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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 1 1 2 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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