as. The camera
et point for cach
(for example,
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ts can also be
is founded. The
telligent for the
of the network
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In practice, the
hows the target
iS, designer can
object. Camera
be changed, if
1aximum of four
amera locations.
t points to be
or points can be
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. The distance
. The visibility
d. If the point is
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ree-dimensional
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e measurement
3.6. The calculation of simulated images and precision
values
After locating the cameras and measuring points with the
MMD tool, the following information can be used in
simulation:
o The (approximated) object coordinates (XYZ) of the points
to be measured
e The exterior orientation of the cameras (the projection
center coordinates and rotations)
e The interior orientation of the cameras. If calibration data
of the cameras is available, it can be used. In other case,
the values defined by the user are used.
e The lens distortions, aspect ratios and possible additional
parameters. Like interior orientation information these can
be get from calibration file or the values defined by the
user can be used.
The simulated image coordinates are calculated from this
measurement model information (camera parameters, possible
camera calibration data, camera orientation, the coordinates of
object points).
The simulation is made by the least-square method. The
precision values (standard errors of intersected 3D-coordinates,
error ellipses and error ellipsoids) are calculated from the
variance-covariance matrix of the unknown parameters. The
accuracy values are visualized in 3D object space and
geometrically weak areas are easily located. The simulation is
explained in more detail in chapter four.
37. Visualization of precision measures and simulated
images
The MMD tool enables the visualization of calculated
precision measures and images in AutoCAD. The simulation
program produces AutoLISP-files needed by the MMD tool's
visualization functions.
The simulated images are visualized. Point distribution on the
images can be evaluated visually. An example of the simulated
images are shown in figure 2. There are two frames in every
image. The outer frame shows the image area and the inner
frame shows the area, where the targets are measurable.
Precision measures like standard errors of the unknown
coordinates, error ellipses in various planes (XY, XZ, YZ),
error ellipsoids or mean radial spherical error (MRSE) can be
drawn for every point. This kind of visualization is very
illustrative compared to precision values expressed only as
numbers. However, for the visualization purposes, the
precision measures have to be scaled and this should always
be kept in mind. Examples of visualization are given in figures
3,4,and 5.
Figure 2. Example of simulated images. The outer frame
Visualize the image area and the inner frame shows the area,
Where the target is able to be measured.
435
Figure 3. Example of visualization of standard errors for the
unknown coordinates of the object points. See chapter 4.2. for
more details.
Figure 4. Example of visualized mean radial spherical errors
(MRSE). See chapter 4.2. for more details.
A |s . 0
| °
bee 9 . e
de lo 2 2
Ll QQ
Figure 5. Example of standard error ellipses in XY-, XZ- and
YZ- planes.
4. SIMULATION OF PRECISION
The simulation is made by the least-square method. The linear
functional and stochastic model of the least squares adjustment
is (see for example, Fraser, 1989) is following:
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B5. Vienna 1996
