ABSTRACT

Inthepast few decades, skepticismabout umpiring follieshasn’tabated.Intheworldofsports, wherestakesare increasingbyeverypassingminuteandanerroneousline-call canmeanchangeoffortunes,thereisanincreasingreliance ontechnologytoensurethatall arbitrationsareunbiased. TheHAWKEYEisoneofthemostcommonlyusedtechnologies inthegameofcrickettoday.Ithasbeenputtoavarietyof uses,suchasprovidingawaytocollectinterestingstatistics, generatevery suggestivevisualrepresentations ofthegame play andeven helpingviewers to better understand the umpiringdecisions,especiallyin the case of LBWs. While the systemprovides for things which weseeevery dayon television,there isvery impressivetechnologygoing into it, which manyof usareobliviousto.In thispaper,weattemptto explainhow the technologyworks, indetail.

CONTENTS

CONTENTS:

  1. Introduction
  2. HAWKEYE– a general overview
  3. Step-by-step details of the HAWKEYE system

4. Applicationsof HAWK-EYE

5. Wagon Wheels

6. Pitch Maps

7. Refrences

8. Conclusions

Introduction

Thegame ofcrickethasattainedgreatcommercial importanceandpopularityoverthepast fewyears.Asa result,therehasbeenfeltaneedtomakethegamemore interestingforthespectatorsandalsototryandmakeitas fairaspossible.Thecomponentofhumanerrorinmaking judgmentsofcrucialdecisionsoftenturnsouttobedecisive. It is not uncommon tosee matchesturning frombeing interestingto being one sided due to a coupleof bad umpiring decisions.Thereisthusaneedtobringintechnologytotry andminimizethechancesofhumanerrorinsuchdecision making.

Teamsacrosstheworldarebecomingmoreandmore professionalwiththewaytheyplaythe game.Teamsnow haveofficial strategistsandtechnical supportstaffwhichhelp playerstostudytheirpast gamesandimprove.Devising strategiesagainstopponentteamsorspecificplayersisalso verycommonin moderndaycricket.Allthishasbecome possible duetotheadventoftechnology. Technological developmentshavebeenharnessedtocollectvariousdata very preciselyand use it for various purposes.

The HAWKEYE is one such technology which is consideredtobereallytopnotchincricket.Thebasicideais tomonitorthetrajectoryofthecricketballduringtheentire durationofplay.Thisdataisthenprocessedtoproducelife likevisualizationsshowing thepathswhichtheballtook. Suchdatahasbeenusedforvariouspurposes,popularuses includingthe LBWdecisionmakingsoftwareandcolorful wagonwheelsshowingvariousstatistics.Thispaperattemptstoexplaintheintricatedetailsofthetechnologywhichgoes behindtheHAWKEYE.Wefirststartoff withageneral overviewofthesystemandanoutlineofthechallengesthat wemightface,thenmoveontothedetailsofthetechnology and end with variousapplicationswhere one sees this technologybeing put to use.

HAWKEYE– a general overview:

Cricketisaballgameplayedwithinapredetermined area.Asystemcomprisingofvideo camerasmountedat specificanglescanbeusedtotakepictures.Thesepictures are then used to locatethe positionof the ball.The images are then put together and superimposed on a predetermined modeltoformacompletevisualizationofthetrajectoryof theball.Themodelincludes,inthiscase,thepitch,thefield, thebatsmenandfieldersetc.Forthistobepossible,weneed tosampleimagesataveryhighrateandthusneedefficient algorithms whichcan process data in real time. Such technologiesarewidelyusedtodayinvarioussportssuchas Tennis,Billiardswhichalsofallinthecategoryofballgames playedwithinarestrictedarea.Ourdiscussionwillmostly containapplicationswhichspecificto thegameofcricket, however in somecases, we will mention how similar techniques are appliedin other games.

Therearevariousissueswhichcropupwhenonetriestodesign andimplementsuchasystem.Inthegameofcricket,thegeneral issues are:

1. Thedistanceatwhichthecamerasseethepitchandthe ballaredependentonthedimensionsof eachground and can vary greatly.

2. Justtheindividualimagesdon’thelptoomuch;forthe systemtobeofpracticaluse,onemustensurethatitcan trackthe3Dtrajectoryoftheballwithhighprecision.In order togetthis accuracy, the fieldof viewofeach camera should be restricted to a small region – this means oneneedsmorecamerastogetthecoverageof the entirefield.

3. Fieldersandspectatorsmightobstructthecamera’sview oftheball andtheball mightget‘lost’inits flight inone ormoreofthecameras.Thesystemshouldberobust enough to handle this, possibly by providing some redundancy.

4. Theballmightgetconfusedwithothersimilarobjects– forinstance,withflyingbirdsortheshadowoftheball itself.The imageprocessingtechniquesusedneedto takecareoftheseissues. Luckily,therearetechniques whichareeasytoimplementandarewellknowntothe ImageProcessingcommunityonthewhole,totakecare of these.

5. TohelpinjudgingLBWcalls,thesystemneedstobe madeawareofthestyleofthebatsman–whetherheis rightorlefthanded.ThisisbecausetherulesofLBW aredependentonthepositionofthestumpsandarenot symmetricalaboutthemiddlestump.Thus,thesystem needs to detect whether a particular ball has pitched outsidethe leg stump of a batsmanor not.

6. Todeterminethepointsatwhichtheballmakescontact withthepitch,thebatsmenorotherobjectsisveryhard. This is because we don’t really know these spots beforehandandthemodelandtherealpicturestakenby camerasneed to be merged to give such a view.

We will see how the HAWKEYE technology successfully treatseach of these issues and provides a robust systemto be used in practice.Thetop-level schematicpicture of the systemanditsvariouspartsis as shown below (each color represents a block of steps which are related):

Figure1: TopLevelview of the Hawk Eye System

Thefigureaboveshowspreciselythestepsthatare involved inthecomputation.Theprocessisstarted withsome calibrationofthecameras.Thisisrequiredtodealwith

the problem raised in1above,aboutthenon-uniformdistance ofthecamerasfromtheplayingarea.Afterthisbasiccalibration isdone andthe systemisup andrunning, we canstart processingthevideoinputwhichwegetfromthecameras.In eachof the imagesobtained,the first aimis to find the ballin it.Oncethisisdone,ageometricalgorithmisusedtolookat multipleimages (whichare2D) andthencombinethem cleverlytogettheco-ordinatesoftheballin3Dspace.This processisnowrepeatedformultipletimeseverysecond (typically at the rateof 100 timesper second).Thus, we havethepositionoftheballin3Dspaceatmanymomentsin everysecond.Thefinalstepistoprocess thesemultiple positions and find a suitable fittingcurve which best describestheflightoftheball.Aswehavesampledthe positionsoftheballatveryshorttimeintervals,theflightof the ballcan be very accuratelydetermined.

Adescriptionoftheexactalgorithmsinvolvedinthe entireprocesswillbeskippedhere. Weinsteadtrytogivean intuitivedescriptionofeachstepingreatdetail,soastogive the reader a feel of what goes into the system, without plunging into the gory details.

Step-by-step details of the HAWKEYE system:

In this section,we go into the technicaldetailsof the stepsinvolvedintheHAWKEYEsystem.The process,as donebefore,canbebrokendownintothefollowing steps(we willdividetheprocessintotheseseeminglydisjointstepssothatitiseasyto explain thedetails, however many of the steps are overlapping):

1The cameras:

Typically,foracricketfield,6camerasareused.These camerasareplacedaroundthefieldat roughlytheplaces as indicatedin the diagrambelow:

Figure 2: Positionof camerasaround the field

Asonecansee,the6camerasinusearepositionedat roughly 60degreefromeachother.Theyareplacedhighin the stands,sothatthereislesserchanceoftheirviewbeing blockedbythefielders.Therearetwocameras,oneeach lookingatthewicketsdirectlyinsidewaysfashion.These6 camerasarecalibratedaccordingtothedistancetheyareat fromthepitch.Inordertogetgoodaccuracy,oneneedsto restricttheviewofeachcameratoasmallerregion.This meanseach cameraimagewouldshowamoreprominent pictureoftheballandhencetheballwillbelocatedmore accurately.However,wealsoneedtokeepinmindthatthe wholefieldofplayhastobecoveredbyjustthe6cameras which are available. This puts some limitation on how restrictedtheviewofacameracanbe.Nevertheless,the accuracyobtainedbyusing6 camerasisacceptabletothe standardsprevalenttoday.

Somefurthersettingupisessentialforthesystemtowork correctly.Thecamerasneedtobefixed tosomeframeof reference,whichisdefinedveryconvenientlyintermsofthe wicketsonthepitch,andthelinejoiningthem.Thisisuseful whenwewanttouseanautomated programtomergeimages from differentcamerasto form one 3D image.

Also,toavoidunnecessarycomputationandmakethesystem moreefficient,thecamerascanbe operatedinactiveor passivemode.Inthepassivemode,noimagingisdoneand hencethesystemismore orlesscompletelyinactive.The cameras can betriggeredintoactivemodeeitherbydetectingsomemotionin the vicinity of the pitch, ormanually by some external trigger.Ineithercase,allthecamerasaresynchronizedandgointoactivemodesimultaneously.Thecamerasarethen designedtostayintheactivemodeforafixedtimebefore goingoffintopassive mode.Thisaction ofgoingintopassive modecanbemanuallyoverriddeninexceptionalcases.The differentmodesforthecamerasareespeciallyeffectivefora gamelikecricketas thegameinvolvessignificantpauses betweenphases of actualplay.

Asdescribedin5inthelistofissues,thesystemneedsto knowifthebatsmanisrightorlefthanded.Thefrontview camerasareusedtodothis.Thisinformation,aspreviously saidisusefulin makingLBWdecisionsandformulating otherstatistics.Forinstance,wecommonlyseetheanalysis ofabowler’spitchingareasdoneseparatelyforaleftanda righthandedbatsman.Whilethis isnotaverydifficult taskto domanuallyeverytimethebatsmanonstrikechanges,the systemdoes provide some way of automatingit.

Oncethissettingisdone,thecamerasarereadytotakepictures in their field of view andhave them sent to a computerwhich processesthem.

2Preparation before starting to process:

Additionalfeaturesmightbeloadedintothesystemto enableittoprocessthedatainamorereliableanduseful manner.Thesemightincludeastatisticalgenerator,whichis usedtoproducestatisticsbasedonthedatacollected.These are the statistics which wesee on television during and afterthematchforanalysis.Suchstatisticscanalsobeused by teamsand players to study their game and devise strategiesagainst their opponents.Indeed, the raw data about the paths of the ballmight be too much for anyhuman to digestand such statisticsturnouttobe easiertohandle andunderstand.Thestatisticsgeneratormightalsoaidin storingdatasuchastheaveragevelocityoftheball.Thisdata iscrucial asitcanhelptheball detection algorithm topredict theroughlocationof theballinanimagegiventheposition inthepreviousimage.Suchconsiderationsareusefulto reduce thecomputationsinvolvedintheprocessingofthe datacollectedfrom thevideocameras.

Oncesuchadditionalmachineryissetupcorrectly,weareall set to startcollectingdataand startprocessingit to churn out tangiblestatisticsandvisualizations.Itmightbenotedatthis stagethatthere is some more informationwhichmight be requiredtoprocessthedatacorrectly.Wewillpointoutsuch things at later points in the paper,where it fits in more appropriately.

3 CoreImage Processing Job:

Thispartofthesystemcanbefurtherdividedinto3major parts:

(1)Identifyingpixelsrepresentingthe ballin eachimage.

(2)Applying some geometricalgorithmon the set of

Imagesat eachinstant.

(3)Coming up with the 3D positionof the ballin space.

We now explaineach of theseoperationsin detail:

(1)Toidentify the pixelsrepresentingthe cricketballin every imagetakenby each of the video cameras:

An algorithmisusedtofindthepixelscorrespondingtothe ballin the imageobtained.The informationwhich is usedinordertoachievethisisthesizeandshapeofthe ball.Itshouldbenotedthatthesystemdoesnotusethe colouroftheballasthatisnotreallysamethroughout the course of a game,nor is it sameacrossall forms of cricket.Ablobdetectionschemecanbeusedtodetecta roundobjectintheimage. Knowingtheapproximatesize of the ball,we can eliminateother round objects,such as helmetsworn by players.The shadow of the ballalsowillresemblethe ballin shape and sizeand thus presents itselfasaveryviablecandidateforablobrepresentinga group of pixelscorrespondingto the ballitself.The positionofthesunatthegiveninstantoftimeandalso informationabout the positionof the ballin previous imagesisusedtomakesurethisconfusionisavoided. Thus, by takingdue care,we can be sure thatthe roundobjectwhichhasbeenlocatedisindeedthecricketball, which is the objectof interest. After this stage,we have as output the x and y coordinatesoftheballineachimage. Insomecases,it mightbethecasethatthesystemisunabletodetermine theexactpositioninsomeimages.Atsuchtimes,“Not Found”isreturnedbythatparticularcamera.Onemust noteat thispoint that 6 camerasareused totakeimages. Actually,intheidealcaseonecandothejobwithjust4 cameras.Thus, we have some redundancyand hence, can afford to have abad resultfrom one of the camerasat some points and stillproduce a completepicture.

(2) GeometricAlgorithm:

The datax and y co-ordinates from eachcamera (or a “Not Found” in some cases,which is ignored) is obtainedby the Geometric Algorithmwhich is at work insidethe HAWKEYE system.The imagetakenfrom eachcamerais just a 2D imageand lacksdepth. Now, knowing the exact positionsof the camerasin space(with respect to thepitch)andthexandyco-ordinatesoftheballinmore thanoneoftheimagestakenbythesecameras,onecan determineaccurately the positionof theballin 3D.

Triangulation:

Triangulation is a process of detemining the location of a point by measuringanglesto it from either end fixed at baseline.

Figure 3-Triangulation

Let usconsider thesimple caseinwhichweassume the camerastobemountedatgroundlevel,positioned with theirvision parallelto the ground.We wish to get informationaboutthe3Dpositionoftheballfromthe positions(x1,y1)and(x2,y2)obtainedbyresolvingthe ball from2Dimages fromCameras 1and2showninthe imagebelow.Theballisactuallyatthepositionshown by the red circle,at some heightabove ground.

Figure 4: Determining3D positionof the ball

The view in the cameraswilllook somethinglikethe one shownbelow.Theviewbelowshowsthepictureasseenby Camera2 in the figure above.

Figure 5: Image takenfrom Camera2

Inthissimplisticscenario,theheightoftheballabove thegroundisgivendirectlybytheyco-ordinateinthe images,y1andy2.Boththesevaluesshouldideallybe equal,but we might want to takethe average in casetheyarenotexactlyequal.Now,theoneparameterwe needtodetermine isthedepthoftheballasmeasuredby Camera2.Oncewehavethatinformation,wewillhave allthedatatoinferthepositionoftheballin3Dspace with respectto the pitch.Note thatwe know thepositionsof the cameraswith respectto the pitchin advance.Letus assumethatthe radialangle,as seen from the wicketsmarkedin the figure, between Camera1 and Camera2isθandtheradiusofthefieldis.Then,the depth of the ballas seen from Camera 2 isas follows:

depth=r-(rcos (θ)+x1|sin(θ))

Thus,weseethatknowingtheco-ordinatesoftheballin twocameras,wecangetthepositionoftheballin3D spacewithrespecttooneofthecamerasandthus,with respecttothewickets.Intherealisticcase,thecameras are mountedhigh above the ground and thus, findingtheheight oftheball abovethegroundisnotastrivial as it was here. One needs to rotatethe axiscorrectlyinordertodothecalculationsthatweresimplehereasit concernedonly planargeometry.In reallife,cricket groundsarenotperfectlycircularandhenceeventhat has to be takeninto consideration.We do not go into those detailshere, but just note thatit is standard mathematics togetthe3Dco-ordinatesoftheballgiven the informationin two images.

(3) 3D positionof the ballin space:The Geometric Algorithmdescribedwiththehelpofanexampleabove providesuswithareadyrecipetofindthe3Dposition of the ballin space.We just use this methodand as a result,nowhavethepositionoftheballascapturedat thatinstant,in 3D space,with respectto any of the referencepointswehadconsideredwhilesettingupthe system.

4Puttingframes at various times together:

Nowwehavetheexactpositionoftheballin3Dspaceata giveninstantoftime.Next,whatneedstobedoneisputting togetherthisdata,collectedatvarioustimeinstantsintoa singlepicturewhichshowsusthetrajectoryoftheball.We cansplitthispartoftheprocessintotwoparts.Again,the reader should understand thatthese parts are verymuch relatedandwesplit themhereinourexplanation justtomake it easilyunderstandable.Thetwopartstothiscomputation are:

(1)Tracking the ballat various instants.

(2)Predictingthe flightor trajectoryof the ball.

(1)Trackingthe ball at various instants.

Suppose the imagesare takenby cameras at times t0,t1.....tn during the play of a singleball.Doing the computationas describedabove at each timeinstantti,0=i=n,we willget n points ,say (xi,yi,zi)for 0<=i<=0Now,on the model thatwe have built previously consistingof a pictureof the pitch,ground and wickets etc.,we plot thesen points.When looked at in their proper sequence,thesepoints tellus about the path followedbytheballwhenittravelledduringthelastball thatwas played.With thesepoints plottedin the 3D space,wecanmoveontothenextandfinalstageinthe processingofasingledelivery,namely,predictingthe flightof the ball.

(2)Predictingthe flight ortrajectoryof the ball:

Wehavenpointsinspacewhichweknowrepresentthe positionof the ballat some particulartimeinstants, which are also known. Now, thereis a standard technique,used commonlyin the fieldof Computer Aided GeometricDesign which can be invoked here. This allowsus to draw as good an approximationas requiredtotheoriginalcurve,passingthroughthegiven points2.This techniquegives us a curve which is continuousand differentiable,meaningit issmooth all along, startingat the first point and ending at the last point among our n points.This smooth curve is an approximationto the originalcurve which the ballwould havefollowed.Themorepointswecangetonthecurve and the higher degreeof polynomial basis we choose touse,wewillendupwithbetterapproximationstothe originalcurve.The betterapproximationsobviously comeat some additionalcost – the added cost of computationoftheapproximation. Hence, thesystemuses some degreesuch thatthe computationtimeis smallenough, at the sametimethe accuracy is acceptable.

Morecan be donewith theinformationabout thepoints. Wecanalsoextendthecurvetopointswhichwehave not been recordedat all– indeed, it might be the case thattheballstruckthebatsmananddeflectedaway,but wewanttoseewheretheballwasheaded,particularly to help adjudgeLBWcases.This extensionuses somebasicmathematicsandensuresthat theextendedcurveis alsosmoothatallpoints,particularlyatthepointfrom where the extendedpart starts,that isthe lastpointwhich we have recordedamong the points. Duringtheflightoftheball,itmightgothroughsome pointswhichareofspecialinterest.Theseincludethe ballhittingthe pitch,the stumps, and the batsmanamong others.Thesepoints are predictedby superimposingthe trajectorywhich we built,ontothe modelthatwe have fed into the system.It should be notedthatthereisapossibilitythatsuchcriticalpoints maynotberecordedinanyoftheimagestakenbythe systemandinsuchcases,therelianceiscompletelyon thepredictedflightoftheball.Also,fortheparticularkey-eventoftheballstrikingthebatsman,thesideways cameras, whichlookdirectlyatthewicketsateitherend of the pitch,are the most reliable sources.

Applications of HAWKEYE:

HAWKEYEhashadfar-reachingconsequencesinmany sports.Primarilyincricket,HAWKEYE is aprocessthat makesthecurrentjudgmentalcallonaLBWdecision,very predictive.WhilenotechnologyisflawlessandHAWKEYE has itsown shareof these, it isup to99.9% accurate.This has madetheLBWdecision,apredictiveone.Moreimportantly, suchtechnologycanbeusedtoevaluatetheskillsofthe umpire as well. The England Cricket Board(ECB) has alreadyset-uptheHAWKEYEsystemnotonlyatabout10 cricketvenuesaroundthecountrybutalsointhetraining academy to aid umpires,as well.

Gatheringstatistics:

WhiletheHawk-Eyehasmadeitsmarkandderivesits appealfromtheabilitytopredicttheflightofthedelivery,it isaveryusefultoolforcollectingstatistics.Theinformation associatedwitheachdeliverybowledisroutinelyprocessed, evenwhentheoutcomeofthedeliveryisnotdoubted.Asa result,the strategy used by a bowler as a functionof bowling spells,deliveryno.intheover,batsmanfacingthedelivery andsooncanbegauged.Similarly,thescoringpatternsofa batsmanaroundthegroundusingwagon-wheelsareroutine inmatchdaytelecasts.Thesearesocleverlygeneratedthat theygiveareal-lifefeeltoit.Commentatorsalsoareableto movethemabouttomakeafinerpoint,aboutabatsman. However appealing and nice that it may seem, a keen cricketing eye will notice that the wagonwheel is less accuratethantheotherdata.Thisisbecausethewagon-wheelis generated fromdata collected from outside the pre- determinedpitcharea.Thelocation,depth,trajectoryofthe ballin-flightatanarbitrarypointonthe groundismore difficultto determine,than when it is on the pitch.As a result, some errorsmanifest

Thesedifficultiesaren’tfacedintennis–where HAWKEYEisusedtodecidewhethertheball,waswithin thecourtlimitsornot.Inthecaseof Tennis,linescallsmade byHAWKEYE arecompletelyaccurate.Tennishasbeen quick to adapt to this technology andHAWKEYE arbitrationsare legal since the NASDAQ-100 tennis tournament. Players can challengelinecalls,followingwhichHAWKEYEdetermineswhethertheball waspitchedinorout!TherecentlyconcludedUSOpenQF matchbetweenFerrerandNalbandianhadamatch-point being decided aftera line-callchallenge.

We now briefly look at the various applications of HAWKEYEwhichthe cricket broadcastersregularlyuse thesedays.

LBWdecisions

As mentioned previously, the HAWKEYE can accuratelycapturethetrajectoryoftheballandalsopredict the future direction of the ball usingmathematical calculations. Thisisputtouseindecidingwhetherabatsman was OUT LBW on a particular ball. Thus, the system determines the exact point at which the ball struck thebatsman.Usingthetrajectoryoftheballuptothatpoint,the systempredictsthepaththeballwouldhavetakenhadthe batsmannotbeenpresentintheway.Thusonecanknowthe lateralpositionoftheballwithrespecttothestumpsaswell astheheightoftheballatthepointwhenitreachestheline of the stumps.The figure below gives an exampleof the trajectoryof theballbeingpredicted. Note that in thispicture, the systemhas got rid of the batsmanfrom the pictureso as to giveusacomplete viewofthepathoftheball since itleftthe bowler’shand.Thisisexactlywhatoneneedstodecideifthe ballwouldhavehitthestumpsandif thatisthecase,the batsmanhas a chanceof being given OUTLBW.

Figure 6: Side-on view to determinea LBWdecision

Thesystem is well equipped to handle the various complex clauseswhichtheLBWrulehas.Forinstance, itcan checkif the ballhad pitchedoutsidethe leg stump of the batsman.Ifthisisthecase,thebatsmanisNOTOUTevenif theballisgoingontothestumps.Recallthatthefrontview camerasareusedtodeterminewhetherabatsmanisrightorl efthanded.Thatinformationisusefulhere.Anotherclause

statesthatthebatsmanshouldnotbegivenOUTifheishit outsidethelineofoff-stumpandisattemptingtoplayashot. Now, the part of whetherthe batsmanis playinga shot has to bedecidedmanuallyandthesystemisnotcapableofdoing it.However,thepointofimpactisaccuratelyknownandone can see exactlywhere the batsmanwas hit

Figure 7:The hit/missballand predictedflightof a ball,after removingthe batsmanfrom the picture

The kind of accuracy which HAWKEYEoffers is difficult to get for any human umpire.The system also includesawaytodoprobabilisticanalysisandhencebringin the factorof “benefit of doubt” which goes to batsman currently.Themainidea behindthisistohavearegionwhich thehumanumpirewouldbelievetheballwouldhavebeenin thisregionisjusttakentobeacirclecenteredattheaccurate positionoftheballandradius.Thevalueofthisradiusis calculatedtakinginto considerationthe distancebetweenthe point ofimpactof theballwiththe batsman and the stumps – thatis,thedistancewhichtheballisyettocover.This modelsquiteaccuratelythe uncertaintywhich the umpires feel while making the decision manually. Thus, if the batsmanisplayingforward,theradiuswillhaveahigher value,than when the batsmanis struck, playingback.To keep the“benefitofdoubt”stillwiththebatsman,thedecision goesinfavourofthebowleronlyifasignificantportionof theprobableregion(circleorradiusdescribedabove)liesin linewiththestumps. Thesystemthusisveryrobustand seemstobebetterthanhumanumpiresasitstands–andit canonly improve.Hencethereisheateddiscussionthese days on whether one shouldcompletely rely on the HAWKEYEforLBWdecisionsWechoosenottogointo those discussionshere, in this paper.

WagonWheels:

Figure 8:WagonWheelgenerated by HAWKEYE

Thetrajectorieswhichtheballhastakenafterbeinghit bythebatsmanarerecordedinthesystem.Thisisusedto generatea graphicshowing 1s, 2s, 3s, 4s, and 6s allin different colours for a batsman. These details allow the commentators,spectatorsand playersto analyzethe scoring areasof the batsmanand also judge if he has playedmore shotsalongtheturforintheair.Suchinformationisvitalfor a fieldingcaptain,whomightalterhisfieldplacementin subsequent matches to adapt to the hitting pattern of a particular batsman.

PitchMaps:

Figure 9: PitchMaps as shown by HAWKEYE

As shown above, the Pitch Map graphi uses informationaboutthepositionwheretheballbouncedonthe pitch.The imageabove clearlyshows the pitchbeing divided intovarious “zones” which the experts consider in their analysis. Itcanbeveryeasily seenwherethebowlerhasbeen pitchingtheballprimarily.Basedonsuchpitchmaps,one can easily see general characteristics of bowlers-for instance,onaparticulardayabowlermightbetakenforalot of runs. HAWKEYEcan show the areasin which the bowler landedtheballsandhemightbeabletofindouthewastoo shortonmostoccasionsandhencewasbeingtakenforruns. Batsmenalsousesuchgraphicstostudythegeneral tendencyof the bowler and can plan to play him in subsequentgames.

DeSpin:

TheDeSpingraphicshelpusinunderstandinghowthe ballhasdeviatedafterpitching.Thegraphicproducedshows the predictedpath of the ball,had it held its lineeven afterpitching.This isparticularlyinterestingto look at, in the case ofspinners,whereonecanseeboththeflightbeinggivenbythe bowler and the spin thathe managesto extractfromthepitch.LookingattheactionandtheDeSpingraphicsforaparticularbowlerisusefulforbatsmantonoticeanychanges inactionwhenthespinnerisbowlinga“trick”ball–which mightbeagooglyorflipperinthecaseofalegspinner,ora “doosra”in the caseof an off spinner.

RailCam:

TheRailCamgraphicsshowasidewaysviewoftheball asitleftthebowler’shand.Thisis useful tocomparethe speeds of various deliveries bowled and the bounce the bowlerwasableto extractfromthepitch.Asasimulation againsttime,theslowerballscanclearlybeseentoreachthe lineof the stumps much later than the fasterballs.

Beehives:

Thisgraphicshowsthepositionofvariousballsinthe planeofthebatsman.So,irrespectiveofwhetherthebatsman playedashotornot,thesystemplacesamarkontheplane showingusthepointat whichtheballpassed/would have passedthebatsman.Atsometimes,thismightbepartofthe actual trajectory, while in other cases, it might bean extrapolatedpath.Toaddtotheusefulness,thesystemcan alsoshowtheballsonwhichthebatsman scored,inone colour and the ones which he defendedin another.Thishelps togetaverygoodideaofthestrengthsandweaknessesofa batsmanandhisscoringzones.Thebowlercaneasilymake outifheneedstobebowlingawayfromthebodyorintothe bodyofthebatsman,whetherheshouldbebouncingithard into the deck or pitchingit up and invitethe drive etc.

TENNIS:

Hawk-eye was first used in tennis in theyear 2004(US opentennis).In tennisHawk-eye generates the impactoftheballwhethertheballis“IN”or“OUT”theline of tenniscourt.

Figure 10 -Tennis ballin motion

Figure 11-Tennis court

Conclusions

WehavelookedatvariousaspectsoftheHAWKEYE technology.Initially,weoutlinedthemainproblemswhich onecouldencounterwhiletryingtoimplementsuchasystem forasportlikecricket.Then,welookedintothedetailsof eachstepoftheprocesswhichfinallygivesusthewonderful lookinggraphicsthatweseeonTVduringcricketanalysis shows.Wegotafairunderstandingofthealgorithms and mathematicswhich goes into the system.With the help of examples,we looked at the applicationswhich the technology findsinmoderndaysport,withcricket beingourmain focus. We got an understanding of how the graphicscan be produced, using the setup, which also was describedin detail.

We have thus seen that the HAWKEYE is a great innovation,whichputstechnologytogooduseinthefieldof sports.Thetechnologyisusedwidelythesedays,insports suchasTennisandCricket. Theaccuracywhichcanbe achieved with the use of the systemis makingthe authorities thinkseriously aboutreducingthehumanerrorcomponent involvedinimportantdecisions.Asthesystemrunsinreal time,thereisnoextratimerequiredtoseethevisualizations andgraphics.Thesystemisalsoagreattoolwhichcanbe usedbyplayers,statisticians,tacticians,coachestoanalyze previousgamesandcomeupwithstrategiesforsubsequent ones.

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