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Stereoscopic Parallax

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If a nearby object is observed alternately with the left and right eye, its location will appear to shift from one position to another. This apparent shift of place is known as parallax.  In other words, parallax is an apparent displacement of an object when seen from two different positions.
Whereas, Stereoscope, optical instrument, through which one may view photographs of objects not merely as plane representations, but with an appearance of solidity, and in relief. The stereoscope is essentially an instrument in which two photographs of the same object, taken from slightly different angles, are simultaneously presented, one to each eye. Each picture is focused by a separate lens, and the two lenses are inclined so as to shift the images toward each other and thus ensure the visual blending of the two images into one three-dimensional image.
Similarly, in aerial photography, an object is photographed from two different positions, this results in an apparent shift in the positions of that object, which is referred to as parallactic displacement. On overlapping prints this displacement can be measured s a linear distance which is related to the height of the object. See image below:
stereoscopic parallax - Forestrypedia


Parallax is of two types:

  1. Absolute stereoscopic parallax (X-parallax)
  2. Y-parallax
  3. Absolute parallax:

It is defined as, “Displacement along or parallel to the line of flight and is represented by the algebraic difference of the distances of corresponding images from their respective nadirs when measured parallel to the line of flight”.
For the sake of convenience, the average photo base length of a stereo pair (i.e. x+x’) is commonly substituted for absolute stereoscopic parallax (P) in the solution of parallax equation.
The parallax eq is:
ho / H – h = d + d’ / (x + x’) + (d + d’)
          =>          ho / H – h = dP / P + dP     
          =>         ho = (H – h) dP / P + dP
                                                Where;  ho        = height of object
P        = absolute parallax at the base of object
dP      = parallax difference
H       = height of camera above sea level
h        = height of datum plane above sea level
 The results are reasonably accurate provided:

  • Tilt is less than (3o).
  • Both nadir (N) and principal point (PP) are at the same ground elevation.
  • Both negatives are exposed from the same flight height.
  • Base of the object and principal point are approximately at the same ground level.
  1. Y- Parallax:

Y-parallax is defined as, “Displacement at right angles to the line of flight.” Since Y – parallax is not commonly used in aerial photography for forestry purposes there no further explanation of Y-parallax is given here.
Parallax difference (dP):
The difference in X-parallax b/w two different image points is a measure of the distance of one point above the other. In other words, parallax difference (dP) is a difference b/w the X-parallax at the top and X-parallax at the bottom.

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Naeem Javid Muhammad Hassani is working as Conservator of Forests in Balochistan Forest & Wildlife Department (BFWD). He is the CEO of Tech Urdu ( Forestrypedia (, All Pak Notifications (, Essayspedia, etc & their YouTube Channels). He is an Environmentalist, Blogger, YouTuber, Developer & Vlogger.

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