Quantitative Method for Evaluating the Coordination between

Sprinting Motions using Joint Coordinates Obtained from the Videos

and Cross-correlations

Masato Sabanai

, Chanjin Seo

, Hiroyuki Ogata

and Jun Ohya

Department of Modern Mechanical Engineering, Waseda University, 3-4-1, Ookubo, Shinjuku, Tokyo, Japan

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

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



𝑓



0𝑐



0𝑓



𝑐



001



𝑟



𝑟



𝑟



𝑟



𝑟



𝑟



𝑟



𝑟



𝑟



𝑡



𝑡



𝑡





𝑋

𝑌

𝑍



(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







𝑇𝑡𝑇𝑁′



0𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

(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

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), 𝑍0.4562 [m], the

mean shoulder width of men (Kouchi, 2005), is

inserted. For the joints of the lower body (ankle, knee,

and hip), 𝑍0.3067





, 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, 𝐿13,𝑇27 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 𝐿13,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 𝐿13,𝑇27; (b) the case of the

coordination between elbow-A and knee-B motions, where

𝐿24,𝑇18.

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 ( 𝑟0.306 ) 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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