# Supervised learning for improving the accuracy of robot-mounted 3D camera
applied to human gait analysis.

Diego Guffanti<EMAIL_ADDRESS>Alberto Brunete  Miguel Hernando
David Álvarez  Javier Rueda  Enrique Navarro  Centre for Automation and
Robotics (CAR UPM-CSIC), Universidad Politécnica de Madrid, 28012 Madrid,
Spain.
Department of Electrical, Electronic and Automation Engineering and Applied
Physics, ETSIDI, Universidad Politécnica de Madrid, 28012 Madrid, Spain.
Department of Human Health and Performance, Faculty of Sports Sciences,
Universidad Politécnica de Madrid, 28040 Madrid, Spain.

###### Abstract

The use of 3D cameras for gait analysis has been highly questioned due to the
low accuracy they have demonstrated in the past. The objective of the study
presented in this paper is to improve the accuracy of the estimations made by
robot-mounted 3D cameras in human gait analysis by applying a supervised
learning stage. The 3D camera was mounted in a mobile robot to obtain a longer
walking distance. This study shows an improvement in detection of kinematic
gait signals and gait descriptors by post-processing the raw estimations of
the camera using artificial neural networks trained with the data obtained
from a certified Vicon system. To achieve this, 37 healthy participants were
recruited and data of 207 gait sequences were collected using an Orbbec Astra
3D camera. There are two basic possible approaches for training and both have
been studied in order to see which one achieves a better result. The
artificial neural network can be trained either to obtain more accurate
kinematic gait signals or to improve the gait descriptors obtained after
initial processing. The former seeks to improve the waveforms of kinematic
gait signals by reducing the error and increasing the correlation with respect
to the Vicon system. The second is a more direct approach, focusing on
training the artificial neural networks using gait descriptors directly. The
accuracy of the 3D camera to objectify human gait was measured before and
after training. In both training approaches, a considerable improvement was
observed. Kinematic gait signals showed lower errors and higher correlations
with respect to the ground truth. The accuracy of the system to detect gait
descriptors also showed a substantial improvement, mostly for kinematic
descriptors rather than spatio-temporal. When comparing both training
approaches, it was not possible to define which was the absolute best.
Therefore, we believe that the selection of the training approach will depend
on the purpose of the study to be conducted. This study reveals the great
potential of 3D cameras and encourages the research community to continue
exploring their use in gait analysis.

###### keywords:

3D camera , mobile robot , gait analysis , machine learning

††journal: XXXX-XXXX

##  1 Introduction

3D cameras have been widely used for gait analysis applications. Most studies
claim that these sensors are not accurate enough to be used for gait analysis
[1, 2]. The low accuracy is more noticeable when analyzing gait kinematics
than spatio-temporal parameters [3]. There are several factors that can
influence the accuracy of these sensors: light conditions, sensor position,
occlusion of different parts of the body, among others [4]. However, the main
advantage of these sensors is undoubtedly their low cost and mode of
operation. As they are markerless systems, they greatly facilitate the work of
clinicians when analyzing gait and avoid disturbing patients when placing
markers.

Machine Learning (ML) is an alternative that has opened the gap to improve the
accuracy of 3D cameras. However, current approaches have only applied ML
together with 3D cameras for the classification of normal and pathological
gait [5], gait recognition [6], or for the classification of different
pathologies [7]. On the contrary, they have not pursued an enhancement of the
accuracy of these sensors. This is highly relevant because for clinicians
dealing with this type of gait pathologies, the classification of the disease
is far less relevant than the quantifiable study of its evolution. For this
reason, as a contribution to current approaches, this study aims to improve
the accuracy of the estimated kinematic gait signals (joint angles) and gait
descriptors when using 3D cameras. For this purpose, artificial neural
networks (ANNs) are used. ANNs allow the system to learn from a gold standard
system through supervised learning. It should be emphasized that in this
study, ANNs do not learn a specific gait pattern. On the contrary, this study
attempts to correct the measurement errors of the 3D camera based on the
examples provided by the gold standard system. To achieve this, a windowing
process is applied to the data and each window represents a training sample.
This means that the ANN never learns the gait pattern as such. Consequently,
it is possible to apply the training result to the analysis of new gait
patterns obtaining better estimations.

In this study, neural networks were trained based on two criteria: training
based on kinematic gait signals, and training based on gait descriptors. The
former seeks to improve the waveforms of kinematic signals in sagittal,
frontal and transverse planes, by reducing the error and increasing the
correlation with respect to a Vicon system. The second is a more direct
approach, focusing on training the networks using gait descriptors (like step
width, stride length, cadence, max. flexions, max. extensions and rotations at
the joints, among other descriptors) directly. In this second approach, 23
most important descriptors for distinguishing pathological from normal gait
were selected for the analysis. This set of descriptors was obtained according
to the recommendations of clinicians Molina and Carratalá [8].

The outline of this paper is organized as follows. Section 2 presents a state-
of-the-art review of current methods applied to improve the accuracy of 3D
cameras. Section 3 is dedicated to the methodology. This section explains the
data collection protocol, as well as the process followed for the definition
of joint kinematics. Section 4 addresses the two training approaches and the
system accuracy achieved in each. Section 5 is focused on the comparison of
both training approaches. Section 6 discusses the results of this study by
comparing them with the current approaches. Finally, Section 7 concludes this
study.

##  2 State of the art

The accuracy of 3D cameras in gait analysis has been a highly discussed topic.
For example, Springer and Seligmann [3] presented a review of 12 studies that
assessed gait analysis with a Microsoft Kinect sensor and a gold standard
system. Results of this review indicated good validity for only some spatio-
temporal parameters, and not enough validity for gait kinematics variables.
For this reason, different approaches have pursued to improve the accuracy of
3D cameras in gait analysis. These approaches have covered, among others, the
fusion of 3D cameras with inertial sensors [9], fusion of multiple 3D
cameras[10, 11, 12], or the use of regression equations [13] to increase
accuracy in the detection of foot-off and foot-contact events. In [12], Müller
et al. applied a multi-camera configuration that was intended to improve the
estimation of spatio-temporal parameters. In the study developed by Matthew et
al. [14], the low accuracy of 3D cameras is attributed to the lack of a gait
model for the data retrieved by the sensor, therefore, the authors propose the
improvement of the estimations applying a new model based on rigid bodies.
Nichols et al. [15] presented another approach based on retro-reflective
markers. The researchers found that retro-reflective markers could be used to
enhance the motion capture process with 3D cameras.

Another approach has been the fusion with inertial sensors. In the study
presented by Alizadegan and Behzadipour [16], the authors proposed a new
method to improve accuracy and real-time performance of inertial joint angle
estimation for upper limb rehabilitation applications. The position
measurements retrieved from a Kinect sensor were used to correct for the
sensor-to-segment misalignment of the inertial sensors. Also in the study
presented by Destelle et al. [17] the authors built an improved skeleton using
information fused from a Kinect sensor and nine inertial sensors fixed to the
subject’s forearms, arms, thighs, shanks and chest. This method proved to
obtain more accurate measurements of joint angles, despite a complex
calibration process prior to each experiment.

Previous studies have also attempted sensor latency compensation. Latency
compensation allows for the suppression of time delays due to data processing
time in 3D cameras. In our previous study [18], the latency of the Kinect V2
sensor was measured and corrected using the Dynamic Time Warping (DTW)
algorithm. The latency compensation process improves the estimation of joint
angles during gait analysis.

ANNs have been another method to improve the accuracy of 3D cameras for gait
analysis. For example, in the study of Kidziński et al. [19], ANNs were
applied to train the detection of foot-contact and toe-off events. Detection
of these events is the initial step in the post-processing of most
quantitative gait analysis workflows. Also, in the study presented by
Bersamira et al. [9], the researchers applied ANNs for the integration of 3D
cameras and inertial sensors. The authors claim that the fusion of these
systems makes it possible to obtain gait data comparable to those produced by
a Vicon system. However, as mentioned above, according to Destelle et al. [17]
the use of IMUs together with 3D cameras is an alternative that requires a
complex calibration prior to each experiment.

The low accuracy of the measurements obtained using 3D cameras in gait
analysis has also been attributed to the joint estimation method. Commonly
used Software Development Kits (SDKs) for skeleton tracking estimate the joint
center using ML techniques. Firstly, ML is applied to label the pixels
corresponding to each body segment. Afterwards, the intersection of these
segments is identified to estimate the joint center location [20]. According
to Matthew et al. [14], by applying this method, the estimated joint centers
may be biologically inconsistent. This can lead to errors in the location of
the ankle, knee, and hip, which complicates their use for later gait analysis
[1]. This problem encouraged the development of a series of deep learning
methods for joint estimation [21, 22]. These methods have been particularly
applied in self-occlusive tasks such as sitting. Unfortunately, these methods
do not study more sophisticated gait descriptors.

In summary, previous studies have attempted to improve the accuracy of the
estimation of joint location, but not the gait kinematics itself. The studies
that have addressed gait analysis have only dealt with spatio-temporal
parameters. However, achieving an accurate enough gait analysis system based
on 3D cameras remains a challenge. In contrast to previous studies, this study
aims to directly improve the estimation of kinematic gait signals and gait
descriptors based on supervised learning through the application of two
training approaches.

##  3 Methodology

###  3.1 Ethics statement

The current study was approved by the ethics committee of the Faculty of
Physical Activity and Sport Sciences INEF (Polytechnic University of Madrid,
Spain). The experiments were performed in the Sports Biomechanics Laboratory
of INEF. All subjects provided written informed consent prior to
participation. In addition, the participants completed an electronic
questionnaire with basic questions related to health problems and
musculoskeletal injuries suffered in recent years.

###  3.2 Data Collection

Thirty-seven healthy participants (16 female and 21 male, Table 1) were
involved in the study. A total of 207 gait recordings were processed.

Table 1: Demographics

Participants: 37 Gait sequences: 207 Male: 21 Female: 16 Mean age: 21$\pm$2
years Mean weight: 67.41$\pm$10.28 kg. Mean height: 172.99$\pm$8.53 cm.

The skeleton tracking task was performed with an Orbbec Astra 3D camera using
the 0.34.1 release of the Nuitrack SDK. For each gait sequence, 15 joint
trajectories were recorded at 30 Hz. During the experiments, the 3D camera was
mounted on a mobile robot Rosbot 2.0 from Husarion. The robot is configured to
maintain 2.5 meters distance from the person while walking. To achieve this, a
controller was implemented in the robot, which was presented in our former
study [23]. We encourage the reader to review the aforementioned study for
more information about the robot configuration and control. The use of the
mobile robot allows to obtain a path long enough to analyze the human gait in
spite of the limited range of the 3D sensor. Consequently, this avoids the use
of multiple sensors and the calibration processes that these configurations
require. Simultaneously, gait information was retrieved with a Vicon system,
which was considered as the ground truth in this study. The Vicon system
consisted of six M2 MCAM cameras recording at a sampling rate of 120 Hz. Fig.
1 shows the data collection environment.

The experiments were conducted in two phases, which are summarised below:

  * 1.

Participant preparation (15 minutes). Thirty-two reflective markers were
placed on anatomical landmarks following the Plug-in-Gait model [24]. The
participant wore running shoes, short tights, a top (in the case of women) and
socks below the ankles. In addition, the participant signed an informed
consent and completed an electronic questionnaire. The height and weight of
each participant was registered. Finally, a warm-up and gait speed
normalization process was done whereby the subject was prepared to walk at an
average speed of 1m/s.

  * 2.

Gait data capture (15 minutes). Gait acquisition was performed in a 15x5-meter
corridor, in a one-way straight line gait. Six iterations per participant were
repeated, giving a total of 222 gait sequences. However, some of these were
discarded due to the loss of markers in the Vicon system, whose trajectories
could not be reconstructed by filling in gaps. As a result, a total of 207
gait recordings were used for the supervised learning stage.

Figure 1: An overview of the experimental setup. Faculty of Physical Activity
and Sport Sciences INEF (Polytechnic University of Madrid, Spain).

###  3.3 Data processing

The robot-mounted 3D camera and the Vicon system started recording data at
different times and through different input streams. The timestamp of the
first heel strike was used to synchronize the data. This point was retrieved
from the anterior-posterior distance between ankle joints (the inter-ankle
distance) according to Ceccato et al. [25]. This event represented the onset
of the recording. The end of the recording is determined by the last timestamp
registered by the Vicon system. The data from both systems was cut between
these limits. Due to the difference in sampling frequencies, the Vicon time
series were linearly interpolated using the timestamps of the 3D camera data.
This process ensures the same query points. Finally, to minimize any
fluctuation, a low pass filter with a cut-off frequency of 4 Hz was applied in
the 3D camera data.

###  3.4 Data analysis

To relate as much as possible the gait model applied by the Nuitrack in the 3D
camera with that applied by the Plug-in-Gait in the Vicon system, it was
necessary to find an equivalence between the landmarks detected by both
systems by defining certain mapping rules. This mapping process is not new.
Mapping rules similar to those used in [26, 27] were adopted, and are shown in
Table 2.

Table 2: Mapping rules to compare the skeleton model of the 3D camera and the
Vicon system.

[t]  3D Camera Vicon Markers Spine base Midpoint [RPSI,LPSI,RASI,LASI] Spine
middle Midpoint [T10,STRN] Spine shoulder Midpoint [C7,CLAV] Left shoulder
Marker LSHO Left elbow Midpoint [LELB marker A,LELB marker B] Left hand
Midpoint [LWR marker A,LWR marker B] Right shoulder Marker RSHO Right elbow
Midpoint [RELB marker A,RELB marker B] Right hand Midpoint [RWR marker A,RWR
marker B] Left hip Hip joint centering algorithm[LASI,LPSI] 1 Left knee
Midpoint [LKNE marker A,LKNE marker B] Left ankle Midpoint [LANK marker A,LANK
marker B] Right hip Hip joint centering algorithm[RASI,RPSI] 1 Right knee
Midpoint [RKNE marker A,RKNE marker B] Right ankle Midpoint [RANK marker
A,RANK marker B] 1 The hip joint center location was calculated with the hip
joint centering algorithm recommended by [24].

Six Vicon markers (LTROC, LTHI, LTIB, RTROC, RTHI and RTIB) were not
considered in this mapping process. For the analysis of gait in this study,
the joint angles from elbow, knee, hip, shoulder, trunk, and pelvis were
analyzed in sagittal plane. Furthermore, the joint angles from hip, and
shoulder were analyzed in frontal plane. In addition, an examination of trunk
and pelvis took place in the transverse plane.

###  3.5 Inverse kinematic model to compute joint angles with the 3D camera

Figure 2: Coordinate systems definition of the body segments used to apply the
inverse kinematics. Four local coordinate systems are shown. For each joint
the coordinate system is indicated where the X-axis is in blue, the Y-axis in
green, and the Z-axis in red.

The inverse kinematics is the process to retrieve joint angles from 3D
coordinates of landmarks. For the inverse kinematics process in the 3D camera,
the coordinate systems definition of the body segments were compatible with
the International Society of Biomechanics recommendations [28]. First, four
local coordinate systems are defined at the joints: $R1=$ ${}^{w}F_{Knee}$,
$R2=$ ${}^{w}F_{Pelvis}$, $R3=$ ${}^{w}F_{Trunk}$, $R4=$ ${}^{w}F_{Elbow}$.
These are the projected knee, pelvis, trunk, and elbow coordinate frames, on
the world frame, and are defined as shown in Fig. 2.

To locate these coordinate systems, vectors V1 and V2 are defined in alignment
with the body segments involved. In Fig. 2, the coordinate axes are color-
coded: X in blue, Y in green and Z in red. In this figure, at the bottom of
each skeleton, the definition of each coordinate axis is indicated according
to the order in which they are defined. For example, in the case of the knee
coordinate system $R1$, first the Z axis is defined as parallel to the vector
V2, which connects knee to hip. Then the Y-axis is defined as the cross
product between V1 and V2, where V1 is the vector connecting knee to ankle.
Finally, X is defined as the cross product between Y and Z. In some cases, in
order to define the coordinate system, it was necessary to calculate a virtual
landmark at the midpoint of two adjacent landmarks. These midpoints are
colored in orange. For example, the midpoint of left and right hip was used to
define the coordinate system $R2$ and the midpoint between left and right
shoulder was used to define the coordinate system $R3$.

Once the local coordinate systems are defined, the mathematical definitions of
the joint angles correspond as closely as possible to the existing clinical
terminology as follows:

  * 1.

The hip joint angles were determined as the Cardan rotation angles in the
sequence YXZ between the pelvic and knee coordinate systems, i.e. the relative
rotation $Eyxz1$, where $Eyxz1=R1\cdot R2^{T}$.

  * 2.

The pelvic angles were calculated using the Cardan rotation angles in the
sequence YXZ between the world and pelvis coordinate frames. This corresponds
to the absolute rotation of $R2$ with respect to the world frame.

  * 3.

The Cardan rotation angles between the world coordinate and the trunk
coordinate frames were used to determine the trunk angles. This corresponds to
the absolute rotation of $R3$ with respect to the world frame.

  * 4.

The angle between the two vectors crossing at the knee joint center was
considered as the knee joint angle. These vectors were rotated according to
$R1$.

  * 5.

The angle between the two vectors crossing at the elbow joint center was
considered as the elbow joint angle. These vectors were rotated according to
$R4$.

  * 6.

The shoulder joint angles were determined as the Cardan rotation angles in the
sequence YXZ between the trunk and elbow coordinate systems, i.e. the relative
rotation $Eyxz2$, where $Eyxz2=R4\cdot R3^{T}$.

##  4 Learning process: Training, Validation and Testing

The large number of experiments performed together with the robot-mounted 3D
camera and the Vicon system allowed the application of supervised learning
algorithms to improve the resulting estimations. This application was only
possible due to the nature of our study in which the signals can be post-
processed before obtaining the final results. There are two basic possible
approaches for training and both have been studied in order to see which one
achieves a better result: training based on kinematic gait signals, and
training based on gait descriptors.

As mentioned above, 37 participants provided 207 gait recordings. Of these,
the recordings corresponding to 20% of the participants were excluded from the
learning process (i.e. were not used for training, validation or testing).
This represents the re-testing group of participants. The data from these
participants was used to make a further comparison between both training
approaches.

###  4.1 Training approach based on joint kinematics

Figure 3: Kinematic gait cycles retrieved from the re-testing group of
participants. The gait cycles are normalized from 0-100% and averaged for all
the iterations. The figure shows the Vicon system (blue line), the raw
estimation of 3D camera (continuous black line), and the learned estimation of
3D camera (dashed black line).

Since the samples from the Vicon system were linearly interpolated using the
timestamps of the 3D camera, the samples from both systems are temporally
aligned. This allowed us to associate each sample of the camera with a
corresponding label on the Vicon signal.

Each kinematic signal was represented by a single vector of dimension Nx1,
where N was the total number of samples collected from all the experiments.
From this single vector, a training matrix was generated by applying a
windowing process. The windowing process is used to split the signal into
several frames, or windows. The skip factor between frames was set to one
sample. Therefore, the final training matrix had a dimension of (N-W+1)xW,
where W was the windowing width. On this basis, each training sample was a
vector of 1xW that had a corresponding target of dimension 1x1 coming from the
Vicon signal.

This data set was randomly split into three classes: training, validation and
testing. The partitioning followed the rule 60/20/20, as follows:

  * 1.

60% of the data was used for training.

  * 2.

20% of the data was used to validate the network and stop training before
overfitting occurs.

  * 3.

20% of data was used as a completely independent test of network
generalization.

Here a two-layer feedforward backpropagation ANN was created and trained per
each kinematic signal. The ANN architecture had 10 neurons per layer, an input
layer with a number of entries equal to the windowing width factor and an
output layer with a single outcome. Experimentally, a windowing width of 3
samples was determined to be the most effective. The training algorithm
updated weight and bias values according to Levenberg-Marquardt optimization.
Mean squared error (MSE) was used as the performance function. The maximum
number of training iterations was set to 1000 epochs.

Table 3 summarizes the accuracy of the system before and after training. When
analyzing the correlations shown in Table 3, it can be seen that before
training, trunk tilt, pelvis tilt, hip add./abd., shoulder add./abd. and
pelvis rotation had correlations lower than 0.70. We can attribute the low
accuracy in shoulder and hip add./abd to the principle of operation of 3D
cameras. Since the 3D camera does not provide useful information for the
detection of motion in frontal plane, the SDK relies on the intrinsic
parameters of the RGB camera for the estimation, so these motions are
approximations of medium quality. However, after training, the improvements
are remarkable. Just trunk tilt and pelvis tilt remain with correlation lower
than 0.70. Despite this fact, considering the low range of motion of these
joints (about 2 degrees), the results are satisfactory.

Table 3: Accuracy of the estimation provided by the 3D camera in sagittal,
frontal and transverse planes before and after training. Results are evaluated
using the root-mean-square error (RMSE) and the Pearson Correlation (r).
Values are displayed in the format mean$\pm$SD.

BEFORE TRAINING AFTER TRAINING RMSE r RMSE r Elbow flex/ext.($\degree$) 3.54
$\pm$ 0.18 0.79 $\pm$ 0.02 2.03 $\pm$ 0.08 0.80 $\pm$ 0.02 Knee
flex/ext.($\degree$) 6.89 $\pm$ 0.29 0.94 $\pm$ 0.01 5.94 $\pm$ 0.31 0.95
$\pm$ 0.01 Hip flex/ext.($\degree$) 11.38 $\pm$ 0.24 0.93 $\pm$ 0.01 4.52
$\pm$ 0.19 0.95 $\pm$ 0.00 Shoulder flex/ext.($\degree$) 10.03 $\pm$ 0.28 0.69
$\pm$ 0.03 6.48 $\pm$ 0.40 0.71 $\pm$ 0.03 Trunk tilt($\degree$) 5.39 $\pm$
0.11 0.45 $\pm$ 0.04 1.94 $\pm$ 0.06 0.55 $\pm$ 0.03 Pelvis tilt($\degree$)
5.81 $\pm$ 0.11 0.43 $\pm$ 0.04 1.91 $\pm$ 0.06 0.55 $\pm$ 0.03 Hip
add/abd.($\degree$) 4.79 $\pm$ 0.11 0.64 $\pm$ 0.03 2.59 $\pm$ 0.10 0.70 $\pm$
0.03 Shoulder add/abd.($\degree$) 7.65 $\pm$ 0.22 0.68 $\pm$ 0.03 3.27 $\pm$
0.25 0.73 $\pm$ 0.03 Trunk rotation($\degree$) 2.77 $\pm$ 0.15 0.82 $\pm$ 0.02
1.72 $\pm$ 0.11 0.87 $\pm$ 0.02 Pelvis rotation($\degree$) 6.95 $\pm$ 0.18
0.62 $\pm$ 0.03 2.71 $\pm$ 0.09 0.71 $\pm$ 0.02

On the other hand, joint kinematics could be affected by the difference in the
gait models between Vicon and the 3D camera. Since the number of markers
detected by the camera is smaller than those detected by the Vicon, the
definition of the coordinate systems of the body segments is in fact different
in each system. While the Vicon uses four markers to detect the kinematics of
the pelvis, the 3D camera uses only two landmarks, plus one belonging to the
middle spine. However, the improvement in the correlation of the signals shown
in Table 3, reflects a fit of the models. Thus, the kinematic signals reported
by the 3D camera more closely resembles that of the Vicon.

Fig. 3 shows the effects of the training process for kinematic signals of gait
in the re-testing group of participants. From the observation of Fig. 3,
another problem arising from the difference in gait models can be noted. In
some of the signals, such as the hip flex./ext., shoulder flex./ext., trunk
tilt, pelvis tilt and shoulder add./abd., there is an offset with respect to
the signal of the Vicon system. The correction of this offset is another
benefit of the learning process that provides a better interpretation of joint
kinematics. In the case of the trunk and pelvis tilt, this offset could not be
corrected completely. The randomness of this offset in the training data and
the small range of motion of these joints (about 2 degrees) made it difficult
for the ANN to correct it. However, a considerable improvement in the
correlation of these signals was obtained.

It is very important to emphasize that the training is not aimed at learning
just the normal gait pattern performed by the participants. This would make
the system unsuitable for the analysis of new gait patterns or pathological
patterns. On the contrary, what the ANN actually learns is how to correct the
measurement errors of the original gait model in the 3D camera, based on the
examples provided by the Vicon system. To achieve this, the ANN does not
receive as input the whole gait cycle in each sample. Instead, it receives
each the information into data frames thanks to the windowing process. This is
extremely important for generalizing learning. Consequently, it is possible to
apply the training result to the analysis of new gait patterns.

###  4.2 Training approach based on gait descriptors

Figure 4: Identification of kinematic descriptors for left knee and hip in
sagittal plane. The reference signal for the detection of heel strike and toe-
off events was the inter-ankle distance [25].

This second approach arises from the concern of whether it would be better to
train the ANN directly with gait descriptors rather than with kinematic
signals divided into data frames. This is a more direct way to teach the ANN
to report gait descriptors more accurately. In order to apply this second
approach, following an in-depth study of gait disturbances in neurological
patients, and on the recommendation of clinicians Molina and Carratalá [8], 27
most important descriptors representing the main differentiators of normal and
pathological gait were selected for the analysis. As listed in Table 4, 11
were spatio-temporal descriptors and 16 were kinematic descriptors.

Fig. 4 illustrates the process followed for the identification of the set of
kinematic gait descriptors. According to Ceccato et al. [25], the reference
signal for the detection of heel strike and toe-off events was the maximal
anterior-posterior distance between ankle joints (or inter-ankle distance). In
this signal there is a characteristic sinusoidal curve when the X coordinate
of the foot markers is graphed versus time. In this curve, the valleys
correlate to the time at which the foot comes into contact with the ground
(the heel strike) and the peaks fit with the initiation of swing phase (the
toe-off) [29]. Fig. 4 illustrates the process followed for the identification
of kinematic descriptors of knee and hip in sagittal plane. The rest of the
kinematic descriptors correspond to instants of maxima and minima in the
corresponding kinematic signals. In addition, the set of spatio-temporal
descriptors were calculated according to established definitions [30, 31, 12].

Table 4: Accuracy of the system for the detection of 11 spatio-temporal and 16
kinematic descriptors. The table shows the results before and after training.
Results are evaluated using the root-mean-square error (RMSE). Values are
displayed in the format mean$\pm$SD.

GAIT DESCRIPTORS BEFORE TRAINING AFTER TRAINING RMSE RMSE SPATIO-TEMPORAL
DESCRIPTORS step width ($m$) 0.022 $\pm$ 0.01 0.021 $\pm$ 0.01 left stride
length ($m$) 0.15 $\pm$ 0.02 0.07 $\pm$ 0.01 right stride length ($m$) 0.13
$\pm$ 0.03 0.05 $\pm$ 0.01 left stride time ($s$) 0.03 $\pm$ 0.01 0.04 $\pm$
0.01 right stride time ($s$) 0.06 $\pm$ 0.02 0.06 $\pm$ 0.02 right step time
($s$) 0.04 $\pm$ 0.02 0.03 $\pm$ 0.01 left step time ($s$) 0.027 $\pm$ 0.01
0.026 $\pm$ 0.01 right cadence ($steps/min$) 4.65 $\pm$ 1.08 4.60 $\pm$ 1.27
left cadence ($steps/min$) 3.60 $\pm$ 1.80 4.01 $\pm$ 1.51 percentage of foot
stance ($\%$) 3.74 $\pm$ 0.78 2.74 $\pm$ 0.73 percentage of foot swing ($\%$)
2.73 $\pm$ 1.41 1.32 $\pm$ 0.29 KINEMATIC DESCRIPTORS trunk max. tilt
($\degree$) 4.22 $\pm$ 0.87 1.68 $\pm$ 0.45 trunk min. tilt ($\degree$) 5.93
$\pm$ 1.21 2.18 $\pm$ 0.35 pelvis max. tilt ($\degree$) 4.31 $\pm$ 0.57 1.33
$\pm$ 0.52 pelvis min. tilt ($\degree$) 6.14 $\pm$ 0.64 1.67 $\pm$ 0.31 hip
max. adduction ($\degree$) 3.86 $\pm$ 0.75 1.37 $\pm$ 0.35 hip min. abduction
($\degree$) 5.02 $\pm$ 0.54 2.22 $\pm$ 0.67 pelvis max. rotation ($\degree$)
6.72 $\pm$ 1.59 2.96 $\pm$ 0.97 pelvis min. rotation ($\degree$) 9.81 $\pm$
0.98 2.02 $\pm$ 0.47 hip max. extension during stance ($\degree$) 14.08 $\pm$
1.53 3.60 $\pm$ 0.83 hip max. flexion during swing ($\degree$) 12.22 $\pm$
1.31 2.61 $\pm$ 0.54 hip max. flexion during stance ($\degree$) 15.10 $\pm$
1.47 3.70 $\pm$ 1.05 knee initial contact position ($\degree$) 7.43 $\pm$ 1.97
4.91 $\pm$ 1.33 knee position at toe-off ($\degree$) 9.85 $\pm$ 1.81 3.29
$\pm$ 1.03 knee max. flexion in load response ($\degree$) 4.10 $\pm$ 1.02 4.52
$\pm$ 1.03 knee max. flexion during swing ($\degree$) 4.06 $\pm$ 1.21 3.39
$\pm$ 1.69 knee max. extension before heel strike ($\degree$) 5.76 $\pm$ 1.68
4.81 $\pm$ 1.52

Each gait descriptor was represented by a single vector of dimension Px1,
where P was the number of gait cycles collected from all the experiments. This
means that one sample of the set of descriptors is extracted for each gait
cycle. Given that 27 descriptors were analyzed, a training matrix of dimension
Px27 was generated. A target matrix of the same dimensions was obtained with
the estimations of the Vicon system. Corresponding columns were used to train
independent neural networks. Each ANN used a feedforward backpropagation
architecture, with two hidden layers, 10 neurons per layer, an input layer
with a single entry and an output layer with a single outcome. The training
algorithm updated weight and bias values according to Levenberg-Marquardt
optimization, and MSE was used as the performance function. The maximum number
of training iterations was set to 1000 epochs. Again the data set was split
into three classes: training, validation and testing, following the rule
60/20/20 (60% for training, 20% for validation and 20% for testing).

Table 4 summarizes the results of this training approach. Results show that
the spatio-temporal parameters have no further improvement after the training
process. An exception occurs in the case of left/right stride length, where a
noticeable correction is observed. Regarding the sixteen kinematic
descriptors, the results are better after training. Especially the descriptors
for hip, pelvis and trunk show remarkable improvements.

##  5 Comparison of training approaches

Figure 5: Process followed to obtain the data for the comparison of the two
training approaches.  Figure 6: Results of the comparison of both training
approaches. The box plots show the 25th percentile, 75th percentile, median,
minimum and maximum values. The mean value is represented with a black dot.
The box plot closest to the Vicon is colored in blue, which is also colored in
blue.

This section is focused on the comparison of both training approaches.
Specifically, it compares the accuracy for the estimation of the sixteen
kinematic descriptors of gait. For this purpose, the re-test group of
participants was used. Fig. 5 shows the process followed to obtain the data
for comparison. On the basis of this process, four estimations can be
compared: the Vicon estimation (V); the 3D camera raw estimation (C); the 3D
camera trained with kinematic signals (CTs); and the 3D camera trained with
gait descriptors (CTd).

Results of this comparison are shown in the Fig. 6. A visual representation of
the data is shown using box plots. These box plots summarize the 25th
percentile, 75th percentile, median, minimum and maximum values of each group
of data. The mean value is also shown with a black dot over the box plots. In
this figure, the box plot belonging to the system with mean value closest to
that of the Vicon is colored in blue, which is also colored in blue.

When analyzing the sixteen kinematic descriptors shown in Fig. 6, it is clear
that the trained systems (CTd or CTs) are always better than the untrained
system (C). When comparing the two training approaches, it is observed that in
62% of the events analyzed (10/16) the approach based on gait descriptors
(CTd) is better than the approach based on kinematic signals (CTs), where only
in 38% of the cases (6/16) it proved to be better. However, it can be observed
that for events of large amplitude, such as maximum knee and hip flexions and
extensions, training based on gait descriptors (CTd) is better. On the
contrary, for kinematics of smaller range of motion, the training based on
kinematic signals (CTs) is superior. This can be noted in the pelvis maximum
and minimum tilt, and in the lower amplitude descriptors of knee kinematics
such as the knee initial contact position, knee maximum flexion in load
response, and in the knee maximum extension before heel strike. Therefore, it
is not possible to define which training approach is completely better.
Despite the fact that training based on gait descriptors (CTd) presented
higher accuracy in most parameters, training based on kinematic signals (CTs)
has an enormous advantage because it allows to know the complete kinematics of
the joint, which is very useful when determining deviations between gait
patterns for clinical purposes. Consequently, the selection of the training
approach will depend on the purpose of the study conducted.

##  6 Discussion

It is interesting to compare the results obtained with other techniques for
improving the estimations of 3D cameras. An in-depth comparison can be made by
analyzing Table 5. Current approaches have attempted to improve the accuracy
of 3D cameras in gait analysis through remodeling the skeleton, sensor fusion,
or applying machine learning techniques. In the study presented by Müller et
al. [12], a validation of enhanced Kinect sensor for gait assessment was
presented. The idea of that study was to compute a spatially averaged skeleton
tracked by two Kinect sensors placed at both sides of the walking path. The
study demonstrated that sensor setups tracking the person only from one-side
is less accurate and should be replaced by two-sided setups. To fuse data from
both sensors, the authors used the iterative closest point method, which adds
imprecision to the model. Similarly, the use of more than one camera suggests
a requirement of a dedicated room where the system can be setup and left
undisturbed between sessions.

Regarding the fusion of 3D cameras with inertial sensors (IMUs), it is
interesting to mention the study presented by Destelle et al. [17]. The
authors built a fused Kinect/IMUs skeleton where the Kinect sensor provided
the positions of the joints and the IMUs provided the orientation information.
The use of IMUs together with 3D cameras required a complex calibration prior
to each experiment. The authors reported a final accuracy of 9.00$\degree$ for
elbow flex./ext., and 7.89$\degree$ for knee flex./ext. In contrast, in our
study considerably higher accuracies were achieved after training
(2.03$\degree$ for elbow flex./ext. and 5.94$\degree$ for knee flex./ext.). It
should also be noted that the study of Destelle et al. [17] was performed for
a simulated kicking motion while in our study a real gait was analyzed.

Table 5: Comparison of our study with current approaches.

[t]  OUR SYSTEM1 RIGID BODIES2 DTW3 MULTI-SENSOR4 MULTI-SENSOR5 3D CAMERA+IMU6
3D CAMERA+IMU7 ROOT MEAN SQUARE ERROR BEF. AFT. BEF. AFT. BEF. AFT. BEF. AFT.
BEF. AFT. BEF. AFT. BEF. AFT. Elbow flex./ext. 3.54 2.03 - - - - - - - - -
5.90 13.33 9.00 Knee flex./ext. 6.89 5.94 9.40 5.20 13.15 10.47 - - - - - -
28.23 7.89 Hip flex./ext 11.38 4.52 11.10 5.60 6.20 2.65 - - - - - - - -
Shoulder flex./ext. 10.03 6.48 - - 9.53 5.80 - - - - - 4.70 - - Trunk
forw./back. tilt 5.39 1.94 3.90 3.50 2.09 1.93 - - - - - - - - Pelvis
ant./post. tilt 5.81 1.91 - 6.10 3.22 3.14 - - - - - - - - Hip add./abd. 4.79
2.59 - - 5.83 4.70 - - - - - - - - Shoulder add./abd. 7.65 3.27 - - 11.76
11.69 - - - - - - - - Trunk int./ext. rot. 2.77 1.72 - - 5.26 5.09 - - - - - -
- - Pelvis int./ext. rot. 6.95 2.71 - - 5.88 4.81 - - - - - - - - step width
(m) 0.022 0.021 - - - - - 0.01 0.0066 0.0039 - - - - AV. stride length (m)
0.14 0.06 - - - - - 0.00 0.0004 0.0020 - - - - AV. stride time (s) 0.05 0.05 -
- - - - 0.01 - - - - - - AV.step time (s) 0.034 0.028 - - - - - 0.01 0.000
0.000 - - - - AV. Cadence (steps/min) 4.12 4.31 - - - - - 0.90 - - 1 Our
trained robot-mounted 3D camera. 2 Matthew et al.[14]. Single Kinect, tested
in a sit to stand task. The original joint data is transformed into a new
model built with rigid bodies. 3 Guffanti et al.[18]. Correction of latency
usind DTW(Dynamic Time Warping). 4 Geerse et al.[11]. Multi-Kinect v2,
10-Meter Walkway for spatio-temporal gait analysis. 5 Müller et al. [12].
Multi-Kinect v2, 7-Meter Walkway for spatio-temporal gait analysis. 6
Alizadegan and Behzadipour[16]. Single Kinect to improve accuracy of inertial
joint angle estimation in upper limb stroke rehabilitation. 7 Destelle et
al.[17]. Single Kinect in front of the person and fusion with IMUs. The RMSE
values were averaged for the two experiments performed by the authors.

In the study presented by Alizadegan and Behzadipour [16], the authors
proposed a new method to improve accuracy of IMUs for joint angle estimation
in upper limb rehabilitation applications. To correct for the sensor-to-
segment misalignment of the inertial sensors, position measurements retrieved
from Kinect sensor were used. The experiment was performed on a mechanical
upper limb stroke rehabilitation device also known as shoulder wheel. The
shaft rotation angle was encoded and this measurement was used as ground
truth. The authors reported accuracies of 5.90$\degree$ for elbow flex./ext.
and 4.70$\degree$ for shoulder flex./ext. Conversely, in our study, the elbow
is reported with higher accuracy (3.54$\degree$ for elbow flex./ext.) but the
shoulder is slightly less accurate (6.48$\degree$ for shoulder flex./ext.). It
should also be noted that the experimental basis in the study of Alizadegan
and Behzadipour [16] is different from ours. While in that study the person
remains static, in our study the person is in constant walking motion.

Matthew et al. [14] proposed the improvement of the estimations provided by 3D
cameras by remodeling the skeleton to a new one based on rigid bodies. The
idea of the authors was to rescale the skeleton detected by the 3D camera,
using the height of the person. Then, the joint centers are recalculated based
on anthropometric approximations. The method was tested only for a sit to
stand task (STS), and the results obtained were satisfactory. However, it
should be noted that, applying joint center relocation based on anthropometric
approximations may not be a robust technique. This is because 3D cameras are
affected by many other factors like light conditions, sensor position,
occlusion, among others [4]. This makes it difficult to relocate joint centers
using only anthropometric approximations. Thus, this method may not be
effective in all experimental conditions. In addition, our method based on ML
obtained better results mainly for trunk and pelvis tilt. While in the study
of Matthew et al. [14] errors of 3.50$\degree$ for trunk tilt and
6.10$\degree$ for pelvis tilt were obtained, in our study 1.94$\degree$ and
1.91$\degree$ were achieved respectively.

Finally, in our previous study [18], latency correction was proposed using
Dynamic Time Warping (DTW). Latency of 3D cameras produces non-symmetrical
temporal variations in signals that directly affects the system performance.
Results showed a noticeable improvement in system performance. However, these
corrections only solve the problem of the temporal disturbances produced by
the variable latency of the sensor. Instead, the application of machine
learning not only corrects these distortions. This can be observed in the
improvement of the correlation in Table 3 and in the correction of waveforms
in Fig. 3. In addition to the above, machine learning can also correct
discrepancies in the gait model applied by the 3D camera with respect to the
Plug-in-gait model applied by the Vicon system. This effect can be observed in
Fig. 3, where the offsets with respect to the Vicon signals were corrected.

##  7 Conclusion

In this study, it was possible to improve the accuracy of 3D cameras for human
gait analysis applications. This was achieved by post-processing raw
estimations of the 3D camera using ANNs trained with the data provided by a
certified Vicon system. The neural networks were trained based on two
different criteria: training based on kinematic gait signals, and training
based on gait descriptors. In the latter approach, 11 spatio-temporal and 16
kinematic descriptors representing the main differentiators of normal and
pathological gait were selected for the analysis.

The accuracy of the estimations with the 3D camera was measured before and
after training. Results showed lower errors and higher correlations with
respect to the gold standard, thus, improving the obtained biomechanical model
with the 3D camera. The accuracy obtained when detecting the main descriptors
of a pathological gait also showed a substantial improvement, mainly for
kinematic descriptors.

When comparing both training approaches, it was not possible to define which
was the absolute best. Regardless, training based on kinematic signals has an
enormous advantage because it allows to know the complete kinematics of the
joint. This is very useful when determining deviations between gait patterns
along a long-term clinical analysis. Therefore, we believe that the selection
of the training approach will depend on the purpose of the study to be
conducted.

This study reveals the great potential of 3D cameras and encourages the
research community to continue exploring their use in gait analysis.

## Conflicts of interest

None of the authors have any conflicts of interest associated with this
research.

## Acknowledgments

The research leading to these results has received funding from
PID2020-118299RB-I00 - SISTEMA ROBOTICO NO INVASIVO PARA EL ANALISIS
BIOMECANICO DE LA MARCHA HUMANA -, “Convocatoria 2020 Proyectos de I+D+i - RTI
Tipo B”, of the Government of Spain. The authors would like to thank Faculty
of Physical Activity and Sports Sciences - INEF, UPM, for the use of Sports
Biomechanics Laboratory.

## References

  * [1] A. Pfister, A. M. West, S. Bronner, J. A. Noah, Comparative abilities of Microsoft Kinect and Vicon 3D motion capture for gait analysis, Journal of Medical Engineering & Technology 38 (5) (2014) 274–280.
  * [2] B. F. Mentiplay, L. G. Perraton, K. J. Bower, Y.-H. Pua, R. Mcgaw, S. Heywood, R. A. Clark, Gait assessment using the Microsoft Xbox One Kinect: Concurrent validity and inter-day reliability of spatiotemporal and kinematic variables, Journal of Biomechanics 48 (10) (2015) 2166–2170.
  * [3] S. Springer, G. Seligmann, Validity of the Kinect for Gait Assessment: A Focused Review, Sensors 16 (2).
  * [4] W. Lemkens, P. Kaur, K. Buys, P. Slaets, T. Tuytelaars, J. Schutter, Multi RGB-D camera setup for generating large 3D point clouds, in: IEEE Int. Conf. Intell. Robot. Syst., 2013, pp. 1092–1099.  doi:10.1109/IROS.2013.6696486.
  * [5] S. Shrivastava, J. Bharti, R. K. Pateriya, Machine learning based gait abnormality detection using Microsoft Kinect sensor, Mater. Today Proc.doi:https://doi.org/10.1016/j.matpr.2020.11.615.
URL https://www.sciencedirect.com/science/article/pii/S2214785320392890

  * [6] H. Zhen, M. Deng, P. Lin, C. Wang, Human gait recognition based on deterministic learning and Kinect sensor, in: 2018 Chinese Control Decis. Conf., 2018, pp. 1842–1847.  doi:10.1109/CCDC.2018.8407426.
  * [7] M. Li, S. Tian, L. Sun, X. Chen, Gait analysis for post-stroke hemiparetic patient by multi-features fusion method, Sensors (Switzerland) 19 (7).
  * [8] M. Francisco, M. Carratalá, La Marcha Humana: Biomecánica, Evaluación y Patología, Editorial Médica Panamericana, Madrid, 2020.
URL https://www.medicapanamericana.com/es/libro/La-marcha-humana-incluye-
version-digital

  * [9] J. N. Bersamira, R. J. A. De Chavez, D. D. S. Salgado, M. M. C. Sumilang, E. R. Valles, E. A. Roxas, A. R. dela Cruz, Human Gait Kinematic Estimation based on Joint Data Acquisition and Analysis from IMU and Depth-Sensing Camera, in: 2019 IEEE 11th Int. Conf. Humanoid, Nanotechnology, Inf. Technol. Commun. Control. Environ. Manag. ( HNICEM ), 2019, pp. 1–6.  doi:10.1109/HNICEM48295.2019.9072775.
  * [10] K.-Y. Yeung, T. H. Kwok, C. Wang, Improved Skeleton Tracking by Duplex Kinects: A Practical Approach for Real-Time Applications, J. Comput. Inf. Sci. Eng. 13 (2013) 41007.  doi:10.1115/1.4025404.
  * [11] D. Geerse, B. Coolen, M. Roerdink, Kinematic Validation of a Multi-Kinect v2 Instrumented 10-Meter Walkway for Quantitative Gait Assessments, PLoS One 10 (10).
URL http://search.proquest.com/docview/1721911213/

  * [12] B. Müller, W. Ilg, M. A. Giese, N. Ludolph, Validation of enhanced kinect sensor based motion capturing for gait assessment, PLoS One 12 (4) (2017) 1–18.  doi:10.1371/journal.pone.0175813.
URL https://doi.org/10.1371/journal.pone.0175813

  * [13] A. Amini, K. Banitsas, An improved technique for increasing the accuracy of joint-to-ground distance tracking in kinect v2 for foot-off and foot contact detection, J. Med. Eng. Technol. 43 (1) (2019) 8–18.
  * [14] R. P. Matthew, S. Seko, R. Bajcsy, J. Lotz, Kinematic and Kinetic Validation of an Improved Depth Camera Motion Assessment System Using Rigid Bodies, IEEE J. Biomed. Heal. informatics 23 (4) (2019) 1784–1793.
  * [15] J. Nichols, M. Sena, J. Hu, O. O’Reilly, B. Feeley, J. Lotz, A Kinect-Based Movement Assessment System: Marker Position Comparison to Vicon, Comput. Methods Biomech. Biomed. Engin. 00 (2016) 1–11.  doi:10.1080/10255842.2017.1340464.
  * [16] A. Alizadegan, S. Behzadipour, Shoulder and elbow joint angle estimation for upper limb rehabilitation tasks using low-cost inertial and optical sensors, J. Mech. Med. Biol. 17 (2) (2017) 1750031.
  * [17] F. Destelle, A. Ahmadi, N. E. O’Connor, K. Moran, A. Chatzitofis, D. Zarpalas, P. Daras, Low-cost accurate skeleton tracking based on fusion of kinect and wearable inertial sensors, in: 2014 22nd Eur. Signal Process. Conf., EURASIP, 2014, pp. 371–375.
  * [18] D. Guffanti, A. Brunete, M. Hernando, J. Rueda, E. Navarro Cabello, The Accuracy of the Microsoft Kinect V2 Sensor for Human Gait Analysis. A Different Approach for Comparison with the Ground Truth, Sensors 20 (16) (2020) 4405.  doi:10.3390/s20164405.
URL https://www.mdpi.com/1424-8220/20/16/4405

  * [19] Ł. Kidziński, S. Delp, M. Schwartz, Automatic real-time gait event detection in children using deep neural networks, PLoS One 14 (1) (2019) 1–11.  doi:10.1371/journal.pone.0211466.
URL https://doi.org/10.1371/journal.pone.0211466

  * [20] Z. Zhang, Microsoft kinect sensor and its effect, IEEE Multimedia 19 (2) (2012) 4–10.  doi:10.1109/MMUL.2012.24.
  * [21] X. Zhou, X. Sun, W. Zhang, S. Liang, Y. Wei, Deep Kinematic Pose Regression, Comput. Vis. – ECCV 2016 Work. (2016) 186–201doi:10.1007/978-3-319-49409-8_17.
  * [22] V.-T. Hoang, K.-H. Jo, 3-D Human Pose Estimation Using Cascade of Multiple Neural Networks, IEEE Trans. Ind. informatics 15 (4) (2019) 2064–2072.
  * [23] D. Guffanti, A. Brunete, M. Hernando, Development and validation of a ROS-based mobile robotic platform for human gait analysis applications, Robotics and Autonomous Systems 145 (2021) 103869.  doi:10.1016/j.robot.2021.103869.
URL
https://www.sciencedirect.com/science/article/pii/S0921889021001548https://linkinghub.elsevier.com/retrieve/pii/S0921889021001548

  * [24] R. B. Davis, S. Õunpuu, D. Tyburski, J. R. Gage, A gait analysis data collection and reduction technique, Hum. Mov. Sci. 10 (5) (1991) 575–587.  doi:https://doi.org/10.1016/0167-9457(91)90046-Z.
URL http://www.sciencedirect.com/science/article/pii/016794579190046Z

  * [25] J.-C. Ceccato, M. de Sèze, C. Azevedo, J.-R. Cazalets, Comparison of Trunk Activity during Gait Initiation and Walking in Humans (Trunk Activity in Walking), PLoS One 4 (12).
  * [26] M. Ma, R. Proffitt, M. Skubic, Y.-K. Jan, Validation of a Kinect V2 based rehabilitation game, PLoS One 13 (8).
  * [27] T. Wei, B. Lee, Y. Qiao, A. Kitsikidis, K. Dimitropoulos, N. Grammalidis, Experimental study of skeleton tracking abilities from microsoft kinect non-frontal views, 3DTV-Conference 2015-July (July).  doi:10.1109/3DTV.2015.7169367.
  * [28] G. Wu, P. R. Cavanagh, ISB recommendations for standardization in the reporting of kinematic data, Journal of Biomechanics 28 (10) (1995) 1257–1261.  doi:10.1016/0021-9290(95)00017-C.
  * [29] J. A. Zeni, J. G. Richards, J. S. Higginson, Two simple methods for determining gait events during treadmill and overground walking using kinematic data, Gait & Posture 27 (4) (2007) 710–714.
  * [30] D. A. Winter, Biomechanics and motor control of human movement, 4th Edition, John Wiley & Sons, Hoboken, New Jersey, 2009.
  * [31] O. Beauchet, C. Annweiler, Y. Lecordroch, G. Allali, V. Dubost, F. R. Herrmann, R. W. Kressig, Walking speed-related changes in stride time variability: Effects of decreased speed, J. Neuroeng. Rehabil. 6 (1) (2009) 32.