J. Biomedical Science and Engineering, 2011, 4, 543-551
doi:10.4236/jbise.2011.48070 Published Online August 2011 (http://www.SciRP.org/journal/jbise/
JBiSE
).
Published Online August 2011 in SciRes. http://www.scirp.org/journal/JBiSE
Discrete wavelet and modified PCA decompositions for
postural stability analysis in biometric applications
Dhouha Maatar1,2, Regis Fournier1, Zied Lachiri2, Amine Nait-Ali1
1Université Paris-Est Créteil, Laboratoire Images, Signaux et Systèmes Intelligents, Créteil, France;
2ENIT, Laboratoire Traitement du Signal de l’Image et Reconnaissance de Formes, Tunis, Tunisie.
Received 3 January 2011; revised 15 March 2011; accepted 29 April 2011.
ABSTRACT
The aim of this study is to compare the Discrete
wavelet decomposition and the modified Principal
Analysis Component (PCA) decomposition to analyze
the stabilogram for the purpose to provide a new in-
sight about human postural stability. Discrete wave-
let analysis is used to decompose the stabilogram into
several timescale components (i.e. detail wavelet coef-
ficients and approximation wavelet coefficients).
Whereas, the modified PCA decomposition is applied
to deco mpose the sta bilogram into thr ee component s,
namely: trend, rambling and trembling. Based on the
modified PCA analysis, the trace of analytic trem-
bling and rambling in the complex plan highlights a
unique rotation center. The same property is found
when considering the detail wavelet coefficients.
Based on this property, the area of the circle in which
95% of the trace’s data points are located, is ex-
tracted to provide important information about the
postural equilibrium status of healthy subjects (av-
erage age 31 ± 11 years). Based on experimental re-
sults, this parameter seems to be a valuable parame-
ter in order to highlight the effect of visual entries,
stabilogram direction, gender and age on the postural
stability. Obtained results show also that wavelets
and the modified PCA decomposition can discrimi-
nate the subjects by gender which is particularly in-
teresting in biometric applications and human stabil-
ity simulation. Moreover, both techniques highlight
the fact that male are less stable than female and the
fact that there is no correlation between human sta-
bility and his age (under 60).
Keywords: Approximation Wavelet Coefficients; Detail
Wavelet Coefficients; Discrete Wavelet Analysis; PCA
Decomposition; Phase; Rambling, Stabilogram,
Trembling; Trend, Biometrics
1. INTRODUCTION
Analysis of postural sway is of great interest because it
can be used to identify changes in balance control
mechanisms. Basically, these changes depend on the age
of the person and they occur due to some diseases.
Except the aging, balance control can also be affected
by gender and different sensory systems, including ves-
tibular, visual, and proprioception systems [1-3].
The postural sway is generally quantified by dis-
placement of the Center of Pressure (CoP) over the time.
This displacement is performed by standing in static
position on a platform based on magnetic field [4,5].
The study of postural control sway is performed by
analyzing the stabilogram which is the representation of
COP’s displacement in anteroposterior (AP) and me-
diolateral (ML) direction. In this paper, we consider the
Gravity Center (GC), instead of COP as described in
[4-7].
Several studies showed that the stabilogram is consid-
ered as non-stationary signal, produced by a non-linear
system [8]. To analyze such a signal, numerous tech-
niques have been proposed. For instance, the Empirical
Mode Decomposition (EMD) has been proposed. The
EMD allows an efficient extraction of intrinsic mode
functions, called (IMF) [6,9-11]. Standard Fourier trans-
form has also been used to analyze human posture sta-
bility. In particular, in has been used to highlight the
correlation between the fear of falling and strategies
produced by human postural control [12].
On the other hand, wavelet analysis [13] has been
employed in numerous studies for the purpose to deter-
mine both short-term and long-term diffusion coeffi-
cients from the stabilogram diffusion control [14-17]. It
has been used also to discriminate chronic ankle insta-
bility [18].
In this work, the stabilogram is analyzed using both
wavelet decomposition and the mPCA decomposition
(mPCA) [4,6]. The main goal of this study is to analyze,

D. Maatar et al. / J. Biomedical Science and Engineering 4 (2011) 543-551 544
using these tools, the effect of: 1) vision on the human
postural control; 2) stabilogram direction; 3) age; 4) gen-
der. For this purpose we have constructed a database of
stabilograms, recorded from healthy voluntary subjects.
This paper is organized as follows: in Section 2, we
describe the experimental protocol. Afterwards, the
mPCA and wavelet decomposition methods are pre-
sented in Section 3. Finally, our results and discussions
are provided in Section 4.
2. MATERIALS AND MEASURES
Experimental measures are recorded while an individual
stand upright on a electromagnetic platform [4]. After
performing a calibration and correction phases on these
measures, we obtained the CG displacement in the hori-
zontal plane.
The representation of this CG displacement in medio-
lateral (ML) or anterioposterior (AP) directions is called
the stabilogram [6] as shown in Fi gure 1.
After the calibration phase, the measures are achieved
with subjects standing in an orthostatic position during
30 seconds. Each recorded signal is sampled at 60 Hz.
The measures are then evaluated for twenty five healthy
subjects, including 8 females and 17 males aged between
19 years and 42 years.
 The first measure is achieved by keeping foot out-
spread and opened eyes fixing a point placed on the
wall in front of the subject (PE_YO),
 The second measure is preformed in the situation of
tighten foot and opened eyes (PS_YO),
 The third measure is achieved by considering out-
spread foot and closed eyes (PE_YF),
 The last measure considers tightened foot and
closed eyes (PS_YF).
(a)
(b) (c)
Figure 1. Displacement of the CG in (a) the horizontal plane; (b) stabilogram in mediolateral (ML) direction; and (c) stabilogram in
anteroposterior (AP) displacement.
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3. METHODS
3.1. mPCA Decomposition
The stabilogram is known to be non-stationary signal,
produced by a nonlinear system. It can be considered as
a superposition of many signals having different charac-
teristics [8]. These signals can be differentiated by tem-
poral and dimensional characteristics.
The mPCA decomposition requires two steps. In the
first step, the signal is decomposed according to a de-
terminist component having a low frequency oscillation
(i.e. trend and rambling) and a chaotic signal (i.e. trem-
bling). This is performed thanks to a temporal estimation
of the signal, followed by a representation in phase space,
then a projection on the first main axes.
In the second step, a polynomial approximation is
achieved in order to separate the trend and the rambling.
Consequently, the following three components are ob-
tained (Figure 2):
 Trend: the displacement of the principal segment of
the considered body;
 Rambling around trend: characterized by a low
frequency and a determinist oscillations;
 Trembling around rambling: this signal presents a
complex structure having a chaotic nature.
3.2. Discrete Wavelet Decomposition
As it is well known, wavelet transform method has the ad-
vantage of analyzing signals in a multi-scale manner by
varying the scale coefficient (representing frequency) [19].
The wavelet function is defined at scale a and location
b as:

,
1
ab
tb
ta
a






,ab t
 is also known as “child wavelets” and are
derived from a basis function referred to as the “mother
wavelet”, ψ(t) [20].
The wavelet transform is given by:
 
,
,d
ab
Tabxtt t 



where x(t) is the time series data and T(a,b) is the
“wavelet coefficient” (WC) at timescale a and time in-
stant b [19].
In this study, Daubechies (db2) wavelet function is
used to decompose the stabilogram. Three decomposi-
tion levels are considered (Figure 3).
3.3. Parameter Calculation
The phase is considered as a relevant parameter. How-
ever, it cannot be always defined for the complexes sig-
nals like stabilogram [6-7]. This is displayed by the
visualization of the trajectory in the complex plan of the
analytic signal z(t) defined as:




ztst iht

where s(t) is the original signal and h(t) is the Hilbert
transform of the signal s(t). It is defined as:
 
1PV d
s
ht t





 

where P·V is the Cauchy principle value [6 ].
As shown in Figure 4, one can notice that the trajec-
tory in the complex plan doesn’t show a unique rotation
center but a multiplicity of centers [6-7]. Consequently,
the phase cannot be defined.
Furthermore, the analytic signal can be expressed as:
 

.
eit zt at
where a(t) is the amplitude of z(t) and
 

arctan ht t
s
t






is the instantaneous phase.
Figure 2. mPCA stabilogram decomposition.
Figure 3. Wavelet stabilogram decomposition.
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(a)
(b) (c)
Figure 4. (a) Trace of a stabilogram s(t); (b) trajectory in the complex plan (s,h,t); (c) projection in the plan (s,h) highlighting multi-
ple rotation centers.
In order to use the unique definition of instantaneous
phase, we have to use a signal having a complex plan
trajectory with a unique rotation center.
The visualization of the trajectory in the complex plan
of the trembling (either rambling) resulting from mPCA
decomposition highlights a unique rotation center (re-
spectively Figures 5 and 6).
This property is similar to that obtained for detail signals
resulting from wavelet decomposition (Figures 7, 8 and 9).
Based on the property of having a unique rotation
centre from the trembling and rambling trajectory from
detail wavelet coefficients trajectory, a specific parame-
ter is defined which consider the area of the circle in
which 95% of the data points are located [10].
This parameter is calculated for AP and ML directions,
for the four measures situations (PE_YO, PS_YO,
PS_YF, PE_YF) and for each of these components:
trembling and rambling resulting from mCPA decompo-
sition and cd1, cd2, cd3 resulting from wavelet decom-
position. So, for each subject we calculate the mean of
all stabilogram area’s values. For this purpose, ANOVA
was used to compare results between conditions, age
categories and gender categories.
4. RESULTS AND DISCUSSION
4.1. Visual Entries Effects
As shown in previous studies, the lack of visual infor-
mation causes degradation in the human balance. In fact,
when considering closed eyes, the human posture is less
stable in comparison to the case of opened eyes (postural
Romberg ) [6,19,20] .
When using mCPA decomposition, the area’s value
for rambling was greater for closed eyes (YF) than for
opened eyes (YO) and this is the case for both situations
PE and PS and both directions ML and AP (Table 1).
This increase is indicative of impairment in the stability
with (YF) than with (YO).
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Figure 5. Trajectory in the complex plan (s,h,t) and projection
in the plan (s,h) related to trembling, highlighting a unique
rotation center.
Figure 6. Trajectory in the complex plan (s,h,t) and projection
in the plan (s,h) related to rambling, highlighting a unique rota-
tion center.
Figure 7. Trajectory in the complex plan (s,h,t) and projection
in the plan (s,h) related to cd1, highlighting a unique rotation
center.
Figure 8. Trajectory in the complex plan (s,h,t) and projection
in the plan (s,h) related to cd2, highlighting a unique rotation
center.
Figure 9. Trajectory in the complex plan (s,h,t) and projection
in the plan (s,h) related to cd3, highlighting a unique rotation
center.
However, when using wavelet decomposition, this is
not clearly noticeable from cd1, cd2, cd3 (Table 2).
4.2. Directional Specificity Effects
The direction (AP or ML) has an effect on the postural
stability based on mCPA decomposition, the areas val-
ues in ML direction are greater than in AP direction (es-
pecially with rambling) (Table 1). So, as the visual tar-
get is in front of the subject standing upright for the
measures, the AP is the direction of their eyesight. So,
subjects can better control their stability in AP direction.
This result is coherent with some previous studies
showing that in the direction of head and gazes, subjects
can better maintain their stability [21-23].
In fact, if we consider the area values in AP direction,
it is clear that with the situations of outspread feet
(PE_YO and PE_YF), areas values are very poor (Table
1). This reflects a high ability to maintain equilibrium in
AP direction with outspread feet [24]. When considering
wavelet decomposition (cd1, cd2, cd3) and as seen from
the previous results, area values are greater in ML than
in AP direction for all situations (Table 2 ).
Table 1. The average mean values of surface for all subjects
for the 4 situations (PE_YF, PE_YO, PS_YF and PS_YO) for
AP and ML displacement for rambling and for trembling.
rambling trembling
ML AP ML AP
PE_YF 1.534087680.0842523 0.64587478 0.67442571
PE_YO 0.946819720.06734606 0.66946591 0.67179009
PS_YF 1.462336590.81462864 0.68186796 0.66420952
PS_YO 0.940709230.49604842 0.6582051 0.6592684
P 0.2034 0.0206* 9.0200e-005*** 0
***
The asterisk denotes significant differences *P < 0.05; **P < 0.01; ***P <
0.001 between the 4 situations.
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JBiSE
4.3. Age Effects
The healthy subjects are divided into two groups ac-
cording to their ages: control subject’s mean age is 22.5 ±
2.5 y and adult subject’s mean age is 34.5 ± 7.5 y.
Based on mPCA decomposition and when we con-
sider the rambling, one can notice that there is a signifi-
cant difference in area values between groups whatever
are the situations, including for AP and ML (Table 3).
One can notice too that, the areas are greater for adult
subjects than for young subjects.
This increase in the values of area with age can be in-
dicative of degradation in the stability due to age effect.
This result is in agreement with previous studies
showing that stability decreases with age: more aged less
stable [25-27].
However, this is in contradiction with the result re-
lated to trembling showing that area’s values for Control
are greater than adult (Table 3). This indicates that the
control subjects group is less stable than adult group.
Consequently, in such a case we conclude that the mPCA
is performant, mainly when considering rambling.
When considering wavelet decomposition, results
show that for cd1, cd2 and cd3 values (Table 4 ), there is
no significant observation related to the age.
Tab le 2 . The average mean values of surface for all subjects for the 4 situations (PE_YF, PE_YO, PS_YF and PS_YO) for AP and
ML displacement; (a) for cd1; (b) for cd2; (c) for cd3.
cd1 cd2 cd3
ML AP ML AP ML AP
PE_YF 0.00039101 0.00015779 0.0060499 0.00250787 0.02664542 0.01034699
PE_YO 0.00040679 0.00015265 0.00613421 0.00234226 0.02874592 0.0109055
PS_YF 0.0004069 0.00017734 0.00628928 0.00269899 0.02982301 0.01296493
PS_YO 0.00038226 0.00017001 0.00598332 0.00301738 0.02691371 0.01166842
P 0.9230 7.9197e-004*** 0.9774 0.2402 0.8790 0.0152*
The asterisk denotes significant differences *P < 0.05; **P < 0.01; ***P < 0.001 between the 4 situations.
Table 3. The average mean values of surface for control and adult subjects for the 4 situations (PE_YF, PE_YO, PS_YF and PS_YO)
for rambling in ML displacement; rambling in AP displacement; trembling in ML displacement and trembling in AP displacement.
rambling trembling
ML AP ML AP
PE_YF 0.91119186 0.05390268 0.63572094 0.70079239
PE_YO 0.46550596 0.05128447 0.68981477 0.68492384
PS_YF 1.12265401 0.81426074 0.68057418 0.66607558
Control
PS_YO 0.57720382 0.49154332 0.6749946 0.66485724
PE_YF 2.10906845 0.11226733 0.50463563 0.03801451
PE_YO 1.39110934 0.08217215 0.9293242 0.09704093
PS_YF 1.77588974 0.81496825 0.6482783 0.20751091
adult
PS_YO 1.27625268 0.50020697 0.51649207 0.15789706
PE_YF 0.8440 0.9066 0.1819 0.7960
PE_YO 0.6251 0.9314 0.6403 0.8034
PS_YF 0.8618 0.4298 0.2564 0.4541
P
PS_YO 0.8466 0.8231 0.3431 0.0331*
The asterisk denotes significant differences *P < 0.05; **P < 0.01; ***P < 0.001 between the Control and adult.

D. Maatar et al. / J. Biomedical Science and Engineering 4 (2011) 543-551 549
Consequently, in order discriminate the age one
should apply the mPCA on rambling which is not the
case when dealing with wavelets. Moreover, neither the
mPCA nor wavelets can provide significant results when
considering the trembling.
From the literature [25-28], one can report that the
stability of an individual deceases after 60 years old.
When using the mPCA on rambling, two groups can be
distinguished which is particularly interesting and prom-
ising.
4.4. Gender Effects
The healthy subjects are now divided into two groups
according to their gender. Female subject’s (mean age is
24.5 ± 5.5 y and male subject’s (mean age is 31 ± 11 y).
For trembling resulted using mPCA decomposition,
results show that there is no significant correlations re-
lated to the gender (Table 5). This is in agreement with
many studies that failed to find a significant correlation
for subjects within in the range 20 - 49 y [19,29].
Table 4. The average mean values of surface for control and adult subjects for the 4 situations (PE_YF, PE_YO, PS_YF and PS_YO)
for cd1 in ML displacement; cd1 in AP displacement; cd2 in ML displacement; cd2 in AP displacement; cd3 in ML displacement and
cd3 in AP displacement.
cd1 cd2 cd3
ML AP ML AP ML AP
PE_YF 0.00033999 0.00015515 0.00508957 0.0026089 0.0209911 0.01032489
PE_YO 0.00033609 0.00014953 0.00492099 0.00225385 0.01974882 0.01001624
PS_YF 0.00032508 0.00018229 0.00482645 0.00273241 0.02046734 0.01280845
control
PS_YO 0.0003267 0.00017172 0.00490177 0.00260945 0.02027565 0.01166333
PE_YF 0.0004381 0.00016021 0.00693636 0.00241461 0.03186478 0.01036739
PE_YO 0.00047205 0.00015554 0.0072541 0.00242386 0.03705093 0.01172635
PS_YF 0.00048244 0.00017276 0.00763958 0.00266814 0.03845901 0.01310937
adult
PS_YO 0.00043355 0.00016843 0.00698169 0.00339393 0.03304114 0.01167312
PE_YF 0.0934 0.5975 0.0728 0.5280 0.0362* 0.9666
PE_YO 0.0454* 0.5223 0.0233* 0.3000 0.0181* 0.3514
PS_YF 0.0102* 0.2797 0.0064** 0.6595 0.0067** 0.7479
P
PS_YO 0.0374* 0.7358 0.0194* 0.3945 0.0178* 0.9904
The asterisk denotes significant differences *P < 0.05; **P < 0.01; ***P < 0.001 between the Control and adult.
Table 5. The average mean values of surface for female and male subjects for the 4 situations (PE_YF, PE_YO, PS_YF and PS_YO)
for rambling in ML displacement; rambling in AP displacement; trembling in ML displacement and trembling in AP displacement.
rambling trembling
ML AP ML AP
PE_YF 0.67627757 0.04937066 0.65769619 0.6774052
PE_YO 0.38120252 0.06368456 0.6749903 0.67972198
PS_YF 0.90836733 0.68712844 0.69408988 0.66514428
Female
PS_YO 0.58459383 0.33275789 0.63608973 0.65382143
PE_YF 1.93776303 0.10066719 0.64031177 0.6730236
PE_YO 1.21299252 0.06906912 0.66686619 0.66805743
PS_YF 1.723028 0.87462874 0.67611646 0.66376963
Male
PS_YO 1.10829294 0.57289102 0.66861233 0.66183168
PE_YF 0.3518 0.3343 0.3468 0.7665
PE_YO 0.8259 0.0581 0.5018 0.4880
PS_YF 0.3740 0.1567 0.5217 0.1152
P
PS_YO 0.4325 0.9297 0.5105 0.1515
The asterisk denotes significant differences *P < 0.05; **P < 0.01; ***P < 0.001 between Female and Male.
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Table 6. The average mean values of surface for female and male subjects for the 4 situations (PE_YF, PE_YO, PS_YF and PS_YO)
for cd1 in ML displacement; cd1 in AP displacement; cd2 in ML displacement; cd2 in AP displacement; cd3 in ML displacement and
cd3 in AP displacement.
cd1 cd2 cd3
ML AP ML AP ML AP
PE_YF 0.0003563 0.00014479 0.00555725 0.00259958 0.02502128 0.00930897
PE_YO 0.0003478 0.00013833 0.00527914 0.0021248 0.02446188 0.00944552
PS_YF 0.0003879 0.00016902 0.00597203 0.00258519 0.02758855 0.01271103
Female
PS_YO 0.00035635 0.00016018 0.00570543 0.00247141 0.02641215 0.0108003
PE_YF 0.00040734 0.0001639 0.00628173 0.00246471 0.02740972 0.01083547
PE_YO 0.00043455 0.00015939 0.0065366 0.00244459 0.03076193 0.01159254
PS_YF 0.00041585 0.00018125 0.00643857 0.00275254 0.03087452 0.01308441
Male
PS_YO 0.00039446 0.00017463 0.0061141 0.00327431 0.02714973 0.01207695
PE_YF 0.4263 0.0531 0.5240 0.6833 0.6816 0.1504
PE_YO 0.2469 0.0282* 0.2740 0.0616 0.4468 0.2729
PS_YF 0.6913 0.1928 0.6963 0.2789 0.6688 0.7095
P
PS_YO 0.5065 0.1585 0.6858 0.4162 0.9043 0.1353
The asterisk denotes significant differences *P < 0.05; **P < 0.01; ***P < 0.001 between Female and Male.
However, if we consider the results related to ram-
bling (Table 5), male’s areas are greater than female’s.
This means that females are more stable than males in
the range varying between 19 y and 42 y.
Using wavelet decomposition, the results show that
for ML direction and AP direction (except few values),
values related to cd1, cd2 and cd3 (Table 6) are greater
for males than for females. This means that females are
more stable than males. However, it is more suitable to
use the features extracted from the rambling using the
mPCA, rather using wavelets.
Based on mPCA decomposition (especially on ram-
bling) and wavelet decomposition, results are in agree-
ment with previous studies showing that females are
more stable than males [1,2,30,31].
5. CONCLUSIONS
In this study, mPCA decomposition has been used to
decompose the stabilogram into trend rambling and
trembling. On the other hand, wavelet decomposition
(db3) has been used to decompose the stabilogram into
approximation signal and 3 detail signals (cd1, cd2,
cd3).
By analyzing the detail signals, namely trembling and
rambling signals in the complex plan, it has been clearly
noticed that each of these signals present a unique rota-
tion center. By considering the circle where 95% of the
points are located, its area is evaluated to provide a sig-
nificant parameter.
The analysis of the parameter (circle area) applied on
the mPCA rambling signal, projected on the plan (s,h),
provided interesting results that allow to distinguish be-
tween the visual entries (opened eyes, closed eyes), the
directions AP vs ML, the aging and genders. This pa-
rameter can be used in some interesting and promising
applications such as biometrics and human stability
modeling and simulation.
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