whole sensor system can be considered as a rigid body. The
This yields six equations for 5 unknown parameters. The least
lepends on GPS observations can yield part of these parameters, and the squares solution yields the object space coordinates of the
algorithm differential coordinates between the GPS antennas and the required point.
. The DLT cameras then can be obtained based on the calibration results (if
he camera the sensor system is leveled). In the future mapping process, the
(7). camera positions are able to compute just based on the GPS 4 EXPERIMENT
observations and these results
4.1 Test Data Description
If no rotation about the x-axis, then there are only two rotations A three dimensional test range of 23 retro-reflective targets was
(6) between sensor frame and mapping frame, i.e. ¢ (clockwise established on an A-shaped canopy, associating pipe and
about y-axis) and k (clockwise about z-axis). The rotation background wall. The target array occupies a volume of
matrix can be expressed as Equation (11). approximately 5m by 4m by 4m (depth). The test range is
shown in Figure 3.
(7) COS@COSK sink -—singcosk
R--cosgsink cosk singsink (11)
sing 0 cos@
Let the left GPS antenna position as the origin of sensor frame a Conan
(8) and its coordinates in the mapping frame as (X,, Y,, Zo), the o
coordinate of any position such as the camera center in sensor
| frame as (AX, AY, AZ). The purpose of calibration is just to
determine these values. If the calibrated coordinates of sensor
position in mapping frame is (X, Y, Z), then the coordinates of
any position in sensor frame can be computed as following
(9) expressions:
AX X- Xo (12) Figure 3 the picture of test range
AYIZR'IY- Y,
AZ L- Lo Three stations were positioned by the Trimble GPS system to a
] precision of Imm. these stations form the control points from
In the future work, by means of the two GPS observations, the which all the targets were intersected by means of one second
| rotation matrix R can be determined, and the camera position theodolite (Wild T2). The estimated precision of the target
then can be computed according to above calibrated values. As points was +5mm.
the same, the differential rotation between sensor frame and
camera exterior orientation also can be obtained by the The GPS observations for camera location (which were
calibration. Thus, based on this differential rotation and the gathered over a period of 1 hour for each stereopair by relative
differential rotation between S-xyz and M-XYZ, the exterior GPS method) were transformed from WGS-84 Cartesian
(10) orientation of camera can be determined at exposure time coordinates to Hong Kong 1980 local coordinates.
without field control.
6. Forward intersection of any object point corresponding to .
their stereo images. This is achieved as follows: T
J ;
* Compute the rotated 3 dimensional coordinates of f r T
antennas image points based on the solved camera parameters: E
es among
ced values, X ads 3 —P E
| geometry Yj-l^b5i: b2? b3'|:x]|»»y
7 cl c 63 Jr Figure 4 Illustration of the control range
f T r (13) at
The accuracy and precision of the geo-referencing process was
X al a2 a3 X evaluated by an experiment. Three stereopairs of the test field
Ye 5! ps5 y were taken. Of the 23 targets, 12 serve as control information
for the calibration, with the others being used as check points.
Z l cl c2 c3 I =f l The test images were taken from 10m to 15m distance away
* As the inversion of collinearity equations, including With the base line of about I.Im. Moreover, as illustrated in
m unknown scale factors K1 and K2 for each point from the ig-4 the N-axis of the object space coordinate system is
two conjugate images, giving: approximately parallel to the camera base. On the other ‚word,
; the light ray is nearly parallel to the E-axis. The precision of
X = K1XXIHXs = K2X Xr+Xs image coordinate measurement was about 0.5 pixel.
. Y = K1X YITYs = K2X Yr+Ys de The resulting data was processed both as single stereopair and
| mapping L-KIXZHZs - K2X Zr+Zs. as multiple stereopairs to examine the potential accuracy and
as precision improvement.
ecause the
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