| Revision as of 21:37, 7 March 2005 editFred Hsu (talk | contribs)Extended confirmed users3,624 edits finished first draft of the Simple Wallpaper subsection← Previous edit | Revision as of 22:13, 7 March 2005 edit undoFred Hsu (talk | contribs)Extended confirmed users3,624 edits →Depth MapsNext edit → | ||
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| === Depth Maps === | === Depth Maps === | ||
| Autostereograms where patterns in a particular row are repeated horizontally with the same spacing can be read either cross-eyed or wall-eyed. In such stereograms, both type of reading will produce the similar depth interpretation, with the exception that the cross-eyed reading produces larger depth differences between planes. | |||
| However, icons in a row do not need to be arranged at identical intervals. By varying the interval between icons across the row, one can create different depth for each icon. The depth for each icon is computed from the interval between it and its neighbor at the left. These kinds of autostereograms are designed to be read in only one way, either cross-eyed or wall-eyed. All autostereograms in this wikipedia entry are encoded for wall-eyed viewing, unless specifically marked otherwise. A stereogram encoded for wall-eyed viewing will produce incoherent 3D patterns when viewed cross-eyed. Most MagicEye pictures are also designed to be viewed wall-eyed. | |||
| The following wall-eyed autostereogram encodes 3 planes across the X-axis. The background plane is on the left side of the picture. The highest plane is shown on the right side of the picture. There is a narrow middle plane in the middle of the X-axis. Starting with a background plane where icons are spaced at 140 pixels, one can raise an icon by shifting it n number of pixels to the left. For instance, the middle plane is created by shifting an icon 10 pixels to the left, effectively creating a spacing consisting of 130 pixels. The brain does not rely on intelligible icons which represents an object or a concept. In this autostereogram, patterns become smaller and smaller down the x-axis, until they become random dots. The brain is still able to matches these random dot patterns. | |||
| ] | |||
| The relationship (distance interval) between any pixel and its counterpart pixel in the equivalent pattern to the left can be expressed in a depth map. A depth map is simply a greyscale image which represents the distance interval of a pixel using a greyscale value between black and white. By convention, the closer the distance, the brighter the color. In an 8-bit greyscale image, there are 256 possible values. Normally 0 represents black, while 255 represents white. | |||
| Using this convention, we can create a greyscale depth map for the above autostereogram using black, grey and white. We can use black, grey and white to represent shifts of 0-pixel, 10-pixels and 20-pixels, respectively. Given any depth map and a small background pattern, a software program can tile the small pattern horizontally at spacing intervals dictated by the depth map. The end result is a autostereogram. | |||
| ] | |||
| ] | |||
| For instance, a program can take the following depth map and the accompanying pattern to produce a autostereogram showing three raised rectangles. | |||
| ] | |||
| ] | |||
| The resulting autostereogram is shown below. | |||
| The following image that every pixel in the resulting autostereogram obeys the distance interval specified by the depth map. | |||
| === Random Dot stereogram === | === Random Dot stereogram === | ||
Revision as of 22:13, 7 March 2005
An autostereogram is a single-picture stereogram, designed to trick human eyes (and brains) into seeing a three-dimensional scene in a two-dimensional image. The Magic Eye series of books featured a type of autostereogram called a random dot stereogram.
History
The first random-dot stereogram was created as an experiment in stereopsis by Dr. Bela Julesz in 1959.
How they work
Simple Wallpaper Autostereogram
The human brain accomplishes stereo vision by a complex set of mechanisms which attempt to relate the two slightly different two-dimensional images seen by the two eyes. The brain tries to assemble a three-dimensional impression by matching each point (or set of points) in one eye's view with the equivalent point (or set of points) in the other eye's view. It therefore assesses the points' positions in the otherwise inscrutable z-axis (depth).
When the brain is presented with a series of very similar points, such as in a repeating pattern like you might see on wallpaper, it has difficulty matching the two eye's views accurately. By looking at a horizontally repeating pattern, but focusing in front of the pattern, it is possible to trick the brain into matching one element of the pattern, as seen by the left eye, with another (similar looking) element, beside the first, as seen by the right eye. This gives the illusion of a plane bearing the same pattern but located behind the real wall. The distance at which this plane lies behind the wall depends only on the spacing between identical elements.
Autostereograms use this dependence of depth on spacing to create three-dimensional images. If, over some area of the picture, the pattern is repeated at smaller distances that area will appear closer than the background plane. If the distance of repeats is longer over some area, then that area will appear more distant (like a hole in the plane).
People who have never seen an autostereogram have a hard time understanding remarks such as, "the image will just pop out of the background, after you stare at the picture long enough", or "the 3D objects will just emerge from the background." The following picture illustrates how virtual 3D objects perceived by a viewer of the autostereogram would look, when viewed from the side, if these virtual 3D objects existed in real world.
The 3D effects in the previous autostereogram were created by repeating the background pattern (the tiger rider icon) every 140 pixels. The second plane displays shark rider icons every 130 pixels. The highest plane displays tiger icons every 120 pixels. The closer a pattern is packed horizontally, the higher is it lifted from the background plane. This distance is referred to as the 'depth' or z-axis value of a particular pattern in the stereogram.
The brain is surprisingly capable of instantly matching hundreds of patterns repeated at different intervals in order to recreate correct depth information for each pattern. The following autostereogram contains some 50 tigers of varying size, repeated at different intervals. Despite the apparent chaotic arrangement of patterns, the brain is able to place every tiger icon at its proper depth.
This is how 3D objects in the above autostereogram appears to a virtual viewer who can scrutinize the virtual scene in a virtual mental universe.
Depth Maps
Autostereograms where patterns in a particular row are repeated horizontally with the same spacing can be read either cross-eyed or wall-eyed. In such stereograms, both type of reading will produce the similar depth interpretation, with the exception that the cross-eyed reading produces larger depth differences between planes.
However, icons in a row do not need to be arranged at identical intervals. By varying the interval between icons across the row, one can create different depth for each icon. The depth for each icon is computed from the interval between it and its neighbor at the left. These kinds of autostereograms are designed to be read in only one way, either cross-eyed or wall-eyed. All autostereograms in this wikipedia entry are encoded for wall-eyed viewing, unless specifically marked otherwise. A stereogram encoded for wall-eyed viewing will produce incoherent 3D patterns when viewed cross-eyed. Most MagicEye pictures are also designed to be viewed wall-eyed.
The following wall-eyed autostereogram encodes 3 planes across the X-axis. The background plane is on the left side of the picture. The highest plane is shown on the right side of the picture. There is a narrow middle plane in the middle of the X-axis. Starting with a background plane where icons are spaced at 140 pixels, one can raise an icon by shifting it n number of pixels to the left. For instance, the middle plane is created by shifting an icon 10 pixels to the left, effectively creating a spacing consisting of 130 pixels. The brain does not rely on intelligible icons which represents an object or a concept. In this autostereogram, patterns become smaller and smaller down the x-axis, until they become random dots. The brain is still able to matches these random dot patterns.
The relationship (distance interval) between any pixel and its counterpart pixel in the equivalent pattern to the left can be expressed in a depth map. A depth map is simply a greyscale image which represents the distance interval of a pixel using a greyscale value between black and white. By convention, the closer the distance, the brighter the color. In an 8-bit greyscale image, there are 256 possible values. Normally 0 represents black, while 255 represents white.
Using this convention, we can create a greyscale depth map for the above autostereogram using black, grey and white. We can use black, grey and white to represent shifts of 0-pixel, 10-pixels and 20-pixels, respectively. Given any depth map and a small background pattern, a software program can tile the small pattern horizontally at spacing intervals dictated by the depth map. The end result is a autostereogram.
For instance, a program can take the following depth map and the accompanying pattern to produce a autostereogram showing three raised rectangles.
The resulting autostereogram is shown below.
The following image that every pixel in the resulting autostereogram obeys the distance interval specified by the depth map.
Random Dot stereogram
Subtle changes in spacing can create the illusion of smooth gradients in distance rather than the simpler-to-achieve jumps in depth. This fine-tuned gradient requires a pattern more complex than a standard repeating-pattern wallpaper, so typically a pattern consisting of repeated random dots is used. This forms what is called a random dot stereogram
How to see them
Much advice exists about 'seeing' an autostereogram (that is, seeing the intended three-dimensional image). The first step is to understand what the intended result is. The aim is to unfocus the eyes so that the image of one iteration of a pattern from one eye overlaps the image of a different iteration of the pattern from the other eye.
Many books recommend the viewer to hold one finger between his eyes and to move it slowly towards the picture, maintaining his focus on the finger at all times, until he is correctly focused on the spot between him and the picture that will allow him to view the illusion.
Other texts recommend staring at 'infinity' - that is, focusing on something distant - and then moving the picture towards or away from the eyes until a comfortable focus is obtained. This method is less practical for viewing autostereograms on a computer screen.
Whichever method works (if either) may depend on whether the viewer is naturally cross-eyed or wall-eyed. It is estimated that some 2% of normally sighted people cannot see the illusion in autostereograms.
Reference
- Pinker, S. (1997). The Mind’s Eye. In How the Mind Works (pp. 211–298) ISBN 0140244913