ich. video
’herefore,
ude some
ch video
ire points
formation
h affine
65)
at frame i.
.. LMedS
iatically.
1g, Least
s on each
ward and
SM result.
image to
image to
1g results
‘he good
(d as the
s.
tie point
Figure 8
the first,
points is
'sidual of
ilt of this
late pass
mage are
this 3D
date pass
linate on
erformed
D image
ing LSM.
iss points
2.6 Robust Bundle Adjustment in Global Coordinate
As the final step of exterior orientation, we perform bundle
adjustment in global coordinate system which using the
corresponding points of still image, the GPS observation of
UAV at waypoint and the minimum GCP. The candidate pass
points and tie points detected automatically as mentioned before
generally include mismatching. Also, the GPS observation often
includes outlier. Therefore, the bundle adjustment of this
investigation is performed using robust regression method
based on M-estimator.
The M-estimator is defined as the least-square method that the
each weighting coefficient is decided to suppress the outlier.
Weighting coefficient of M-estimator w” is obtained from
following equation.
w zy(z)(z)]w,
zuy/ e, (6)
where w: weighting coefficient of least-square method
v: residual error of each observation equation
0: RMS of each observation equation.
z: normalized residual error
y: influence function
The influence function y of this investigation is Tukey’s
Biweight that defined as follows.
v(z)s zl -(z/ey] when |z| « C
0 when lz2c (n
The constant C in equation (7) is selected as 5-9.
Therefore, the robust bundle adjustment using M-estimator is
performed by minimizing the following error function.
Ts off 4f
Es 22% X fo -xs| +> wi |G,
p Fr
Ep
g
(8)
where Xp: image coordinate of point p
on the /-th image
Xp: re-projected image coordinate of point p
on the /-th image
Gy: 3-D coordinates of GPS at
the f"-th waypoint
G’r: Computed 3-D coordinates of GPS at
the f"-th waypoint
P,: 3-Dcoordintaes at the g-th GCP.
P',: Computed 3-Dcoordintaes at the g-th GCP.
wy : Weighting coefficient of M-estimator
for re-projection error
wy. : Weighting coefficient of M-estimator
for GPS
w, 7 : Weighting coefficient of M-estimator
for GCP
From this procedure, exterior orientation parameter of each still
image and 3D coordinate of each common feature point are
obtained in global coordinate system, and also the influence of
error observation such as mismatching points or outlier
positioning of GPS at waypoint is suppressed by this procedure.
International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Volume XXXIX-B7, 2012
XXII ISPRS Congress, 25 August — 01 September 2012, Melbourne, Australia
3. EXPERIMENT
In order to evaluate the effectiveness of proposed automatic
corresponding point detection method and robust exterior
orientation method, some experiments were performed. These
experiments performed at the embankment of Arakawa river
side located near the TOKYO. The area of interest was about
80m x 40m. In this area, 11 check points for accuracy
evaluation were constructed before by VRS-GPS surveying.
In this experiment, two kinds of following flights were planned.
The first flight type was planed as photography from constant
altitude like conventional aerial photogrammetry. The second
flight was photography from constant height from the ground
surface.
3.1 Constant Altitude Flight
Figure 9 shows the result of the first flight experiment. In this
case, 33 still images were acquired by UAV. The height from
UAV to ground was changing from about 10m to 20m due to
the altitude of this flight was constant.
The positioning data of each still image were obtained by DGPS
(SBAS) on UAV. From still images, 1029 corresponding points
were obtained automatically with our proposed method using
video image and still image. The exterior orientation of this
experiment was performed by proposed robust bundle
adjustment using still image position and only 3 ground control
points. The outlier in still image position from GPS observation
and miss matched points were suppressed automatically with
our proposed robust bundle adjustment. The RMSE of 3D
measurement for 11 check points from aerial triangulation in
this experiment was 16mm in XY axis and 22 mm in Z axis.
Figure 10 shows the 3D texture model which generated from
automatic corresponding points.
3.2 Topography Trace Flight
Figure 11 shows the result of second flight. The height from
UAV to ground surface was about 15m and UAV flied as trace
the topography of embankment. In this case, 33 still images
were obtained and 1489 common feature points were obtained
automatically. The RMSE of 3D measurement for 11 check
points was 20mm in XY axis and 24 mm in Z axis. Figure 12
shows the 3D texture model of second flight.
* 1 common feature points
: computed still image position
Figure 9. Result of First Flight