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Seeing in 3-D Stereo

Prior to the 1930s, most topographic maps were made exclusively from field surveys. With the advent of aerial photography, and specifically in stereo pairs, planimetric maps became possible and special instruments could draw contours. Ground surveying is still necessary to precisely locate calibration points within photo scenes.. To understand how we apply stereophotogrammetry to contouring requires mastery of the concepts behind stereographic viewing.

This style of viewing is as familiar as seeing. When we alternately blink our eyes, objects appear to move slightly sideways. This shift is even more dramatic when we hold an index finger about 30 cm (18 in) in front of our nose and perform the above eye activity. This apparition comes from the principle of parallax. Parallax is the apparent displacement of a viewed point or small object at a distance that results from a change in the point of observation. For a person, that change in the point of observation could simply be from one eye to the other at a fixed location or from relocating from one viewing spot to another. Our line of sight from each eye is not quite parallel to the line between our nose and the selected target, but converges from the eye pair, so that the left eye sees a bit of the left side of the target not seen by the right eye, while the right eye sees a bit of the right side, missed by the left eye. In this way our eyes send a signal to the brain which, on further processing, creates the impression of depth.

This same effect lies at the heart of stereo viewing of photo pairs, taken either from two lateral positions on the ground, or, in aerial photography, as successive photo pairs with about 50% overlap along a single flight line, or with similar sidelap between pairs from adjacent flight lines, with some of the scene in common (see Section 10 for further details). When we position the stereo pair properly left-right and then view them through a stereoscope, the eye-brain reaction is an impression of surface curvature or relief, as though weÕre looking down from a plane at the ground. A pocket stereoscope consists of two lenses that we can adjust along a slide bar to be as far apart as our eyes, placed in a raised mount (on collapsible legs) about six inches above the central region of the stereo pair.

The sense of relief may be exaggerated relative to reality. The degree of vertical exaggeration (VE) depends on the base to height ratio (B/H), which depends on the scale of the photos. The scale, in turn, shows the actual horizontal ground distance (B) between any two equivalent points, identifiable in the two photos, and the height (H) of the camera, during the exposure of each photo in the pair. These points will, of course, not occupy the same position in the two photos because of the forward motion of the imaging platform. The vertical exaggeration also depends on the apparent height (h) of the viewer's eyes and the breadth (b) between the eye centers of the particular viewer. So VE = (B/H)(h/b). VE typically ranges between 1+ and 6+ for B/H ranges between about 0.2 and 1.2.

11-7: Calculate the vertical exaggeration of this set of conditions: Distance on ground = 1800 meters; Height of camera above ground = 4000 meters; Apparent height of viewer's eyes = 40 cm; width between eyes = 6 cm. ANSWER

If you have a pocket stereoscope, you may see the stereo effect by placing it, with legs extended, against the image below as it appears on the screen. This viewing usually doesn't work for most observers, so, it is probably necessary to print the pair, cut them apart, and then view them with the stereoscope. You likely will have to move one or the other laterally until the area viewed in common fuses visually into the stereo effect.

Stereoscopic pair of a mature topography in a dissected hilly terrain.

We extracted the pair, showing mature topography in a dissected hilly terrain, from their proper positions in the full photos and placed them in juxtaposition, separated enough for stereo viewing. You may see the slight differences in shape (and shadowing) of the same hills in the two photos that result from the changed viewing positions.

11-8: In the above stereo pair, assuming you have viewed them stereoscopically, where is the apparent highest peak? ANSWER

If you do not have a stereoscope, you still may be able to get the 3-D effect without one. Many people can see in stereo with their unaided eyes. To test the likelihood of doing this, contact your two index fingers tip to tip at eye level about 20 cm (12 in) in front of your nose. You may see not only them, but an illusory "sausage," about an inch long, consisting of the two finger tips, that appears to "float" between the two real fingers. Moving the fingers closer to or farther from your eyes causes the sausage to expand or shrink. This wonÕt work if you focus directly on the fingers, but should happen if you focus on "infinity," that is, gaze at long distance, so as to focus well beyond the fingers (the "vacant stare"). If this doesn't occur for you, it means you either have some physical eye limitation, or you psychologically don't believe that you can do this. Try this natural stereo viewing either on the image pair above or the one below (or print them, if you need to). Position yourself about 30-45 cm (12-18 inches) from the monitor screen, and stare at the image pair as though you are looking into "virtual space" some distance beyond. Relax. You may need to move your eyes in or out from the screen, as well. If this viewing works, the two images will seem to fuse into a third image between them that has the desired 3-D effect. (Don't be discouraged if nothing happens; some people can see in stereo without a scope with ease but they see only a poor stereo representation on a monitor.)

Stereoscopic image pair.

11-9: Which way do the strata (bands of rocks) appeared to be inclined (the geologist says "dipping"), to the upper right or to the lower left? ANSWER

So, if you do not succeed in seeing stereo on the screen, but have a stereoscope, you may print the above views and examine them on a table. And, perhaps you will need to move the images independently (cut them apart) to find the right separation. Again, we have scanned a pair of photos of an anticline (upward arching fold) in Wyoming and reproduced them below at rather large size. After printing and cutting apart, put the top one to the left of the bottom one and check its stereo expression. It may show up just fine or it may look funny. The positioning relative to the sequence in the flight line must be proper for normal stereo to take place. Since there was no information available to the writer as to whether the top photo was taken first or second, you will have to experiment with choosing which photo to place left of the other, switching until the normal effect leaps out at you.

Stereoscopic image (A) of an anticline in Wyoming. Stereoscopic image (B) of an anticline in Wyoming.


These you must print as movable products. The upper photo is the left one. Hold one in place and move the other laterally until stereo appears. You may have to bend (curl) the paper of one to see the corresponding area in the other. Be sure to trim any borders to eliminate any white effect.

11-10: In stereo, which is lower: the elongate hill within the anticline or its rim? ANSWER

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Primary Author: Nicholas M. Short, Sr. email:

Collaborators: Code 935 NASA GSFC, GST, USAF Academy
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