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Close-range imaging, long-range vision

ntrast to camera
e point accuracy
The orientation
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iss the different
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tension of the
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lanning rescue
ut through a
1 by errors, one
cal image point
with different
joints, tracking
essential. The
nplex as if head
position and head orientation are used as observed parameters,
because for each image point a own head position and
orientation has to be assumed. As shown in the following
sections, these problems can be handled by special design
patterns used by object oriented programming. In the last
chapter the following questions are discussed: Which
calibration procedure is the optimal one? How can the
calibration effort be optimised? Which calibration parameters
are redundant?
The results presented in this paper are produced using the
Ascensions Flock of Bird (FOB) Tracking System and the i-
glasses-Protec STHMD (see figure 2). The basic source co-
ordinate system is realised by a transmitter that is building a
magnetic field. The two sensors of the system, further also
referred to as "birds", are used as mobile sensors that can
compute their orientation and position from measurements of
the magnetic field of the transmitter. In figure 2 the first bird is
attached at the glasses. The second bird is lying on the table
between the glasses and the transmitter. The measurements of
the sensors are the position in the source (transmitter) co-
ordinate system and the orientation of its co-ordinate system in
the source co-ordinate system.

birds ~~

Figure 2. The components of the studied augmented reality
2.1 Estimation of the sensor and image point accuracy
A fast method to approve the manufacture’s specification [1] of
a sensors accuracy is to compare it with other sensors of
superior accuracy [6],[8],[10]. For this study there was not a
device of superior accuracy available. For that reason the
accuracy was estimated by experiments. The accuracy of the
position measurements was estimated by forcing the centre of
the sensor to lie physically on a sphere. The centre of the sphere
and its radius have been estimated as unknown parameters, the
position measurements were used as observations. The mean
errors of the measured position was estimated separately in
various distances to the transmitter. The results are given in
figure (3). The dispersion in the right upper corner is a result of
gross errors.
For the estimation of the accuracy of the measured angles, the
sensor was lying on a plane surface and turned around on the
same place, while permanently measuring the orientation of the
sensor. All measurements can be described as a rotation about
the same axis. All angle measurements can further be referred
to an initial fixed orientation. This model can now be used to
estimate the error of the observed angles again, separately for
different distances to the transmitter (see figure 4). The
resulting equations are not linear a solution is computed using
the Newton method. Gross error cause a divergence in the
Newton method. As a result of the divergence some outliers are
automatically identified. That is the reason, why the number of
outliers is not as large as in figure 3.
The image point accuracy is determined empirically using the
differences of a point that is displayed on the screen and ist
corresponding image point, that was measured by a user with a
cross-hair. The control points have been determined with
superior accuracy. They are assumed to be error free in
comparison to all other occurring errors.

x 10?
5 T : 7 T
4.5} +
3.5} * -
= 3r
E * +
© 2.5 4
E + +
* 5 à
1.5} + + 4
+ +
js * +
* *
* *
0.5 3e À + E
* *
x *
0 L 1 1 1 1 1 1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
distance point to transmittter [m]
Figure 3. Positioning accuracy in different distances.

x 10
8 T T
7r a
6r J
S sl ]
24} 1
o *
3 + 3 .
+ + ; + +
2} + + + + + 1
* *
4 1 1 1 n 1 1
0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distanz [m]
Figure 4. Accuracy of the angles in different distances.
In the following parameter estimation theory (e.g. explained in
[4]) 1s used for the accuracy estimation of the observations and
for the estimation of the unknown parameters. The
implementation of the parameter estimation program is
employing the general case described in [4]. This general case
assumes that there are equation systems with conditions
between several observations and unknowns, extended by
restrictions between the unknowns.
The goal is to find the minimum of the weighted square sum of
the errors. To describe the problem in a formal framework one
has to formalise the following concepts. Let x be the vector of