Society of Experimental Psychologists.

References

  1. ↑ Westheimer, Gerald (2011). "Three-dimensional displays and stereo vision". Proc. Roy. Soc. B, 278, 2241-2248. doi : 10.1098/rspb.2010.2777.
  2. ↑ v. Rohr, Moritz (1907). Die Binokularen Instrumente. Berlin: Julius Springer.
  3. ↑ Wallach, H. and Zuckerman, C. (1963). "The constancy of stereoscopic depth". Am. J. Psychol., 76, 404–412.
  4. ↑ Gogel, W.C. (1960). "Perceived frontal size as a determiner of perceived binocular depth". J. Psychol., 50, 119–131.
  5. ↑ Foley, J.M. (1968). "Depth, size and distance in stereoscopic vision". Percept Psychophys, 3, 265–274.
  6. ↑ Johnston, E.B. (1991). "Systematic distortions of shape from stereopsis". Vision Research, 31, 1351–1360.
  7. ↑ Westheimer, Gerald (2011). "Depth rendition of three-dimensional displays", J. Opt. Soc. Am. A 28, 1185–1190.
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