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- rotation (X-axis, Y-axis, Z-axis, positive
directions)
- principal distance
An implementation of an algorithm for finding
initial values based on the method described in
(Haralick et al, 1991) is planned.
43.4 The calibrated parameters The result from
the calibration phase can be divided in two parts:
- Inner orientation parameters
- Outer orientation parameters
The inner orientation parameters are the principal
distance, the principal point, radial distortion
coefficients and the scale difference in x and y. In a
metric camera with fiducial marks these parameters
are defined and constant and indifferent to camera
movement. In a high speed camera this is not the
case. It is especially the principal point which is
unstable due to the lack of fiducial marks. In the
present version the principal point is not regarded as
constant while the other parameters are.
The outer orientation describes the position and the
direction of the camera in the object coordinate
system. If the calibration is done with the same set-up
of the cameras as the actual test set-up, these outer
orientation values can be used as approximate values
for the 3D calculations. They are not used for any
other purpose.
4.4 3D - Calculations
The actual 3D calculation is done either as a result
from the bundle adjustment or as a resection from
the known orientation parameters and image
coordinates. There are two reasons not to make a new
bundle adjustment for each frame: time and stability.
The time requirements for the system will probably
permit an adjustment for each frame, but if a few
hundred frames are measured the time saving is still
considerable. Another reason is the stability of the
system. If a new adjustment is done for each model,
the measuring noise might give a larger instability
than using a constant setting for all frames. An error
in the constant settings will obviously create an error,
but this error will have a uniform structure through
the sequence and the local errors between frames
might be smaller than with a new bundle adjustment
for each frame.
The 3D coordinates are calculated from, at least, two
images. The coordinates for the point is measured in
the images and the object space coordinates are
computed as the intersection of the rays. To be able to
do this, the inner and outer orientation of the
cameras must be known. The inner parameters are
taken from the calibration phase as well as the
approximate values for the outer orientation if the
calibration is done with the same set-up as the test
run. When using high speed film cameras, the inner
orientation is normally not stable since there are no
reference marks (fiducial marks) to define the
principal point. Due to this, the principal point must
be re-calibrated during the 3D calculations. If the
cameras are fairly stable, i.e. the inner and outer
orientation parameters do not change, the 3D
calculations are performed without recalculating the
outer orientation for each image frame. If the
deviations to the known object points are too large
the outer orientation parameters will be recalculated.
fig6 Control point configuration
4.4.1 Control point configuration The purpose of
the control points in the 3D calculation are to connect
the image coordinate systems to the object coordinate
system. In the case of additional calibration of the
principal point they also serve this purpose. The
minimum configuration for the control points are
three points, but in order to achieve some
redundancy and control of the calculations this
number should be increased to at least six points,
preferably three behind the test object and three in
front of the object. They should be as well distributed
as possible under the given practical conditions over
the image plane. An example of acceptable control
point configuration is shown in fig 6.
4.5 Self Diagnosis and Quality Reports
The philosophy of the system is that an operator
should be avle to run through an image sequence
with as little interaction as possible. This means that
errorneous measurements or changes in the inner or
outer orientations must be diagnosed and corrected
automatically as fas as possible by the system. Two
types of diagnosis is made:
4.5.1 Internal Diagnosis By looking at the residu-
als for each computed 3D point indicates if an error
are present. If more than two cameras are used it will
normally be possible to detect the erroneous
measurement. In the camera calibration on known
test-fields, a re-weighted least squares procedure is
used to reduce the effect of the errors.
45.2 External Diagnosis In each frame a few stable
known coordinates will always be seen. They will be
used as a measure of stability during the sequence.
When the 3D calculations are done, these points will
be compared with their true values and if drifted