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International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV , Part B3. Istanbul 2004
available. Like in close range photogrammetry one could
imagine that points can be reconstructed if the image co-
ordinates of the points are measured from different positions.
Of course, choosing points by an ARS when the image is
moving continuously is difficult. It is e.g. not possible to
visualise both views at the same time. In section 4 a method is
developed that simplifies the creation of three-dimensional
objects for ARS applications.
33 Simulated Data
To test the ARS, data were simulated, containing the geometry
of damaged buildings according to the methodology described
by Schweier et al. (2003). Simulation at the scale of building
parts should not be misunderstood in this context as the
prediction of damages at buildings after an earthquake. Such an
simulation seems to be impossible as there exist various aspects
that cannot be modelled easily. For instance the failure of
building parts can be caused by bad workmanship, poor
material as well as deficiencies in the statics. Furthermore,
furniture inside the buildings could alter the building's
behaviour in the case of an earthquake. The location of cavities
- a place where trapped persons survive more probably - can be
influenced by furniture. That means a realistic simulation of a
real collapse is not possible since too many things are unsure.
However, simulated damages make sense being used for SAR
training purposes.
4. METHODS
Next to hardware and data, a software is needed to run an ARS.
The tasks of the software are to perform the superposition and
to enable the user to interact with the virtual world. To handle
these tasks the following photogrammetric methods have been
developed: a method of computing the needed calibration-
parameters to calculate the superposition and a method of
simplifying the creation of shapes for new virtual objects.
4.1 Superposition
The superposition is achieved by mixing a picture of the reality
with a synthetically generated image rendered by 3D computer
graphics software. The picture of the reality is taken by a
camera or directly observed by the retina of the user of the
retinal display. If the retinal display option is used, the process
of mixing is solved by hardware since the user sees both
pictures through the transparent display at the same time. If the
camera option is used, the video stream of the camera is simply
used as the background of the scene displayed by the 3D
graphics software. The remaining problem is to render the 3D
image geometrical correctly. For this one has to know the
correct mapping, defined by a combination of transformations
and referring transformation parameters. The process of
determining these parameters can be interpreted as a calibration
process.
While indoor AR calibration is widely studied in literature (a
Survey is given by Leebmann (2003)), no detailed description
for outdoor AR calibration can be found in literature. Outdoor
AR calibration has analogies to airborne photogrammetry using
INS and GPS for measuring the exterior orientation of the
camera (Cramer et al., 2002). The functional model for ARS
can be described by a concatenation of several transformations.
The transformation of the point:
911
A)
reference—system
in homogenous co-ordinates is expressed by the product of
several four-by-four matrices of the form:
10
10 aa 2
from
Jrom
with 7, being components of a rotation matrix and [, being the
components of a translation. A three-by-four projection matrix
C 0 Xo 0
Po =ld ¢, yw Q0
070 1 0
is used to transform the point from the camera or eye-system
into the display-system: where C, and C, represent the scale
in the row and the column direction respectively (these scales
are often expressed as focal length and aspect ratio), X, and
Y, are the principal point co-ordinates and d is the skew of
the image. The projection of the point X
u=(n m h):
is the point
nm dites X (1)
GaussKrüger""GaussKrüger
The perspective projection is the non-linear function
pD which transforms the display co-ordinates to image co-
ordinates:
X
x/w (2)
y
yz| y/w |- pD
zZ
z/w
Ww
Since the three rotations between rover and eye-system are not
commutative they have to be kept separate and cannot be
combined.
eye— system T IMU qe rover ( 3)
qnas or pre
EE source rover “GaussKrüäger
world eve—system ~ IMU
The combination of the equations (1), (2) and (3) leads to an
equation that can be used for the bundle adjustment. If the
: J 3 TT source eye— system A d
transformation parameters for rover: * IMU an
p^ Hes are introduced as unknowns in the bundle
eye— system
adjustment, they can be determined and used as calibration
: . ; IMU
parameters. The parameters of the transformations T c and
