Hawk-Eye is a computer system that uses multiple cameras and trigonometry to visually track the path of a ball and display its most likely trajectory. It was developed in the UK and is now used in sports like cricket, tennis, and snooker to aid in decisions. Hawk-Eye systems use cameras placed around the field that triangulate the ball's position to create 3D representations and projections of its path. This technology helps minimize human error in close calls and allows players to review and analyze past performances. While expensive, Hawk-Eye brings more accuracy and fairness to many sports.

1. Hawk-Eye
Presented by: Guided by:
Khyati Rajput (14014081007) Prof. D.S.Pandya
UVPCE-Ahmedabad Prof. Menka Patel

2. Contents
• Introduction
• Principle & Components
• Hawk-Eye in Sports
• Other Applications
• Advantages
• Disadvantages
• References

3. Introduction
• Hawkeye is a computer system used in cricket, tennis, snookers and
other sports to visually track the path of the ball and display a record
of its most spastically likely paths as moving image[2]
• Hawkeye as the most innovative technology provider in sports
broadcasting
• It is a development that will reinforce the groups presence and
influence
• It was developed in UK by Dr. Paul Hawkins.

4. Why Hawk-Eye?
• Sports has a great commercial importance and popularity. As a result,
there is a need to make it as fair as possible
• Human error plays a vital role in decision making at decisive
moments
• There is need to bring a technology to minimize the chances of
human error in such decision making
• Help players to study their past games and improve

5. Principle of Hawk-Eye
• A Hawk-Eye system is based
on the principle of “Triangulation”.
• In trigonometry and geometry,
triangulation is the process of
determining the location of a point
by measuring angles to it from known Fig 1. Triangulation[1]
points[1].

6. Theory of Triangulation
• Triangulation is the process of determining
three-dimensional world coordinates for
an object given two-dimensional views of
it from multiple cameras[1]
• The diagram shows the three-dimensional
views of it from multiple cameras
Fig 2. 3D Triangulation of Camera rays

7. • Using equation of line
𝑋 = 𝐶′ + 𝑀 𝑎 𝐷′ − 𝐶′ _____(1)
𝑋′ = 𝐶 + 𝑀 𝑏 𝐷 − 𝐶 ______(2)
• To find the minimum cord between the
two vectors
𝑋 − 𝑋′ 2 (by 1 & 2)
• We know that the dot product of two
perpendicular vectors is zero.
i.e. (𝑋 - 𝑋′). 𝐷 ′ − 𝐶′ = 0 _____(3)
(𝑋 - 𝑋′). 𝐷 − 𝐶 = 0 ______(4) Fig 3. Intersection of two rays[1]

8. • Expanding X and X’ gives:
𝐶 − 𝐶′ + 𝑀 𝑎 𝐷′ − 𝐶′ − 𝑀 𝑏 𝐷 − 𝐶 ∗ 𝐷′ − 𝐶′ = 0 _____(5)
𝐶′ − 𝐶 + 𝑀 𝑎 𝐷′
− 𝐶′
− 𝑀 𝑏 𝐷 − 𝐶 ∗ 𝐷 − 𝐶 = 0 _____(6)
• The above two equations (i.e.(5) & (6)) can be used to solve 𝑀 𝑎 and
𝑀 𝑏 which in turn can be used to calculate points 𝑋 and 𝑋′.
• Once the points are obtained, we can find 𝑃 as:
𝑃 =
𝑋+𝑋′
2
_____(7)
• The above formula can find the position of the object in 2 dimension
but we require the position in 3 dimension. So, what next??

9. The Epipolar Geometry[3]
Fig 4. Projection of Camera[3]
• C, C’, x, x’ and X are coplanar. What if only C, C’, x are known?

10. Fig 5. All points on p project on l and l’. Family of planes p and
lines l and l’ intersection in e and e’[3]

11. • Epipoles are e & e’
= intersection of baseline with plane
• An epipolar plane = plane containing baseline
• By this we have obtained the third point as well.
• Now we can find the exact location of the object
in 3 dimension[3]
𝑙 =
𝑑
𝑡𝑎𝑛 𝛼
+
𝑑
tan 𝛽
𝑑 = 𝑙
1
𝑡𝑎𝑛 𝛼
+
1
tan 𝛽
Fig 6. Triangulation with l and d[1]

12. Components
• The hawk-eye system consists of two significant parts:
 Tracking System.
• Camera
• Speed gun
 Video Replay System.

13. Tracking System
• The system will automatically calculate the following information:
 The speed of the ball leaving the bowler's hand
 The swing of the ball from the bowler's hand to where the ball
pitched
 How much the ball bounced
 How much the ball deviated sideways off the wicket
 A prediction of where the ball would have passed the stumps

14. Hawk-Eye Camera & Speed Gun
Fig 7. Camera Fig 8. Speed Gun

15. Video Replay System
• Hawk-Eye system can incorporate more
video replay cameras for analysis form
different angles, which can be controlled
remotely.
• The video is captured and stored digitally
on hard disks.
• This uses display unit like monitor and
projector screens. Fig 9. Video Replay System

16. Hawk-Eye in Cricket
• It is based on the principles
of triangulation using the
visual images and timing
data provided by high-speed
video cameras located at
different locations and angles
around the area of play[1]
Fig 10. Position of Camera

17. Application in Cricket
• LBW Decisions Pitch Maps
Fig 11. LBW Decisions Fig12. Pitch Maps

18. • DeSpin Beehives
Fig 11. DeSpin Fig12. Beehives

19. Wagon Wheel
• The wagon wheel gives you an idea of the different areas where the
batsman has been targeting to score.
Fig 13. Wagon Wheel

20. Hawk-Eye in Tennis & Badminton
• The Hawk-Eye system in badminton
and tennis is a binocular stereo
visual system[4].
• Three-dimensional information is
obtained with epipolar constrain
after the cameras of the system
are calibrated.
Fig 14. Tennis & Badminton[4]

21. IN and OUT decisions
• Hawk-Eye generates the impact of the ball whether the ball is “IN” or
“OUT” which is important for decision making[5].
Fig 15. IN and OUT decisions

22. Other Applications
Hawk-Eye in Military Hawk-Eye in Automobiles
Fig 11. Military Fig12. Automobiles

23. Advantages
• This technology is being used in many sports like cricket, tennis and
snooker.
• Used by players, statisticians, tacticians, coaches to analyse previous
games and come up with strategies for subsequent ones.
• It reduces human efforts.
• Hawk-Eye officials are working towards making it more cost effective
so that it can be used in more premier tournaments around the
world[6].

24. Disadvantages
• It is highly expensive.
• It is not 100% accurate.
• It challenges the umpire decision.
• Incompatible with certain natural factors : Wind, Bright Sunlight,
Shadow, Artificial floodlights, etc.

25. Conclusion
The Hawk-Eye technology is a wonderful invention as far as
sports like Cricket, Football, Snooker, etc. are concerned. It is still in its
infancy, but the day is not far when we can say that, all umpiring
decisions are completely accurate and correct. This technology helps to
have correct decisions in any kind of game.

26. References
[1] B.Favre-bulle, J. Prenninger, and C. Eitzinger, “Dynamic Triangulation,” Instrum. Meas
Technol. Conf. 1998. IMTC/98. Conf.Proceedings. IEEE, vol. I, pp. 446-449, 1998.
[2] B.Bailey and S.T. Field, “Real Time 3D Motion Tracking For Interactive Computer Simulations,”
Citeseer, 2007.
[3] A.Z. Richard Hartley, “Epipolar Geometry and the Fundamental Matrix,” in Multiple View
Geometry in Computer Vision 2nd Edition, 2004, pp. 219-243.
[4] L. Li, “Application of the Three-Dimension Information Acquisition Technology In The
Badminton Hawk-Eye System,” Int. Conf. Educ. Manag. Comput. Technol., 2015
[5] Huo Fang “The application of instant reviewing system in tennis match.”Bulletin of Sport Science
& Technology., 2007
[6] Kenneth H. Wong “Development of Quantitative Imaging Methods for the GE Hawkeye
CT/SPECT System.” Journal of Nuclear Cardiology, vol. V, pp. 2170-73, 2002