Photogrammetry . Lecture 8

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• Lecture 8 Content

• Stereoscopic parallax

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• Nadir an Isocenter on a photo
• Nadir point vertically beneath the camera lens
  at the time of exposure (where a plumb line
  extended from the camera lens to the ground
  intersects the photo image)
• Isocenter point on the photo that falls on a
  line approximately halfway between the principal
  point and nadir

Principal Point
Isocenter
Nadir
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• K-Factor
• The ratio of the air base length to the altitude
  at which a pair of aerial photographs were taken
  (i.e. BH)

B
O2
O1
H
Terrain
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• Stereoscopic parallax
• Parallax is the distance between images of the
  same object on the two photographs forming a
  stereopair

px
A2
z
py
y
A1
x
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• Stereoscopy refers to the ability to perceive the
  object space in three dimension using your two
  eyes
• Using one eye, a persons perception of depth is
  hampered
• Using one eye ? monocular viewing
• Using two eyes ? binocular viewing
• Binocular viewing allows the viewing from two
  different locations due to the separation between
  the eyes (eye base)

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• Convergence angle

b
L
R
H1
F1
H2
P1
h
F2
P2

• Because angle F1 is larger than F2 the observer
  will perceive point P1 as closer than point P2
• difference in distance from observer, (H2-H1h)
  is a function of the difference in convergence
  angle, F1- F2

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• Comparing binocular and stereoscopic viewing

b
Stereoscopic Viewing
Convergence Angle
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• Angle F is called the parallactic angle and its
  linear equivalent is called parallax
• Assuming no tilts, both photos are taken at the
  same altitude, and any rotation of the camera
  from one photo is accommodated by replacing the
  fiducial system of axis by another, then the x
  parallax (or simply parallax) is defined by
• P x-x
• Where x and x are the coordinates on the left
  and right photographs

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• Stereoscopic parallax enables perception of
  height differences
• This is defined by the x-parallax
• Y-parallax once removed, defines the straight
  line between two consecutive photos

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• Height difference using parallax

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• Photos are H above the datum
• Point A is h above the same datum
• Coordinates x and x are defined by the location
  of a and a on image using the principal point on
  each photo as the origin
• That is C1a is equal to x
• Parallax (p) is given by x - x and is the line
  segment aa

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• ? aaE and ? EEA are similar

• To determine elevation of point A requires
• Flying height
• Value of air base
• Camera focal length

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Ground Coordinates formulae

• Determining the ground coordinates of a point
  with respect to an arbitrary coordinate system
  whose origin is vertically below the left
  exposure station and with a positive X in the
  direction of flight

Flight direction
Air Base B
E
E
f
f
x
c1
c2
a
p
x
a
a
(H-h)
XA
O
A
h
Datum
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• Triangles EOA EC1a are similar
• Coordinate for A is (XA,YA) using the arbitrary
  coordinate system
• (x is the distance on the photo for point
  a)

Substituting for h (derived before), we get
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• Recall scale (S) at a point of elevation is given
  by

• Substituting for h which is defined by the
  parallax height equation into the scale equation
  gives

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• Parallax Measurement (Manual method)
• Two photographs are fastened to a base aligned
  along the flight line
• The flight line is derived by locating the
  principal points of the two photographs. Each
  photo with have two points (one for its principal
  point and the other principal point for the
  neighboring photo). Connecting these four points
  a straight line will be formed which is
  indicative of the flight line
• Parallax can then be measure from a single
  measurement using a parallax bar (Such a bar
  measures the linear distances at a very high
  accuracy)
• The distances measured are used in the equations
  derived previously
• Once the photographs are properly secured and is
  in line with the flight line, the distance
  between the two principal points between the two
  photographs is measured and noted
• Parallax is then measured off by selecting
  identifiable common points on the two photographs

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• The End