The gait profile score and movement analysis profile.
ABSTRACT The Gait Deviation Index (GDI) has been proposed as an index of overall gait pathology. This study proposes an interpretation of the difference measure upon which the GDI is based, which naturally leads to the definition of a similar index, the Gait Profile Score (GPS). The GPS can be calculated independently of the feature analysis upon which the GDI is based. Understanding what the underlying difference measure represents also suggests that reporting a raw score, as the GPS does, may have advantages over the logarithmic transformation and zscaling incorporated in the GDI. It also leads to the concept of a Movement Analysis Profile (MAP) to summarise much of the information contained within kinematic data. A validation study on all children attending a paediatric gait analysis service over 3 years (407 children) provides evidence to support the use of the GPS through analysis of its frequency distribution across different Gross Motor Function Classification System (GMFCS) and Gillette Functional Assessment Questionnaire (FAQ) categories, investigation of intrasession variability, and correlation with the square root of GGI. Correlation with GDI confirms the strong relationship between the two measures. The study concludes that GDI and GPS are alternative and closely related measures. The GDI has prior art and is particularly useful in applications arising out of feature analysis such as cluster analysis or subject matching. The GPS will be easier to calculate for new models where a large reference dataset is not available and in association with applications using the MAP.

Conference Paper: SAR image filtering using wavelet transform
[Show abstract] [Hide abstract]
ABSTRACT: This paper presents a novel multiresolution waveletbased algorithm for filtering SAR images in order to remove speckle noise. The basic idea is to apply to the wavelet coefficients a sizedecreasing halfinterpolated median filter. The size of the median filter is adapted to the noise energy reduction between the image pyramid levels and different filter shapes are used in each wavelet subbands according to the dominant frequencies. Experimental results showed, that the proposed algorithm results in significant noise removal while the edges are preserved in the imagesAcoustics, Speech, and Signal Processing, 1995. ICASSP95., 1995 International Conference on; 06/1995  Annals of Physical and Rehabilitation Medicine 10/2011; 54(S154):146.
 Annals of Physical and Rehabilitation Medicine 10/2011; 54(S154):143.
Page 1
Runner Up of the ESMAC 2008 Best Paper Award
The Gait Profile Score and Movement Analysis Profile
Richard Bakera,b,c,d, Jennifer L. McGinleya,c,*, Michael H. Schwartze,f,g, Sarah Beynona,
Adam Rozumalskie,g, H. Kerr Grahama,h, Oren Tirosha
aMurdoch Childrens Research Institute, Royal Children’s Hospital, Melbourne, Australia
bDepartment of Mechanical and Manufacturing Engineering, The University of Melbourne, Australia
cSchool of Physiotherapy, The University of Melbourne, Australia
dSchool of Physiotherapy and National Centre for Prosthetics and Orthotics, La Trobe University, Australia
eGillette Children’s Speciality Healthcare, St Paul, MN, USA
fDepartment of Orthopaedic Surgery, University of Minnesota, USA
gDepartment of Biomedical Engineering, University of Minnesota, USA
hDepartment of Orthopaedics, The Royal Children’s Hospital, Melbourne, Australia
This paper was selected by an ESMAC Reading Committee headed by Professor Maria Grazia Benedetti. The present paper was edited by Dr. Tim Theologis.
1. Introduction
Instrumented threedimensional gait analysis generates kine
matic measurements of a wide range of variables across the gait
cycle. These span different joints and different planes. Clinical
decisions are generally based on an interpretation of the complex
information contained in these highly interdependent data. It can
oftenbeuseful,however,tohaveasinglemeasureofthe‘quality’of
a particular gait pattern. Such a measure can quantify the overall
severity of a condition affecting walking, monitor progress, or
evaluate the outcome of an intervention prescribed to improve the
gait pattern.
Although other measures have been proposed, the only one to
have widespread clinical acceptance is the Gillette Gait Index [1]
(GGI, originally referred to as the Normalcy Index), which
quantifies the difference between data from one gait cycle for a
particular individual and the average of a reference dataset from
people exhibiting no gait pathology. The GGI, however, has several
shortcomings. These have been well documented and largely
overcome in a recent paper proposing an alternative, the Gait
Deviation Index [2] (GDI). The GGI incorporates temporal spatial as
well as kinematic parameters. The GDI uses only kinematic
variables, and might thus be taken as a cleaner reflection of gait
quality. The entire variability in kinematic variables across the gait
cycle is used, rather than a small number of discrete parameters,
thereby removing much of the subjectivity in choosing those
parameters. Selection of the parameters for the GGI was specific to
children with cerebral palsy whereas the GDI would appear to be a
more general measure of gait pathology.
Gait & Posture 30 (2009) 265–269
A R T I C L EI N F O
Article history:
Received 15 March 2009
Received in revised form 28 April 2009
Accepted 18 May 2009
Keywords:
Gait pathology
Outcome
Gait Profile Score
Gait Deviation Index
Movement Analysis Profile
A B S T R A C T
TheGaitDeviationIndex(GDI)hasbeenproposedasanindexofoverallgaitpathology.Thisstudyproposes
an interpretation of the difference measure upon which the GDI is based, which naturally leads to the
definition of a similar index, the Gait Profile Score (GPS). The GPS can be calculated independently of the
feature analysis upon which the GDI is based. Understanding what the underlying difference measure
represents also suggests that reporting a raw score, as the GPS does, may have advantages over the
logarithmic transformation and zscaling incorporated in the GDI. It also leads to the concept of a
MovementAnalysisProfile(MAP)tosummarisemuchoftheinformationcontainedwithinkinematicdata.
A validation study on all children attending a paediatric gait analysis service over 3 years (407
children) provides evidence to support the use of the GPS through analysis of its frequency distribution
across different Gross Motor Function Classification System (GMFCS)and Gillette Functional Assessment
Questionnaire(FAQ)categories, investigationofintrasessionvariability,andcorrelationwiththesquare
root of GGI. Correlation with GDI confirms the strong relationship between the two measures.
The study concludes that GDI and GPS are alternative and closely related measures. The GDI has prior
art and is particularly useful in applications arising out of feature analysis such as cluster analysis or
subject matching. The GPS will be easier to calculate for new models where a large reference dataset is
not available and in association with applications using the MAP.
? 2009 Elsevier B.V. All rights reserved.
* Corresponding author at: Murdoch Childrens Research Institute, Hugh
Williamson Gait Laboratory, Flemington Road, Parkville, Victoria 3052, Australia.
Email address: jennifer.mcginley@mcri.edu.au (J.L. McGinley).
Contents lists available at ScienceDirect
Gait & Posture
journal homepage: www.elsevier.com/locate/gaitpost
09666362/$ – see front matter ? 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.gaitpost.2009.05.020
Page 2
It has been shown that the GGI requires a reasonably large
number of people in the reference dataset [3], and that values can
vary significantly between different reference datasets [4]. In
contrast, values of the GDI appear much less sensitive to
differences in the reference data [5]. The GDI proceeds naturally
from the gait feature analysis, which provides considerable data
compression and provides a framework for other analytical
techniques such as cluster analysis for gait classification [6].
Finally, the GDI has been demonstrated to correlate well with GGI
and the Functional Assessment Questionnaire (FAQ) in a compre
hensive validation study [2].
As with any other measure, the GDI does have some limitations.
The technique depends on the preliminary analysis of a large
dataset containing examples of all likely gait deviations (3351
subjects were used in the original study [2]). Although the authors
have made the gait features derived from this analysis available for
use, this does limit the potential for this technique to be expanded
to other applications. Deriving a similar index for a new
biomechanical model based on a different marker set, incorporat
ing functional calibration, or including more complex modelling of
the foot, for example, would be a considerable undertaking.
The GDI is a scaled version of the Euclidean distance of a
subject’s kinematics from the average of a reference dataset
calculated ina basis comprised of 15gait features.At first sight this
appears a somewhat abstract quantity and the clinical interpreta
tion of the measure is based upon its scaling relative to the
reference dataset. That scaling has been chosen to ensure a
measure with good statistical properties.
This paper proposes a simpler interpretation of the distance
measure underlying the GDI, which leads to the proposal of a
modified measure that can be calculated independently of the
feature analysis. This adds to our understanding of how it can be
interpreted clinically, and suggests that there may be advantages
in using a raw score (as opposed to a scaled index). The paper thus
presents data to validate such a raw score, and uses the new
understanding of the distance measure as a basis for considering
the relative advantages and disadvantages of raw scores or scaled
indices.
2. Method
2.1. Interpreting the difference measure of the GDI
Thekey tounderstand the differencemeasureused inthe GDIis torecognise that
the feature analysis is based on projecting the original gait data onto the gait
features usingan orthonormal transformation. By definition, theEuclidean distance
–andthereforetheRMSdifference–betweenanytwogaitvectorswillbepreserved
by any such transformation. Thus, if all 459 gait features were used in the GDI
(rather than just the first 15), the difference measure used in the GDI would be the
RMS difference between the patient’s data and the average from the reference dataset
taken over all relevant kinematic variables, for the entire gait cycle. For reasons which
willemergebelow,thisquantitywillbereferredtoastheGaitProfileScore(GPS).As
only the first 15 features are used in the GDI (because this represents a close
approximation to the original gait data), the actual distance measure will be a close
approximation to the GPS. A more formal proof of this is attached as an electronic
appendix.
2.2. Definition of Gait Variable Scores (GVS), the Movement Analysis Profile (MAP) and
the Gait Profile Score (GPS)
Appreciating that the fundamental quantity on which the GDI is based is the
RMSdifferencebetweenthegaitvectorandtheaveragegaitvectorforpeoplewith
no gait pathology suggests that there may be value in considering the RMS
difference between a similar quantity calculated for a single gait variable rather
than the entire gait vector. This will be referred to as a Gait Variable Score (GVS).
The GVS for nine key relevant kinematic variables for the right and left legs can be
combined to form a Movement Analysis Profile (MAP, Fig. 1). The RMS average of
all the variable scores for a particular side will then equal the GPS calculated from
the entire gait vector. It is also possible to calculate an overall GPS from the
variable scoresfromboth sides. Given that the pelvis is common to both segments
it is sensible to include pelvic kinematics from one side only (the left is used by
convention in this paper).
2.3. Validation of the Gait Profile Score
The GPS already has high face validity. The formal validation focuses on its
statistical properties, how it is distributed, its intrasession reliability, and its
concurrent validity compared to the FAQ, Gross Motor Function Classification
System (GMFCS), GDI, and GGI. The data upon which this is based came from all
patients under the age of 18 attending for an instrumentedgait analysis at a tertiary
paediatric hospital during the years 2005–2007. If patients attended more than
once during this period, then only data from their first visit were included. Data
from a sample of convenience of 38 children under 18 years of age with no known
gait pathology were used to form the reference dataset.
All data had been captured using a VICON 512 or MX system and processed with
the PluginGait component for Workstation software (Vicon, Oxford, UK) based on
the required marker set with the use of knee alignment devices during a static trial.
Two AMTI force plates were used to capture force plate data. Trials were processed
sequentially.Ifvalidforce platedatawere availablethen thefirstthreeleft andright
gait cycles identified as having valid kinematic and kinetic data for each patient
were included in the analysis (although no reference was made to kinetic data in
this particular study). If valid force plate data was not available then the first three
left and right gait cycles identified as having valid kinematic data for each patient
were included. Data was uploaded into Gaitabase (http://gaitabase.rch.org.au)
which includes modules for calculating the GGI, GDI and GPS from gait data.
Examination of the distribution of the GPS follows the method of Schwartz and
Rozumalski [2] in assessing concurrent validity with the FAQ, GMFCS, GGI and GDI.
The FAQ is a tenpoint scale rating gait function which is not specific to a particular
pathology [7]. The fivelevel GMFCS is now the standard classification of severity of
cerebral palsy [8]. The frequency distributions of the first recorded GPS score for
each side of all children in each FAQ category and each GMFCS category were
plotted, as were those of the reference dataset of children with no gait pathology.
A Euclidean distance such as the GPS is likely to have a chidistribution so results
are reported in terms of the median value and interquartile ranges (IQR). The GDI,
which involves a logarithmic transformation, was found to be normally distributed
by Schwartz and Rozumalski, and thus both the raw GPS and its logarithmic
transform were assessed for normality using the Kolmogorov–Smirnov test.
Intrasession variability was calculated as the IQR of the GPS for each child
estimated from the three trials.1The median of this was estimated similarly for all
patients and for each category of GMFCS and FAQ.
Concurrent validity was examined by comparing the GPS against other measures
of gait pathology. The GGI is the only widely accepted continuous measure of gait
pathology [2]. Following Schwartz’s observation that the derivation of the GGI
suggests that the metric actually represents the square of the deviation from
normal, the correlation between GPS and the square root of GGI ð
dimensional gait speed (normalised by dividing through by
length and g is the acceleration due to gravity) were examined using Spearman’s
rank correlation and with GDI using exponential regression. As these correlations
are essentially between two measurements made on a single gait cycle, all gait
cycles (i.e. threerightand threeleftforeachchild)areincluded.Analysis ofvariance
(of the logarithmic transform of the GPS to ensure a normal distribution) was used
to determine whether it distinguished between levels of the GMFCS and FAQ. Post
hoc tests were used to identify where the differences occurred.
ffiffiffiffiffiffiffiffiffi
GGI
p
Þ and non
ffiffiffiffiffi
gL
p
, where L is the leg
Fig. 1. The Movement Analysis Profile. Each column corresponds to one of the
kinematic variables. Its height represents the (RMS) average difference across time
between a specific gait cycle and the average gait cycle from people with no gait
pathology. The black area at the foot of the columns represents the average value of
this for people with no gait pathology. The GPS for left side, right side and overall
gait pattern are displayed in the rightmost column.
1Medians and interquartile ranges were estimated on the assumption that the
logarithmic transform of the GPS is normally distributed. Thus the mean (m) and
standard deviation (sd) of ln(GPS) were calculated and exp(m), exp(m ? 0.67sd),
and exp(m + 0.67sd) taken as estimating the median, and lower and upper quartiles
of the GPS.
R. Baker et al./Gait & Posture 30 (2009) 265–269
266
Page 3
The final part of the analysis was to investigate the properties of the individual
GVSs which comprise the MAP, and to determine the relationship of the individual
GVS scores with each other and with the GPS. A Spearman’s rank correlation was
performed between each GVS and the GPS and for each pair of GVSs.
3. Results
Data from the 407 children were used. 271 had cerebral palsy,
88 had general orthopaedic conditions (such as Perthes disease,
slipped upper femoral epiphysis and rotational malalignment), 43
had other neurological conditions (such as spina bifida, hereditary
spastic paraplegia and acquired brain injuries) and five were
idiopathic toe walkers (Table 1).
The frequency distributions of the GPS for the categories of the
FAQ (levels 6–10) and GMFCS (I–III) and also for the children with
no gait pathology (there were too few children in other categories
for meaningful analysis) exhibit skewed distributions as expected
(Fig. 2). Kolmogorov–Smirnov tests showed significant differences
from a normal distribution in the raw GPS scores for all categories
(all p values < 0.05) but no such evidence for any category of the
log transformed data (all p values > 0.05).
For intrasession variability, the median IQR was 0.678. Only 6%
of all patients showed an IQR of greater than 2.08.
A moderate correlation (r = .79) between GPS and
found, suggesting that the two measures are similar (Fig. 3a). The
correlation between GPS and walking speed is weak (r = ?.28,
Fig. 3b) suggesting that the overall effect of walking speed is only
weakly reflected in the kinematics. This suggests that the GPS and
speed may serve as complementary outcome measures reflecting
differentdomains ofgait quality.Thereisa very strongexponential
correlationbetweenGPS andGDI (r = 0.995, Fig.4),confirmingthat
the strong mathematical relationship between them. The oneway
ANOVA confirmedGPSdiffers with bothFAQ (p < .001)and GMFCS
(p < .001) and post hoc tests showed differences between all levels
of the FAQ and GMFCS (p < .02), except for between FAQ levels 7
and 8.
Table 2 shows the Spearman rank correlations of the GVSs with
GPS and with each other. It can be seen that none of the GVSs
correlates particularly strongly with the GPS (knee flexion shows
the highest correlation, r = .72) and that none of the GVS pairs
ffiffiffiffiffiffiffiffiffi
GGI
p
was
correlate particularly strongly (pelvic tilt and hip flexion showing
the strongest correlation, r = .66).
4. Discussion
The GPS has strong face validity being based on the RMS
difference between gait data for an individual child and the
average data from children with no gait pathology. Analysis of
intrasession variability suggests that it is also a reliable measure
(within a single session). The moderate correlation with
the significant differences in GPS between both FAQ and GMFCS
levels provide further evidence of validity.
The extremely strong correlation between the GPS and the GDI
confirms the theoretical conclusion that the two are based on
essentially similar measures of difference. A consequence of this is
that any evidence validating one will automatically stand as a
validation of the other. Indeed, in this context this paper can be
read as independently replicating the study of Schwartz and
Rozumalski [2] in a different laboratory and population, and
strengthening the conclusion that both the GDI and the GPS are
valid and largely equivalent measures of gait pathology. Reporting
of a raw score for GPS and a transformed and scaled index for GDI,
however, results in them having quite different properties. The
decision as to whether one or other is preferable thus rests on a
consideration of these differences.
TheGDI isderivedfromgaitfeature analysiswhichisbasedona
very large dataset of subjects with a wide range of gait pathologies.
Schwartz and Rozumalski [2] have made their gait features
publicly available so that this makes little practical difference to
calculating either measure for data derived from the conventional
gait model. It does, however, impose a considerable barrier to
extending similar techniques to data derived from different gait
models or different activities (running, stair climbing, etc.). The
GPS is independent of the feature analysis and can be calculated
directly from the data of an individual and the averaged data of
people with no gait pathology. On the other hand, Schwartz and
Rozumalski [2] have outlined several interesting properties of
feature analysis and having a measure of gait pathology that
derives directly from the analysis has its attractions.
Another potential advantage of the GPS is the decomposition
referred to here as the MAP. The MAP provides useful insights into
which variables are contributing to an elevated GPS. The lack of
strong correlations of the individual GVSs with the GPS and with
each other suggests that there is considerably more information
contained within the MAP than in the GPS alone. There is a simple
mathematical relationship between the GPS and GVSs as the GPS is
the RMS average of the GVSs. Whilst it is possible to conceive of a
similar decomposition of the GDI it does not have the same
elegance. The extension of logarithmic transform and zscoring to
the constituent gait variables, in particular, would lead to a
complex relationship between component scores and the GDI.
The other major difference between the two scores is that the
GPS is defined as a raw score whereas the GDI is transformed and
ffiffiffiffiffiffiffiffiffi
GGI
p
and
Table 1
Characteristics of study cohort and reference subjects. Mean and standard
deviations are quoted where an assumption of normally distributed data seems
reasonable, median and interquartile range are quoted otherwise.
Summary statisticsCohortReference
Number
Age (years)
BMI (kg/m2)
Nondimensional walking speed
GPS (8)
GGI (no units)
GDI (no units)
407
12 (3)
20 (5)
1.1 (0.3)
9.7 (4.9)
105 (164)
78 (13)
38
11 (3)
19 (5)
1.3 (0.2)
5.2 (1.9)
17 (11)
100 (10)
Mean (sd)
Mean (sd)
Median (IQR)
Median (IQR)
Median (IQR)
Mean (sd)
Table 2
Correlations between GPS and GVS and between the different pairings of GVS expressed in terms of Spearman’s rank correlations (r).
Pel Tilt Hip FlexKnee Flex Ank Dors Pel OblHip Abd Pel RotHip Rot Foot Prog
GPS
Pel Tilt
Hip Flex
Knee Flex
Ank Dorsi
Pel Obl
Hip Abd
Pel Rot
Hip Rot
.47 .63
.66
.72
.34
.54
.60
.26
.36
.56
.44
.29
.30
.36
.31
.44
.24
.26
.35
.32
.61
.47
.19
.21
.34
.31
.28
.36
.44
.09
.15
.10
.09
.14
.18
.17
.57
.10
.15
.31
.23
.24
.18
.22
.12
R. Baker et al./Gait & Posture 30 (2009) 265–269
267
Page 4
Fig. 2. Frequency distribution of the GPS across different levels of the GMFCS (left column), FAQ (right column) and from children with no gait pathology (bottom left).
R. Baker et al./Gait & Posture 30 (2009) 265–269
268
Page 5
scaled. The GPS is reported in the same units (degrees) as the
kinematic variables and its interpretation is based upon this. The
interpretation of the GDI is based on the scaling which has an
average score of 100 for people without gait pathology and ?10
units for every standard deviation away from this. Choice of which
is more appropriate may be dependent on the purpose for which
such scales are being used and also on personal preference.
ThelogarithmictransformationusedtoderivetheGDIresultsin
it having better behaved statistical properties than the GPS. The
normal distribution of the GDI within different categories of the
FAQ does provide a basis for using parametric statistics directly. To
be rigorous it makes sense to perform parametric statistics on the
logarithmic transform of the GPS or nonparametric statistics on
the raw scores. On the other hand the linear relationship between
the GDI and difference from the average data for people with no
gait pathology is lost. A person whose data is twice as different
from that of people with no gait pathology than another person’s
will have twice the GPS.
5. Conclusion
The study concludes that GDI and GPS are alternative and
closely related measures. The GDI has prior art and is particularly
useful in applications arising out of feature analysis such as cluster
analysis or subject matching. The GPS will be easier to calculate for
new models where a large reference dataset is not available and in
association with applications using the MAP.
Acknowledgements
The authors acknowledge funding support from the National
Health and Medical Research Council of Australia [Centre for
Clinical Research Excellence in Gait Analysis and Gait Rehabilita
tion Grant No 264597].
Conflict of interest
Authors Richard Baker, Jennifer L. McGinley, and Oren Tirosh
have filed a patent through their employers for an invention
making use of some of the ideas described in this paper. Otherwise
none of the authors have any financial and personal relationships
with other people or organisations that could inappropriately
influence (bias) their work.
Appendix A. Supplementary data
Supplementarydataassociatedwiththisarticlecanbe found,in
the online version, at doi:10.1016/j.gaitpost.2009.05.020.
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Fig. 3. Correlations of GPS with ð
ffiffiffiffiffiffiffiffiffi
GGI
p
Þ and nondimensional walking speed displaying linear regression line.
Fig. 4. Correlation of GPS with GDI displaying exponential regression line.
R. Baker et al./Gait & Posture 30 (2009) 265–269
269