an image processing technique for lbw decision making based on 2 dimensional analysis

8/11/2019 An Image Processing Technique For LBW Decision Making Based on 2 Dimensional Analysis

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International Journal of Image Processing and Visual CommunicationVolume 1 , Issue1, August 2012

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stump is noted (say hx, hy ). Substitutehx for x in the parabolic equation andobtain the corresponding y value. ThisThe other camera is placed as shown inthe figure below. It gives the top view of

play. Play is continuously recorded inthis camera as well. Whenever a closeLBW . value of y is compared with thevalue of hy . If this value of y is lesserthan hy then it can be concluded that the

ball is within the height of the stumpselse the ball is above the height of thestumps.

In the figure below

the curve which traces the ball is therequired parabolic equation. The value

of x at the stumps hx is substituted in the parabolic equation. The obtained valueof y is compared with the value of y atthe top of the stumps (i.e.) hy . If y islesser than hy it can be concluded thatthe ball is within the height of thestumps else the ball is above the heightof the stumps.The other camera is placed as shown inthe figure below. It gives the top view of

play.

Play is continuously recorded in thiscamera as well. Whenever a close LBWappeal occurs the video of that particulardelivery is cut. The pixel value of the

ball in consecutive frames is then

obtained using a MATLAB program.From the various pixel values of the balla parabolic curve is fit. This equationgives the equation of motion of the ballin a 2 dimensional plane parallel to the

plane of the top camera(x-z plane). Theequation of this parabolic curve is of theformz = f(x) = ax^2 + bx +c =0.

By the method of interpolation thevalues of the coefficients a and b areobtained using MATLAB. Havingobtained the equation of motion of the

ball we can say that if the ball hadnt hitthe pads it would have continued in itsequation of motion. Therefore by tracingthe equation of the ball to the stumps wecan say if it would have gone to hit thestumps. To do this from any of theframes the pixel values of the leftextreme and right extreme of the stumpsare noted (say ( sx, sz1 ) and ( sx, sz2 )).Substitute sx for x in the above parabolicequation and obtain the corresponding zvalue. If the z value lies within sz1 andsz2 (i.e.) within the left and the rightextremes of the off stump and the legstump resp. then the ball will hit withinthe range of the stumps. If the z valuedoesnt lie within the left and rightextremes of the stumps then the ball willhit outside the range of the stumps.


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From the top camera the framecorresponding to the instant at which the

ball hits the batsmens pads is captured.

The value of the z co-ordinate at thisinstant is compared with the z co-ordinate of the off stump or the legstump, depending upon the delivery. Ifthe ball hits the batsmens pads outsidethe range of the stumps i.e. if the pointof impact is outside the stumps the

batsmen can straight away be declared NOT OUT.

If the ball pitches outside the leg stump

it can be determined in a similar way asexplained above.

Hence from the above arguments it can be concluded that, if all the conditions of both the cameras evaluate to TRUE (i.e.)if the ball lies within the height of thestumps, the ball lies within the expanseof the stumps (within the leg stump andoff stump), the point of impact is withinthe stumps and if the ball doesnt pitch

outside the leg stump the ball will surelygo on to hit the stumps and the batsmenis declared OUT. If even any one of theconditions evaluates to false the ballwont hit the stumps and the batsmen is

NOT OUT. This technology is so simplethat it can be implemented in televisionsets. For customers using television

services from DTH service providers,they can demand video coverage fromany of the camera. Hence when aspectator watching a cricket match fromhis home has any doubt if it was an

LBW he can demand the top camera andthe side camera videos of the previous ball. The demand of the spectator isaccepted and the top and the side cameravideos of the previous ball is displayedon the television. During this time avideo recorder when attached to thetelevision records these videos. Thevideos thus recorded are processed asdescribed above. This processing can beaccomplished even by means of a low

end processor which can be built withinthe television as a new appendage.

A software can be developed whichobtains the pixel information of the ballfrom those samples and uses theseinformation to predict whether the ballwould have hit the stumps.

Advantages of this technologyThe present hawk eye technology thatis being used tracks the ball 3dimensionally. The image here, isdigitized and in the process sampled andquantized and so the accuracy of

prediction is reduced. On the other handthe method proposed in this paper tracksthe ball two dimensionally. No samplingor quantization is employed and thus themethod proposed here doesntcompromise on accuracy.Moreover this method is very simple toimplement. A high degree of accuracy isachieved at a very low cost.

At present a minimum of 3 cameras arerequired to locate a point in space. But inthis technique we are able to track themotion of the ball with just two cameraswhich is an advancement in technology.


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LimitationsUmpires or some fielders may restrictthe view of the ball from the camera. Inthis case the view of the ball is blocked

by the fielder for an instant of time.Hence we won t be able to obtain the pixel information of the ball during thatinstant. This may reduce the accuracy of

prediction.

Real time problems encounteredWhen the sampled video signals are

projected two dimensionally on the

computer screen the pixel value of the pitch at different places will be different.This implies that the y co-ordinate of the

Another problem is the fixing of topcamera. As seen in the figure above thetop camera which gives the top view isfixed to a rod that runs along the

diameter of the cricket field. But now adays in ICL cricket matches such type ofcameras fixed in such positions are used.Further the position of the camera on therod is controlled by a remote control.

pitch is different at different places(consider the side view). But in realitythe whole pitch is on the ground andhence it should have only one uniquevalue as its y co-ordinate.To solve this problem a simple solutionwould be to place the side camera at the

same level as the pitch (i.e.) on theground. In this case the pitch would beseen as a straight horizontal line and thestump would be seen as a straightvertical line. Also the base of the camerashould be placed parallel to the pitch.

When the camera is placed in this waythe edge of the pitch has a single uniquevalue as its y co-ordinate.

ConclusionFrom the idea presented in this paper itcan be concluded that, this idea wouldyield higher accuracy as compared to the

present hawk eye system. At the sametime it is much cheaper than the hawkeye system. Implementing this idea is

not difficult. Simple MATLAB codingwill do.

an image processing technique for lbw decision making based on 2 dimensional analysis

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