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Fig. 2.6
Hand-forearm
model.
Left
: Definition of the
cones.
Right
: Dependencies
of the radii derived from
human anatomy
W
p
2
=
W
p
1
+
T
R
Z
(β
1
)
·
R
Y
(α
1
)
·
l
forearm
·[
1
,
0
,
0
]
(2.8)
W
p
3
=
W
p
2
+
T
,
R
Z
(β
2
)
·
R
Y
(α
2
)
·
l
hand
·[
1
,
0
,
0
]
(2.9)
where
l
forearm
and
l
hand
are the predefined lengths of the human hand-forearm limb.
The
x
and
y
axes are running in the horizontal and vertical directions parallel to
the image plane, respectively, while the
z
axis denotes the depth. The matrix
R
Y
(α)
represents a rotation around the
y
axis by the angle
α
, and
R
Z
(β)
a corresponding
rotation around the
z
axis.
The lengths
l
hand
and
l
forearm
of the hand and forearm are set to uniform fixed
values for all image sequences regarded in the experimental evaluation described in
Sect.
7.4
. Although human hands and forearms may actually have fairly different
lengths, it is shown in Sect.
7.4
that the hand-forearm limb of all test persons is
tracked successfully, and we found that differences between the modelled and the
actual lengths of 100-200 mm are easily tolerated by the system. Such differences
may even occur as short-term variations within a sequence, e.g. when the hand is
grabbing, holding, and depositing a tool.
The shapes of the hand and the forearm relative to the maximal radii
r
1
and
r
4
were derived from human anatomy, as shown in Fig.
2.6
, and are defined according
to
r
2
=
0
.
8
·
r
1
r
3
=
0
.
65
·
r
1
(2.10)
r
5
=
1
.
1
·
r
4
r
6
=
=
0
.
026 m
const
.
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