Mechanical Engineering Journal

Transcription

1 56789 Bulletn of the JSME Mechancal Engneerng Journal Vol., o., 6 Measurement of three-dmensonal orentaton of golf club head wth one camera Wataru KIMIZUKA* and Masahde OUKI* * DULOP SPORTS CO. LTD. Waknohama-cho -6-9, Chuo-ku, Kobe, 65-7 Japan E-mal: wataru-kmzuka@dunlopsports.co.jp Receved Aprl 5 Abstract Golfers swngs vary wth each ndvdual and golf club manufacturers provde the servce called Fttng, to select an approprate golf club for each swng, to an each golfer. In order to fnd the approprate golf club for each golfer, t s necessary to measure the poston and orentaton of a golf club head. It can be supposed that the measurement error needs to be less than.5 degree. There s an exstng method whereby the three-dmensonal (D) orentaton of a golf club head s measured from the D postons of ponts on the golf club head. Ths method s generally used n the area of moton analyss, and has problems n that the system has many restrctons n ts nstallaton, large nstallaton space s requred, and costs are ncurred to the future expanson of the fttng servce to many locatons, as two or more cameras are needed. The Fttng servce requres a method that needs small space, low cost and lttle calculaton tme. Therefore, A method was developed, whereby the D orentaton of a golf club head was calculated based on one mage from just one camera usng the ewton-raphson method, whch needs lttle calculaton tme, and the measurement accuracy was valdated compared wth the expermental results. It was proved that the developed method s useful to a golf club fttng servce because the measurement error s less than.5 degree of our target even when varous golfers swngs are measured, whereby markers are attached possbly near the outlne of the head n the case of the farthest dstance between markers from 8 to 95 mm, and then the coordnates of the marker center are dentfed by calculaton from lumnance and coordnates of each pxel n an area surroundng the marker. Key words : Measurement, Orentaton, Golf club, Image processng, Accuracy, ewton-raphson method. Introducton Golfers swngs vary wth each ndvdual and golf club manufacturers provde the servce called Fttng, to select an approprate golf club for each swng, to an each golfer. The selecton of club has been tradtonally conducted based manly on the measurement results on the launch condtons of a golf ball ht by a golfer, such as the velocty, trajectory and spn rate. However, the launch condtons of the ball depend on poston, orentaton, speed and trajectory of a golf club head at the mpact wth a ball (Yamaguch, 8) and the approprate fttng servce for golfers depends on what factor determned the launch condtons. For example, consderng the case of when a golf ball was launched to the rght drecton, f a large face angle, as shown n Fg., determned the launch condton, a golf club wth an adjusted face angle needs to be recommended. On the other hand, f a large le angle, as shown n Fg., determned the launch condton, a golf club wth an adjusted le angle needs to be recommended. Therefore, t s necessary to measure the poston and orentaton of a golf club head n order to fnd the approprate golf club for each golfer. Requred measurement accuracy can be consdered based on adjustable unt of the head specfcatons. In many cases n the market, lne-ups of a drver have a loft angle n one-degree ncrement and a le angle of an ron can be adjusted by one degree. To take one example from golfer s swng wth a drver at the head speed of m/s at mpact, the dfference n the face angle by one degree brngs 5 to yard devaton of the ball landng pont (Kawamura, 97). Paper o.5-5 J-STAGE Advance Publcaton date: Aprl, 6 [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers

2 Kmzuka and Onuk, Mechancal Engneerng Journal, Vol., o. (6) For these reasons, for golfers who wantt ther ball dstance and drecton as theyy want, t s necessary to adjust the head specfcatons at least by degree ncrement. Then tt can be supposed that the measurement m error needs to be less than.5 degree whch s a half of the above degree. The drect lnear transformaton (DLT) method s known as one of the establshedd method to measure the three-dmensonal (D) postonal coordnates of a pont. In ths method, a pont n space s photographed by two or more cameras fxed n the space, and the coordnatess of the pont n space are dentfed fromm the postons of the pont n the mages (Abdel and Karara, 97) ) (Ikegam, ett al., 99). Identfyng the poston and orentaton off an object by calculatng the coordnates of a multple of ponts on the object usng ths method s wdelyy performed n the feld of moton analyss (D.Gordon, 8). There s also technology whereby the above method ss appled to golf club head orentaton measurement. akasuga et al. developedd a method to measure the D orentaton of a golf club head wth two or more cameras (akasuga and Hashmoto, 996). However, These systems wth two or more cameras c have problems n that the system has many restrctons n ts nstallaton and large nstallaton space ss requred as photographs from several dfferent drectons are needed. Also, consderng the future expanson of the fttng servce to many locatons, a low cost system wth fewer cameras s desred. For these reasons, t s desrable to measure the D orentaton of a golf club head wth one camera. There s reported technology whereby the D orentaton of an object s measured from mages from f just one camera, usng a genetc algorthm (Toyama, et al., 998) (Kayanuma and Hagwara, 999). Ueda et al have appled ths method to golf ball measurement, and developed technology whereby the D orentaton of golf ball s measured usng a genetc algorthm (Ueda, et al., ). Although t can be supposed that a genetc algorthm s used because the measurement ponts on the ball are hdden by the ball s rotaton, the rotaton off a golf club head s not so great that the measurement ponts are not hdden, so t s not thought that there s any need to use such a tme consumng method as a genetc algorthm. In order to reduce the golfer s watng tme when carryng out fttng,, a method that needs lttle calculaton tme s requred. Therefore,, A method was developed, whereby thee D orentaton of a golf club c head was calculated based on one mage from just one cameraa usng the ewton-raphson method, whch needs lttle calculaton tme. It s reported n ths paper that the measurement error was nvestgated andd confrmed tt was less than.5 degree.. Theory. DLT method Fg. Three-dmensonall orentaton of golf club head httng golf ball The DLT method s known as one of the establshed method to measure the D postonal coordnates of a pont (Abdel and Karara, 97) (Ikegam, et al., 99). Fg. shows the relatonshp between the coordnatess X,Y,Z n spatal coordnate system and the coordnates U, V on a dgtzng plane when a pont P s photographed by a camera. The center of the camera lenss s pont O, whch s taken to be the orgn of a coordnate system X Y Z, and a coordnate system wheren the U and V axes on thee dgtzng plane are parallel to the X and Y axes respectvely s X Y Z. L s the dstance on the Z axs between thee pont O and the pont P, F s the dstance on the Z axs between the pont O and a pont Q (the map of the pont P), and a pont U, V s thee ntersecton of a straght lne l ncludng the Z axs and the dgtzng plane. The components of vectors OP and OQ n thee coordnate system s X Y Z are expressed n Equaton (). M s the rotaton matrx for transformng the coordnate system from XYZ to X Y Z. [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers

3 Kmzuka and Onuk, Mechancal Engneerng Journal, Vol., o. (6) X - X U -U OP M Y -Y, OQ V -V () Z - Z - F Also, OP and OQ are of the relatonshp OQ F/L OP, and when the equaton s wrtten for each component, elmnatng L usng the Z component equaton, the followng two equatons are derved. ote that the row column j component of M. U U V V m F m m F m ( X X ( X X ( X X ( X X ) m ) m ) m ) m ( Y Y ) m ( Y Y ) m ( Y Y ) m ( Y Y ) m ( Z Z ( Z Z ( Z Z ( Z Z ) ) ) ) m j s () When organzng constants determned by the postonal relatonshp between the lens and flm n the equaton, the followng two equatons are derved. The constants A to A, B to B, and C to C are called camera constants. A X AY A Z A U C X C Y C Z B X BY BZ B V C X C Y C Z () In order to calculate the eleven camera constants, sx or more ponts whose spatal coordnates X,Y,Z are already known are photographed by a camera and ther coordnates U,V on the dgtal plane are obtaned, a total of twelve or more equatons are made by assgnng the coordnates X,Y,Z and U,V of each pont to the above equaton, and the eleven camera constants are calculated usng a least-squares method. Ths operaton of calculatng the camera constants s called calbraton. In order to calculate the spatal coordnates X,Y,Z, the pont s photographed usng two or more cameras whose camera constants are already known, four or more equatons are made by assgnng the obtaned U, V, U, V, and so on to the above equaton, and X,Y,Z s derved usng the least-squares method. F L U (U, V ) V Dgtzng Plane (Flm) Q(U, V) Fg. Drect Lnear Transformaton method. Method to derve the three-dmensonal orentaton of an object wth one camera X Y O(X, Y, Z ) X Z Z P(X, Y, Z) Object Plane Y Spatal coordnate system As explaned above, two or more cameras are needed n order to calculate the spatal coordnates of one ndependent pont usng the DLT method. Wth regard, however, to the spatal coordnates of a multple of ponts fxed to an object of some sze, provded that the postonal relatonshp between the ponts (that s, the coordnates of each pont n the object coordnate system) s already known, a relatonal expresson can be added to the equaton for [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers

4 Kmzuka and Onuk, Mechancal Engneerng Journal, Vol., o. (6) calculatng the spatal coordnates X,Y,Z, and the spatal coordnates of the multple of ponts (that s, the poston and orentaton of the object) can be calculated based on one mage from just one camera. Hereafter, the spatal coordnates X,Y, Z of a representatve pont on the object and the orentaton,, of the object are defned as unknowns and solved. The orentaton,, of the object n ths study ndcates the rotatonal angles, and when the spatal coordnate system XYZ are caused to concde wth the object coordnate system X Y Z by frst rotatng around the Y axs, next rotatng around the Z axs, and fnally rotatng around the X axs. When changng Equaton (), the followng equatons are derved. ( A C U ) X ( A ( B C V ) X ( B C U ) Y ( A C V ) Y ( B C U ) Z ( A C V ) Z ( B U ) V ) () Heren, usng vectors, r from the representatve pont to - ponts n the object coordnate system, the spatal coordnates of each pont on the object are expressed as R X,Y,Z ) T r ( (5) T s the coordnate transformaton matrx for transformng from the coordnate system XYZ to X Y Z, and conssts of the, and. That s, R conssts of the spatal coordnates X,Y, Z of the representatve pont of the object and the orentaton,,. By assgnng X,Y, Z and U, V of the representatve pont, R and ( U,V ) of the other ponts to Equatons (), nonlnear smultaneous equatons are derved, as shown below. Heren, R x, R Y and R Z represent the X, Y and Z components of R respectvely. ( A C U ) X ( B ( A C U ( B ( A C U ( B C V ) X C V C V ( A C U ( B C V ( A ( B,X,X,X,X,X,X ( B ( B C U ) Y C V ) Y C V C V ( A C U ( A C U ( B C V ( A C U ( A ( B,Y,Y,Y,Y C V ) Z ( B ( B,Y C U ) Z ( B C V C V ( A C U ( A C U,Y ( A ( B C V ( A C U,Z,Z U ) V ),Z,Z ( B ( B ( A U ) V ) ) V ) ( A U,Z,Z ( B V ( A U ) ) (6) Therefore, provded that s three or more, that s, provded that the object coordnates of three or more ponts on the object are already known, the sx unknowns, that s, the spatal coordnates X,Y, Z of the representatve pont of the object and the object orentaton,,, can be derved by applyng the ewton-raphson method to the smultaneous equatons.. Experment. Preparaton An expermental apparatus (jg) were desgned and manufactured to valdate the accuracy of the D orentaton of the club head estmated by the proposed method, as shown n Fg.. The jg can set the club head n the ntended orentaton: the face and le angles whch are adjusted usng the rotaton mechansms ndcated by the blue and green crcles, respectvely, n Fg.. Wth ths confguraton, the face and le angles when the club head s set at a certan standard orentaton can be changed wth an accuracy of. or better. Markers were attached to sx ponts on the head angle settng jg n order to carry out calbraton. As explaned n., the spatal coordnates of the sx ponts need to be already known when conductng an experment. Therefore, one [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers

5 Kmzuka and Onuk, Mechancal Engneerng Journal, Vol., o. (6) of the sx ponts was taken as the spatal coordnate system orgn, each coordnate axal drecton was fxed as n Fg., and the spatal coordnates of each marker were measured usng a D measurng machne (GOM s ATOSSO). As explaned n., the coordnates n the head coordnate system of three or more markers fxed to the club head need to be known already n order to calculate the head orentaton. Therefore, two markers were attached to ponts on the face lne, and one to a pont on the face surface but not on the face lne. Also, a multple of markers were attached to the face surface and the body n order to nvestgate the relatonshp between the marker postons and measurement accuracy of head orentaton. The coordnates of each marker were measured wth the D measurng machne. The head coordnates r of each marker was obtaned by takng one pont on the face lne to be the head coordnate system orgn, and defnng a drecton followng the face lne as the head coordnate system X axs, a drecton perpendcular to the face surface as the head coordnate system Y axs, and a drecton perpendcular to both the X axs and Y axs as the head coordnate system Z axs. A camera used n ths experment has 6-by-8 pxels resoluton. Photographs of club head are taken wth a strobe lght trggered by a sensor at the mpact wth a ball n order to prevent moton blurrng. In ths experment, photographs of a statc head are taken wth a strobe lght manually n order to make the lght ntensty to be the same level at the tme of swng. And t has been confrmed that the mage qualty of photographs of swngs s equvalent to of statc heads. Z Markers X Y Fg. Jg for settng club head angle. Measurement Steps A club head s fxed n the angle settng jg, and the face and le angles scales are adjusted to. ext, the jg s set under fxed camera, and an mage s taken for calbraton. At ths tme, all calbraton markers should be wthn the range of the fxed camera. From ths pont, the poston and angle of the camera, and the poston of the jg, should not be changed. The rotatng and nclned stage adjustment unts are rotated so that the club head s at the ntended face and le angles, one photograph s taken n each case, and the photographs are used to valdate accuracy. Examples of the photographs are shown n Fg.. For calbraton, the calbraton mage s read by the mage processng software Dpp-Image (DITECT Co.), and the coordnates U,V of the sx markers fxed to the jg are obtaned. The camera constants are calculated from the coordnates U,V and X,Y,Z of the sx markers. For calculatng the head orentatons, the mages for valdatng accuracy are read by Dpp-Image, and the coordnates U,V of the markers fxed to the club head are obtaned. The head orentatons are calculated from the coordnates U,V and r of the markers. The face and le angles at each orentaton relatve to the face and le angles when settng adjusted to are taken as measurement values. [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers 5

6 Kmzuka and Onuk, Mechancal Engneerng Journal, Vol., o. (6) Markers for Calbraton Markers for Calbraton Fg. Examples of photographs taken n experment. Accuracy valdaton In the experment, the effect on measurement accuracy of () the postons of the markers, () the scale of the change n head poston and orentaton, and () the method of dentfyng the coordnates of the marker center was nvestgated... Effect of marker poston on measurement accuracy Wth the poston of the jg such that the ball s ht wth the center of the club head, and the head orentaton at face and le angles of, -, and -5, respectvely, photographs were taken n each case. c In order to dentfy thee marker coordnates on the mages, the marker center c was dentfed vsually, and the pxel poston taken to be UU,V. The effect of marker poston on measurement accuracy was examned by changng the combnaton of markers used n head orentaton calculaton as shown below. Combnaton :the markers are attached over a relatvely wde area (the four markers surrounded by red crcles n Fg. 5(a)) the farthest dstancee between markers of 95 mmm for a drverr and 8 mm for an ron Combnaton :the markers are attached over a relatvely narrow area (the four markers surrounded by blue crcles n Fg. 5(b)) the farthest dstancee between markers of 5 mmm for a drverr and 5 mm for an ron (a) Combnaton Fg. 5 Marker Combnatons (b) Combnaton [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers 6

7 Kmzuka and Onuk, Mechancal Engneerng Journal, Vol., o. (6).. Effect on measurement accuracy of scale of change n club head poston and orentaton Wth the poston of the jg such that the ball s ht wth the toe or heel of the club head, and the head orentaton at face angles of, -5, and 5 and le angles of and 5, photographs were taken n each case. In order to dentfy the marker coordnates on the mages, the marker center was dentfed vsually, and the pxel poston taken to be U,V. The marker combnaton used n head orentaton calculaton was Combnaton (wheren the markers are attached over a relatvely wde area)... Effect on measurement accuracy of marker center coordnate dentfcaton method Wth the poston of the jg such that the ball s ht wth the toe or heel of the club head, and the head orentaton at face angles of, -5, and 5 and le angles of and 5, photographs were taken n each case. In order to dentfy the marker coordnates on the mages, the coordnates of the marker center were calculated as below, and taken to be U,V. Fg. 6 shows an mage taken n the experment dgtalzed wth lumnance 5 as a threshold, and a dagram n whch a marker porton s enlarged. Owng to the dgtalzng process, the lumnance of the black porton became, and the lumnance of the whte porton 55. The coordnates of the marker center were calculated by usng the equaton below from the coordnates U, V and a lumnance M of all the pxels n an area (red frame) surroundng the marker. The marker combnaton used n head orentaton calculaton was Combnaton. U, V U M M, V M M (7) Coordnates (U, V ) Lumnance M Fg. 6 Example of photograph data dgtalzed to dentfy the coordnates of the marker center. Results and Dscussons. Effect of marker poston on measurement accuracy Table and Table show the face and le angles set n the angle settng jg, the face and le angles calculated wth each marker combnaton, and measurement error, whch s the absolute value of a dfference between set angle and calculated angle. The fgures shown n Table are for a drver head, and those n Table for an ron head. In the case of the drver, the average errors wth Combnaton, wheren the markers are attached over a wde area, are face angle., le angle.5, whle the average errors wth Combnaton, wheren the markers are attached over a narrow area, are face angle., le angle.8. Ths shows that both face and le angles measurement errors are smaller when the markers are attached over a wde area. In the case of the ron, the average errors wth Combnaton, wheren the markers are attached over a wde area, are face angle., le angle., whle the average errors wth Combnaton, wheren the markers are attached over a narrow area, are face angle.9, le angle.8. Ths shows that, as n the case of the drver, both face and le angles measurement errors are smaller when the markers are attached over a wde area. [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers 7

8 Kmzuka and Onuk, Mechancal Engneerng Journal, Vol., o. (6) It can be supposed that ths s because the effect of errors n dentfyng the marker center on the mage s smaller owng to the dstances between markers beng greater when the markers are attached over a wde area. In addton, measurement errors of le angle compared wth the face angle tend to be larger n a drver than an ron. Due to the markers of the drver are attached on the crown, these markers are roughly arranged on the parallel plane to the camera lens. In ths knd of marker arrangement, t s advantageous to dentfyng an orentaton whch s on a parallel plane to the camera lens such as the face angle, n terms of accuracy. On the other hand, t s dsadvantageous to dentfyng an orentaton whch s on a depth drecton to the camera lens such as the le angle, because the dsplacement of markers on the mage s so small. Therefore, t s consdered that the measurement error of the le angle s larger than that of the face angle. Related to the markers of the ron, the markers are manly attached on the face, and arranged to the depth drecton to the camera lens. Therefore, t s advantageous to dentfyng an orentaton whch s on a depth drecton to the camera lens such as the le angle, because the dsplacement of markers on the mage s so large, n terms of accuracy. And, t s consdered that the measurement error of the le angle s approxmately equal to that of the face angle. Wth these results, t was found that target level of measurement error wthn.5 can be acheved by attachng markers possbly near the outlne of the head n the case of the farthest dstance between markers of 95 mm for a drver and 8 mm for an ron. It was also found that the measurement accuracy of le angle s rased when markers are arranged to the depth drecton to the camera lens. Table Effect of marker combnaton on drver measurement accuracy Drver Combnaton Drver Combnaton Settng Measurement Error Face Le Face Le Face Le Assume Face Le Face Le Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] ht wth Angle[ ] Angle[ ] Angle[ ] Angle[ ] Assume ht wth Center Center Center Center Center Center Center Center Average..5 Settng Measurement Error Face Le Angle[ ] Angle[ ] Center Center Center Center Center Center Center Center Average..8 Table Effect of marker combnaton on ron measurement accuracy Iron Combnaton Iron Combnaton Settng Measurement Error Face Le Face Le Face Le Assume Face Le Face Le Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] ht wth Angle[ ] Angle[ ] Angle[ ] Angle[ ] Assume ht wth Center Center Center Center Center Center Center Center Average.. Settng Measurement Error Face Le Angle[ ] Angle[ ] Center Center Center Center Center Center Center Center Average.9.8. Effect on measurement accuracy of scale of change n club head poston and orentaton Table shows the face and le angles set n the angle settng jg, the face and le angles calculated wth marker combnaton, and measurement error, whch s the absolute value of a dfference between set angle and calculated angle, when the head poston and orentaton are subjected to a large change. In the case of the drver, the average errors are face angle., le angle.8, and n the case of the ron, the average errors are face angle., le angle.. [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers 8

9 Kmzuka and Onuk, Mechancal Engneerng Journal, Vol., o. (6) These errors are larger than that of Combnaton n.. Based on ths, t can be sad that when the head poston and orentaton are subjected to a large change wth respect to the standard, measurement accuracy decreases compared wth when there s lttle change. Furthermore, when the le angle of the drver s subjected to a large change, the measurement error ncreases. It can be supposed that ths s because the markers are on only the crown of the drver, meanng that the effect on le angle calculaton of the dstance between markers n the toe-heel drecton s greater than n the case of the ron. When the le angle s subjected to a large change, the dstance between markers n the toe-heel drecton decreases, and the effect of errors n dentfyng the marker center on the mage ncreases. As golf swngs vary dependng on the person, t can be supposed that some head orentaton may sgnfcantly devate from the standard orentaton. Therefore, t was found that the measurement accuracy of ths system, n the case of measurement from varous golfers swngs, s lower than the target as the average of measurement errors of le angle for a drver s larger than.5. Table Effect on measurement accuracy of scale of club head orentaton change Drver (Combnaton ) Iron (Combnaton ) Settng Measurement Error Face Le Face Le Face Le Assume Face Le Face Le Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] ht wth Angle[ ] Angle[ ] Angle[ ] Angle[ ] Assume ht wth Toe Toe Toe Toe Heel Heel Heel Heel Average..8 Settng Measurement Error Face Le Angle[ ] Angle[ ] Toe Toe Toe Toe Heel Heel Heel Heel Average... Effect on measurement accuracy of marker center coordnate dentfcaton method Table shows the face and le angles set n the angle settng jg, the face and le angles calculated wth marker combnaton, and measurement error, whch s the absolute value of a dfference between set angle and calculated angle, when the coordnates of the marker center are dentfed by calculaton. In the case of the drver, the average errors are face angle., le angle., and n the case of the ron, the average errors are face angle., le angle.. These errors are smaller than that of results n.. Based on ths, t s supposed that dentfyng the coordnates by calculaton can reduce readng error rather than vsually dentfyng each pxel of the marker center poston. It was proved n ths paper that the developed method s useful to a golf club fttng servce because the averages of measurement errors ncludng those of drver s le angle are less than the target value of.5. Table Effect of measurement accuracy on marker center coordnate dentfcaton method Drver (Combnaton ) Iron (Combnaton ) Settng Measurement Error Settng Measurement Error Face Le Face Le Face Le Assume Face Le Face Le Face Le Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] ht wth Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] Angle[ ] Assume ht wth Toe Toe Toe Toe Heel Heel Heel Heel Average.. Toe Toe Toe Toe Heel Heel Heel Heel Average.. [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers 9

10 Kmzuka and Onuk, Mechancal Engneerng Journal, Vol., o. (6) 5. Concluson A method to measure the D orentaton of a golf club head based on one mage from just one camera has been developed, whereby the orentaton s calculated from the coordnates of markers attached to the head n the head coordnate system and the coordnates of markers on the mage. By upgradng ths method, the velocty and trajectory of head are possble to be calculated by takng two or more photos before mpact. Also, the followng was confrmed regardng measurement accuracy: () Measurement errors can be reduced by attachng the markers possbly near the outlne of the head and arrangng markers to the depth drecton to the camera lens () When the head poston and orentaton are subjected to a large change wth respect to the standard, measurement accuracy decreases compared wth when there s lttle change. () Identfyng the coordnates of the marker center by calculatng from lumnance and coordnates of each pxel n an area surroundng the marker can reduce measurement errors rather than vsually dentfyng each pxel of the marker center poston. It was proved that the developed method s useful to a golf club fttng servce because the measurement error s less than.5 of our target even when varous golfers swngs are measured, whereby markers are attached possbly near the outlne of the head n the case of the farthest dstance between markers from 8 to 95 mm, and then the coordnates of the marker center are dentfed by calculaton from lumnance and coordnates of each pxel n an area surroundng the marker. References Abdel-Azz, Y. I. and H. M. Karara, Drect lnear transformaton from comparator coordnates nto object space n close-range photogrammetry, ASP Symposum on Close-Range photogrammetry, Amercan Socety of Photogrammetry, Falls Church (97). D.Gordon E.Robertson, Research Methods n Bomechancs (8), pp. 9-8 (n Japanese). Ikegam,Y., Sakura, S., Yabe, K., D.L.T. method, Japanese Journal of Sports Scence, - (99), pp (n Japanese). Kawamura, R., Bran Exercse of Golf (97), pp. 5- (n Japanese). Kayanuma, M., Hagwara, M., A new system to detect object and estmate the poston and orentaton from an mage usng a -D model havng feature ponts, IEEE Internatonal Conference on Systems Man and Cybernetcs, vol. IV (999), pp akasuga, M., Hashmoto, R., The D-Measurement of Golf Club Head Movement, Symposum on Sports Engneerng : Symposum on Human Dynamcs, Vol.996 (996) pp (n Japanese). Toyama, F., Shoj, K., Myamch, J., Pose estmaton from a lne drawng usng genetc algorthm, Japanese Journal of Electroncs, Informaton and Communcaton Engneers, vol.j8-d-ii, no.7 (998), pp Ueda, M., Tsunoda, M., Onuk, M., Hroyasu, T., and Mk, M., Detecton of Rotaton Angle of Golf Ball wth Genetc Algorthm Mechansm, Symposum on Sports Engneerng : Symposum on Human Dynamcs, Vol. () pp.-7 (n Japanese). Yamaguch, T., Real Scence of Club and Ball for Long Dstance and ot Curve (8), pp (n Japanese). [DOI:.99/mej.5-5] 6 The Japan Socety of Mechancal Engneers