Point-Cloud-to-Point-Cloud Technique on Tool Calibration for Dental Implant Surgical Path Tracking

Transcription

1 Pont-Cloud-to-Pont-Cloud Technque on Tool Calbaton fo Dental Implant Sugcal Path Tackng Auanuch Losakul, Jackt Suthakon and Chanja Snthanayothn Abstact Dental mplant s nomally used n posthetc dentsty. Computeze navgaton system whch conssts of peopeatve sugey and ntaopeatve suppot ae povded to enhance the accuacy n ths hgh sk sugey. Dental tool tp calbaton s one of mpotant pocedue to fulfll the complete navgaton system nteventon. A hghe accuacy to fnd the elatonshp wth espect to make and tool tp can be pefomed by usng SVD to mnmze the least-squaes soluton. The hghe accuacy esult s expessed by compang the eale tool tp calbaton method and the based lne tackng smulaton. Methodology n optcal tackng and mage pocessng s accomplshed to complete the system. D I. INTRODUCTION ENTAL IMPLANT s the most fequent method of tooth oot eplacement used n posthetc dentsty. Computeze navgaton system s offeed to mnmze potental sk of damage to ctcal anatomc stuctues of patents. The methodology based on CIS nteventons ncludes peopeatve and ntaopeatve pocedues. The peopeatve sugey s to use 3D vews as povded to enhance aw mages obtaned fom the patent befoe opeaton. Ths helps to get famla wth the anatomy of the patent. The technques ae to ende the taget egon and elatve ogans ncludng the pathway by CT data. Whle ntaopeatve suppot can be used dung the eal sugcal pocedue both as a navgaton and decson ad. The tackng systems, a steeo scope calbaton, and a set of specal desgned efeence makes attached on the dental hand-pece tool and patent s jaw, ae assocatvely egsteed togethe n the system. Dental tool tp calbatng s bascally an mpotant pocedue to detemne the elaton between the hand-pece tool tp and hand-pece s makes whch can be fomed as vecto b tp. Wth the tansfeng coodnates fom peopeatve data to ealty, ths paamete s a pat of components n typcal egstaton poblem. A hgh accuacy s equed, and ths elaton s aanged by Pont-cloud-topont-cloud gd tansfomatons and sngula value decomposton (SVD) fo mnmzng gd egstaton eos [], [2]. The poposed pocedue s to use the pontng devce o hand-pece to touch the pont on the pvot and the tansfomaton matx s calculated evey tme when t moves to the new poston whle the tool tp stays at the same pont. Then the tansfomaton matx s fomed by 3x3 otaton matx whch descbes a fame otated by R elates to the efeence fame, and tanslaton vecto ntepetng of actually tanslatng the pont n space. Regadng to hgh accuacy of equement, and ths tansfomaton matx s aanged by pont-cloud-to-pontcloud gd tansfomatons and sngula value decomposton (SVD) fo mnmzng gd egstaton eos [], [2]. The methodology n ths system s to fnd the elaton between the hand-pece tool tp and hand-pece s makes. Then vefy the accuacy by compang to the eale tool tp calbaton algothm and smulatng the path tackng fom ths elatonshp. Manuscpt eceved Apl 6, Ths wok was suppoted n pat by the Cente of Bomedcal and Robotcs Technology (BART LAB), Mahdol Unvesty, Thaland. A. Losakul s cuently a gaduate student n the Depatment of Bomedcal Engneeng, Mahdol Unvesty, Salaya, Thaland. She eceved he Bachelo s Degee n Electcal Engneeng fom the Chang Ma Unvesty n (e-mal: g @student.mahdol.ac.th). J. Suthakon s cuently the decto of the Cente fo Bomedcal and Robotcs Technology, Faculty of Engneeng, Mahdol Unvesty, Salaya, Thaland. He eceved hs Ph.D. n Robotcs fom the Johns Hopkns Unvesty, USA, n 2003 (coespondng autho to povde phone/fax: Ext e-mal: egjst@mahdol.ac.th). C. Snthanayothn s cuently the eseach leade at Advanced Dental Technology Cente, Natonal Scence and Technology Development Agency. She eceved he Ph.D. n Physcs (Imagng) fom the Kng s College, London, U.K. n 999. Fg.. Navgaton System Dagam (Coutesy [2]) II. SYSTEM DESCRIPTION OF TOOL TIP CALIBRATION A. Calbaton Concept The poposed pocedue s to use the pontng devce calbaton technque to fnd the homogenous tansfomaton matx between the IR-LED make, attached to the end of the tool holde, and the tp of the nstument.

2 Ths elatonshp has a lot of nfluence n the navgaton system as llustated n Fg.. Ths paamete fulflls the navgaton path fom CT data to the tool tp of the nstument F Ctp. The elatonshp F Ctp can be calculated by F Ctp = F eg F - eff tool F tp () whee F eg s the egstaton tansfomaton wth espect to the CT data fame and efeence fame, F - ef s the nveson of the efeence tansfomaton wth espect to the camea fame, F tool s the tool tansfomaton wth espect to tool s make fame and the camea fame, and F tp s the tool tp tansfomaton wth espect to the tool s make fame and tool tp. The pncpal pocedue to fnd the F tp s that to use the pontng devce o hand-pece to touch the pont on the pvot and the tansfomaton matx s calculated evey tme when t moves to the new poston whle the tool tp stays at the same pont. Fg. 2. Pontng Devce Calbaton Technque Fg. 2 shows the method used to fnd the vecto b tp, whch epesents the elatonshp between tool s make and tool tp. Fo each measuement k, we have b post = R k b tp +p k.wth new aangement, Rb b = p. Set up a least squae poblem M M M btp R I k pk b post M M M Ths can be epesented as k tp post k Ab % % = p% wtten as b= ( A% T A% T ) A% T % p%, whee ( T AA % % ) A % s pseudo nveson. B. System Ovevew (2) and the vecto can be mage s pocessed to obtan the 3D coodnate of make postons. Thesholdng and mophologcal mage pocessng technques have been pefomed to complete the stuctung elements of object egon. All centods of make egon n left and ght steeo mages, and ntnsc and extnsc steeo paametes ae nput nto steeo tangulaton functon to fnd the 3D postons whch ae equvalent to the wold coodnate system. Wth these two sets of pont cloud, the tansfomaton matx s calculated by SVD. III. OPTICAL TRACKING AND IMAGE PROCESSING STAGE A. Optcal Tackng ) Steeo Camea Calbaton: The steeo camea calbaton has been done by Camea Calbaton Toolbox fo MATLAB. It s based on plana checkeboad pas of coespondng left and ght mages. The ntal values fo the ntnsc camea paametes ae shown n addton to an estmate fo the extnsc paametes chaactezng the elatve locaton of the ght camea wth espect to the left camea. Ths pocess s known as steeo tangulaton [3]. In ths pape, the 3D coodnates of the ponts n the left camea ae teated to be efeence fames. 2) Tackng Devce: The actve optcal tackng IR-LEDs s used as makes o tacked objects n the system. The man pupose of a tackng system s to detemne the 3D coodnate of an object. Ths method nvolves on magng wth cameas mounted at a fxed locaton and mage pocessng [5]. In ths system employs the nfaed optcal tackng system to extact the dffeences between makes and backgound. The two set of actve makes ae utlzed as efeence fame, F ef, and the othe s on the top of the tool holde whch called the pontng fame, F pt. Wth these two sets of makes, they epesent the two set of pont clouds {a } and {b } as llustated n Fg. 4. Fg. 3. System Ovevew Fg. 3 llustates the system confguaton. The calbated steeo camea wth nfaed flte s used to eteve mage shown n Fg. 3. The Image Acquston has been mplemented to captue monochome mage though MATLAB. Moeove, the steeo-snapshot of left and ght mages fo each measuement, k have been stoed, each b tp Fg. 4. Example of make and tool holde 3) Image Acquston: The mage acquston stage s the fst stage of the vson system. Bascally, Bumblebee camea connects to a PC tansmsson va an IEEE-394 nteface (FeWe). The mage s satsfactoly obtaned by softwae whch mplemented on Dgclops and Tclops, Bumblebee Lbay to captue monochome mages though MATLAB. Dgclops s used to contol the steeo vson

3 camea settngs and mage acquston, whle Tclops pefoms mage ectfcaton and steeo pocessng [6]. Whle calbatng, the left and ght mages ae necessay to be captued smultaneously n each pool of measuement. The examples of mage whch pass IR-Flte s llustated n Fg. 5(a) and 5(b). (a) Fg. 5. (a) Example of captue mage fom camea, (b) Gaphc ndcates the components of pontng calbated technque B. Image Pocessng If the mages have been acqued satsfactoly, then the ntended tasks ae achevable wth the ad of some fom of mage enhancement. ) Thesholdng: The acqued mages ae changed to bnay mage by thesholdng technque. Thesholdng s a method to dstngush the equed objects n an mage fom backgound by ceatng a bnay pattonng of the mage ntenstes. The pocedue s accomplshed by compang the desed ntensty value called theshold to ntenstes of all pxels n mage. The pxels that have ntensty value geate than the theshold ae assgned to one class. Othewse, they ae assgned to anothe class [5]. 2) Dlaton and Eoson: The use of combnaton of dlaton and eoson, togethe wth openng and closng s employed to enhance the stuctue of the nteestng egon. Dlaton s to gadually enlage the boundaes of egons of foegound pxels. Openng tends to emove some of the foegound pxels fom the edges of egons of foegound pxels, whle closng tends to enlage the boundaes of foegound egons n an mage, but t s less destuctve of the ognal bounday shape [7]. 3) Labelng and Fndng Centod: Wth these mpoved egons n mages, the centods of the objects pesent n both left and ght mages ae calculated. Befoe fndng centod, the connected components labelng s pefomed by scannng an mage and goups ts pxels nto components based on pxel connectvty. All pxels n a connected component have the same ntensty values and connect to each othe though ts neghbos. Afte the labelng s pefomed to locate the aea of makes, centods of makes ae detemned to epesent the poston of the make accodngly. (b) IV. PARAMETER OPERATION STAGE A. Pont-cloud-to-pont-cloud gd tansfomaton Typcally, a set of ponts {a } n one coodnate system and anothe set of ponts {b } n a second coodnate system ae gven. The goal s to fnd [R,p] that mnmze η = e e, whee e ( = R a + p ) b (3) To fnd the least-squaes soluton of R and T, the centods of each pont cloud and SVD of a otaton matx ae pefom as followng algothms. B. Algothm to fnd gd tansfomatons Step : Compute centod of each pont cloud N a= a N b= b N = N = a=a % a b % =b b Step 2: Fnd R that mnmzes 2 ( R a% b % ) Step 3: Fnd p p=b R a Step 4: Desed tansfomaton s F=Fame(R, p ) To fnd otaton matx R that mnmze 2, the nonteatve algothm nvolves the sngula value decomposton (SVD) of a 3x3 matx s calculated. C. Algothm to fnd mnmzed otaton R Step : Compute a b a b a b, x, x, x, y, x, z H = a b a b a b, y, x, y, y, y, z a b a b a b, z, x, z, y, z, z Step 2: Compute the SVD of H=USV t Step 3: X=UV t Step 4: Vefy Det(X) If Det(X) = +, then X s otaton (R=X). If Det(X) = -, X s a eflecton. In case that X s a eflecton, then R=V'U t, whee V' = [v, v 2, -v 3 ]. Ths can be poved n method due to K. Aun, et. al. [] V. EXPERIMENTAL RESULT AND ANALYSIS A. Tools and Equpments. Bumblebee2 steeo vson camea system (BB2- BW-60), monochome, 640x480 at 48 FPS, 6.0 mm focal length lens, two /3 pogessve scan CCD sensos, and both the left and ght mages to a PC tansmsson va an IEEE-394 nteface. 2. Infaed flte coves the steeo cameas 3. Two makes wth 4-IR-LEDs fo each 4. Pvot 5. Tool Holde

4 6. MATLAB pogam fo calculaton 7. Camea Calbaton Toolbox fo MATLAB B. Smulaton and Results ) Testng calbaton wth standad calbaton: Compute smulatons have been caed out on MATLAB. The esult has been compaed wth espect to the nomal pontng devce calbaton. 7 measuements of pontng changes wth poston ae pefomed n the expement. The left and ght mages have been loaded by optcal tackng component and have been pocessed by mage pocessng component. The postons of objects wth espect to theedmensonal coodnates ae pefomed as set of pont clouds {a } and {b }. [R,p] s calculated by the least squae poblem T T settng up n ode to compute b tp n b= % ( A% A% ) A% p %. Ths esult has been compaed wth the standad pontng devce calbaton and found that the expected esult dffes fom the standad method wth the eo %. 2) Testng calbaton wth tackng system: b tp b mak b = b + b es mak tp (a) (b) Fg. 7. (a) System envonment setup, (b) Model of vectos b tp Fg. 6. Tackng system smulaton concept. The tackng smulaton usng the b tp that obtaned fom tool tp calbaton by pont-cloud-to-pont-cloud method. Fg 6 llustated the system concept n tackng smulaton. Ths smulaton envonment setup s shown n Fg. 7(a). The eal tme mages ae acqued by mage acquston softwae whch ntefaces between Dgclops and Tclops, and MATLAB. Each fame of eal tme mages s pefomed by mage pocessng pat to enhance and eteve the thee-dmenson coodnate of the make poston wth espect to the steeo camea fame whch employed as efeence fame n ths smulaton. Vecto b mak s the nfomaton that obtans fom mage pocessng stage. Vecto b es can be calculated by the elatonshp b es = b mak + b tp. Fg. 7(b) shows the model of vectos. The anmaton of elatonshp between make poston and tool tp s establshed by MATLAB when movng the tool holde to vaous postons. The expement has been aanged by usng the tool tacks the based lne whch s ceated n the wokspace n MATLAB as modeled n Fg. 8. Regadng to the expement, the obtaned esult s coect n usng the tool holde to tack the based lne dsplayed n gaphc anmaton. Ths based lne can be assumed to be the guded navgated path n sugey. The tool holde s equvalent as hand-pece fo the opeaton. Fg. 8. Tackng Path Anmaton VI. CONCLUSION Ths pape gves a systemc ntoducton about ou ongong poject, the dental navgaton system. In ths wok, we constuct and fulfll some smple expements on tool tp calbaton wth Pont-Cloud-to-Pont-Cloud Technque and the Least-Squae Soluton whch compaed to the eale tool tp calbaton method and obtan % eo. Fo tackng smulaton, t found that ths elaton s able to accomplsh to tack the based lne whch assumed as the gudance n navgaton system. The expement acqued the nfomaton of tackng devce, mage acquston and mage pocessng algothm. Futue tasks consst of the ntegated system wth peopeatve sugey and ntaopeatve tackng systems. A sees of expements of oveall system wll be caed out n ode to valdate the pefomance of the system and algothm. VII. ACKNOWLEDGEMENT The fst Autho s suppoted by TGIST Scholashp (TG M). Ths eseach s funded by MTEC, Thaland (MT-B-48-BMD E). Addtonal thanks to BARTLAB, Thaland and specal thanks to A. Kunapnun. VIII. REFERENCES [] K. S. Aun, T. S. Huang, and S. D. Blosten, Least-Squaes Fttng of Two 3-D Pont Sets, IEEE Tansactons on Patten Analyss And Machne Intellgence, Sep. 987, pp [2] Russell Taylo Compute-Integated Sugey ( Engneeng Reseach Cente fo Compute Integated Sugcal Systems and Technology, Johns Hopkns Unvesty, USA.

5 [3] Danal Stoyanov, Camea Calbaton Toolbox fo Matlab, Royal Socety/Wolfson Foundaton Medcal Image Computng Laboatoy, Impeal College London, UK. [4] Rafael C. Gonzalez, Rchad E. Woods, Steven L. Eddns, Dgtal Image Pocessng usng MATLAB, Peason Pentce Hall [5] T. Kusalanukhun, Optcal Thee-Dmensonal Coodnaton fo Medcal Applcatons, Maste Thess, Depatment of Bomedcal Engneeng, Faculty of Engneeng, Mahdol Unvesty, [6] Pont Gay Reseach Inc., Steeo Vson Poduct Dgclops SDK, Avalable: [7] B. Fshe, S. Pekns, A. Walke and E. Wolfat, Hypemeda Image Pocessng Refeence, Depatment of Atfcal Intellgence, Unvesty of Ednbugh, UK, Avalable: