TOOTH ALIGNMENT OF THE DENTAL CAST USING 3D THIN PLATE SPLINE

Transcription

1 TOOTH ALIGMET OF THE DETAL CAST USIG 3D THI LATE SLIE Chanjira Sinhanaohin, Wisaru Bholsihi, Wichi Tharanon aional Science and Technolog Developmen Agenc (STDA 111 Thailand Science ark, hahon-yohin d, Klong 1, Klong Luang, ahumhani, 11, Thailand ABSTACT This aricle has described he process for ooh alignmen using 3D hin plae spline. Firs sep is o simulae he individual ooh and is landmarks and fi i ino he denal cas b geomeric ransformaion of individual ooh. ex sep is o align he simulaed eeh ino proper arch form. Afer ha, record pairs he landmarks of simulaed eeh before and afer ooh alignmen. The final sep is o creae he new denal cas (warping denal cas b appling 3D hin plae spline echnique hrough pairs of landmarks on simulaed eeh as inpus. The resuls of he ooh alignmen and he comparison wih he denal cas before ooh alignmen have shown ha he eeh aligned along he curve while he gum was slighl deformed o show he smoohness of ransformaion on eeh and gum. KEY WODS Visualisaion, Simulaion, Thin plae spline, Teeh Alignmen 1. Inroducion The orhodonics analses have relied upon denal cass made from plaser of aris wih silicone mold for a long ime. The saes-of-he-ar echnologies have allowed orhodonic diagnosic, analses and reamens planning in 3D images of denal cass hrough commercial sofware on personal compuers. OrhoCAD of Caden Inc. [1], 3Dxer of Dimemnex Digial Lab [] and e-model from Geodigm Corp. [3] and Applicaion Visualiaion Ssem Express of Advanced Visual Ssem Inc.[4] are a few examples of sofware for 3D orhodonic planning and analses. However, exising commercial sofware for 3D orhodonic analses has a limiaion of displaing onl crown secion of he denal cas wihou aking anaom informaion of denal roos ino accoun. [5] Even hough here are some researches for he complee 3D model of human jaw including denal crowns and roos [6], i requires rigid regisraion and hen maching on boh denal crowns and roos wih he 3D Freeform Deformaion (FFD denal models which is a imeconsuming process. Macchi [7] has developed he echnique for 3D superimposiion of anaomic eeh and cas model. However, he sofware menioned in Macchi s paper is no eas o use and also required he significan user skill. Furhermore, we have found he similar problem when we ried o perform image regisraion beween CT images and model image due o he sheer amoun of 3D daa which complicae he difficul o segmen he 3D CT model.. Mehod.1 egisraion beween Denal Cas and Simulaed Teeh This secion, firs he simulaed eeh were creaed using 3D Sudio Max [8]. The enamel-crowns emplae shown in Fig. 1(A was scanned and segmened o be a emplae of 3D crowns. The denal roos were designed and aached o he crowns as shown in Fig. 1(B. The resul of he simulaed 3D eeh model can be shown as in fig. 1 (C, which shows he side and op views respecivel. Also he eeh landmarks of each ooh have been locaed on he surface of he simulaed eeh as can be seen in fig 1(C as well. ex sep is o locae he occlusal landmarks on he op of each ooh or a some seleced eeh and appl cubic spline echnique [9] o fi he landmark as he race line posiions in 3D. To locae he occusal landmarks, user needs o click on he 3D objec o locae he landmarks. ormall he sofware recognies he landmarks locaed b user on screen as screen coordinaes. Therefore, i is needed o call gluunprojec funcion from opengl librar o conver screen coordinaes ino o 3D model coordinaes. To appl he D-o-3D coordinae conversion on mouse coordinaes, several variables has o pass ino he funcions such as funcion for viewpor origin and exen, modelview Marix, projecion marix and he windows

2 screen coordinae which can be obained using some opengl funcions. [1] he denal cas b using he funcion provided in our sofware. Once ever ooh has been moved o mach he cas, hen he user can saved i and open i laer on wihou regisraion ever ime running. Translaion expression can be seen in (1. (A (B x1 + x T T +.. (1 x + x + + The roaion abou x-axis, -axis and -axis can be seen in (A, (B and (C according o Euler angles. [1] (C Fig. 1: Simulaed Teeh wih roos using 3D Sudio Max. A The enamel-crown emplae used in he denal lab. B 3D Crowns creaed from he emplae. C Side and op view of Simulaed Teeh wih roos. Once locaing occlusal landmarks, he cubic spline algorihm will be execued o generae race line and he landmarks. The cubic spline consiss of secions of polnomial curves conneced a hese landmarks. The polnomials of a given spline all have he same degree in X, Y and Z and fi he conrol poins as 3D line. The spline is obained b calculaing he second derivaives of he inerpolaing funcion a he abulaed poins based on he formulaion given in umerical ecipes in C. [11] The resul of fiing he 3D line wih cubic-spline inerpolaion can be seen as in Fig.. X Y Z X,, Y Z Y, Z X 1 cos( θ sin( θ cos( θ sin( θ cos( θ x sin( θ (A x sin( θ cos( x θx 1 sin( θ cos( θ sin( θ cos( θ 1 (B (C The scaling echnique can be expressed as (3 where S is he scaling value. S * x1 S * 1 S * 1 S S (3 S * x S * S * The regisraion ool ha has been developed for his projec le he user be able o move, roae and scale he eeh emplae o mach he denal cas as shown in Fig 3. Fig. 3(A shows he resul before he regisraion while Fig. 3(B shows he resul for moving, roaing and scaling individual eeh on he eeh emplae. Fig 3(C shows he final resul of image regisraion of eeh emplae on denal cas while program in Fig 3(D shows he cas wih 6 % ranslucen o enable user o see he roos inside he cas along wih he mechanic for moving he individual ooh. Fig. : Cubic spline fiing line on he occlusal landmarks The occlusal line was applied o calculae he saring posiion of he 3D simulaed eeh. Then, each ooh was ranslaed, roaed and scaled in o he righ posiion o fi (A (B (C 56

3 Afer simulaing he final posiions for eeh emplae, he nex sep is o compare he landmarks of he iniial simulaed eeh wih corresponding landmarks on he aligned eeh emplae as shown in Fig. 6. Fig. 6(A shows he resul of paring landmarks wih he denal cas while Fig 6(B shows he resuls of paring wihou denal cas. (D Fig 3: Simulaed eeh regisering on he denal cas.. Simulaed Teeh Alignmen (A (B Fig. 6: The resuls of paring landmarks..3 Denal Cas Warping based on 3D Thin lae Spline (A (B Fig. 4: Iniialiing he eeh alignmen. In he experimen of ooh alignmen wihou causing denal roos proruding ou of he gum in he denal cas, he firs sep is o seup he iniial posiion for simulaing eeh alignmen. esearchers have defined he occlusal landmarks in red for each ooh in he denal cas in o draw he race line and hen superimpose he eeh emplae on he denal cas as shown in Fig. 4(A o se he iniial eeh posiions before performing eeh alignmen as shown in Fig. 4(B Afer he iniialiaion, he nex sep is o se he final posiions for he eeh alignmen. This can be done b appling a eeh emplae wih geomeric ransformaion ino he proper alignmen as shown in Fig. 5(A. Comparison of he proper simulaed eeh alignmen and he denal cas can be seen as in Fig. 5(B. To generae he new denal cas, i becomes necessar o appl algorihms o creae he new model from he eeh movemen daa. One of he algorihms for his ask is Thin lae Spline (TS. Thin plae spline (TS [13] is he echnique for esimaing he random daa from paring ses of daa o consruc spline map from he affine facor for linear disorion and weighing facor for nonlinear disorion for image regisraion. The firs sep of TS is o solve (4 o calculae boh affine facor A and weighing facor W. K ˆ T ˆ W V O(4,4 A O(4,3 T O(r,w is ero marix of 4x4 and 4x3 respecivel. ˆ is a marix ˆ ha has rows and columns swiched (ransposed ˆ marix. ˆ is an iniial landmark posiion se marix before moving wih he addiional value 1 in ever row defined in (5 while K is a marix U (r defined as a funcion of disance beween each landmark r for image disorion b 3D Thin lae Spline process as defined in (6 and (7 respecivel, and V is an final landmark posiion se marix afer moving he landmarks defined in (8 wih is he number of sar-sop landmark pairs. (4 1 x ˆ [ Ones(1,, ] (5 1 x 1 (A (B Fig 5: Simulaing he final posiions for eeh emplae. 57

4 1 K U ( r( ( 1 U U 1( 1 ( 1 ( 1 1 ( 1 (6 e. g.: r (7 1, ( x x1 + ( 1 + ( 1 x V (8 x Fig. 7 shows he resul from 3D Thin lae Spline applied on he skeleon model wih 1 pairs of landmarks as demonsraed in [14]. Fig. 7(A showed he skeleal before appling 3D TS while Fig. 7(B shows he final resul afer 3D hin plae spline. (A (B Fig. 7.TS Applicaion in 3D on he Skeleal Model 3. esuls The experimen resuls show he denal cas before ooh alignmen as Fig. 8(A while Fig 8(B shows he final resuls afer performing ooh alignmen using 3D Thin lae Spline echnique. (A (B Fig. 8 Comparing he Teeh Alignmen esuls The resuls showing in Fig. 9 are he superimposiion of he final eeh alignmen wih he iniial denal cas in differen angles. The resul has shown ha here is no denal roo proruding ou of he old and he new denal cas as well. Fig. 9 The superimposiion of he resuls eeh alignmen However, here are some disorions on he individual eeh afer performing ooh alignmen due o he effec of 3D Thin lae Spline. The individual eeh are no supposed o be disored shapes since he are inelasic compared wih he gum secion. Furher developmen is o perform segmenaion on individual eeh as shown he case of markerconrolled mesh segmenaion [15] or auomaic segmenaion b using range images o deec boh denal arch and ooh inersices before segmenaion [16]. ex sep afer segmenaion is o applied proper 3D cubic spline inerpolaion algorihms on he model mesh o fill he missing pars of individual eeh. These algorihms would allow users o perform eeh alignmen wih minimied shape disorion on each ooh b separaing eeh ou of he model before performing 3D Thin plae Spline. 4. Conclusion We have proposed an approach o align eeh on he denal cas for orhodonic planning b appling 3D hin plae spline echnique. This mehod has used a se of eeh wih crowns and roos as a emplae o mach wih eeh on he denal cas o se he iniial posiions for landmarks on denal emplae. Afer performing eeh alignmen o se he final posiions for landmarks on denal plae, we perform 3D hin plae spline o creae he new model of denal cas. Our approach depends onl on he changing posiions of landmarks on he emplae wihou reling upon CT scan daa which are expensive imaging. The applicaion of image regisraion is o mach he denal emplae wih denal cas wih he bes fi wih available upper pars of eeh. The applicaion of 3D hin plae spline is o creae he new denal model afer orhodonic reamen o appl orhodoniss o predic he final resuls of he reamen in advance. 58

5 Acknowledgemen Thanks o Dr. Kanoknar Chinakanon and Orhodoniss eam a ADTEC for heir advices in he projec. Also hanks o all ADTEC & ECTEC s members for heir friendship and encouragemen. eferences [1] M. Meer, Comparison of peer assessmen raing (A index scores of plaser and compuer-based digial models, American Journal of Orhodonics and Denofacial Orhopedics, 18(4, 5, df [] C. Li. e. al, Orhodonic Simulaion and Diagnosis: An Enhanced Tool for Deniss, roc. 7 h IEEE Conf. on IEEE Engineering in Medicine and Biolog, Shanghai, China, 5, ieeexplore.ieee.org/iel5/1755/339/ pdf [3] B. heude e. al., An Evaluaion of he Use of Digial Sud Models in Orhodonic Diagnosis and Treamen lanning, Angle Orhodonis, 75(3, 5, [4]. Moohashi e. al., A 3D compuer-aided design ssem applied o diagnosis and reamen planning in orhodonics and orhognahic surger, European Journal of Orhodonics, 1(3, June 1999., Available online a ejo.oxfordjournals.org/cgi/reprin/1/3/63.pdf [5] A.A. Goshasb, A Ssem for Digial econsrucion of Gpsum Denal Cass, IEEE Transacions on Medical Imaging, 16(5, Ocober ieeexplore.ieee.org/iel3/4/1397/64757.pdf [6] H. Hassan e. al., A Complee Volumeric 3D Model of he Human Jaw, roc. of Compuer Assised adiolog and Surger (CAS, Berlin, German, June 5, ub_df/5/cmi_hossam5.pdf [7] A. Macchi e. al, Three-dimensional digial modeling and seup, American Journal of Orhodonics and Denofacial Orhopedics, 19(5, Ma 6, [8].Ensio e. al., The virual craniofacial paien: 3D jaw modeling and animaion. roc.11h Medicine Mees Virual eali, ew or Beach, California, USA, Januar 3, hp://graphics.usc.edu/cgi/pdf/papers/eciso_jawani m_mmv_fial.pdf [9] J. V. Hajnal, e. al, A regisraion and inerpolaion procedure for subvoxel maching of seriall acquired M images, Journal of Compuer Assised Tomograph, 19(, Februar 1995, [1] Mason Woo e. al., OpenGL rogramming Guide: The Official Guide o Learning OpenGL, Version 1.1, Second Ediion, (ew York, Addison-Wesle ublishing, Januar [11] W.H. ress. e. al., Cubic Spline Inerpolaion, umerical ecipes in C: The Ar of Scienific Compuing, (Cambridge, UK: Cambridge Universi ress, hp:// [1] E. Lengel, Mahemaics for 3D Game rogramming and Compuer Graphics, Second Ediion, (Boson, MA, USA: Charles iver Media, 3. [13] F. L. Booksein, rincipal Warps: Thin-lae Splines and he Decomposiion of Deformaions, IEEE Transacion on. aern Analsis and Machine Inelligence, 11(6, June 1989, Available online a www-cse.ucsd.edu/classes/sp3/cse5/booksein.pdf [14] C. Sinnhanaohin e. al, Image Warping based on 3D Thin lae Spline, roc. 4 h Inernaional Conf. on Informaion Technolog in Asia, Kuching, Malasia, 5, [15] Z. Chi e. al., Marker-conrolled ercepion-based Mesh Segmenaion, roc. 3 rd Iner Conf. on Image and Graphics, Hong Kong, China, Available online a graphics.pku.edu.cn/papers/download/mms.pdf [16] T. Kondo e. al., Tooh Segmenaion of Denal Sud Models Using ange Images, IEEE Transacion on Medical Imaging, 3(3, March 4, ieeexplore.ieee.org/iel5/4/8414/ pdf 59