Quantitative Method for Evaluating the Coordination between
Sprinting Motions using Joint Coordinates Obtained from the Videos
and Cross-correlations
Masato Sabanai
1
, Chanjin Seo
1
, Hiroyuki Ogata
2
and Jun Ohya
1
1
Department of Modern Mechanical Engineering, Waseda University, 3-4-1, Ookubo, Shinjuku, Tokyo, Japan
2
Faculty of Science and Technology, Seikei University, 3-3-1, Kichijoji-kitamachi, Musashino-shi, Tokyo, Japan
Keywords: Sprinting Motion, Coordination, Evaluation Method, Coaching System.
Abstract: This paper proposes a method for quantitatively evaluating sprinting motions using the videos of runners.
Specifically, this paper explores the coordination between physical motions, which has been recognized as
very important in sprinting. After detecting and normalizing the joint coordinates from sprinting videos, the
cross-correlations of two windowed time-series data are calculated using the windowing cross-correlation
function, and the coordination between the motions of the two joints is quantified. Experiments that use 20
subjects are conducted. As a result of classifying the cross-correlation obtained from the subjects’ data into
two clusters using k-means clustering, conditions in which the obtained cluster includes a high percentage of
inexperienced sprinters are found. To verify whether the motions corresponding to these conditions are valid
as the evaluation criterion of sprinting, Spearman’s rank correlation coefficients between cross-correlations
and 30-m time records are calculated. The results show a weak correlation with respect to the coordination
between the elbow and knee motions. Therefore, it can be said that the cross-correlation corresponding to the
coordination can be used as a quantitative criterion in sprinting.
1 INTRODUCTION
Improving the quality of runners’ sprinting motions
in physical education or athletics requires objective
and appropriate evaluation of motion quality. Suzuki
et al. (2016) and Kaji et al. (2017) proposed methods
for evaluating the quality of sprinting motions using
qualitative criteria. Using such qualitative criteria,
evaluators can assess a runner’s motion by directly
observing it or by reviewing the recorded video.
However, the evaluation of motions based on
qualitative criteria does not allow for consistent
evaluations because of variations in interpreting such
criteria by different evaluators, such as the runner
himself and the coach. Therefore, if details of the
motion can be evaluated using quantitative criteria,
rather than the qualitative criteria, the runner’s
motion can be evaluated more consistently.
However, it is difficult for humans to
quantitatively evaluate the details of the motion
through visual observation. In recent years, many
technologies have been developed to acquire athletes’
motion data using video processing or sensor
information processing and evaluating their motions
quantitatively by computer (Pirsiavash et al., 2014,
Parmar et al., 2019). However, these studies aimed to
automate experts’ traditional evaluation or scoring of
the sports motion using computers, and none of them
proposed new evaluation criteria that determine
athletes’ body portions and the timing to be focused
for improving the athletes’ motions, while only
qualitative approaches by Suzuki et al. (2016) and
Kaji et al. (2017) can be seen.
In addition, although many studies have analyzed
sprinting motions from the perspective of
biomechanics (Maeda et al., 2010, Fukuda et al.,
2010), few studies have aimed at proposing new
evaluation criteria. For sprinting motion, this paper
proposes a quantitative evaluation criterion obtained
by computer-based analysis of the time-series
information of joint coordinates obtained from the
video. One of the items, whose quantitative
evaluation criterion can be clarified only when
assuming computer evaluation, is the coordination
between physical motions in sprinting. With regard to
the coordination between physical motions, Tellez
Sabanai, M., Seo, C., Ogata, H. and Ohya, J.
Quantitative Method for Evaluating the Coordination between Sprinting Motions using Joint Coordinates Obtained from the Videos and Cross-correlations.
DOI: 10.5220/0010243105310539
In Proceedings of the 10th International Conference on Pattern Recognition Applications and Methods (ICPRAM 2021), pages 531-539
ISBN: 978-989-758-486-2
Copyright
c
2021 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
531
emphasized its importance in the 1980s (Muraki et al.,
2015), and in recent years, Nobuoka (2010) and
Takano (2008) incorporated the awareness of it into
their sprinting training methods. However, few
studies have quantitatively evaluated the coordination
between physical motions in sprinting, and whether
physical motions are well-coordinated has not been
clarified.
Therefore, in this paper, we clarify the sprinting
motion features that indicate whether physical
motions are well-coordinated, and based on the
results, we propose a quantitative sprinting evaluation
method.
The rest of this paper is organized as follows.
Related studies are described in Section 2. In Section
3, our proposed methods are explained. Section 4
shows experiments to quantify the coordination of
physical motions and to determine the characteristics
of the motions of experienced and inexperienced
runners. In Section 5, the details and validity of the
evaluation criteria are discussed and our proposed
methods are validated. Finally, this paper is
concluded in Section 6.
2 RELATED WORK
Most studies that proposed methods for evaluating
sprinting motions assumed that the motions were
evaluated by visual observation, and the criteria only
described the sprinting motions qualitatively. Suzuki
et al. (2016) and Kaji et al. (2017) proposed some
evaluation methods for sprinting in elementary-
school education. These evaluation methods were
based on biomechanical findings on sprinting, and the
effectiveness of the proposed criteria was
demonstrated by correlating their candidate criteria
with sprinting speed. These studies evaluated the
sprinting motions on a scale of A to C (where A is the
best) by seeing a runner’s motion using qualitative
criteria, such as “putting the elbow forward or not.”
However, such qualitative evaluation criteria include
unclear phrases that can be interpreted differently by
each evaluator. This situation makes it difficult to
consistently evaluate the sprinting motions. The
reason why sprinting evaluations are limited to
qualitative criteria is that sprinting motions have
generally been evaluated visually by humans.
However, in other areas than sprinting, many
methods for evaluating sports motions using
computational methods have been developed in
recent years. Pirsiavash et al. (2014) proposed a
machine-learning method to predict the performance
scores given by experts to skaters and divers using
videos of their performance. In addition, Parmar et al.
(2019) predicted not only experts’ scoring but also
their evaluation of athletes’ motion skills from the
video of diving. However, these proposed methods
only predict the evaluation of sports motions by
experts and do not propose new evaluation criteria
that determine athletes’ body portions to be focused
for improving the athletes’ motions.
Several studies have analyzed the motions of
sprinters from the perspective of biomechanics.
Maeda et al. (2010) analyzed the role of arm swinging
in sprinting by comparing the angular momentum of
each body part, sprint speed, pitch (number of steps
per unit time), and stride width with and without fixed
arm swinging. In addition, Fukuda et al. (2010)
analyzed the characteristics of the motions of top
sprinters in terms of sprint speed, pitch, stride width,
and angle and angular velocity of each body part with
respect to the motions of the swinging and kicking
legs. However, these studies did not propose new
quantitative criteria for evaluating motions.
Our previous study (Sabanai et al., 2019) focused
on the coordination between physical motions, as in
this paper, and proposed quantitative evaluation
methods for sprinting using joint coordinates detected
from videos. However, it is unclear what kind of
relationship exists between the coordinating parts of
the body because the joint coordinate data are
converted into frequency components. Therefore, it is
difficult to interpret the evaluation criteria.
In this paper, we propose a method that can
interpret the relationship between coordinating body
parts using the windowing cross-correlation function
(WCCF).
3 PROPOSED METHOD
3.1 Overview of the Proposed Method
An overview of the proposed method is shown in Fig.
1. First, the time-series information of the joint
coordinates is obtained from the video data of
sprinting motions. For that, person detection
algorithms for videos and the method of Yang et al.
(2017) are used. Second, an athlete’s motion data
used for exploring the coordination are obtained.
Specifically, information of two motion items (e.g.,
elbow motion and knee motion) that are expected to
coordinate with each other is extracted from the
time-series of joint coordinates and normalized so as
to be used in the subsequent analysis. Third,
the coordination between the two motion items
is quantified. For that, the WCCF is applied to the
ICPRAM 2021 - 10th International Conference on Pattern Recognition Applications and Methods
532
Figure 1: Overview of the proposed method.
information obtained in the above-mentioned
processes. Finally, differences in the features of the
coordination between the physical motions of
experienced and inexperienced runners are identified.
For that, k-means clustering is used for the calculated
cross-correlations to classify the dataset into two
clusters, and the percentage of experienced and
inexperienced runners in each cluster is explored.
3.2 Obtaining Information from Video
First, the video data of sprinting captured from the
side are divided into frame-by-frame images. The
person is detected from each of the images, and the
joint coordinates are obtained from the detected
person area. Methods such as YOLOv3 (Redmon et
al., 2018) and Faster R-CNN (Ren et al., 2015) can
be used for the person detection. Next, in the person
area in each image, the method of Yang et al. (2017)
is performed to extract 16 joint coordinates.
In this case, some of the joint coordinates might
be falsely detected. The false detection can affect the
analysis proposed in this paper. Therefore, the
method used in our previous study (Sabanai et al.,
2019) is used to correct the false detection.
Furthermore, if the video is captured with a
general camera from the side, the coordinates away
from the center of the image are affected by the
perspective projection of the camera: e.g. if the
horizontal coordinates of two points with different
depths in the real world are same, the horizontal
coordinates of the two points projected to the image
are different. To correct the effect of the perspective
projection, Eq. (1), which transforms the real-world
coordinate system (𝑋,𝑌,𝑍) to the image coordinate
system (𝑢,𝑣) is used. In Eq. (1), f is the focal length, 𝑐
is the image center, 𝑟 is the rotational parameter, and
𝑡 is the translation parameter, where 𝑥 and 𝑦 denote
the horizontal and vertical directions in the image
coordinate system before the correction respectively,
and 1, 2, 3 are suffixes.
𝑢
𝑣
1

𝑓
0𝑐
0𝑓
𝑐
001

𝑟

𝑟

𝑟

𝑟

𝑟

𝑟

𝑟

𝑟

𝑟

𝑡
𝑡
𝑡

𝑋
𝑌
𝑍
1
(1)
Expanding Eq. (1) yields
𝑢𝑐

𝑋𝑐

𝑌𝑐

𝑍𝑐

(2)
where 𝑐 denotes the coefficient.
When videos of sprinting motions are captured,
the origin of the real-world is set, and four real-world
coordinates are measured at each of the right and left
halves of the videos. By substituting the four points’
coordinates into the (𝑋,𝑌,𝑍) of Eq. (2) and solving
the simultaneous equations, 𝑐

, 𝑐

, 𝑐

, and 𝑐

can
be determined. Since 𝑐

is smaller than the other
coefficients, the term including 𝑐

is ignored.
Figure 2: Examples of angles used for motion items.
In this study, the horizontal coordinates of the
joints on the right side are assumed to be correct, and
that of left side are corrected. The linear equation is
solved by substituting the horizontal coordinate of the
joint to be corrected into 𝑢 and the distance between
the joint to be corrected and its counterpart joint into
𝑍 in Eq. (2). The real-world coordinate 𝑋 of the joint
to be corrected is determined by solving the linear
equation. Finally, the corrected horizontal coordinate
is obtained by substituting 𝑋 and 𝑍0 into Eq. (2).
3.3 Extraction of Motion Items and
Normalization
From the information of the obtained joint
coordinates, two motion items that are expected to
coordinate are extracted. Specifically, as shown in Fig.
2, the two motion items include the time-series
information of values such as 𝜃
, which represents the
angle between the line segment passing the thorax
and elbow and the trunk line passing the thorax and
pelvis, and 𝜃
, which represents the angle between
the line segment passing the pelvis and knee and the
vertical line passing the pelvis.
Quantitative Method for Evaluating the Coordination between Sprinting Motions using Joint Coordinates Obtained from the Videos and
Cross-correlations
533
After the time-series data of the two motion items
are obtained, the acquired data are divided into cycles.
The moment at which one foot is grounded is defined
as the beginning of a cycle, and the moment at which
the same foot is grounded again defined as the end of
the cycle (Sabanai et al., 2019), so that the motions of
the right and left feet are included in one cycle. In
addition, the time-series data are automatically
divided into cycles by detecting the grounding using
our method (Sabanai et al., 2019).
Since the number of frames per cycle depends on
the time-series data, linear interpolation is used to
unify the number of the sampled data to 𝑁, which is
the number of dimensions of the data inputted to the
analysis using the WCCF described in Section 3.4.
3.4 Quantification of Coordination
using the Windowing
Cross-correlation Function
A cross-correlation function is applied to each cycle
having 𝑁 data to quantify the coordination between
the two motion items. The cross-correlation function
can calculate the agreement of two time-series data.
For example, the coordination between arm and leg
motions can be expressed by applying changes in arm
and leg positions per unit time to the cross-correlation
function. The cross-correlation function is applied to
each cycle because the characteristics of sprinting
motions change from the first to later cycles, and the
same cycles, which have similar characteristics,
should be compared. Furthermore, since variations in
sprinting motions are large immediately after the start
of the running, the second or later cycles in which the
motion is more stable and the motion variation is
smaller are analyzed.
In this paper, when the coordination between two
motion items is calculated using the cross-correlation
function, we compare the coordination of two items
not only at the same time point, but also at two
different time points such as the leg motion after the
arm motion. Let 𝐿 be the time difference between the
two time points. Regarding the coordination at the
same point: i.e., 𝐿0, the data of the two motion
items of the first to 𝑁th values of 𝑛th cycle are
compared. In contrast, regarding the coordination at
two time points: i.e. 𝐿0, the cross-correlation
function is applied to the first to 𝑁th values of the 𝑛th
cycle of one motion item 𝑖, while for the other motion
item 𝑗, in case of 𝐿0, the function is applied to the
𝐿 1 to 𝑁th values of the 𝑛th cycle and the first to
𝐿th values of the (𝑛 + 1) cycle, and in case of 𝐿0,
the function is applied to the first to (𝑁𝐿) values of
the 𝑛th cycle and the (𝑁 + 𝐿 + 1) to 𝑁th values of the
(𝑛 − 1) cycle.
Furthermore, in this paper, the coordination of
one cycle’s entire length (𝑁) is not quantified; instead,
portions of one cycle are focused on and compared to
quantify the instantaneous coordination. Therefore,
the window function 𝑊
𝑡
in Eq. (3) is introduced
into the cross-correlation function, assuming that the
𝑇th to (𝑇 + 𝑁′) values of one motion item 𝑖 are
focused on. In this paper, the cross-correlation
function in which the window function is introduced
is called the WCCF (Windowing Cross-Correlation
Function).
𝑊
𝑡,𝑇

1
𝑇𝑡𝑇𝑁
0𝑜𝑡𝑒𝑟𝑤𝑖𝑠𝑒
(3)
Let 𝐹
𝑡 and 𝐹
𝑡 𝐿 be time-series functions
of the two motion items; then, the WCCF 𝑅
,
𝐿,𝑇
of the items i and j is defined as
𝑅
,
𝐿, 𝑇
𝐹
𝑡 ∗ 𝐹
𝑡  𝐿 ∗ 𝑊
𝑡,𝑇
∗


∗
𝐹
𝑡 ∗ 𝑊
𝑡,𝑇
∗


∗
𝐹
𝑡  𝐿 ∗ 𝑊
𝑡,𝑇
∗


∗
(4)
This function contains three parameters 𝑛, 𝑁, and
𝑁
, whose values are set based on our preliminary
studies. In addition, values of the cross-correlation are
analyzed by changing the two variables 𝐿 and 𝑇. The
time range to which the WCCF is applied (in case of
𝐿0) is shown in red in Fig. 3. In Eq. 3 and Fig. 3,
𝑡 is the time when each cycle is divided, and in Eq. 4,
𝑡 is the time when all cycles are connected.
Figure 3: Range of time-series to which the WCCF is
applied.
3.5 Analysis of the Differences in
Coordination between Experienced
and Inexperienced Runners
To find out what sprinting motions coordinate well or
not well, differences in motion coordination between
experienced and inexperienced runners are analyzed.
In this paper, subjects with two years or longer
experiences in athletics are defined as the experienced,
otherwise, as the inexperienced.
By calculating the cross-correlation for a data set
in Section 3.4, a set of numbers between −1 to 1 is
obtained. By performing k-means clustering to the set
ICPRAM 2021 - 10th International Conference on Pattern Recognition Applications and Methods
534
of numbers, the data set is classified into two clusters.
In the classification result, by calculating the
percentage of the experienced and inexperienced
subjects in each cluster, we clarify the two body parts
and the timings that show difference characteristics of
physical motions between experienced and
inexperienced runners. For example, as a result of
performing the clustering for the coordination for the
leg swing soon after the arm swing, if clusters for the
experienced and inexperienced subjects are separate
from each other, the coordination for the experienced
and inexperienced subjects are different.
4 EXPERIMENTS AND RESULTS
4.1 Capturing Video of Sprinting
Motions
Videos of sprinting motions of 20 male subjects (7
experienced and 13 inexperienced, 20-25 years old)
were taken under the conditions shown in Fig. 4. Each
subject ran 30 meters (along a straight line) as soon as
he heard the start signal. We instructed that the
subjects should not slow down till they reach the finish
line. Each subject ran five to six times in average. The
subjects were provided adequate warm-up time before
the initial run, and sufficient time was given between
successive runs so that fatigue caused by one run does
not affect the next run. A total of 115 runs (45
experienced and 70 inexperienced subjects) were
video-recorded. The first 15 meters of each 30 meters
run was video-recorded and used for the analysis. The
Figure 4: Video capture conditions in this study.
time for the 30 meters run was recorded. The camera
used was a Handycam HDR-CX680 (Sony Inc.,
Japan). The frame rate is set to 60 fps, and the video
resolution is set to 1920 × 1080 pixels.
4.2 Obtaining Information from Videos
The obtained video data are split into frame-by-frame
images, and the runner was detected from each image
using YOLOv3 (Redmon et al., 2018). The length of
the larger side (width or height) of the detected
bounding box of the runner is scaled to 256 pixels, so
that the size of all the images is 256 × 256 pixels by
multiplying the same magnification as the longer side
to the shorter length and by filling black to the void
areas caused by the multiplication as shown in Fig. 2.
Next, the joint coordinates are detected from the
obtained images using the method of Yang et al.
(2017). Then, as explained in Section 3.2, false
detections and replacements of the coordinates are
automatically corrected.
In addition, the influence of the perspective
projection on the horizontal coordinates of the
runners’ right and left joints is corrected using Eq. (2).
To obtain 𝑐

, 𝑐

, 𝑐

, and 𝑐

in Eq. (2), the real-
world coordinates (𝑋,𝑌,𝑍) and the corresponding
image coordinates 𝑢 of four points in each of the right
and left halves of the videos are needed. In this study,
𝑐

, 𝑐

, 𝑐

, and 𝑐

are calculated using the real-
world coordinates and corresponding image
coordinates of the six points: the start point, the 15-m
point, two points in front of the camera, and two
arbitrary landmarks, as shown in Table 1. Since the
videos were taken over four days in the experiment,
the image coordinates 𝑢 changes depending on the
day (only on the fourth day, the arbitrary landmark
was used instead of the 15-m point). Since 𝑋 = 6.35
[m] is in front of the camera and located at the center
of the field of view of the image, the corresponding
two points in Table 1 were used to correct both the
right and left halves of the images.
Table 1: Image coordinates and real-world coordinates used
to correct the effect of perspective projection (image
coordinates 𝑢 are represented in the order of the first to the
fourth day of data collection).
Part of
video
Position
Image
coordinates
𝑢
Real-world
coordinates
(
𝑋
,𝑌,𝑍)
Left
half
Start
65, 37,
410, 453
(0, 0, 0)
Arbitrary
landmark (1)
565, 539,
839, 892
(0, 0, 67.00)
Common
In front of
camera (1)
On all four
days,
960
(6.35, 0, 0)
In front of
camera (2)
On all four
days,
960
𝑋
6.35,
𝑌 and 𝑍 are
arbitrarily small
p
ositive values
Right
half
Arbitrary
landmark (2)
1418, 1453,
1476, 1575
(31.20, 0, 52.50)
15-m point
(on fourth day,
arbitrary
landmark (3))
1902, 1908,
1741, (1467)
(15.00, 0, 0)
(on fourth day,
(12.70, 0, 0))
Quantitative Method for Evaluating the Coordination between Sprinting Motions using Joint Coordinates Obtained from the Videos and
Cross-correlations
535
To calculate the real-world coordinates 𝑋 of the
(left) joints of the runner’s left side (left ankle, knee,
hip, wrist, elbow, and shoulder), the values of 𝑢 and
𝑍 are inserted into Eq. (2) (𝑌 values need not be
inserted, because 𝑐

is small enough to be ignored
compared with the other coefficients, as described in
Section 3.2). The horizontal coordinates of each
joint in the image are inserted into 𝑢. Regarding 𝑍, all
the 𝑍-coordinates of the right joints are set to 0, and
the 𝑍 -coordinates of the corresponding left joints are
replaced by the difference in 𝑍 between each two
joints. Specifically, for the joints of the upper body
(wrist, elbow, and shoulder), 𝑍0.4562 [m], the
mean shoulder width of men (Kouchi, 2005), is
inserted. For the joints of the lower body (ankle, knee,
and hip), 𝑍0.3067
m
, the mean great trochanter
width of men (Kouchi, 2005) is inserted. From these
values, 𝑋 is calculated, and the corrected horizontal
coordinates are derived using this value as explained
in Section 3.2.
4.3 Extraction of Motion Items and
Normalization
To analyze the coordination between physical
motions in sprinting using the time-series data of joint
coordinates acquired and corrected as described in
Section 4.2, in this study, the amounts of changes per
unit frame in the angle 𝜃
formed by the thorax,
pelvis, and elbow (the angle of the shoulder joint) and
the angle 𝜃
formed by the perpendicular line in the
𝑦-axis direction, the pelvis and knee (the angle of the
hip joint), are used as the two motion items to be
extracted. This approach enables the quantitative
expression of the coordination between the upper and
lower body; for example, when the elbow is moving
forward and the knee is also moving forward, the
cross-correlation is high. The (right or left) joints on
the same side as the arm that is put forward when
starting are defined as the joint-A, and joints on the
other side are defined as the joint-B (e.g., elbow-A,
knee-B). In Chapter 5 and later, the same definition is
used for foot. The coordination between the elbow-A
and knee-A motions and the coordination between the
elbow-A and knee-B motions are analyzed as follows.
After the two motion items were extracted, the
time-series information was divided into cycles and
sampled to unify the number of dimensions per cycle
as explained in Section 3.3. The number of frames per
cycle is approximately 30 in most of the collected
data of sprinting motions. Therefore, the number of
dimensions of sampling is set to 𝑁 = 30 to minimize
the effect of sampling.
4.4 Quantification of Coordination
using Cross-correlation and
Analysis of Differences between
Experienced and Inexperienced
Sprinters
By applying the WCCF in Eq. (4) to the data obtained
as described in Section 4.3, the coordination between
the elbow and knee motions was quantified. This
paper analyzes the 𝑛 = 4 cycle, which is relatively
accelerated cycle in the sprinting motions in our
experiment and for which sufficient data were
obtained. The coordination between instantaneous
motions of the elbow and knee is analyzed, with 𝑁
=
1. Here, 𝐿 is varied from −29 to 29; 𝑇 is varied from
1 to 29; thereby, a total of 59 × 30 cross-correlations
are calculated for each data of the sprinting motions.
Moreover, the set of the cross-correlations
obtained for each 𝐿 and 𝑇 is classified into two
clusters using k-means clustering, and the
percentages of experienced and inexperienced
subjects in each cluster are obtained.
4.5 Results of the Application of
WCCF and k-Means Clustering
An example of the distribution of the obtained cross-
correlations (𝐿 = 15), for the coordination between
the elbow-A and knee-A motions, is shown in Fig. 5.
Regarding each 𝑇 and cross-correlation, the intensity
of the red color indicates the number of experienced
subjects, and that of the blue color indicates the
number of inexperienced subjects. In Fig. 5, for
example, it can be seen that around 𝑇 = 25, the
number of inexperienced subjects is large if the cross-
correlation is close to −1, and the number of
experienced subjects is relatively large if the cross-
correlation is close to 1. Thus, for some 𝐿 and 𝑇
values, characteristic distributions of experienced and
inexperienced subjects can be seen, depending on
values of the cross-correlation.
Figure 5: Distribution of experienced and inexperienced
subjects regarding the size of 𝑇 and the cross-correlation
between the elbow-A and knee-A (𝐿15).
ICPRAM 2021 - 10th International Conference on Pattern Recognition Applications and Methods
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Figure 6: 𝐿 and 𝑇 values for which the percentage of
inexperienced subjects in the cluster with small cross-
correlations was more than 75% when the set of cross-
correlations was divided into two clusters, where (a) the
coordination between the elbow-A and knee-A motions,
and (b) the coordination between the elbow-A and the knee-
B motions.
As a result of the classification of the obtained set
of the cross-correlations into two clusters using k-
means clustering for each 𝐿 and 𝑇, clusters with small
and large cross-correlations are obtained. The plot of
𝐿 and 𝑇 is shown in Fig. 6, where the percentage of
inexperienced subjects included in the cluster with
small cross-correlations is more than 75%. Figure 6
(a) shows the result of the coordination between the
elbow-A and knee-A motions, and Fig. 6 (b) shows
the coordination between the elbow-A and knee-B
motions. The points are relatively more concentrated
around (𝐿, 𝑇)= (13,27) in Fig. 6(a), and near (24,18)
in Fig. 6(b).
5 DISCUSSION
As described in Section 4.5, the coordination between
the elbow-A and knee-A motions and the
coordination between the elbow-A and knee-B
motions are quantified using cross-correlation, and
the quantified values are used to classify the sprinting
dataset into two clusters. As a result of the
classification, we found the conditions (variables 𝐿
and 𝑇) in which a large percentage of inexperienced
subjects are included in the cluster with the
smaller cross-correlations, as shown in Fig. 6;
specifically, 𝐿13,𝑇27 for the coordination
between the elbow-A and knee-A motions, and
𝐿24,𝑇18 for the coordination between the
elbow-A and knee-B motions are such conditions.
To visualize what sprinting motions these
conditions correspond to, examples of the image data
are shown in Fig. 7. In Fig. 7, in case of 𝐿13,𝑇
27 for the coordination between the elbow-A and
knee-A motions, the specific motions are the elbow-
A motion at the moment the foot-B is grounded and
then the knee-A motion just before the foot-A is
grounded. In case of 𝐿24,𝑇18 for the
Figure 7: Specific motions corresponding to the variables 𝐿
and 𝑇 for which the cluster of the smaller cross-correlation
includes the higher percentage of inexperienced runners: (a)
The case of the coordination between elbow-A and knee-A
motions, where 𝐿13,𝑇27; (b) the case of the
coordination between elbow-A and knee-B motions, where
𝐿24,𝑇18.
coordination between the elbow-A and knee-B
motions, the specific motions are the elbow-A motion
at the moment the foot-A leaves the ground and then
the knee-B motion at the moment the foot-A is
grounded. Under these conditions, motions with
small cross-correlation values tend to correspond to
inexperienced runners’ motions; therefore, it can be
considered that if inexperienced runners improve
their motions so that the cross-correlation values get
larger, quality of their motions can be better. Based
on these, it might be possible to evaluate the
coordination quantitatively using the cross-
correlation.
Meanwhile, to validate evaluation methods for
sprinting motions, Suzuki et al. (2016) and Kaji et al.
(2017) investigated correlation between sprinting
speed and their proposed evaluation criteria. In this
paper, the validity of our evaluation criteria is
investigated by calculating the correlation between
the cross-correlations and the subjects’ 30-m
sprinting time records. The cross-correlations are not
normally distributed, while the 30-m time records are
normally distributed in the data collected in our
experiment. Therefore, Spearman’s rank correlation
coefficient is used to derive the correlation. After
obtaining the rank correlation coefficients 𝑟 out of all
𝐿 and 𝑇 values, the 𝐿 and 𝑇 values are plotted for 𝑟
larger than 0.300 (the relatively large values), as
shown in Fig. 8. Figure 8(a) illustrates the case of the
coordination between the elbow-A and knee-A
motions, and (b) shows the case of the coordination
between the elbow-A and knee-B motions.
Points relatively densely exist near (𝐿 , 𝑇) = (14,
27) in Fig. 8(a); 𝑟 = 0.306 for (14,27) in (a). The
motions corresponding to (14, 27) mostly coincide
with the motions shown in Fig. 7 (a). Thus, under the
condition in which the percentage of the
inexperienced subjects included in the cluster with
Quantitative Method for Evaluating the Coordination between Sprinting Motions using Joint Coordinates Obtained from the Videos and
Cross-correlations
537
Figure 8: 𝐿 and 𝑇 values for which Spearman’s rank
correlation coefficient between cross-correlations and 30-m
time records was larger than 0.300: (a) The case of the
coordination between the elbow-A and knee-A motions,
and (b) the case of the coordination between the elbow-A
and knee-B motions.
small cross-correlations is large, a weak correlation
between the cross-correlations and 30-m time records
can be seen. Therefore, the case of 𝐿14 and 𝑇
27 in Fig. 8 (a), which corresponds to the
coordination between the elbow-A motion at the
moment the foot-B is grounded and then the knee-A
motion just before the foot-A is grounded, is related
to the sprinting velocity and is considered to be valid
as a criterion to evaluate the sprinting motions.
Therefore, it could be possible to evaluate sprinting
motions by the quantitative and consistent criterion
unlike the qualitative criteria proposed by related
studies. However, to achieve a more valid criterion, it
is necessary to verify the reproducibility of the
evaluation with different datasets, increase the
number of data, and verify the criterion based on
mechanical analyses.
6 CONCLUSIONS
This paper has developed a quantitative method for
evaluating the coordination between sprinting
motions, which has been considered to be important
in sprinting. The joint coordinates of the runner are
detected from the videos of runners and are
normalized, and the WCCF is applied to the two time-
series data of the elbow and knee motions obtained
from the normalized joint coordinates; then, the
coordination between their motions is quantified.
In our experiments that use 20 subjects as runners,
as a result of classifying the cross-correlation
obtained from the subjects’ data into two clusters
using k-means clustering, we found conditions for 𝐿
and 𝑇 in which the obtained cluster includes a high
percentage of inexperienced sprinters. To verify
whether the motions corresponding to these
conditions are valid as the evaluation criterion of
sprinting, Spearman’s rank correlation coefficients
between cross-correlations and 30-m time records are
calculated. The results show a weak correlation near
𝐿14,𝑇27 ( 𝑟0.306 ) with respect to the
coordination between the elbow-A and knee-A
motions. Therefore, it can be said that the cross-
correlation corresponding to the coordination
between the elbow-A motion at the moment the foot-
B is grounded and then the knee-A motion just before
the foot-A is grounded can be used as a quantitative
criterion to evaluate the coordination between
physical motions in sprinting. This criterion may be
applicable in evaluating sprinting motions in physical
education or athletics.
In the future, it is necessary to validate the
reproducibility using different datasets. We need to
increase the data size to ensure more validity, verify
based on mechanical analyses, extend the running
distance, obtain three-dimensional motion
information, and verify the motion items other than
the angles 𝜃
and 𝜃
in Fig. 2. In addition, this study
involves only a proposal of an evaluation criterion of
motions, not a proposal of how to improve the
motions based on the criterion. Therefore, we need to
develop training methods to improve the motions
based on the proposed criterion.
ACKNOWLEDGEMENTS
This study was part of the research activities of the
Human Performance Laboratory, Organization for
University Research Initiatives, Waseda University.
In addition, the authors would like to express their
sincere thanks to Mr. Yuta Goto of Waseda
University for his advice from the viewpoint of sports
science.
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