喜歡這套資料就充值下載吧。資源目錄里展示的都可在線預(yù)覽哦。下載后都有，請(qǐng)放心下載，文件全都包含在內(nèi)，圖紙為CAD格式可編輯，有疑問(wèn)咨詢QQ:414951605 或 1304139763p Available online at Procedia Engineering 00 (2009) 000000 Procedia Engineering Conference of the International Sports Engineering Association (ISEA) Validation of a live, automatic ball velocity and spin rate finder in tennis J. Kelleya*, S. B. Choppina, S. R. Goodwilla, S. J. HaakeaaSports Engineering Research Group, Centre for Sport and Exercise Science, Faculty of Health and Wellbeing, Sheffield Hallam University, Collegiate Crescent Campus, Sheffield, S10 2BP, United Kingdom Received 31 January 2010; revised 7 March 2010; accepted 21 March 2010 Abstract Software designed to quickly and easily calculate the 3-dimensional speed and the spin rate of a tennis ball from high speed video footage from a single camera was validated. The software values were compared to speed values from light gates and spin rate values found by manually tracking the ball logo. The respective ranges were 18-31ms-1 and 65-165rads-1. The speed values had a mean percentage error of 4.47% (1.08ms-1). The spin rate values had a mean percentage error of 4.14% (4.71rads-1). 2009 Published by Elsevier Ltd. Keywords: Tennis; Analysis Software; Validation; Ball speed, Ball spin rate 1. INTRODUCTION There are several parties for which obtaining data on tennis ball speeds and spin rates is desirable. The International Tennis Federation (ITF) continually monitors many aspects of tennis match play. It is advantageous for them to obtain accurate data on the tennis ball as quickly and easily as possible. It could also be of use for players and coaches if ball speed and spin rate data was easy to obtain and readily available from matches and during practice. A method for obtaining both spin rates and speed values using simple equipment set up and calibration, and providing results quickly with minimum user input would be ideal. A method capable of producing live results would satisfy all parties; live results would be available when required and when analysis takes place after footage collection, such a method capable of giving live results would naturally enable fast and efficient analysis. Previous work on obtaining ball spin rate data from match play has been carried out by Kelley et al. 1 at the 2007 Wimbledon Qualifying Tournament and Goodwill et al. 2 at the 2007 Davis Cup tie between Switzerland and Spain. Both studies were carried out on behalf of the ITF; examples of how the ITF monitor the game of tennis. Kelley et al. 1 and Goodwill et al. 2 recorded high speed video clips of tennis shots using Vision Research * Corresponding author. Tel.: +44-114-225-5634; fax: +44-114-225-4356. E-mail address: J.Kelleyshu.ac.uk c ? 2010 Published by Elsevier Ltd.Procedia Engineering 2 (2010) c ? 2010 Published by Elsevier Ltd.doi:10.1016/j.proeng.2010.04.096Open access under CC BY-NC-ND license.Open access under CC BY-NC-ND license.2J. Kelley et al. / Procedia Engineering 00 (2010) 000000 Phantom high speed cameras. Manual analysis was used to measure ball spin rates, which is a time consuming process, and not suitable for live analysis. An automatic spin finding method is required in order to carry out live analysis or speed up analysis carried out after footage collection. There are obvious methods for obtaining 3-dimensional ball speed. One of these is the use of a radar gun, as used by Mavvidis et al. 3 and often employed courtside at tennis tournaments to give speed values of Serves. However radar guns lose accuracy if the moving object is not moving in a direct line (on a collision course) with the radar gun. This is called the cosine effect (Scientific American 4). Essentially, radar guns just give the closing speed between the moving object and the radar gun. This restricts the radar guns use to shots that move on a direct line towards the radar gun. Another method for obtaining ball speed is three-dimensional reconstruction of footage from 2 cameras. Such a method was used by Choppin et al. 5 using 2 calibrated and synchronized high speed cameras. This method used a calibration procedure that requires a number (20) synchronized images of a checkerboard from each camera once set up is complete. The calibration procedure and use of two cameras mean that this method is not suitable here. Software was designed to calculate ball speed and spin rates using the footage from a single Vision Research Phantom high speed camera. The software can provide results within 15 seconds of the footage being recoded. The software requires only a simple calibration using a single image of a tennis ball a known distance from the camera. Ideally the ball should be approximately in the centre of the calibration image at a similar distance from the camera to the distance from the camera to the ball in the clips that are analyzed. The calibration image can be taken at any time, even away from the tennis court, as long as the camera lens settings remain the same for the calibration image and the recorded footage. The calibration procedure takes less than 1 minute. If no calibration is possible, the software can still give spin value results as the calibration is only required for speed calculation. This software was validated in this study. 2. METHOD Tennis balls were projected from a pitching machine (BOLA) and video clips of the ball trajectory were recorded using a Vision Research Phantom high speed camera. Old tennis balls were used to reduce the likelihood that the ball properties would change during testing. The BOLA could be adjusted so that the ball speed and spin rate varied. Video clips were recorded at a frame rate of 1000fps. The ball speed calculated by the software was compared to the speed measured using light gates. The light gates were positioned at the start of the ball trajectory. The software measures the average speed over a specified number of frames. The clips were analyzed so that the ball position was 3m away from the light gates in the middle frame of the analysis. This point, 3m from the light gates, is referred to as point A and was the approximate ball position for which the average speed calculated by the software applies. The reduction in speed of the ball between the light gates and point A was estimated by comparing the velocities found when the light gates were at point A to those found when the light gates were in the set up position for. This test found that there was a consistent reduction in ball speed for each BOLA setting of approximately 6.5%. All light gate velocities were therefore reduced by 6.5% before they were compared to the velocities calculated by the software. Therefore the light gate speed values contained a certain amount of error due to the approximate 6.5% reduction. Another source of error was the error in the values given by the light gates. However this was assumed to be small in magnitude compared to the error in the reduction value. The ball spin rates calculated by the software were compared to manually calculated spin rates using the same manual analysis method as Goodwill et al. 2. The number of frames it took for the logo to rotate twice was counted. Dividing the frame rate by half the number of frames for two revolutions (essentially the number of frames for a single revolution) gives the ball spin rate in revolutions per second. This can be easily converted into rads-1. To assess the accuracy of the manual analysis method, five repeated manual analyses of 5 clips were carried out. The maximum variability between repeated analyses of the same clip was found to be 1.5%. There is no other method of obtaining spin rate values other than tracking the rotation of the logo or some other marker attached to the ball. 2968J. Kelley et al./Procedia Engineering 2 (2010) 29672972J. Kelley et al. / Procedia Engineering 00 (2010) 000000 3Two lens settings were used; lens setting 1 was less zoomed in than lens setting 2. Three different trajectory directions were used by positioning the BOLA in 3 different positions. One with an angle of approximately 10 to the direction in which the camera is pointing, one with an angle of approximately 45 and one with an angle of approximately 90. For each angle, the BOLA was targeted so the flight of the ball was over point A. Two camera positions were used, position 1 was 6m from the point A and position 2 was 8m from point A. The ball spin rotation axis was approximately vertical and was not varied since the method of spin rate measurement does not depend on rotation axis orientation. The set-up is shown in figure 1. Fig. 1. The equipment set-up showing 3 different trajectory angles and 2 camera positions. Nine sets of 10 video clips were recorded with the ball speed and spin rate varied within each set of 10. The modified light gate speed values ranged from 18 to 31ms-1 (40 to 70mph). The spin rates calculated manually ranged from 63 to 170rads-1 (600 to 1600RPM). The trajectory angle, camera position and lens settings for each set of 10 clips are shown in table 1. Table 1. Details of the set-up for each set of 10 video clips Set 1 2 3 4 5 6 7 8 9 Angle 10 10 10 45 45 45 90 90 90 Camera Position/lens setting 1/1 2/1 2/2 1/1 2/1 2/2 1/1 2/1 2/2 The video clips were analyzed using the software after all the clips were recorded to speed up the footage collection process. It took approximately 1 hour to analyze all 90 video clips using the analysis software. The manual spin rate analysis took approximately 2 hours. 3. Results 3.1. Ball speed The analysis software successfully analyzed 88 out of the 90 video clips (98%) and returned N/A for the remaining 2 clips. The mean, standard deviation and confidence interval for the differences between the reduced light gate velocities and the velocities measured by the software are shown in table 2. Table 2. The mean, standard deviation and 95% confidence interval of the difference between the reduced light gate and software speed values. Mean Standard Deviation 95% Confidence Interval. -0.12ms-1 1.42ms-1 -0.17 to 0.42ms-1J. Kelley et al./Procedia Engineering 2 (2010) 2967297229694J. Kelley et al. / Procedia Engineering 00 (2010) 000000 The confidence interval contains zero so there is no statistical evidence that the population mean difference is non-zero. This indicates there is no systematic difference between the reduced light gate speed values and the speed values calculated by the software. For any sample, 95% of the values are within 1.96 sample standard deviations of the sample mean. Therefore 95% of the error values found in this sample were in the range -2.66 to 2.91ms-1. This gives an indication of the accuracy expected by the software when analyzing future clips. A scatter graph of the speed values calculated by the software against the reduced speed values from the light gates is shown in figure 2. Fig. 2.Speed values calculated by the software plotted against the modified light gate velocity values. The straight line is the y=x line. Figure 2 shows that the majority of the points are close to the y=x line. To assess the errors numerically, the percentage error is used since it is more meaningful than the mean squared error in this case. The mean and maximum percentage error is shown in table 3. Table 3. Mean and maximum percentage errors for speed. Mean Maximum 4.47 % 15.6 % The maximum error was found at a low speed value (18.4ms-1). For velocities greater than 20ms-1 the maximum error was 11.8%. The proportion of analyses with error less than 10% error was 91%. Repeating the analysis on the same frames for each clip would provide identical results. Therefore, to assess the repeatability, the clips were re-analyzed with the start frame of the analysis moved forward 5 frames. Since the analysis was effectively 0.005s later for each clip, a slight decrease in speed was expected. The mean, standard deviation and confidence interval of the differences between the first analysis and the re-analysis are shown in table 4. Table 4. The mean, standard deviation and 95% confidence interval of the difference between the first and repeated analysis speed values. Mean Standard Deviation 95% Confidence Interval. -0.19ms-1 0.78ms-1 -0.36 to -0.03ms-1The mean is close to zero and the standard deviation is small. Also, 94% of the differences were less than 5%. This suggests that the difference between the analyses is small. Therefore the repeatability of the speed measurements is good. The confidence interval is wholly below zero, which suggests than the re-analysis gives values slightly lower than the first analysis, as expected. 2970J. Kelley et al./Procedia Engineering 2 (2010) 29672972J. Kelley et al. / Procedia Engineering 00 (2010) 000000 53.2. Spin The software analyzed the spin rate in 71 clips. Manual analysis was successful in 81 out of the 90 clips. This was because the logo was not visible for long enough in 9 of the clips. Therefore the software analyzed 88% of the clips that could be analyzed manually. For all remaining clips, the software returned an N/A result. One clip was analyzed incorrectly and can be seen as the outlier in figure 3. Fig. 3. Spin rate values calculated by the software against the manually calculated spin rate values. The straight line is the y=x line Apart from the outlier in figure 3, all of the points are very close to the y=x line. The mean, standard deviation and confidence interval for the differences between the manual analysis and the software spin rate values are shown in table 5. Table 5. The mean, standard deviation and 95% confidence interval of the difference between the manual and software spin rate values. Mean Standard Deviation 95% Confidence Interval. With outlier 0.55rads-1 9.99rads-1 -1.77 to 2.88rads-1Without outlier -0.49rads-1 4.77rads-1 -1.60 to 0.63rads-1The confidence intervals both with and without the outlier contain zero so again there is no statistical evidence that the population mean difference is non-zero. This again indicates there is no systematic difference between the manual analysis and the spin rates calculated by the software. Again using the sample mean and 1.96 times the sample standard deviation not including the outlier, 95% of the error values found in this sample were in the range -9.83 to 8.86 rads-1. The mean and maximum percentage error is shown in table 6. Table 6. Mean and maximum percentage errors for spin rate. Mean Maximum With outlier 4.14% 52.8% Without outlier 3.44% 11.8% Table 6 shows that the maximum error when the outlier is omitted is quite low at 11.8%. The proportion of spin rate analyses with error less than 10% error was 92%. The repeatability of the software spin rate measurement was assessed in the same way as the speed measurement. The mean, standard deviation and confidence interval of the differences between the first analysis and the re-analysis are shown in table 7. J. Kelley et al./Procedia Engineering 2 (2010) 2967297229716J. Kelley et al. / Procedia Engineering 00 (2010) 000000 Table 7. The mean, standard deviation and 95% confidence interval of the differences between the first and repeated analysis spin rate values. Mean Standard Deviation 95% Confidence Interval. -1.34rads-1 8.36rads-1 -3.33 to -0.65rads-1The mean is close to zero and the standard deviation is small. Also, 93% of the differences were less than 5%. This suggests that the difference between the first analysis and the repeated analysis is small. Therefore the repeatability of the spin rate measurements is good. The confidence interval contains zero, suggesting there is no evidence that the difference between the first analysis and the repeated analysis is not zero. 4. Discussion The repeatability of both the speed measurements and the spin rate measurements was good. The reliability of the speed measurements was good, with the software able to analyze 98% of the clips. These analyses had an average percentage error of 4.47% and 91% of the analyses had an error less than 10%. The reliability of the spin rate measurements was slightly less good, but the accuracy was higher. The software was able to analyze 88% of the clips, but one had major error. Including this major error, the average percentage error was 4.14% and 92% of the analyses had an error less than 10%. The user of the software can be confident that the speed and the spin rate measurements are accurate to within 10% for the velocities 18 to 31ms-1 (40 to 70mph) and spin rates 63 to 170 rads-1 (600 to 1600 RPM). The scatter graphs in figures 2 and 3 show that the spread of the data points does not change with speed or spin rate magnitude. Therefore the accuracy levels are expected to be the same for higher spin rates and velocities. The software was designed for use in match play situations, where its use would be to obtain typical speed and spin rates. The software was not designed for detecting small changes in speed and spin rate in a laboratory environment. Therefore an error of 10% is acceptable. 5. Conclusion The software has been validated so that the user is confident that the speed and spin rate measurements are accurate to within 10%. This is suitable for the use the software is designed for. The software was used at a Davis Cup in Barcelona at the end of 2009. Ideally it would be preferable to repeat the validation process for higher speeds and spin rates. Spin rates of up to 450rads-1 have been recorded (Goodwill et al. 2) and the word record serve is 69ms-1. For velocities and spin rates this high, a more powerful BOLA would be required. Acknowledgements Thank you to the ITF and Heather Driscoll for assisting with this work. References 1 Kelley, J., Goodwill, S., Capel-Davies, J., Haake, S. Ball Spin Generation at the 2007 Wimbledon Qualifying Tournament. In: The Engineering of Sport. Biarritz. 2008;1:649657. 2 Goodwill, S., Capel-Davies, J., Haake, S., Miller, S. Ball spin generation by elite players during match play. In: Tennis Science and Technology 3. London: ITF; 2007, p. 349-352. 3 Mavvidis, A., Koronas, K., Riganas, C., Metaxas, T. Speed Differences between Forehand and Backhand in Intemediate-Level Tennis Players. In: Kinesiology 37, 2005, 2 281304. 4 Scientific American. http:/ Choppin, S., Goodwill, S., Haake, S. Miller, S. Speed 3D Player Testing at the Wimbledon Qualifying Tournament. In: Tennis Science and Technology 3. London: ITF; 2007, p. 333-340. 2972J. Kelley et al./Procedia Engineering 2 (2010) 29672972