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CMRT09: Object Extraction for 3D City Models, Road Databases and Traffic Monitoring - Concepts, Algorithms, and Evaluation 
Looking across track (camera tilt perpendicular to base) 
Looking along track (camera tilt parallel to base) 
►x 
Figure 1: Geometry of across track (left) and along track (right) baseline in oblique stereo images 
2 STEREO GEOMETRY AND ACCURACY IN 
OBLIQUE IMAGES 
The dense matching results in point correspondences in a stereo 
pair 5 . The image rays as resulting from those matching image 
pairs are forward intersected in order to compute 3D points in ob 
ject space. In this section a brief theoretic approximatoin of the 
expected accuracy from the given intersection geometry in obli 
que airborne images is derived. Two cases can be distinguished: 
A) the two cameras used for the stereo intersection are oriented 
across track, i.e. they inclose a right angle with the base, and B) 
the cameras are looking in flight direction. The intersection ge 
ometry of the first case can be derived from the standard normal 
case, but the varying scale and the tilt of the camera coordinate 
system wrt the actual coordinate system need consideration. The 
second case can be compared with the longitudinal tilt-setup (Al- 
bertz and Kreiling, 1980), i.e. the normal case with different ca 
mera heights. Only here the whole base is tilted. In Fig. 1 both 
camera geometries are sketched. 
The scale within an oblique image depends on the flying height 
H, the focal length c the tilt angle t, and the angle between the 
viewing ray to a target and the vertical ß (symbols according to 
(Höhle, 2008)): 
H ■ cos(ß — t) 
TO = — - 
c • cos ß 
(1) 
where to: scale at target point. At the principal point 0 equals f, 
whereas at the fore- and the background /3 is determined from t 
and the half field of view a: 0f O re = t — a and ftback = t + a. 
A: tilt across track (side-looking) In the vertical image case, 
the accuracy for triangulated points in height (s' H ), and in X-Y 
plane (sx,y) can be estimated by: 
Finally, the respective error components need to be projected 
from the tilted system to the actual coordinate system: 
sh ~ yj(s' H ■ cos t) 2 + (s[ x y ■ sinf) 2 , (5) 
Sx,y ~ yj{s’ H ■ sini) 2 + (s' x Y ■ cost) 2 , (6) 
thus for a tilt angle of 45° both components will be identical. 
B: tilt along track (forward-looking) To derive the accuracy 
in the tilted system H, X', Y 1 , first the necessary parameters for 
the case of longitudinal tilt need to be computed: Base B' in the 
tilted system and the heights of the cameras I and //: 
H 
= B ■ cos t, 
(7) 
AH' 
= B-sint, 
(8) 
Hi = to • c, 
and H'u = Hi- AH'. 
(9) 
Applying partial derivation wrt the image and parallax measure 
ments to the formulas given in (Albertz and Kreiling, 1980), the 
accuracies for the coordinate components in the tilted system can 
be derived: 
s'hj ~ s' HlI « y/(™) 2 ' s p x + '5, 00) 
s'x,Y ~ ~ ■ S x - (11) 
Note that the actual parallax needs to be computed for the estima 
tion. In the approximations for the given data, see below, a mean 
parallax according to a mean depth in fore- and background was 
assumed. For the planar accuracy the more pessimistic estima 
tion, assuming the smaller image scale, is given here. Finally, the 
planar and height components in the actual coordinate system are 
computed according to equations 5 and 6. 
3 METHODS ADOPTED 
sh ~ -g--m-s px , (2) 
s 'x,y ~ s x ■ to « s y • to, (3) 
where s x « s y « 0.5 • s px are the standard deviations for image 
coordinate and parallax measurements; the errors in the orienta 
tion components are neglected. In the case of the tilted camera 
system, these formulas are applicable to the tilted system, so the 
varying scale needs to be considered, according to equation 1, 
also H' needs to be adopted accordingly: 
H' — to • c. (4) 
5 For the combination of multiple views see the experiment section 
3.1 Block adjustment for multiple platforms 
In (Gerke and Nyaruhuma, 2009) a method to incorporate scene 
constraints into the bundle block adjustment is described and tested. 
The bundle block adjustment algorithm uses horizontal and ver 
tical line features, as well as right angles to support the stability 
of block geometry. Those features can be identified at building 
façades, as visible in oblique images. In addition, the approach 
is able to perform self-calibration on all devices which are incor 
porated in the block. This is an important issue in the case of 
oblique images, as those are often acquired by non-metric came 
ras. The extension to the setup used for this paper where images 
from different platforms are involved is done without any change 
to the core approach.