Single Viewpoint Stereography

B.P. Johnson, Nov. 23, 2004

Single Viewpoint Stereography is a new method for creating stereographic images whereby a scene consisting of horizontal rows of regularly spaced similar objects is photographed from a single viewpoint. When the resulting image is viewed by the cross-eyed free-viewing technique, the viewer perceives a dimension of depth in the two-dimensional image.

The scene may consist of real objects and be captured by a camera. However, the scene may consist of virtual objects and digitally captured by a computer.

The stereographic effect may be increased or decreased by adjusting the distance of the camera from the scene and the field of view.

Deviations from the basic method may be employed for artistic purposes, but must be balanced with the distortion they may introduce.

Single Viewpoint Stereography has valuable potential for many uses in a wide range of endeavors including, but not limited to: advertising, marketing, packaging, animation, visual arts, education, television, movies, the internet, etc.

Background

Stereography in the broadest sense is the term used for methods to create an illusion of depth from a two-dimensional image. Although some traditional methods involving monocular depth cues in images such as perspective, shading, shadows, relative size, etc. may give the viewer a sense of depth, they are not usually described as stereographic methods. There are also some stereographic methods which utilize mechanisms such as Holography, Chromastereography, the Pulfrich Effect and Wobble , but they will not be discussed further. Rather, stereographic methods usually rely heavily on binocular disparity, which is the main focus of this paper.

Human eyes, being separated approximately 2.5 inches, provide two different views of a real object or scene. Our brains fuse these views into one. While doing so, it uses the slight differences in images from the left and right eyes to provide a depth cue.

This cue is combined with monocular cues, motion cues, physiological cues such as eye muscle contraction and convergence, and information stored from previous experience in order for the brain to arrive at a complete evaluation of depth. All cues need not be present for the brain to put together a coherent picture, but the sense of depth will be lessened with fewer cues, and confusion results if one or more of the cues actually contradicts the others. Many optical illusions are dependant on this principle.

When looking at a photograph or flat image, there is no binocular disparity to provide a depth cue. However, if many monocular cues are present we can still detect depth. For example, excellent computer graphics with models, character and scene shading, reflection, shadows, and in the case of animation, motion parallax, can give, with a bit of imagination on the viewer’s part, quite a sense of realism. Although not quite 3D (though some use this term loosely), this effect has come to be referred to more often as 2¹/₂D.

Although some believe there is evidence from ancient Greece and some renaissance era paintings of the use of binocular disparity to create a depth effect, the first documented, widely accepted and popular use was by Sir Charles Wheatstone in the mid-1800s with the introduction of stereo pairs viewed with the aid of his reflecting Stereoscope. In this case, two pictures were taken of the same scene from positions a few inches apart, thereby replicating the views of a right and a left eye. The Stereoscope presented the corresponding picture to the correct eye and the viewer would perceive depth. It was quite a hit in Victorian England.

Over the years innovations were made to cameras, picture taking, and presentation methods. One method for viewing, “free-viewing” or “free-fusion” actually required no equipment, but simply had the viewer relax the eyes (parallel viewing) or cross them (cross-eyed viewing). But the underlying concept for stereographic imaging remained the same: take two pictures of the same scene from two viewpoints and present the appropriate picture to each eye. In the most general term, this technique is described as Stereo Pairing or Stereo Photography.

About the same time as Wheatsone, Sir David Brewster discovered that while free-viewing a repeating pattern in Victorian wallpaper, it appeared to sink away from the wall. Small imperfections in the wallpaper sometimes caused the horizontal spacing of repeating elements to vary slightly. Where this happened the elements seemed to sink or float at different focal planes. This is now termed the "wallpaper effect" and stereographic images utilizing this principle are deemed Wallpaper Type Stereograms. They are made by displaying a repeating pattern of horizontally aligned elements and controlling the depth effect by varying the spacing between them.

In the late 1950s, Dr. Bela Julesz demonstrated a sense of depth could be developed from a flat image using binocular disparity with no other depth cues present. He did this by placing two similar images of random dots side by side. On one of the images he horizontally displaced some of the dots. When examined by free-viewing, the images merged to one, but binocular disparity created by the displaced dots caused the viewer to perceive the dots floating in front of or sinking below the focal plane containing the non-displaced dots.

Later in 1979, Christopher Tyler, a very clever fellow, placed several similar random dot images adjacent to one another to look like a single image, then manipulated the dots in such a way that when free-viewed, a hidden image emerged. Although in reality this was just a variation of Wallpaper Type Stereograms this became known as SIRDS, Single Image Random Dot Stereogram, and was the basis for the stereogram craze in the 1990s.

Because the depth effect was determined by horizontal displacement of dots, the math involved to create a hidden figure was quite intensive. Computers became essential. Algorithms were developed by Tyler and others to calculate the displacement of dots to create the desired effect. Many of these involved using a grayscale image, or “depth map”, of the hidden object, with the degree of shading indicating the desired depth of any particular point. The program would evaluate the brightness of a pixel in the depth map, calculate the displacement needed to create the binocular disparity to cause the correct sense of depth, then shift the pixels accordingly.

Prior Art

Technique 1: Stereo Photography

The practitioner uses two cameras to photograph the scene (Fig 1). The scene may consist of one or more objects and can include a background if desired.

The cameras are separated by some distance. Usually, they are set so that the lenses are approximately 2.5 inches apart, the average distance between the eyes of an adult person. However, the practitioner may elect to vary the distance to change the stereographic effect (Fig 2). Also, common practice is to align the cameras to be parallel to each other, but again, depending on conditions and the desired effect, the practitioner may elect to change the angle, to “toe in” or “toe out” (Fig 3).

Each camera records an image. Because the viewing angles are different for the cameras, the images will differ slightly. These images are then set side by side and presented to the viewer. Depending on how the images are lined up, either the right image on the right or left, the viewer then uses special equipment or will use one of two “free viewing” techniques, parallel of cross-eyed to look at the images.

While one eye is focused on one image and the other eye is focused on the other image, the viewer will perceive three virtual images instead of two real images. Because the middle virtual image is a composition of two real images, the brain uses binocular disparity depth cues and the viewer perceives the scene as if it was three dimensional. The effect can be enhanced by normal monocular depth cues such as perspective, objects overlapping, size disparity, color intensity, shadows effects, etc.

A variation of this technique is to use only one camera, but move it between shots (Fig 4). Also, special cameras with the ability to shoot two photos at once are available. Still however, two images are produced from different viewing angles.

A variation of the above technique is to use one camera and rotate one or more objects between shots (Fig 5). This technique results in a loss of realism, but can produce interesting results.

Stereo Photography has been used for many years to produce stereo pairs which have been viewed by millions of people. In many cases stereoscopic devices, such as ViewMaster, have been developed to relieve the viewer of the task of free viewing.

Sometimes more than two cameras are used producing images from multiple viewpoints. The images are presented side by side, and are viewed as multiple stereo pairs (Fig 6).

More recently computers have replaced cameras and 3D software such as 3DS Max, Lightwave, Maya, Cool3D, and others, are able to produce virtual three dimensional objects, so the scene can now be created on a computer screen and the image digitally captured. The viewing point can then be adjusted, equivalent to moving the camera, and another image is then captured, creating a stereo pair.

Also, as a parallel to real photography, one or more objects can be rotated slightly to produce stereographic effects.

The important thing to note is that even with the use of computers, the technique is the two camera technique, or a variation thereof.

Technique 2: Wallpaper Stereograms

The brain is capable of perceiving depth when no discernable depth cues other than binocular disparity are present. When presented with a plurality of identical (or nearly identical) two dimensional images aligned parallel to the viewer’s eyes, and if the spacing of the objects is not uniform, a person using a free viewing technique (or aided by a stereoscopic device) will perceive the images to be at different depths.

Images of this type are mostly referred to as “wallpaper type stereograms”. Later, variations of this technique were developed into quite sophisticated Random Dot Stereograms, and still later, Single Image Random Dot Stereograms, which caused a pop culture craze in the form of Magic Eye posters.

The technique is pretty simple. Replicate an image several times, align the images horizontally, and vary the spacing between elements. If using parallel viewing (Fig 7), images which are closer together will appear to be closer to the viewer. Just the opposite is true for cross eyed viewing (Fig 8).

An important variation of this technique is to break down the elements into sub-elements and vary the spacing. This allows for much more interesting stereograms.

A simple, non-animated wallpaper stereogram can be hand drawn, or easily constructed on a computer using basic graphic tools. However if the scene becomes more complex with multiple objects and sub-elements, better depth precision is desired or animation is introduced, the task of getting everything in the right spot gets very tough very quickly. Fortunately, algorithms have been developed and incorporated into software to do the calculations and placement of pixels.

Here is the important point. The algorithms all deal with the spacing of objects, sub-elements, or pixels, on a flat plane. That is, the stereogram calls for an element to be at a certain depth. This information is supplied to the program, usually by means of a depth map. The software then computes the spacing of pixels, and then manipulates the screen to produce the desired effect.

Animation is the hardest task. So far, there are programs to do only limited stereographic animation. Of course as computing power increases, the task will become easier.

Other depth cues have to be supplied by the practitioner separately. For instance, in real life, objects which are farther away will be smaller and dimmer. This is not addressed by spacing adjustment algorithms.

Also, in the case of parallel viewing, perspective cues actually contradict the binocular disparity cues. In real life, perspective causes things farther away to look closer together. When using parallel viewing, objects which are spaced closer together appear nearer to the viewer.

Single Viewpoint Stereography

Uniformly arrange identical (or near identical) real objects in horizontal rows. If desired, create more than one row. Different objects may be utilized for different rows, but the horizontal spacing of objects is the same for all rows. Arrange all rows parallel to each other.

With the camera lens perpendicular to the rows, make a photograph.

Because of perspective, objects in rows farther away will be captured on film as being closer together than those in rows closer to the camera. In effect, a stereogram is created. However the spacing of objects, which establishes the depth effect, is not determined by algorithm, but rather by perspective.

The degree of perspective, hence the depth effect, is controlled by (1) the distance the camera is from the scene, and (2) the field of view. When the distance is large and the field of view is narrow, binocular disparity caused by perspective is low, so the image looks relatively flat. As the camera is moved closer and the field of view is widened, the effect of perspective grows and image looks more three dimensional. If the camera is extremely close and the field of view is very wide, perspective causes vast distortion, sometimes such that there is too much binocular disparity for the brain to resolve and the scene is not coherent (Fig 9).

The same technique is used when employing computer software to construct the scene to be digitally captured. 3D modeling software such as 3DS Max, Lightwave, Maya, Cool 3D Studio, Zuma and others are excellent for creating scenes with realistic looking objects and many monocular cues. The scenes consist of rows of 3D models which are uniformly spaced horizontally, and placed at the desired depth, Z.

Adjustments are then made to the distance the camera is away from the scene and the field of view to achieve spacing between elements as a natural consequence of perspective.

When viewed using the cross eyed technique, the non-uniformity of spacing results in the stereographic effect and depth is perceived.

The normal depth cues created by the 3D software, perspective, size, color intensity, shadows, deviation from the horizon, etc. are maintained (maybe not perfectly in some cases, but close enough for the brain to accommodate).

Animation is very simple using the animation capabilities of the software. As long as the scene or elements within the scene are moved so that corresponding elements are aligned horizontally, the stereographic effect is maintained. Actually, as discussed below, strict horizontal alignment isn’t necessary.

Variations

Our brains have great capability to resolve discrepancies and present pleasing, coherent images even when things aren’t perfect. For example, if the scene is rotated a bit around the Y-axis, the rows are no longer viewed as absolutely horizontal and the apparent sizes of objects in each row vary. Yet, even under these conditions, the image may just look great. It depends on the skill of the practitioner in laying out the scene, adjusting the viewpoint, and working the camera. For instance in the example just mentioned, moving the camera back and narrowing the field of view will help minimize distorting effects, but will sacrifice some depth perception. The balance between the two is an artistic choice.

So, with that in mind, here are some examples of deviations from the basic technique.

• Rotation of rows or scene about Y-Axis
• Rotation of rows or scene about Z-Axis
• Combination of rotations about X,Y,Z Axes
• Vary the sizes of objects in a row
• Vary the color of objects in a row
• Vary the shape of objects in a row
• Rotate objects in a row
• Vary spacing between objects in the same row
• Vary object spacing between rows
• Vary depth of objects within a row