2. Introduction
◼ 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.
◼ This motion is another example of parallax. Caused by shifting the
location of the observation point.
◼ 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.
◼ Either moving the head keeping the finger
or blinking one eye at a time.
◼ Closer the finger is held to the eyes, the
greater will be its apparent shift. Apparent
motion of the finger is parallax, it is due
to the shift in the position of observation.
◼ Images of objects would be seen to move
across the field of view in viewfinder.
3. Introduction
◼ Points A and B are imaged at a and b on the left-hand photograph.
◼ Images move laterally across the camera focal plane parallel to the flight
line, so that on the righthand photo they appear at a′ and b′.
◼ Because point B is higher (closer to the camera) than point A, the
movement of image b across the focal plane was greater than the
movement of image a;
◼ The parallax of point B is greater than the parallax of point A.
◼ Two important aspects of stereoscopic parallax:
◼ (1) The parallax of any point is directly related to the
◼ elevation of the point.
◼ (2) parallax is greater for high points than for low points.
◼ Variation of parallax with elevation provides the fundamental basis for
determining elevations of points from photographic measurements.
pa= xa-xa’ pa= 27.41- (-28.66) = 56.07
pb= xb-xb’ pb= 34.40- (-41.50) = 75.90
5. Photographic Flight-Line Axes for
Parallax Measurement
◼ Parallax is occurred along the flight-line.
◼ Photographic x and x′ axes for parallax measurement must be parallel
with the flight line.
◼ Flight line is the line connecting the two principal points.
◼ The y and y′ axes for parallax measurement pass through their respective
principal points and are perpendicular to the flight line.
6. Monoscopic Methods of Parallax
Measurement
1. Direct measurement of x and x′ on the left and right photos,
respectively.
2. By fastening the photographs down on a table.
1. flight lines o1o2 and o1′o2′ are marked as usual.
2. Now parallax is pb=D-db
7. Stereoscopic Methods of Parallax
Measurement
◼ Stereoscope is used with a parallax bar, or a stereometer for calculation.
◼ D = spacing between principal points.
◼ C= the parallax bar constant.
◼ K = the distance from the fixed mark to the index mark of the parallax.
◼ Parallax pf Point A =
◼
8. Parallax Equations
◼ X,Y, Z can be calculated
from parallax.
◼ The XY origin at the
datum principal point P
on left photo.
Similarity triangles
Similarity triangles
Eq (a)
Eq (b)
10. Parallax Equations
hA = the elevation of point A above datum, H is the flying height above datum.
B = the air base.
f = the focal length of the camera.
Pa = the parallax of point A.
XA and YA = the ground coordinates of point A in the previously defined unique
arbitrary coordinate system,
xa and ya = the photo coordinates of point a measured with respect to the flight-
line axes on the left photo.
parallax equations (d, e, & f) enable calculation of air base B and flying height H
with moderate accuracy if sufficient ground controls are available.
X and Y ground coordinates in the unique arbitrary coordinate system of the
stereopair.
This coordinate system is not related to any standard 2D-coordinate system.
2D transformation can be applied to convert from stereo coordinate system to
standard system if two common points are available.
