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the proposed method is sensitive to occlusions and self-intersections if they appear
excessively. It is limited to lines and tube-shaped objects, which is useful for a
variety of applications, e.g. in the field of industrial quality inspection. As real-
world applications of the three-dimensional ziplock ribbon snake method, the three-
dimensional reconstruction of a cable and of a glue line on a car body part are
addressed in Sect.
6.2
.
2.2.3 Three-Dimensional Spatio-Temporal Curve Fitting
As an example of three-dimensional pose estimation of articulated objects, this sec-
tion addresses the problem of markerless pose estimation and tracking of the motion
of human body parts in front of a cluttered background. The multiocular contract-
ing curve density (MOCCD) algorithm inspired by Hanek and Beetz (
2004
) and its
spatio-temporal extension, the shape flow algorithm, are introduced by Hahn et al.
(
2007
,
2008b
,
2010a
) to determine the three-dimensional pose of the hand-forearm
limb.
Due to the limited resolution of the trinocular greyscale camera setup it is un-
feasible in the system to model each finger of the hand, as is possible e.g. in the
work by Stenger et al. (
2001
). On the other hand, a cylindrical model of the forearm
as proposed by Schmidt et al. (
2006
) is too coarse due to the variability of human
appearance, e.g. clothes. Hence, the methods described in this section are based on
a three-dimensional hand-forearm model which represents the three-dimensional
contour by an Akima spline (Akima,
1970
) using control points defined by a param-
eter vector. The MOCCD algorithm is computationally too expensive to be used in a
particle filter framework. Hence, it is integrated into a Kalman filter-based tracking
framework which estimates more than one pose hypothesis at a single time step.
The presentation in this section is adopted from Hahn et al. (
2010a
). Further details
are provided by Hahn (
2011
).
2.2.3.1 Modelling the Hand-Forearm Limb
In the application scenario of safe human-robot interaction described in Sects.
7.3
and
7.4
, a three-dimensional model of the human hand-forearm limb will be used
which consists of a kinematic chain connecting the two rigid elements forearm and
hand. The model consists of five truncated cones and one complete cone, as shown
in Fig.
2.6
. The cones are defined by nine parameters according to
T
.
T
=[
p
1
x
,p
1
y
,p
1
z
,α
1
,β
1
,α
2
,β
2
,r
1
,r
4
]
(2.7)
W
p
1
=[
The three-dimensional point
defines the beginning of the
forearm and is part of the pose parameter vector
T
.Thewrist(
W
p
2
) and finger-
tip (
W
p
3
) positions are computed according to
p
1
x
,p
1
y
,p
1
z
]
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