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1. CHAPTER 4
STEREOSCOPIC PARALLAX
4.1 Depth perception
In our daily activities we unconsciously measure
depth or judge distances to a vast number of
objects about us through our normal process of
vision.
 Methods of judging depth may be classified as
either stereoscopic or monoscopic.
Persons with normal vision (those capable of
viewing with both eyes simultaneously) are said to
have binocular vision, and perception of depth
through binocular vision is called stereoscopic
viewing.
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2. Monocular vision is the term applied to viewing
with only one eye, and methods of judging
distances with one eye are termed monoscopic.
A person having normal binocular vision can, of
course, view monocular by covering one eye.
Monoscopic methods of depth perception
enable only rough impressions to be gained of
distances to objects.
With stereoscopic viewing, on the other hand, a
much greater degree of accuracy in depth
perception can be attained.
2

3. Stereoscopic depth perception is of
fundamental importance in photogrammetry ,
for it enables the formation of a three-
dimensional stereo model by viewing a pair of
overlapping photographs.
The stereo model can then be measured and
mapped.
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4. 4.2 Parallactic angle:
With binocular vision, when the eyes are
focused on a certain point, the optical axes of
the two eyes converge on that point
intersecting at an angle called the parallactic
angle.
 The nearer the object, the greater the
parallactic angle and vice versa. In fig 5.2, the
optical axes of the two eyes L and R are
separated by a distance be, called the eye base.
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5. For the average adult, this distance is between 63
and 69 mm, or approximately 2.6".
When the eyes are focused on point A, the
optical axes converge, forming parallactic angle
a.
Similarly, when sighting an object at B, the optical
axes converge, forming parallactic angle b.
The brain automatically and unconsciously
associates distances Da and Db with
corresponding parallactic angles a and b.
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6. The depth between objects A and B is (Db -Da) is
perceived as the difference in these two
parallatic angles.
The ability of human beings to detect changes
in parallactic angles, and thus judge differences
in depth, is quite remarkable.
Although it varies somewhat among individuals,
the average person is capable of discerning
parallactic angle changes of about 3" of arc, but
some are able to perceive changes as small as
1".
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7. This means that photogrammetric procedures
for determining heights of objects and terrain
variations based on depth perception by
comparisons of parallatic angles can be highly
accurate.
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8. 8

9. Viewing photographs stereoscopically
Suppose that a pair of aerial photographs is
taken from exposure stations LI and L2 so that
the building appears on both photos.
Flying height above grounds is HI and the
distance between the two exposures is B, the
air base.
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10. Object points A and B at the top and bottom
of the building are imaged at a1 and bl on the
left photo and at a2 and b2 on the right photo.
Now, if the two photos are laid on a table and
viewed so that the left eye sees only the left
photo and the right eye sees only the right
photo as shown in fig 5.2.2, a three-
dimensional impression of the building is
obtained.
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11. The three-dimensional impression appears to lie
below the table top at a distance h from the
eyes.
The brain judges the height of the building by
associating depths to points A and B with the
parallactic angles a and b, respectively.
 When the eyes gaze over the entire overlap
area, the brain receives a continuous three-
dimensional impression of the terrain.
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12. This is achieved by the continuous perception
of changing parallactic angles of the infinite
number of image points, which make up the
terrain.
 The three-dimensional model thus formed is
called a stereoscopic model or simply a stereo
model, and the overlapping pair of
photographs is called a stereo pair.
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14. 4.3 y-parallax
An essential condition that must exist for clear
and comfortable stereoscopic viewing is that
the line joining corresponding images be
parallel with the direction of flight.
 When corresponding images fail to lie along a
line parallel to the flight line, y parallax (P y) is
said to exist.
Any slight amount of y parallax causes
eyestrain, and excessive amounts prevent
stereoscopic viewing altogether.
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15.  If a pair of truly vertical overlapping photos
taken from equal flying heights is oriented
perfectly, no y parallax should exist anywhere
in the overlap area.
Failure of any of these conditions to be
satisfied will cause y parallax.
 In fig 5.3.1, for example, the photos are
improperly oriented and the principal points
and conjugate principal points do not lie on a
straight line.
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16. As a result, y parallax exists at both points a and
b.
This condition can be prevented by careful
orientation.
In fig 5.3.2 the left photo was exposed from a
lower flying height than the right photo, and
consequently its scale is larger than the scale of
the right photo.
Even though the photos are truly vertical and
properly oriented, y parallax exists at both points
a and b due to variation in flying heights.
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17. To obtain a comfortable stereoscopic view, the
y parallax can be eliminated by sliding the
right photo upward transverse to the flight
line when viewing point a and sliding it
downward when viewing point b.
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18. 18

19. 4.4 x-parallax
Parallax is the apparent displacement in the
position of an object, with respect to a frame
of reference, caused by a shift in the position
of observation.
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20. The change in position of an image from one
photograph to the next caused by the aircraft's
motion is termed stereoscopic parallax, x
parallax, or simply parallax.
 Parallax exists for all images appearing on
successive overlapping photographs.
 In fig 5.4.1, for example, Images of object
points A and B appear on a pair of overlapping
vertical aerial photographs, which were taken
from exposure stations Ll and L2.
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21. Points A and B are imaged at 'a' and 'b' on the
left-hand photograph.
 Forward motion of the aircraft between
exposures, however, caused the images to
move laterally across the camera focal plane
parallel to the flight line, so that on the right-
hand photo they appear at a' and b'.
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22. Because point A is higher (closer to the
camera) than point B, the movement of image
'a' across the focal plane was greater than the
movement of image 'b' ; in other words, the
parallax of point A is greater than the parallax
of point B.
 This calls attention to two important aspects
of stereoscopic paraIIax :
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23. (1) the parallax of any point is directly related to
the elevation of the point, and
(2) (2) parallax is greater for high points than for
low points.
 Variation of parallax with elevation provides
the fundamental basis for determining
elevation of points from photographic
measurements.
 In fact X, Y and Z ground coordinates can be
calculated for points based upon their
parallaxes. 23

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25. 4.5 Principle or floating mark
• Parallaxes of points can be measured while
viewing stereoscopically with the advantages
of speed and accuracy.
• Stereoscopic measurement of parallax makes
use of the principle of floating mark.
25

26. When a stereo model is viewed through a
stereoscope, two small identical marks etched
on clear glass called half mark may be placed
over the photographs -one on the left photo
and one on the right photo, as illustrated in
5.5.1 .
The left mark is seen with the left eye and the
right mark with the right eye.
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27. The half marks may be shifted in position until
they fuse together into a single mark, which
appears to exist in the stereo model and to lie
at a particular elevation.
 If the half marks are moved closer together,
the parallax of the half marks is increased and
the fused mark will therefore appear to rise.
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28. Conversely, if the half marks are moved apart,
parallax is, decreased and the fused mark
appears to fall.
 This apparent variation in the elevation of the
mark as the spacing of half marks is varied is
the basis for the "floating mark."
The spacing of the half marks (parallax of the
half marks) may be varied so that the floating
mark appears to rest exactly on the terrain.
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29. This produces the same effect as though an
object of the shape of the half marks had
existed on the terrain when the photos were
originally taken.
 The floating mark may be moved about the
stereo model from point to point, and as the
terrain varies in elevation, the spacing of the
half marks may be varied to make the floating
mark rest exactly on the terrain.
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30. Figure 5.5.1 demonstrates the principle of the
floating mark and illustrates how the mark
may be set exactly on particular points such as
A, B and C by placing the half marks at a and
a', b and b' and c and c', respectively.
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