Information Technology Reference
In-Depth Information
Both homogeneity and symmetry are calculated using a similarity function
(
,
)
(
,
]
F
x
y
, which is defined using Eq. 11.6 and provide values in the interval
0
1
.
In Fig. 11.6, can be seen the shape of this function.
x
if
x
≥
y
>
0
F
(
x
,
y
)=
(11.6)
x
y
if 0
<
x
<
y
11.3.1
Homogeneity (
H
)
The homogeneity (
) is obtained by comparing a gait with itself and it is calculated
for every state using two cycles. Therefore, a gait will be homogeneous for a state
q
i
in the cycle
j
if the area of its rectangle in this cycle (
A
i
j
) is similar to the area of its
rectangle in the next cycle
j
H
1(
A
i
j
+
1
) as shown in Eq. 11.7. The total homogeneity
+
H
|
) is calculated as the average value of the homogeneities of the
four states as shown in Eq. 11.8.
for each cycle
j
(
j
A
i
j
,
A
i
j
+
1
)
H
=
F
(
(11.7)
4
i
=
1
H
1
4
i
H
j
=
(11.8)
j
11.3.2
Symmetry (
S
)
The symmetry (
) is obtained by comparing the movement of both legs. Symmetry
is based on comparing the areas of the rectangles which summarize the states
q
1
and
q
2
(stance and swing phase of the reference foot) versus the areas of the rectangles
which summarize the states
q
3
and
q
4
(stance and swing phase of the opposite foot).
A gait will be symmetric if the areas of the states
q
1
and
q
2
are similar to the areas
of the states
q
3
and
q
4
.
S
The Symmetry in a cycle
j
(
S
j
) is calculated using the
as can be seen in Eq. 11.9, where
A
j
,
A
j
,
A
j
,
A
j
are the
areas of the rectangles corresponding to states
q
1
,
q
2
,
q
3
,and
q
4
in the cycle
j
.
similarity function
F
(
x
,
y
)
A
j
+
A
j
,
A
j
+
A
j
)
S
j
=
F
(
(11.9)
11.3.3
Linguistic Report
To automatically generate a linguistic report on the quality of the gait of a person, we
will use the methodology proposed by Yager [16] and developed also by Kacprzyk
[7], which is based in the concept of fuzzy cardinalities introduced by Zadeh [21].
The idea is to produce a set of natural language (NL) sentences of the type: “Most
times the homogeneity is low” or “Few times the symmetry is high”. First of all,
we have to fuzzify the values of the homogeneity and the symmetry within the set
