TennisEye: Tennis Ball Speed Estimation using a Racket-mounted Motion Sensor

TennisEye: Tennis Ball Speed Estimation using a

Racket-mounted Motion Sensor

Hongyang Zhao

College of William and Mary

Williamsburg, VA

[email protected]

Shuangquan Wang

College of William and Mary

Williamsburg, VA

[email protected]

Gang Zhou

College of William and Mary

Williamsburg, VA

[email protected]

Woosub Jung

College of William and Mary

Williamsburg, VA

[email protected]

ABSTRACT

Aggressive tennis shots with high ball speed are the key factor in

winning a tennis match. Today’s tennis players are increasingly

focused on improving ball speed. As a result, in recent tennis tour-

naments, records of tennis shot speeds are broken again and again.

The traditional method for calculating the tennis ball speed uses

multiple high-speed cameras and computer vision technology. This

method is very expensive and hard to set up. Another way to cal-

culate the tennis ball speed is to use motion sensors, which are

lower cost and easier to set up. In this paper, we propose an ap-

proach for tennis ball speed estimation based on a racket-mounted

motion sensor. We divide the tennis strokes into three categories:

serve, groundstroke, and volley. For a serve, a regression model is

proposed to estimate the ball speed. For a groundstroke or volley,

two models are proposed: a regression model and a physical model.

We use the physical model to estimate the ball speed for advanced

players and the regression model for beginner players. Under the

leave-one-subject-out cross-validation test, evaluation results show

that TennisEye is 10.8% more accurate than the state-of-the-art

work.

CCS CONCEPTS

• Human-centered computing → Ubiquitous computing

;

Mo-

bile computing; Mobile devices;

KEYWORDS

tennis ball speed estimation, motion sensor, regression model, phys-

ical model

ACM Reference Format:

Hongyang Zhao, Shuangquan Wang, Gang Zhou, and Woosub Jung. 2019.

TennisEye: Tennis Ball Speed Estimation using a Racket-mounted Motion

Sensor. In Proceedings of the 18th ACM/IEEE Conference on Information

Processing in Sensor Networks (IPSN’19). ACM, New York, NY, USA, 13 pages.

https://doi.org/10.1145/nnnnnnn.nnnnnnn

Permission to make digital or hard copies of part or all of this work for personal or

classroom use is granted without fee provided that copies are not made or distributed

for prot or commercial advantage and that copies bear this notice and the full citation

on the rst page. Copyrights for third-party components of this work must be honored.

For all other uses, contact the owner/author(s).

IPSN’19, April 2019, Montreal, Canada

ACM ISBN 978-x-xxxx-xxxx-x/YY/MM.

https://doi.org/10.1145/nnnnnnn.nnnnnnn

1 INTRODUCTION

With the advance of ubiquitous computing, cyber physical systems,

and human computer interaction, wearable devices are becoming

more and more popular nowadays [

] [

]. Applications of wear-

able devices have been widely extended to the eld of sports. For

example, Hao et al. propose a running rhythm monitoring system

based on the sound of breathing through smartphone embedded

sensors [

]. Kranz et al. propose an automated assessment system

for balance board training called Gymskill, which provides feedback

on training quality to the user based on smartphone integrated sen-

sors [

]. In addition, there are several studies in other sports like

running [

], skiing [

], climbing [

], cricket [

], football [

and table tennis [

]. In addition to these research publications, the

industrial wearable devices market is also evolving at a rapid pace.

The global industrial wearable devices market has reached a value

of 1.5 billion dollars in 2017, and is expected to have a compound

annual growth rate (CAGR) of 9

6% [

]. The wearable devices

market in sports is expected to register a CAGR of 9.8%, during the

forecast period (2018 - 2023) [13].

There are also applications of wearable devices in tennis training.

Several commercial tennis assistant systems are available on the

market that aim to improve players’ performance [

] [

These products either integrate the motion sensors inside the racket [

or require users to attach the motion sensors to the racket [

] [

They analyze the motion sensor data and compute the key perfor-

mance metrics for each swing, such as stroke type, ball speed, ball

spin, and ball impact location. In addition to these commercial prod-

ucts, there are also several existing research works on analyzing the

performance of tennis shots. For instance, Srivastava et al. analyze

the consistency of the tennis shots [

]. The authors provide recom-

mendation on wrist rotation based on the shots from professional

players. Sharma et al. analyze the tennis serve [

]. By comparing

the serve phases of a user to those of professionals, the system

provide the user with corrective feedback and insights into their

playing styles.

Tennis ball speed is an important metric in assessing the skill

level of a tennis player. There are two main ways to calculate the

tennis ball speed. One way is to use multiple high-speed cameras

to capture ball movement and calculate speed, such as Hawk-eye

technology [

] [

] and PlaySight [

]. These systems use advanced

This work is supported by U.S. National Science Foundation under grants CNS-1253506

(CAREER).

IPSN’19, April 2019, Montreal, Canada Hongyang Zhao, Shuangquan Wang, Gang Zhou, and Woosub Jung

image processing and analytical algorithms to capture ball move-

ment and calculate speed. However, high-speed cameras are very

expensive and hard to set up. Therefore, most players cannot get

access to these systems, which limits their popularity. Another way

is to use motion sensors. Compared with camera-based method, the

motion sensors-based method is lower cost, more energy ecient,

not inuenced by lighting environment, and easier to set up. There

are some commercial products on the market that assess the perfor-

mance of the players and estimate the ball speed [

] [

However, none of these commercial products open their algorithms

to the public. In addition, to our knowledge, no previous publication

has used motion sensors to calculate the tennis ball speed. There-

fore, we are motivated to explore how to use a motion sensor to

calculate the tennis ball speed.

There are several research publications and commercial prod-

ucts that use motion sensors to analyze tennis shots. However,

none of them open their source codes and datasets to the public.

Source codes and tennis dataset sharing are valuable as they allow

researchers to build their works upon others rather than repeat

already existing research work. In addition, they encourage more

connection and collaboration between researchers, which promotes

the tennis research. Therefore, we are motivated to open our source

codes and tennis dataset to the public

We present TennisEye, a tennis ball speed calculation system

using a racket-mounted motion sensor. We apply a simple threshold-

based method to detect if there is a tennis stroke. Once a tennis

stroke is detected, we use a time window to extract stroke data and

interpolate the sensor readings if the true value exceeds the mea-

surement limit. We apply the Random Forest classier to classify

each tennis stroke into one of three stroke types: serve, ground-

stroke, and volley. A serve is a shot to start a point. A groundstroke

is a shot that is executed after the ball bounces once on the ground,

while a volley is a shot that is executed before the ball bounces on

the ground. If the tennis stroke is a serve, we apply a regression

model to calculate serve speed. If the tennis stroke is a groundstroke

or volley, we propose two models: a physical model and a regression

model. For advanced players, they have correct and constant stroke

gestures. We use the physical model to calculate the ball speed for

them. For beginner players, they have incorrect and varying stroke

gestures. We use the regression model to calculate the ball speed.

We summarize our contributions as follows:

(1)

We propose a tennis ball speed calculation system, Tennis-

Eye. It is the rst research publication to calculate the serve,

groundstroke and volley speed of a tennis ball using a racket-

mounted motion sensor.

(2)

We propose two models to calculate the groundstroke or

volley speed: a physical model and a regression model. We

apply the physical model to calculate the ball speed for ad-

vanced players, and the regression model to calculate the

ball speed for beginner players.

(3)

We evaluate the proposed system using the tennis shot data

from players of dierent levels. Our experiment results show

that TennisEye is 10.8% more accurate than the state-of-the-

art work.

https://hongyang-zhao.github.io/TennisEye/

Stroke

Detection

Regression Model

Physical Model

Accelerometer

Readings

Gyroscope

Readings

Serve Speed

Calculation

Groundstroke/Volley Speed Calculation

ball speed

BLE

Sensor

Groundstroke/

Volley

Serve

Stroke

Data

Segmentation

Data

Interpolation

Stroke

Classiﬁcation

Beginner?

Yes

Stroke

data

Figure 1: Data Processing of TennisEye

(4)

We collect an accurate and high-quality tennis dataset. We

open our source codes and tennis dataset to the public.

The remainder of this paper is organized as follows. First, we

introduce the system design in Section 2. In Section 3, we evaluate

the system performance. We discuss the system and future work

in Section 4. We summarize the related works in Section 5. Finally,

we draw our conclusion in Section 6.

2 TENNISEYE DESIGN

We introduce the system design of TennisEye in this section. First,

we introduce the data processing in Section 2.1. Then, we introduce

the sensor deployment and data collection in Section 2.2. Following

that, modules in the data processing are introduced from Section 2.3

to Section 2.8.

2.1 Overview of TennisEye

The data processing of TennisEye is shown in Fig. 1. A motion

sensor is deployed on a racket handle to collect the accelerometer

and gyroscope readings, which are real-time transmitted to a smart

phone through Bluetooth Low Energy (BLE). Based on the collected

motion data, a threshold-based method is proposed to detect tennis

strokes. Once a tennis stroke is detected, we apply a peak detection

algorithm to nd the impact time when a ball hits the racket. Once

the impact time is found, we use a sliding window with a length of

2 seconds to extract the stroke data. For the stroke data, we apply

a cubic spline interpolation to compensate the sensor readings if

the sensor saturates. Then, we use the Random Forest classier to

classify each tennis stroke into one of three stroke types: serve,

groundstroke, and volley. If the tennis stroke is a serve, we propose

a serve speed estimation method to calculate serve speed. If the

tennis stroke is a groundstroke or volley, we propose two models, a

regression model and a physical model, to calculate the ball speed

for the beginner player and the advanced player, respectively. We

train the models and evaluate the performance of the system using

a laptop.

TennisEye: Tennis Ball Speed Estimation using a Racket-mounted Motion Sensor IPSN’19, April 2019, Montreal, Canada

Side A

Side B

0.31m 0.21m

Side A

Figure 2: Sensor placement and coordinate system

Figure 3: Birdview of the tennis court from a PlaySight cam-

era

2.2 Sensor Deployment

The motion sensor we used is a UG sensor [

]. It includes a triaxial

acceleration sensor and a triaxial gyroscope. The measure range

of the accelerometer and the gyroscope were set to be

and

2000

◦

/sec

, respectively. Both sensors were sampled with 100 Hz.

The UG sensor was xed at the handle of the players’ rackets. Fig. 2

shows the sensor position and the coordinate system. We call the

side with the UG sensor side A, and the side without the UG sensor

side B.

We collected data in a tennis court that was equipped with a

PlaySight system [

], which included six high denition (HD)

cameras. The PlaySight system uses image processing algorithm

to recognize stroke type, ball speed, and more. We use the stroke

type and the ball speed calculated by the PlaySight system as the

ground truth. The birdview of the tennis court from a PlaySight

camera is shown in Fig. 3.

2.3 Stroke Detection

When a player plays tennis, he/she not only swings a racket, but

also performs some non-stroke actions during a match. For example,

he/she may run on the court, use the racket to pick up a ball from

the court surface, or twirl the racket in his/her hands while waiting

for an opponent to serve. The aim of the stroke detection is to detect

stroke behaviors, rather than those non-stroke actions.

We nd that when a player hits a ball, the player swings the

racket in a circular motion. In this circular motion, the racket is

aected by a centripetal acceleration that points to the human torso.

This centripetal acceleration generates a spike in the accelerometer

readings in X-axis,

. Fig. 4 shows

when a player plays tennis.

0 5 10 15 20 25 30 35 40 45

Time (second)

-40

-20

100

120

140

160

Acceleration (m

/s)

twirl a racketlateral run pick up a ball

Figure 4: Accelerometer readings in the X-axis when a player

plays tennis

Each spike in the gure is a tennis stroke. Other non-stroke actions,

such as lateral run, twirling a racket, or picking up a ball, do not

generate large values in

. Therefore, we use

to detect stroke

behaviors. If

is larger than a threshold, i.e. 9

, it is regarded as a

stroke.

2.4 Data Segmentation

After a stroke is detected, the next step is to nd the start and end

time of a tennis stroke and extract this interval of sensor data as

stroke data. The extracted stroke data will be used for ball speed

calculation.

There are mainly four phases for a tennis stroke: backswing,

acceleration, impact, and follow-through. In a backswing phase, a

player moves a racket behind his/her body and prepares to swing

forward. In an acceleration phase, the player moves the racket

forward. The speed of the racket increases in this phase. At the

end of the acceleration phase and the start of the impact phase,

the speed of the racket reaches maximum. In an impact phase, the

racket hits a tennis ball. Due to impact, the speed of the racket

decreases rapidly. Finally, in a follow-through phase, the player

slows down the racket after hitting a ball.

Based on our study, we nd that the impact phase occurs in the

middle of these four phases. In addition, the speed of the racket

reaches maximum at the start of the impact phase. Therefore, by

looking for the time when the speed of the racket reaches maximum,

we nd the start of the impact phase. In our coordinate system, no

matter which stroke (serve, forehand, backhand) a player plays, the

racket always rotates around Y-axis. Therefore, the position with

the max absolute value of the gyroscope readings in the Y-axis is

the start of the impact phase.

Fig. 5 shows the gyroscope readings of a tennis serve. From the

gure, we nd that the valley of

is the start of the impact phase.

We apply a peak detection algorithm with a sliding window on

the absolute values of the gyroscope readings in the Y-axis,



to nd the impact start time. As the minimum interval between

two consecutive strokes is 2 seconds, the time window size is set

to be 2 seconds. Specically,



(t)



is a peak if it is larger than

all of the samples in the time window of

[

t − 1s, t + 1s

]

. Since the

IPSN’19, April 2019, Montreal, Canada Hongyang Zhao, Shuangquan Wang, Gang Zhou, and Woosub Jung

0 0.5 1 1.5 2

Time (sec)

-1500

-1000

-500

500

1000

Gyroscope (degree/sec)

1 1.05 1.1 1.15

-1500

-1000

-500

500

1000

tstart

Backswing

Acceleration

Follow-through

Impact

tend

tstart tend

Impact

Figure 5: Gyroscope readings of a serve

minimum of



for a stroke in our dataset is 814.5 degree/sec, the

detected peak of



should be larger than 814.5 degree/sec. After

the impact start time

star t

is detected, we use a time window of

[

star t

− 1s, t

star t

+ 1s

]

to extract the stroke data.

2.5 Data Interpolation

In our dataset, we nd that the gyroscope readings in the Y-axis

sometimes saturate when a player serves with a high speed. This

saturation happens when a sensor measures a value that is larger

than its measurement range,

2000

◦

/sec

. The blue line in Fig. 6

shows an example of the sensor saturation. In the gure, we nd

that the raw gyroscope readings in the Y-axis saturate from 0.52

seconds to 0.54 seconds. To deal with this problem, we apply the

cubic spline interpolation [

] to interpolate the saturated gyroscope

readings in the Y-axis. Specically, we use the gyroscope readings

in the Y-axis within the range of



sat _st ar t

− tw, t

sat _st ar t



and



sat _end

, t

sat _end

+ tw



to construct new data points within the

range of



sat _st ar t

, t

sat _end



sat _st ar t

and

sat _end

are the start

and end times of the saturation, which are 0.52 seconds and 0.54

seconds in this case.

is empirically set to be 100ms. The gyro-

scope readings in the Y-axis after interpolation are shown as the

red dashed line in the gure.

2.6 Stroke Classication

After data interpolation, the next step is to classify the stroke type

for each stroke data segment. First, we extract a series of features

from each data segment. The features include mean, standard devi-

ation, skewness, kurtosis, minimum, and maximum of each axis of

accelerometer and gyroscope readings. The amplitude of accelerom-

eter and gyroscope readings are also computed. In total, 38 features

for each data segment are calculated and normalized between

[

0, 1

]

Second, we apply a machine learning classier to classify each

data segment into one of three stroke types: serve, groundstroke,

and volley. We compare the performance of ve classiers: Naive

Bayes, AdaBoost, Support Vector Machine (SVM), Decision Tree,

and Random Forest. Since the Random Forest performs best as

shown in Section 3.4, we choose the Random Forest classier for

stroke classication.

0 0.25 0.5 0.75 1

Time (second)

-3000

-2500

-2000

-1500

-1000

-500

500

1000

Gyroscope (degree/sec)

raw gy

gy after interpolation

Figure 6: Interpolation of the gyroscope readings in the Y-

axis

2.7 Serve Speed Calculation

For a tennis serve, the initial speed of a ball is quite small and

mainly depends on the racket speed. The larger the racket speed,

the higher the ball speed. This motivates us to use the racket speed

to calculate the serve speed. When a player serves a tennis ball,

the racket swings in a circular motion with the human shoulder

as the center. Because the racket rotates around the Y-axis in our

coordinate system,

measures the angular speed of the racket.

We use

at the impact start time to model the ball serve speed

b_serve

by a linear regression model as:

b_serve

= k ·



(

star t

)



+ b, (1)

where

and

are the parameters of the linear regression model.

All of the tennis serve data are used to train the serve model.

and

are calculated by using the method of least squares [

and

are 0.025 and 20.06, respectively.

2.8 Groundstroke/Volley Speed Calculation

We propose two models to calculate the ball speed: a physical model

and a regression model. The physical model is built based on the

physical impact between a racket and a ball, while the regression

model applies a linear regression model to estimate the ball speed.

For advanced players, they have correct stroke gestures, and similar

gestures for the same type of the stroke. We propose a physical

model to calculate the ball speed for them. For beginner players, it

is hard to build the physical model due to two reasons. First, their

stroke gestures are incorrect. With incorrect stroke gestures and

terrible tennis skills, they often swing the racket in an awkward way,

which is hard to build the physical model. Second, for the same type

of the stroke, they may perform dierent gestures and swing the

racket in dierent ways. The big variance in their stroke gestures

reduces the accuracy of the physical model. Therefore, instead of

building a physical model, we propose a simple regression model

to calculate the ball speed for the beginner players.

2.8.1 Physical Model. The impact between a racket and a tennis

ball is governed by some physical laws and mechanical principles.

By applying these laws and principles, we propose a physical model

TennisEye: Tennis Ball Speed Estimation using a Racket-mounted Motion Sensor IPSN’19, April 2019, Montreal, Canada

"_$%&"%

"_$%&

!"#$%&'()*%+!&,%

Before impact After impact

"_$%

Figure 7: Physical impact process between a tennis racket

and a tennis ball

to estimate ball speed. The outgoing ball speed is mainly inuenced

by two factors: the racket speed and the incoming ball speed. The

racket speed can be calculated using motion sensors, while the

incoming ball speed is unknown. Without the incoming ball speed,

the outgoing ball speed cannot be calculated by a physical model.

To solve this problem, we apply a physical law (conservation of

linear momentum [

]) and a mechanical principle (Coecient

of Restitution [

]). Both the physical law and the mechanical

principle contain the incoming ball speed parameter. We combine

these into one by eliminating the incoming ball speed parameter to

get the outgoing ball speed.

Because of the diculty in characterizing the physical impact

process using only one racket-mounted motion sensor, we make

several assumptions to simplify the physical model.

(1)

The tennis ball horizontally hits and bounces o the racket.

(2) The ball impacts at the center of the racket face.

(3)

During impact, there is a constant hand force on the racket.

There are four reasons to these three assumptions. (1) The physi-

cal impact process between a racket and a tennis ball is very compli-

cated. Without these assumptions, it is extremely dicult to build

a physical model only using motion sensors. (2) Even if we build

a model without these simplied assumptions, this model will be

very complicated. A complicated model may require much more

computation and energy cost than the simplied model. This is not

feasible for the small-size device embedded into the racket. (3) As

shown in Section 3, the evaluation results demonstrate that our

proposed models perform quite well already. A complicated model

may only increase the accuracy a little. (4) These assumptions are

made based on our observations on tennis matches. We nd that

the angle between a ball and the normal to the racket string plane is

typically quite small. Otherwise, the ball will either move towards

the ground or move towards the sky. Accordingly, we assume that

the ball horizontally hits and bounces o the racket. In addition,

we nd that tennis balls usually hit at the center of the rackets for

advanced players. Therefore, we assume that the ball impacts at the

center of the racket face. Finally, we nd that the duration of the

impact is roughly 20ms, as shown in Fig. 5. Thus, it is reasonable

to assume a constant hand force during this short period of time.

Based on these assumptions, the physical impact process is

shown in Fig. 7. Before impact, there is a hand force

exerted on

a racket. Under the inuence of the hand force, the racket of mass

is moving at velocity

r _st ar t

towards a tennis ball. At the same

time, this tennis ball of mass

is moving at velocity

b_in

towards

the racket. After impact, the tennis ball bounces o the racket at

velocity v

b_out

, reducing the velocity of the racket to v

r _end

By conservation of linear momentum, we get:

e nd

s t ar t

HFdt = M ·



r _end

− v

r _st ar t



+m·



b_out

+ v

b_in



, (2)

where

star t

and

end

are the start and end times of impact. In

this equation,

star t

, and

are known.

star t

is calculated in

data segmentation module, as shown in Section 2.4.

and

are

300

and 50

. To calculate

b_out

, we need to calculate the other

unknown parameters rst. They are

end

r _end

− v

r _st ar t

and v

b_in

Calculating t

end

The impact starts when a ball hits a racket,

and ends when the ball leaves the racket. During the impact, due to

the momentum lost by the ball, the speed of the racket decreases

rapidly. After the ball leaves the racket, the speed of the racket

increases again. By searching for the change of the racket speed,

we nd the end time of impact as shown in Fig. 8. More specically,

by searching from t

star t

, t

end

is calculated as:

end

= t i f



(

)



(

t + 1

)



(3)

Calculating v

r_end

− v

r_start

. v

r _end

− v

r _st ar t

can be calcu-

lated as the integration of the accelerometer readings in the Z-axis.

However, as there are two sides of the rackets, the accelerometer

readings in the Z-axis will have opposite values when the tennis

ball hits on the dierent sides. The motion sensor is attached on

the side A of the racket, as shown in Fig. 2. When the side A of the

racket hits the tennis ball, the movement direction of the racket

is the same as the positive direction of the Z-axis of the sensor.

r _end

− v

r _st ar t

is calculated as the integration of the accelerom-

eter readings in the Z-axis. However, when the side B of the racket

hits the tennis ball, the movement direction of the racket is oppo-

site to the positive direction of the Z-axis of the sensor, as shown

in Fig. 7.

r _end

− v

r _st ar t

is calculated as the integration of the

inverse of the accelerometer readings in the Z-axis. Therefore, to

calculate the ball speed, we need to reorientate the motion sensor

so that the positive direction of the Z-axis of the sensor is the same

as the movement direction of the racket.

There are eight possible impact types between a tennis ball and

a racket, which are summarized in Table 1. From the table, we nd

that when the

(

star t

) is larger than 0, the positive direction of

the Z-axis of the sensor is the same as the movement direction of the

racket. When the

(

star t

) is smaller than 0, the positive direction

of the Z-axis of the sensor is opposite to the movement direction

of the racket. This motivates us to use

(

star t

) to reorientate the

sensor readings in Z-axis. The reoriented accelerometer readings

in the Z-axis a

′

is calculated as:

′



(

star t

)

> 0

−a

(

star t

)

< 0

(4)

The change of the racket speed

r _end

− v

r _st ar t

in Eq. 2 is

calculated as the integration of the reoriented acceleration readings

IPSN’19, April 2019, Montreal, Canada Hongyang Zhao, Shuangquan Wang, Gang Zhou, and Woosub Jung

0 0.5 1 1.5 2

Time (sec)

-1500

-1000

-500

500

1000

1500

Gyroscope (degree/sec)

start

end

0 0.5 1 1.5 2

Time (sec)

-50

100

150

200

Acceleration (m/s

)

start

end

Figure 8: Acceleration data (left gure) and gyroscope data (right gure) of a forehand shot performed by a left-hand player.

The start time of impact t

star t

is marked as the red dashed line.The end time of impact t

end

is marked as the black dashed line.

Table 1: Eight impact types between a tennis ball and a racket

Dominant Hand Forehand/Backhand Side that a ball hits a racket д

star t

) Direction

Z −axis

and Direction

r acket

Left

Forehand Side A > 0 Same

Forehand Side B < 0 Opposite

Backhand Side A > 0 Same

Backhand Side B < 0 Opposite

Right

Forehand Side A > 0 Same

Forehand Side B < 0 Opposite

Backhand Side A > 0 Same

Backhand Side B < 0 Opposite

in the Z-axis during impact as:

r _end

− v

r _st ar t

e nd

s t ar t

′

(

)

dt (5)

Calculating HF.

This hand force causes the racket to move in

an accelerated motion, which is measured by the Z-axis of the

accelerometer. As we assume that the hand force is constant during

impact, we use the adjusted accelerometer readings in the Z-axis

′

at the start time of impact

star t

to model the hand force. The

larger the hand force, the larger the acceleration. Thus, we choose

a linear function to model this relationship as shown below:

HF = k

H F

· M · a

′



s t ar t



+ b

H F

, (6)

where

H F

and

H F

are the model parameters. After substituting

Eq. 3 through Eq. 6 into Eq. 2, Eq. 2 has four unknown parameters:

H F

, b

H F

b_in

b_out

. We use the incoming ball speed

b_in

and

outgoing ball speed

b_out

calculated from the PlaySight system to

train this model. First, we get the incoming and outgoing ball speeds

for each tennis shot from the PlaySight system. Then, we feed the

incoming and outgoing ball speeds of all the tennis shots into Eq. 2.

Finally, we use the method of least squares [

] to calculate

H F

and b

H F

. k

H F

and b

H F

are 0.236 and 65.83, respectively.

Calculating v

b_in

After

H F

and

H F

are determined, there are

two unknown parameters in Eq. 2:

b_in

and

b_out

. To calculate

b_out

, we need to calculate

b_in

rst. However,

b_in

is hard

to be calculated using a motion sensor. To solve this problem, we

apply the coecient of restitution (COR) to build another equation

between

b_in

and

b_out

. We combine these two equations into

one by eliminating v

b_in

parameter to calculate v

b_out

The COR is dened as the ratio of the nal velocity to the initial

velocity between two objects after their collision [

]. The COR is

a measure of how much kinetic energy remains after the collision

of two bodies, with the value that ranges from 0 to 1. If the COR is

close to 1, it suggests that very little kinetic energy is lost during

the collision; on the other hand, if it is close to 0, it indicates that a

large amount of kinetic energy is converted into heat or otherwise

absorbed through deformation. In our case, the COR is calculated

as:

e =

b_out

− v

r _end

r _st ar t

+ v

b_in

(7)

To calculate the outgoing ball speed

b_out

, we need to calculate

r _st ar t

r _end

, and

b_in

rst. The racket speed before impact

r _st ar t

is calculated by the gyroscope readings in the Y-axis:

r _st ar t



(

star t

)



· R

swinд

, (8)

where

swinд

is the swing radius of the circular motion, which is

the distance between the center of the racket face and the rotation

center. Howard Brody measured the swing radius among a number

of players [

]. He found that the average radius between the butt

end of the racket and the rotation center is 0.2m. As the distance

TennisEye: Tennis Ball Speed Estimation using a Racket-mounted Motion Sensor IPSN’19, April 2019, Montreal, Canada

0 0.2 0.4 0.6 0.8 1

COR

0.02

0.04

0.06

0.08

0.1

0.12

Probability

Figure 9: Distribution of COR values

between the center of the racket face and the butt end of the racket

is 0.52m, as shown in Fig. 2. Therefore, R

swinд

is set to be 0.72m.

By substituting

r _st ar t

into Eq. 5, we calculate the racket speed

after impact v

r _end

as:

r _end

= v

r _st ar t

e nd

s t ar t

′

(

)

dt (9)

We feed the incoming ball speeds and outgoing ball speeds cal-

culated from the PlaySight system into Eq. 7 to calculate

. The

distribution of all calculated COR values is shown in Fig. 9. We

nd these COR values obey a normal distribution with a mean of

0.16. Because there are many impact factors for COR estimation

(such as ball speed, stroke force, string tension and impact position)

and the correlations between these impact factors and the COR

are unknown, it is extremely dicult to explicitly dene the COR

model. In addition, most COR values are close to the mean of this

normal distribution. Therefore, we assume COR to be a constant

value, 0.16, for all the tennis shots to simplify the model.

We then combine Eq. 9 and Eq. 2 by eliminating the incoming

ball speed to get the outgoing ball speed as:

b_out

1 + e



m · v

r _st ar t

− M ·



r _end

− v

r _st ar t



· v

r _end

e nd

s t ar t

HFdt



(10)

From the above equation, we nd that the outgoing ball speed

b_out

depends on

r _st ar t

r _end

star t

end

, and

. The in-

coming ball speed

b_in

does not appear in the equation as it is

eliminated when we combine Eq. 2 and Eq. 7. Though

b_in

does

not appear in Eq. 10, it indirectly inuences the outgoing ball speed

via

r _end

, which is calculated based on the integration of accelera-

tion data in the Z-axis during impact as shown in Eq. 9. The larger

incoming ball speed, the larger uctuation of the acceleration data

during impact. Therefore, the inuence of the incoming ball speed

is considered in our model.

2.8.2 Regression Model. When a player performs a groundstroke

or volley, he/she swings the racket in a circular motion. In our

coordinate system, the racket rotates around the Y-axis for both

strokes. Similar to the serve speed model, we use

to calculate

the outgoing ball speed v

b_out

by a linear polynomial model as:

b_out

= k ·



(

star t

)



+ b, (11)

where

and

are the parameters of the linear regression model.

We use all the tennis groundstroke and volley data to train this

model by the method of least squares [

and

are 0.039 and

3.94, respectively.

3 PERFORMANCE EVALUATION

We evaluate the performance of TennisEye in this section. We

rst introduce the data set in Section 3.1. Then, we introduce the

performance of the physical model and regression model using

leave-one-subject-out cross validation, self test, and 5-fold cross

validation in Section 3.2.1, Section 3.2.2, and Section 3.2.4, respec-

tively. After that, we evaluate the performance of stroke detection

in Section 3.3 and stroke classication in Section 3.4. Finally, we

evaluate the overall performance of TennisEye in Section 3.5.

3.1 Data Set

We collected data from 7 players. Based on their self-report infor-

mation, we divided the subjects into three categories: coach, regular

player, and casual player. The coaches play several times per week,

the regular players play one time per week, and the casual players

play 0

∼

2 times per month. Table 2 shows the summary of tennis

data we collected with a UG sensor. In total, we collected 569 serves,

1398 groundstrokes, and 18 volleys.

No previous publication has used motion sensors to estimate

tennis ball speed. However, we are aware that there are some ten-

nis sensors on the market, such as Zepp [

], Sony Sensor [

Usense [

], and Babolat Play [

]. These sensors are attached to

the tennis racket. By analyzing the tennis data, they compute the

key performance metrics for each swing, such as stroke type and

ball speed. Among them, Sony Sensor and Usense are no longer

manufactured. Babolat Play does not compute the ball speeds of

groundstroke and volley shots, which we focus on. Zepp is a popu-

lar tennis sensor that recognizes stroke types and calculates serve,

groundstroke and volley speeds. Therefore, we choose Zepp as

state-of-the-art work. To compare with the ball speed calculation al-

gorithm in Zepp, we collected tennis data using both a UG and Zepp

sensor. Table 3 shows the summary of the tennis data collected.

3.2 Ball Speed Calculation Accuracy

3.2.1 Leave-one-subject-out Evaluation. To evaluate the perfor-

mance of the proposed ball speed models. First, we use the video

data to locate each tennis stroke in the dataset collected with a

UG sensor as shown in Table 2. Then, we calculate the tennis ball

speeds for each stroke based on the proposed ball speed models.

Finally, we compare the ball speeds calculated by our model with

the ball speeds calculated by other models. Here, we use the leave-

one-subject-out cross validation to evaluate the performance of

the proposed ball speed models. The leave-one-subject-out cross

validation uses the tennis shot data from 6 subjects to train the

ball speed estimation model, and then applies this model to esti-

mate the ball speed from the remaining subject. Mean and standard

deviation of error are considered as the evaluation metrics. The

results are shown in Fig. 10. For the serve ball speed estimation,

IPSN’19, April 2019, Montreal, Canada Hongyang Zhao, Shuangquan Wang, Gang Zhou, and Woosub Jung

Table 2: Dataset collected with a UG sensor

Player

Player Dominant

Data Collection Time # Serve # Groundstroke # Volley

Description Hand

# 1 Male Coach Right 5/8/2018 36 0 0

# 2 Female Coach Left 5/15/2018; 5/22/2018 75 214 5

# 3 Female Coach Right 8/13/2018 50 136 0

# 4 Regular Player Right 5/23/2018 0 302 3

# 5 Casual Player Left 7/7/2018; 7/15/2018; 7/22/2018 0 628 10

# 6 Casual Player Right 5/7/2018; 8/13/2018; 9/7/2018 263 118 0

# 7 Casual Player Right 9/7/2018 145 0 0

Table 3: Dataset collected with both a UG and a Zepp sensor

Player Data Collection Time # Serve # Groundstroke # Volley

# 3 8/13/2018 50 136 0

# 5 7/22/2018 0 209 6

# 6 9/7/2018 46 118 0

# 7 9/7/2018 145 0 0

Serve Groundstroke+Volley Serve+Groundstroke+Volley

Mean/Std of Error (miles/hour)

Phy

Reg

Phy

Reg

Zepp

Phy

Zepp

Player 1

Player 2 Player 3

Player 4

Player 5 Player 6 Player 7

Figure 10: Performance of ball speed estimation models under leave-one-subject-out cross validation

the error of the proposed regression model is 4.3

4.0 miles/hour.

The accuracy is 93.4%. For the groundstroke and volley ball speed

estimation, the error of the proposed physical model and regression

model are 5.0

4.9 miles/hour and 4.9

4.4 miles/hour respectively.

The accuracy are 88.4% and 88.8% respectively. For all the tennis

shot data, the error of the proposed physical model and regression

model are 4.8

4.7 miles/hour and 4.7

4.3 miles/hour, respectively.

The accuracy are 90.0% and 90.2%, respectively. From Fig. 10, we

nd that the performance of the physical model is similar to that of

the regression model. For the casual players, the regression model

is slightly better. For the regular players, two models have simi-

lar performances. For the coaches, the physical model performs

slightly better than the regression model. Therefore, we use the

regression model to estimate the ball speed for beginner players

and the physical model to estimate the ball speed for advanced

players.

We compare our ball speed models with two works: the ball

speed model in Zepp and a table tennis ball speed model [

]. There

are two reasons to choose this table tennis ball speed model for

comparison. (1) Both tennis and table tennis belong to racket sports.

Compared with other racket sports, table tennis is most similar to

tennis. (2) As far as we know, this table tennis model is the only mo-

tion sensors-based ball speed model for racket sports. We evaluate

the performance of these three models using leave-one-subject-out

(LOSO) cross validation. The dataset used for evaluation is collected

with both a UG and Zepp sensor, as shown in Table 3. The evalua-

tion results are shown in Table 4. From the table, we nd that the

proposed physical model and regression model have similar perfor-

mance. Both of them perform much better than Zepp and the table

tennis model. For all the tennis shot data, the proposed physical

model is 7.8% more accurate than the table tennis model and 11.7%

more accurate than Zepp. The proposed regression model is 8.2%

TennisEye: Tennis Ball Speed Estimation using a Racket-mounted Motion Sensor IPSN’19, April 2019, Montreal, Canada

Table 4: Comparison with State-of-the-art Ball Speed Models

Ball Speed Mo del Evaluation Metric Serve Groundstroke + Volley Serve + Groundstroke + Volley

Peter et al. [3]

Mean±Std 11.6±7.1 miles/hour 7.6±6.9 miles/hour 9.1±7.3 miles/hour

Accuracy 81.4% 81.2% 81.3%

Zepp

Mean±Std 5.2±5.7 miles/hour 10.6±miles/hour 8.9±7.8 miles/hour

Accuracy 91.8% 70.8% 77.4%

Phy

Mean±Std N/A 5.3±5.7 miles/hour 4.9±5.1 miles/hour

Accuracy N/A 86.7% 89.1%

Reg

Mean±Std 4.3±3.9 miles/hour 5.1±4.9 miles/hour 4.8±4.6 miles/hour

Accuracy 93.1% 87.4% 89.5%

Serve

Groundstroke+Volley

Serve+Groundstroke+Volley

Mean/Std of Error (miles/hour)

Player 1

Player 2 Player 3

Player 4

Player 5 Player 6

Player 7

Phy

Reg

Phy

Reg

Figure 11: Performance of ball speed estimation models under self test

more accurate than the table tennis model and 12.1% more accurate

than Zepp. The table tennis model performs better than Zepp, es-

pecially in groundstroke and volley speed estimation. However, it

is still outperformed by our models. We think there are two main

reasons. (1) Table tennis and tennis are two racket sports that dier

a lot in terms of the size, mass, and material of the ball and racket.

In addition, the techniques of swinging the rackets are dierent. In

table tennis, a player swings the racket with a lot of wrist action.

However, in tennis, a player swings the racket with a lot of body

rotation and less wrist action. Therefore, the table tennis model

may not be appropriate for tennis. (2) In this table tennis model, the

racket speed is modeled as the sum of the wrist linear speed and

wrist rotation speed. However, in tennis, the racket speed mainly

depends on the rotation of the arm and body. Therefore, our models

are more accurate than the table tennis model in characterizing the

tennis racket speed.

3.2.2 Self Evaluation. The self test partitions the dataset for each

player into 5 randomly chosen subsets of equal size. Four subsets

are used to train the model, and the remaining one is used to val-

idate the model. This process is repeated 5 times, such that each

subset is used exactly once for validation. The results of the self

test are shown in Fig. 11. Mean and standard deviation of error

are considered as the evaluation metrics. For the serve ball speed

estimation, the error of the proposed regression model is 4.0

3.6

miles/hour. For the groundstroke and volley speed estimation, the

error of the proposed physical model and regression model are

4.6

4.6 miles/hour and 4.2

3.9 miles/hour. For all the tennis shot

data, the error of the proposed physical model and regression model

are 4.4

4.3 miles/hour and 4.2

3.8 miles/hour. Under the self test,

both the regression model and the physical model perform better

than that under leave-one-subject-out cross validation. In addition,

under the self test, the regression model always performs slightly

better than the physical model for all the players.

3.2.3 Cross Evaluation. The 5-fold cross-validation test uses all the

data to form the dataset. It partitions the dataset into 5 randomly

chosen subsets of equal size. Four subsets are used to train the

model, and the remaining one is used to validate the model. This

process is repeated 5 times such that each subset is used exactly once

for validation. The results of the 5-fold cross validation are shown

in Fig. 12. Mean and standard deviation of error are considered as

the evaluation metrics. For the serve ball speed estimation, the er-

ror of the proposed regression model is 4.1

3.8 miles/hour. For the

groundstroke and volley speed estimation, the error of the proposed

physical model and regression model are 4.8

4.8 miles/hour and

4.6

4.0 miles/hour. For all the tennis shot data, the error of the pro-

posed physical model and regression model are 4.6

4.5 miles/hour

IPSN’19, April 2019, Montreal, Canada Hongyang Zhao, Shuangquan Wang, Gang Zhou, and Woosub Jung

Mean/Std of Error (miles/hour)

Serve

+Groundstroke

+Volley

Groundstroke

+Volley

Reg

Phy

Reg

Groundstroke

+Volley

Serve

+Groundstroke

+Volley

Figure 12: Performance of ball speed

estimation mo dels under 5-fold cross

validation

0~9

10~19

20~29

30~39

40~49

50~59

60~69

70~79

80~89

90~99

Incoming ball speed (miles/hour)

100

Accuracy (%)

Advanced players

Beginning players

Figure 13: Performance of the phys-

ical model under dierent incoming

ball speeds

0~9

10~19

20~29

30~39

40~49

50~59

60~69

70~79

80~89

90~99

Racket speed (miles/hour)

100

Accuracy (%)

Advanced players

Beginning players

Figure 14: Performance of the phys-

ical model under dierent racket

speeds

and 4.4

3.9 miles/hour. Under the 5-fold cross-validation test, both

the regression model and the physical model perform better than

that under leave-one-subject-out cross validation, and worse than

that under self test. In addition, under the 5-fold cross-validation

test, the regression model always performs slightly better than the

physical model.

3.2.4 Influence Factors on the Physical Model. We evaluate the

performance of the physical model under dierent incoming ball

speeds and racket speeds using the leave-one-subject-out cross

validation. The results are shown in Fig. 13 and Fig. 14. From Fig. 13,

we nd that the physical model performs well for both advanced

and beginner players under various incoming ball speeds. Therefore,

the incoming ball speed factor does not have signicant inuence

on the accuracy of the physical model. From Fig. 14, we nd that the

physical model performs well for advanced players under various

racket speeds. However, when the racket speed is too low (

miles/hour) or too high (

≥

60 miles/hour), the physical model does

not perform well for beginner players. The reduction of the accuracy

results from the awkward and incorrect swing gestures performed

by beginner players when they swing the racket too slow or too

fast.

3.3 Stroke Detection Accuracy

Fig. 15 shows the performance of the stroke detection under dier-

ent thresholds. Three evaluation metrics are considered: precision,

recall, and F-measure. F-measure considers the balance between

precision and recall as described in Eq. 12:

F -measure = 2 ∗

Precision ∗ Recall

Precision + Recall

(12)

From the gure, we nd that as the threshold increases, the

precision increases and the recall decreases. When the threshold is

, the F-measure is at highest value: 97.8%. Therefore, we choose

as the threshold for stroke detection. Under this threshold, the

precision and recall are 98.5% and 97.2%. The promising results

show the eectiveness of the proposed stroke detection method.

3.4 Stroke Classication Accuracy

We apply the WEKA machine-learning suite [

] to train ve com-

monly used classiers. The classiers include AdaBoost (run for 100

Table 5: Comparison of Machine Learning Algorithms for

Stroke Classication

Algorithm Precision Recall F-Measure

AdaBoost 92.1% 92.5% 92.3%

Naive Bayes 79.6% 71.6% 73.9%

SVM 92.1% 94.2% 92.9%

Decision Tree 83.4% 85.3% 84.4%

RandomForest 96.2% 98.2% 97.2%

iterations), Naive Bayes, SVM (with polynomial kernels), Decision

Tree (equivalent to C4.5 [

]), and Random Forests (100 trees, 4

random features each) [

]. Table 5 shows the performance of these

ve classiers under 5-fold cross validation test. Same as stroke

detection, precision, recall, and F-measure are considered as the

evaluation metrics. From the table, we nd that the Random Forest

classier performs the best. The precision, recall, and F-measure

are 96.2%, 98.2%, and 97.2%, respectively. Therefore, we choose the

Random Forest classier for stroke classication.

3.5 TennisEye Performance

Fig. 16 shows the overall performance of TennisEye system and

Zepp using the leave-one-subject-out cross validation. Mean and

standard deviation of error are considered as the evaluation metrics.

The cumulative distribution functions of TennisEye and Zepp are

shown in Fig. 17. The error of TennisEye is 5.6

4.9 miles/hour,

while that of Zepp is 8.9

7.8 miles/hour. The accuracy of TennisEye

is 88.2%, while that of Zepp is 77.4%. Therefore, TennisEye is 10.8%

more accurate than Zepp in terms of the accuracy.

4 DISCUSSION AND FUTURE WORK

In our physical model, we make several assumptions. For example,

we assume that the tennis ball horizontally hits and bounces o the

racket. In addition, we assume that the ball impacts at the center

of the racket face. We make these two assumptions based on the

observations that coaches always swing the racket horizontally and

hit the tennis ball at the sweet spot of the racket. However, we also

observe that the casual players often swing the racket at dierent

angles and hit the tennis ball at bad positions, i.e., racket frame.

TennisEye: Tennis Ball Speed Estimation using a Racket-mounted Motion Sensor IPSN’19, April 2019, Montreal, Canada

4g 5g 6g 7g 8g 9g 10g 11g 12g 13g 14g

Stroke Detection Threshold

100

(%)

Precision

Recall

F-measure

Figure 15: Performance of stroke de-

tection under dierent thresholds

TennisEye

Zepp

1 2 3 4 5 6 7

Player Index

Mean/Std of Error (miles/hour)

Figure 16: Performance of TennisEye

0 5 10 15 20 25 30 35 40

Error (miles/hour)

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

CDF

TennisEye

Zepp

Figure 17: Cumulative distribution func-

tions of TennisEye and Zepp

For casual players, the large variance of their tennis swings and

bad hit positions signicantly reduce the accuracy of the proposed

physical model. Thus, the physical model does not perform well

for casual players. We plan to further improve the accuracy of the

physical model by releasing these two assumptions.

In our study, we only consider the horizontal impact between

a tennis racket and a tennis ball. However, the racket not only

moves horizontally, but also vertically. During impact, the vertical

momentum of the racket converts to the vertical speed and spin

speed of the tennis ball. It would be interesting to explore how

much momentum are converted to the vertical speed and how much

momentum are converted to the spin speed. We plan to take the

vertical speed of the racket into consideration to further improve

the accuracy of the ball speed estimation model. In addition, we

also plan to estimate ball spin speed in the future.

In addition, the impact process between a tennis ball and a tennis

racket is very short. To accurately measure the racket vibration

during the impact, a high sampling rate of the UG sensor is needed.

The sampling rate in our system is set to be 100Hz. It would be

interesting to investigate whether the accuracy will be further

improved or not with a higher sampling rate. This will be explored

in the future.

5 RELATED WORK

There are mainly two ways to analyze tennis shots. One way is to

use computer vision technology. The other way is to use wearable

motion sensors.

In computer vision technology, some researchers use one camera

to study the trajectory of tennis ball. For example, Yan et al. intro-

duce a methodology to process low quality single camera videos

and track a tennis ball with the aid of a modied particle lter [

Qazi et al. combine machine learning algorithms with computer

vision techniques to predict ball trajectories [

]. Wang et al. em-

ploy a neural network approach to predict ball trajectories [

These one camera-based methods can only capture video data in

two dimensions. The lack of the video data in the third dimension

makes data not usable for high precision applications such as line

calling or player performance analysis. For this reason, some re-

searchers use multiple dimensional video data to study the tennis

shots. Pingali et al. are pioneers to build a multiple camera real time

ball tracking system based on six cameras [

]. So far, there have

been several commercial products for three dimensional tennis ball

tracking and line calling, such as Hawk-eye technology [

] [

] and

PlaySight [

]. Hawk-eye technology achieves extremely precise

results (mean error rating of 2.6 mm) as it employs 6 to 10 high-

dimensional cameras to equip the court. This technology has been

applied by many researchers [

] [

]. In addition to Hawk-

eye, PlaySight is another multi-camera based sports video-review

and analytics system [

]. This system is equipped with six high-

dimensional cameras, and uses advanced image processing and

analytical algorithms to capture and log stroke type, ball trajectory,

speed and spin, in-depth shot data, player movement and more.

The computer vision-based technology requires that a tennis court

is equipped with camera systems. However, most tennis courts

are not equipped with such systems. Therefore, most players can

not get access to these systems, which limits the popularity of this

technology.

Recent trends show that inertial motion sensors are being used to

analyze tennis shots. Some works focus on the stroke behaviors clas-

sication. They classify tennis stroke types into forehand, backhand,

serve, volley, smash, top spin, and back spin [

] [

A variety of machine learning algorithms have been applied, in-

cluding SVM [

], longest common subsequence [

], Random For-

est [

], CNN, and Bidirectional Long Short-Term Memory Net-

works (BLSTM) [

]. In addition to stroke classication, some re-

searchers assess the performance of tennis strokes and provide

recommendations to improve tennis skills [

][

]. Srivastava

et al. study the consistency of tennis shots [

]. The authors provide

recommendations on wrist rotation based on shots performed by

professional players. TennisMaster used Hidden Markov Model to

segment a tennis serve into 8 phases [

]. By studying the power,

gesture, and rhythm for each phase, the authors build a regression

model which outputs the score of a serve. Sharma et al. segment a

tennis serve into various phases, including backswing, pronation,

and follow-through [

]. By comparing the serve phases from a

user and that from professionals, the system provide the user with

corrective feedback and insights into their playing styles. Dierent

from stroke behaviors classication and performance assessment,

we investigate the interaction between the racket and the ball. To

our knowledge, none of the previous works use motion sensors to

estimate tennis ball speed.

IPSN’19, April 2019, Montreal, Canada Hongyang Zhao, Shuangquan Wang, Gang Zhou, and Woosub Jung

In addition to these research works, there are also some com-

mercial products on the market that assess the performance of

the players, such as Zepp [

], Usense [

], Babolat Play [

], and

Babolat Pure Drive [

]. These products either integrate the motion

sensors inside the racket [

], or require users to attach the motion

sensors onto the racket [

] [

]. They analyze the tennis data

and compute the key performance metrics for each swing, such as

stroke type, ball speed, ball spin, and sweet spot. However, none of

these commercial products opens their algorithms to the public. In

addition, we compare our proposed ball speed calculation algorithm

with the ball speed calculation algorithm in Zepp. The evaluation

results show that our algorithm is more accurate than that in Zepp.

6 CONCLUSION

In this paper, we propose TennisEye, a tennis ball speed calculation

system using a racket-mounted sensor. It detects tennis strokes,

recognizes stroke types, and calculates the ball speed. We propose

a regression model to estimate the serve speed. In addition, we

propose two models, a regression model and a physical model,

to estimate the groundstroke and volley ball speed for beginner

and advanced players, respectively. For the leave-one-subject-out

cross-validation test, experiments with human subjects show that

the TennisEye is 10.8% more accurate than the state-of-the-art

work. TennisEye is promising and has commercial potential as it

is lightweight and more accurate than the existing commercial

product.

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