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Photogrammetry . Lecture 4

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Only one line is common to both the vertical and tilted photographs ... Each epipolar line in a pair of photographs is conjugate to the other ... – PowerPoint PPT presentation

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Title: Photogrammetry . Lecture 4


1
  • Lecture 4 Content
  • Errors on photo
  • Relief
  • Tilt
  • Collinearity

2
  • Errors on photograph
  • A map is an orthogonal projection of the ground
    surface onto a sea level sphere
  • Camera errors
  • Projection is reduced further to a plane
  • Small extent areas, gives a good approximation to
    the terrain.However, it is not so for large
    extents
  • A vertical projection is a central projection
  • Therefore, if a map and a photo is overlaid,
    there will be little coincidence over the whole
    photo
  • Discrepancies are due to the terrain relief and
    camera tilt

3
Internal Sensor Errors
  • Lens distortion and errors cause the light rays
    to deviate

4
  • All aerial cameras have a calibration report
    (Continued)

5
  • All aerial cameras have a calibration report
    (Continued)

6
  • All aerial cameras have a calibration report
    (Continued)

7
  • All aerial cameras have a calibration report

8
Planimetrically Correct
Orthorectification creates planimetrically
correct images, which display no relief
displacement
3D View
9
  • Relief

Map Scale
C
d
f
Two triangles AAA and Coa are similar,
therefore
a
o
a
Nadir Point
H
r
A
rh
D
or

f
h
Substituting
rhf
d
fH
or
A
A
D
10
  • Relief
  • This error is the shift of photographic position
    of an object with respect to the photographic
    position of its orthogonal projection onto the
    datum plane
  • Caused by the variations in the terrains relief
  • Relief error occurs along the radial lines from
  • the nadir point

11
  • Tilt
  • This is the shift of photographic position of an
    object with respect to its image taken from the
    same exposure station with truly vertical camera
    axis

A
B
A
B
12
C
f
b
a
Vertical Photo
d
e
H
D
E
A
B
13
  • Only one line is common to both the vertical and
    tilted photographs
  • Called the isoline or axis of tilt
  • Intersection with principal line is the isocenter

y
Principal line and tilt axis on a tilted photo
e
Isoline (axis of tilt)
e
s
i
o
x
i
n
i
a
Principal line
(180-s)
a
14
  • Points a and b, being on the downside of the
    isoline, are displaced radially from the
    isocenter (i)
  • Points d and e, are shifted radially towards (i)
    because they are above the isoline
  • When tilt and relief displacements compound each
    other, the geometric treatment becomes impractical

15
  • Epipolar lines and planes

16
  • Two photos, a ground point, G, and its images, g1
    and g2
  • Camera locations are C and C
  • Points C, C and G all lie on a plane and such a
    plane is called an epipolar plane
  • Such a plane intersects the two photos along a
    line and on each photo
  • Such a line on the photo is called an epipolar
    line
  • Each epipolar line in a pair of photographs is
    conjugate to the other
  • This concept is useful for digital photogrammetry

17
Collinearity Condition
  • A line extending from

the exposure station
to the image point
and to the ground point
must be linear
This condition is used to mathematically relate
image and ground measurements to the Exterior
Orientation parameters
18
  • Collinearity
  • to reconstruct a model in the object space from
    measurements on photographs, use is made of
    mathematical models that represent the
    relationship between points in the object space,
    the perspective center, and parameters of the
    camera
  • X,Y,Z Cartesian coordinate system is used as a
    reference for object space
  • x,y,z Cartesian coordinate system is used to
    reference the image space
  • Object coordinates of the perspective center is
    Xc, Yc, Zc where Zc is the flying height of the
    camera above the datum
  • Object coordinates of the ground point A is XA,
    YA, ZA

19
Need to get the coordinates of the point a
defined on the image coordinate system and also
get the coordinate of the similar point A on
the object coordinate system (ground control)
20
  • The image vector from the perspective center
    C to the image point and the object vector
    from to the object point
  • are collinear
  • These points should also be collinear during
    photogrammetric reconstruction and data reduction
  • Two vectors are said to be collinear if one is a
    scalar multiple of the other

a
C
A
21
  • a kA equation 1
  • Where k is a scalar that is equal to the ratio of
    the length of a to the length A
  • If the two vectors are referred to the same
    coordinate system then
  • Substituting into equation 1

Where M is the orientation matrix defined to
rotate the image system to become parallel to the
object system
22
(No Transcript)
23
  • The End
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