Photogrammetry ' Lecture 5

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• Lecture 5 Content

• Camera Calibration Report
• Coplanarity

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Camera Calibration Report

• On Calibration Report, PP is usually defined as

Principal Point of Autocollimation

• Given as Xo, Yo

• Other information is obtained from the camera
  calibration report which is used to compute the
  orientation parameters

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Camera Calibration Report
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Camera Calibration Report
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Camera Calibration Report
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• The relationship between the image and object
  coordinate systems is expressed by a 3x3
  orthogonal matrix (M)
• Rotation around the x axis ? ? (omega)
• Rotation around the y axis ? F (phi)
• Rotation around the z axis ? ? (kappa)
• Azimuth ? a
• Tilt ? t
• Swing ? s

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C

• a azimuth is the clockwise angle from the
  ground Y-axis to the principal plane
• t tilt is the angle between the vertical line
  through the exposure point and camera axis
• s swing is the angle measured in the plane of
  the photograph clockwise from the y axis to the
  nadir point of the principal line

f
y
t
Z
x
s
n
Y
a
X
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• For the orientation matrix (m) the nine elements
  are functions of ?,F,? or a,t,s
• The elements are the nine cosines of the spatial
  angles that each of the axes x,y,z makes with the
  axes X,Y,Z

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• Substituting into the colinearity equation
  (akMA) for M

• Multiplying through the RHS and equating the
  terms on the LHS

• Dividing the first and second equation by the
  third

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Least Squares Adjustment

• Collinearity Equations can be solved using the
  Least Squares Adjustment approach
• This technique adjusts your measurements and
  estimates the unknowns by minimizing and
  spreading errors throughout a set of sequential
  photos (called a block)
• Statistical techniques automatically identify,
  distribute, and remove error

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Least Squares How it works?
We measure
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Measurement Quality
Can be thought of as the POSSIBLE ERROR in your
measurements Quality estimates are inputted into
the Block Tool
For the ground measurements
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Measurement Quality
For the ground measurements
We define a standard deviation which indicates
the quality of the measurement
Eg. SD of 5m GCP is within 5m of its true
location (X,Y,Z)
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Measurement Quality
Perspective Centers also need estimates of
quality (X,Y,Z)
Also entered as standard deviation values
For Image measurements We define a standard
deviation which indicates the quality of the
digitizing
e.g. SD of 1 pixel Point is within 1 pixel of
its true location
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Quality Estimates What they do
Adjustment process will move your points until
the best solution is found
Inputted Standard Deviations (Measures of Quality)
The points fluctuate only within the limits of
the specified standard deviation values
Adjustment takes place in the X, Y AND Z direction
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What is the Best Solution ?

• Based on the residuals of the adjustment

This is only ONE residual Least squares approach
tries to minimize measurement residuals across an
entire block...
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• Coplanarity
• Object points are recorded on two or more
  photographs
• Since two rays of light originally emanate from
  the same object point at the time of photography,
  they must therefore be coplanar
• Enforces the fact that two camera stations, two
  image points, and object point all lie on one and
  the same plane

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Building The Relationship

• A mathematical relationship between Image Space
  and Object Space relies on the measurement of
  Control Points

Mathematics can build a relationship between
these values these values
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Epipolar Plane

• Created using the Triangulation Results
• A triangle formed between two perspective centers
  and a ground feature
• Trying to find X, Y, Z for point on the ground

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• Coplanarity (Continued)

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• Using the polygon rule of vector algebra the
  following are the vector format of the coplanar
  condition
• B A1 A2 0
• B ?1 a1 ?2 a2 0
• Where ?1 and ?2 are scalar factors (using the
  colinearity condition)

Airbase components
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• Referring a1 and a2 to the same coordinate system
  for the two photos

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• Substituting into the coplanarity equation
• B ?1 a1 ?2 a2 0
• removes ?1 and ?2 leaving only one equation
  which is written as a determinant

• Which is expanded to give

L1L2 ? camera stations a1a2 ? image points
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• The End