2. SOFTWARE AND HARDWARE ASPECTS
For the integration and operation of the system specialised
software was developed, involving all photogrammetric
problems, for the adequate metric exploitation of the video
data.
2.1 Camera calibration
Camera calibration of the video camcorders used is obviously
of utmost importance, in order to ensure high accuracy for the
measurements. It may accurately be performed with the use
of a self-calibrating least squares bundle adjustment. Each
camera setup introduces 15 unknowns into the adjustment. Six
of them are station dependent unknowns, and are usually
referred to as exterior orientation parameters. These are the
three space coordinates of the perspective centre (X,, Y,, Ze)
of the camera lens and the three rotation angles (uw, «p, K) of
the lens axis. Since the commercial camcorders used could
not be considered as metric, each camera introduces 9
additional station dependent unknowns. The set of the
additional unknowns includes the location of principal point (x,,
y,) on the image plane, the camera constant (c), two
parameters for radial distortion, two for decentering distortion
and two affine transformation parameters. The mathematical
model is based on the well known photogrammetric collinearity
equations enhanced with additional correction terms Ax, Ay,
in order to compensate for camera lens distortion errors (He
et al. 1992, Snow et al. 1992):
Ax = x, *x(r^-1)a, « x(r^-1)a, + (r^-2x))a, «2xya, * xa, * ya,
" " iis ii = (1)
by - y,*y(r-)a, » y(r^-1)a; * 2xya, « (r^-2y^)a, - yas
where:
Xp Vo the image coordinates of the principal point
X, y the image coordinates with respect to the
principal point
r the radial distance of the point from the
principal point
a, a, radial distortion parameters
a, a, decentering distortion parameters
A5, A affine transformation parameters
In order to enable the algorithm to solve for the unknown
parameters, a test field including at least 8 suitably signalised
control points is necessary. These control points should be
stable and placed surrounding the moving object. Their location
in space is determined with the help of precise geodetic
measurements.
For the determination of the control points' image coordinates,
an automatic target detection algorithm is used. Firstly image
processing tools, such as average filtering and contrast
stretching, may be used in order to remove the noise
introduced during the digitization of the frames and improve the
quality of the images. Initial target image coordinates are
determined by using a cross correlation algorithm which
matches the observed targets with a predefined target
template (Vernon 1991). It has been found thet the use of
circular black targets on white background facilitates this
phase of the work, because they are not distorted
considerably from different angles of view. To improve the
accuracy, a centroid detection algorithm has been finally used,
which computes the centre of gravity of the black circles with
sub-pixel accuracy.
112
Object coordinates in 3-D space are determined by a two
camera triangulation algorithm (Snow et al. 1992). Image
coordinate measurements of signalised points of interest are
performed automatically on synchronised stereoscopic video
frames of the object, in order to avoid manual identification of
the targets separately on each frame. Synchronisation is
achieved by matching the frames with the same clock
indication, which is present on each recordered frame.
Absolute synchronization of the two cameras requires
specialized hardware which is not usually available for
commercial video camcorders.
The image coordinates of the observed targets are introduced
into the computation as tie points with unknown positions. For
each tie point 3 additional unknowns and 4 observation
equations are added.
2.2 Rectification to the normal case
The production of epipolar images definitely simplifies the
process of stereoviewing and measuring. The rectification of
a stereo pair to the normal case is achieved by using epipolar
geometry and image processing techniques. The basic idea is
simple: if the left and right image planes are coplanar and the
horizontal image coordinates axes are collinear (no k rotation
about the optical axes), then the epipolar lines are parallel in
both images and the corresponding lines have the same y
coordinate. Since such a condition is quite difficult to achieve
in practice, a geometric transformation should be employed in
order to transform both left and right images to the desired
coordinate system of the common plane.
In the following, the algorithm used to rectify a stereo pair of
video images to the normal case will be described. First of all,
the elements of the relative orientation should be determined.
Assuming that the left photo is fixed in position and orientation,
i.e. the three translation displacements and three rotations are
equal to zero, five relative orientation parameters have to be
calculated. The translation displacement dX in the X direction
is fixed at a value approximately equal to the image base, in
order to establish the scale of the stereo model approximately
equal to the image scale. The five unknown parameters are
then computed for the right image. They are the three rotation
angles do, dp, dk and the two translation displacements dY
and dZ.
In the ideal normal case, the right image is considered as
"vertical" (dw=de=dk=0) and no displacements exist in Y and
Z directions, i.e. dY=dZ=0. This means that the right image is
parallel to the left one and the epipolar lines are parallel to the
image coordinate fiducial axis system. Although this ideal case
does not actually exist, it is possible to rotate a gemerally tilted
right photo to a coordinate system that is parallel to the fixed
coordinate system of the left photo by using the following
relations (Chen & Scarpace 1990):
x^, E myX, f ma, T Imc
Ver = MX, + may, - mage (2)
ee -
Z par Maar 7 Mag
where:
Xp y, right image coordinates in coordinate system of the
tiled image
m, elements of rotation matrix
A
Since this transformation produces a different z^, for each
image point, the right image must also be transformed to the
common plane. In this study, a common plane at (-c-dZ) has
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B2. Vienna 1996
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