Biomedical Engineering Reference
In-Depth Information
people to compare their results to previously published ones [
39
,
40
]. The key idea is
to place markers on accurate anatomical position where skin markers do not signifi-
cantly slide over the bones. The problem is then to retrieve the location of the internal
joints according to the external position of the markers. In this chapter we describe
the methods commonly used to process motion capture data in order to compute joint
centers and angles.
Let us consider that the position of all themarkersm
i
is known (assuming that there
is no missing information due to occlusions) as shown in Fig.
8.2
. There are mostly
three approaches to deduce the joint centers according to this marker placement. The
first approach consists in applying regressions that express joint centers as a linear
function of external markers' positions [
12
,
29
]. For example, the right shoulder joint
rShoJC could be expressed as:
⎧
⎨
rShoJC
x
=
RSHO
x
11
π
180
)
||
rShoJC
y
=
RSHO
y
+
0
.
43 cos
(
CLAV
−
C
7
||
⎩
11
π
180
)
||
rShoJC
z
=
RSHO
z
−
0
.
43 cos
(
CLAV
−
C
7
||
where RSHO, CLAV and C7 are markers depicted in Fig.
8.2
.
The main advantage of this type of method is simplicity. However this approach
is not very accurate as it is based on average values while anthropometric data in
humans can vary very significantly from one user to another.
The other approach, named functional approach, consists in searching for the joint
centers that would generate the observable displacements [
5
,
7
,
9
]. For example, the
right hip joint (rHip) is assumed to be a ball and socket. Its joint center should be the
center of a sphere that covers the various positions of a point of the femur expressed
in the pelvis reference frame. For example, any position of RKNE should satisfy the
following constraint in the pelvis reference frame:
RKNE
x
−
rHip
x
2
+
RKNE
y
−
rHip
y
2
+
RKNE
z
−
rHip
z
2
l
2
−
=
0
where l is the distance between the hip joint center and RKNE (length of the femur).
Thus recovering the joint center consists in solving an optimization problem:
RKNE
x
(
rHip
x
2
+
RKNE
y
(
rHip
y
2
ar
g
min
rHip
,
l
i
)
−
i
)
−
l
2
2
+
RKNE
z
(
rHip
z
2
i
)
−
−
Of course, to find a good solution, RKNE should have large displacements in all the
possible directions, in order to cover most of the sphere's surface. As a consequence,
this method is generally applied to “range of motion” protocols where the user is
moving each joint in all directions and with large displacements. However if the hip
joint is actually not a ball and socket joint, the result could be inaccurate. Because of
