Towards Automated Pose Invariant 3D Dental Biometrics

Transcription

1 Towards Automated Pose Invarant 3D Dental Bometrcs Xn ZHONG 1, Depng YU 1, Kelvn W C FOONG, Terence SIM 3, Yoke San WONG 1 and Ho-lun CHENG 3 1. Mechancal Engneerng, Natonal Unversty of Sngapore, , g @nus.edu.sg. Faculty of Dentstry, Natonal Unversty of Sngapore, School of Computng, Natonal Unversty of Sngapore, Abstract A novel pose nvarant 3D dental bometrcs frame s proposed for human dentfcaton by matchng dental plasters n ths paper. Usng 3D overcomes a number of key problems that plague D methods. As best as we can tell, our study s the frst attempt at 3D dental bometrcs. It ncludes a mult-scale feature extracton algorthm for extractng pose nvarant feature ponts and a trplet-correspondence algorthm for pose estmaton. Prelmnary expermental result acheves 100% rank-1 accuracy by matchng 7 postmortem (PM) samples aganst 100 ante-mortem (AM) samples. In addton, towards a fully automated 3D dental dentfcaton testng, the accuracy acheves 71.4% at rank-1 accuracy and 100% at rank-4 accuracy. Comparng wth the exstng algorthms, the feature pont extracton algorthm and the trplet-correspondence algorthm are faster and more robust for pose estmaton. In addton, the retreval tme for a sngle subject has been sgnfcantly reduced. Furthermore, we dscover that the nvestgated dental features are dscrmnatve and useful for dentfcaton. The hgh accuracy, fast retreval speed and the facltated dentfcaton process suggest that the developed 3D frame s more sutable for practcal use n dental bometrcs applcatons n the future. Fnally, the lmtatons and future research drectons are dscussed. 1. Introducton Dental bometrcs utlzes dental features for vctm dentfcaton. The use of teeth n postmortem (PM) dentfcaton has ganed ncreasng attenton over the last half-century. In forensc dentstry, the postmortem dentfcaton of a deceased ndvdual s based on the dental records when other evdences of the vctm (e.g. clothng, jewelry, pocket contents, gender, estmated age, heght, buld, color of skn, scars, moles, tattoos, abnormaltes, DNA, fngerprnts, rs etc.) are not avalable [1]. Due to the survvablty and dversty of dental features, dentfcaton by dental records outperforms that by DNA [] n severe condtons and mass dsasters because DNA s fragle that ts structure s easly altered or destroyed through tme, heat, chemcal or other forces. Tradtonally, the dentfcaton based on dental radograph comparsons s labor-ntensve and low n effcency. There are several computer-aded postmortem (PM) dentfcaton systems, such as the famous CAPMI [3] and WnID [4]. However, these systems are text-based searchng of records and do not provde hgh level of automaton as the feature extracton, codng, and mage comparson are stll carred out manually. Extensve efforts have been put nto the research towards automated two-dmensonal (D) radograph-based dental dentfcaton n the last decade. The D frame manly nvolves four steps [5]: mage segmentaton [6], feature extracton [6, 7], atlas regstraton [8, 9] and matchng [10, 11]. Fg. 1 Dental plasters an AM madbular plaster of a lve person a PM mandbular plaster of a dry skull However, many unsolved problems and challenges lmt the dentfcaton capablty and accuracy of the D methodology, ncludng: 1) radographs are often blurred mages, makng t very dffcult to extract the tooth contours accurately wth mnmal geometrc dstortons. Moreover ths process s often tme-consumng. Chen et al. [1] reported that 14 of the 5 subjects n ther database could not be dentfed due to poor mage qualty, varaton of the dental structure and nsuffcent number of AM mages for matchng. ) D radographs are projectons of 3D teeth. Dstortons n tooth shape arsng from dfferent magng angles are often sgnfcant, whch causes ncorrect matchng, namely tooth contours extracted from genune samples (pared PM and AM samples of a vctm) could not be matched together. In contrast, 3D dental dentfcaton based on the dgtzed dental plaster s able to overcome the /11/$ IEEE 1

2 AM Dentton AM Plaster Casts AM Dgtzed Model Decmaton AUTO PCA-plane Segmentaton PM Dentton PM Plaster Casts PM Dgtzed Model Decmaton Manual or AUTO PCA-plane Segmentaton(Experm ent I and II) Feature Pont Detecton Feature Pont Detecton Correspondence(algorthm comparson Experment III and IV) Fne Matchng Matchng Score Rank Lst Fg. An overvew of 3D dental bometrcs frame aforementoned lmtatons because 1) laser-scanned 3D dental plasters are hgh-resoluton surface data; ) projecton from 3D to D s not requred, thus no dstorton of the tooth shape occurs. The problem arsng from dfferent magng angles n 3D s what we call pose varaton problem whch we am to solve n ths paper. Trends n 3D dental bometrcs There has been much nterest and development n the nvestgaton of 3D dental bometrcs. Wth the development of real-tme scannng and 3D reconstructon technologes from D mages or vdeo sequences, the acquston of 3D models has become effortless and fast. 3D bometrcs s recevng ncreasngly more attenton than D bometrcs. For nstance, 3D face and ear recognton [13, 14] showed a promsng future. In addton, there are some emergng dental research s n assstng 3D reconstructon of teeth from CT mages [15] and 3D automatc teeth segmentaton for dental bometrcs [16]. Therefore, the present study ams to nvestgate 3D dentfcaton scheme n dental bometrcs by matchng dental plasters, such as the two shown n Fg. 1. Our paper makes the followng contrbutons: 1. We propose a novel 3D pose nvarant dental bometrcs frame. As best as we can tell, ours s the frst attempt at 3D dental bometrcs; all exstng s use only D mages. It overcomes a number of key hurdles n tradtonal D methods, thus makng our method more useful.. Our method s fast and could be fully automatc and thus can be used for rapd dentfcaton of large groups of people. It takes about 1.7 hours to retreve one subject from 33 subjects and 7 hours to retreve from 133 subjects (PC wth a.99 GHz Pentum 4 processor) [17]. In contrast, t takes only 5 mnutes on average to retreve one subject from 100 subjects. (PC wth Duo CPU.33 GHz 1.96GB RAM). 3. Our method s faster and more robust to pose varatons, whch s shown n Experment III and IV. 4. The dental arch (the curvng structure formed by the teeth n ther normal poston), tooth crown shape and the arrangement of teeth (teeth neghborng poston) are used drectly wthout projecton to D n our study. We dscover that the dscrmnablty of these dental features s useful and dstngushable enough to provde potental denttes among ndvduals wthout tedous sngle tooth segmentaton and contour extracton requrements. In addton, our method s more robust because we can use the dental arch for dentfcaton even when ndvdual teeth have been damaged.. System Approach An overvew of the 3D dental bometrcs frame s shown n Fg.. Ante-mortem (AM) database The AM database comprses 100 mandbular teeth samples scanned usng Mnolta VIVID 900 Surface Laser Scanner (Konca-Mnolta Corporaton, Osaka, Japan). Postmortem (PM) database The PM samples used to match wth the AM samples consst of 7 plasters of mandbular teeth whch are separately prepared and scanned by a dfferent nvestgator usng the same scanner wthout knowng the prevous scannng parameters. The ntal orentatons are seldom the same when genune samples are prepared and scanned by dfferent nvestgators. In addton, t s observed that even the appearances of the genune samples are dfferent as can be seen n Fg. 3. The PM sample n Fg. 3 looks smooth compared wth ts AM sample (Fg. 3 ), e.g. some holes are presented n the AM sample. The reason of these dfferences could be 1) the physcal dental plasters are made

3 by dfferent nvestgators; ) the dfferent resolutons of scannng; and 3) handlng errors durng scannng. To facltate effcent and accurate matchng of correspondng AM and PM samples, preprocessng of the dgtzed samples s requred to reduce the sze of the sample. The preprocessng comprses three operatons: 1) decmaton for both AM and PM samples; ) PCA-plane segmentaton for 100 AM samples; and 3) manual/ auto PCA-plane segmentaton for 7 PM samples (two experments). Decmaton for both AM and PM samples Each dgtzed sample s 14~30MB, comprsng of 340k~400k trangles and so s decmated by 90% to acheve hgher computatonal speed. Only 10% of the orgnal mesh s used for dentfcaton n our present study. We want to show that a compettve accuracy can be acheved by usng our proposed approaches even after such large-scale decmaton. The decmaton algorthm n [18] was utlzed. The decmated samples are shown n Fg. 3. Fg.3 Dfference n genune samples after decmaton AM sample of vctm I PM sample of vctm I PCA-plane segmentaton for 100 AM samples. For a large AM database, the automatc segmentaton s necessary. As best as we know, no fully automatc 3D segmentaton method acheves a promsng accuracy. Ths s the most tedous and tme-consumng step both n 3D and D dental bometrcs. Some researchers are ng towards ths goal n orthodontcs plannng studes. Kondo et al. [19] proposed a hghly automatc tooth segmentaton method. The dental arch s used to calculate the panoramc range mage. However, four reference ponts need to be manually specfed by users at the begnnng. Kronfeld et al. [0] presented a hghly automatc segmentaton method for separaton of teeth from the mesh model by applyng an actve contour algorthm. However, they reported that manual adjustment s stll needed when the ntal snakes are not approprately located at the transton between teeth and gum. Both methods fal where the boundary between tooth and gum s very smooth or n severe maloccluson cases. In ths study, nstead of sngle-tooth segmentaton, a fast automatc processng method s proposed for a large AM database to elmnate the bottom part of the plaster whch does not contan tooth nformaton. The Prncpal Component Analyss (PCA)-plane passng through the centrod of the plaster was calculated for each AM plaster as shown n Fg. 4. A dental plaster was segmented by ts PCA-plane nto the crown part and bottom part as llustrated n Fg.4 and Fg.4(c) respectvely. Manual/auto segmentaton for 7 PM samples. The gum and teeth for the PM samples are to be exactly segmented. It s manually performed because segmentaton for a PM sample, whch stll contans tooth gum, s dfferent from that for the mandbular teeth of a human skull as shown n Fg. 5. Most of the 3D segmentaton methods detect the nterstce between gum and teeth (gngval margn) by computng the ponts located at mnmum curvatures on meshes. If ths mnma rule s appled to madbular teeth of a skull as shown n Fg.5, the dash lne n Fg. 5 wll be detected whch s the nterstces between the teeth and alveolar bone, nstead of the expected sold lne whch s the real nterstce between teeth and gum (gngval margn) as shown n Fg. 5. Thus one porton of the tooth root, whch does not exst n ts correspondng AM plaster sample, wll be ncluded n PM sample. It wll produce error n the matchng process. Accordng to forensc dentsts experence, gum begns to decay wthn two or three days after death. Therefore, t s qute common to see PM samples wthout gums. Based on the aforementoned reasons, manual segmentaton s mplemented to segment madbular teeth of skulls accordng to the gngval margn. The segmented teeth are shown n Fg. 5(c). In addton, we also test fully automatc dentfcaton process n experment II by applyng the same PCA-plane segmentaton method to the 7 PM samples n experment II. (c) Fg. 4 PCA-plane segmentaton for an AM sample PCA-plane segmented tooth crown (c) bottom part of a dental plaster (c) Fg. 5 Manual segmentaton of a human skull a human skull the expected detected nterstces (sold lne) and the nterstces obtaned by mnma curvature rule (dash lne) (c) a set of manual segmented mandbular teeth of a human skull Feature pont detecton. The prncple of key feature pont or salent feature pont detecton s well-establshed n D mage processng [1, ]. Durng the last decade, several studes have extended t to the 3D doman [3-5]. Inspred by these studes, a mult-scale feature pont detecton algorthm s presented to extract feature ponts on dgtzed 3

4 dental surfaces. Fg.6 shows the dfferences between the exstng [3-5] and ths. The man steps are gven below. The frst step of the feature pont detecton s computng mult-scale representatons for dental mesh surface by applyng N Gaussan flters on t. For each vertex v n the surface model, the neghborhood Nv (, ) s pont x wthn dstance. As the Eucldean dstance gves better results than the geodesc dstance[3], equaton N ( v, ) x x v, x : vertex (1) s used for calculatng the neghborhood ponts. A representaton of the surface model Gv (, ) can be obtaned usng equaton x exp x v / ( ) xn ( v, ) Gv (, ). () exp x v / ( ) xn ( v, ) The second step of feature pont detecton s salency map computaton of dental mesh surfaces. To compute the mesh salency, the Dfference-of-Gaussan (DoG) for each vertex v s defned: DoG( v) G( v, ) G( v, k) (3) as the dfference between ts Gaussan-weghted representaton at scale ( ) and scale ( k ). DoG( v ) s actually a 3D vector whch denotes the dsplacement between dfferent scales. Sx scales were used σ {1ε, ε, 3ε, 4ε, 5ε, 6ε }, where ε s 0.3% of the length of the dagonal of the boundng box of the dental surface model. In order to promote the small number of dstnctve hgh peaks whle suppressng the large number of smlar hgh peaks n the salency map, each salency map s normalzed usng the non-lnear suppresson operator S proposed by Itt et al [1]. The thrd step s boundary effect removal. The followng algorthm s appled: 1) search for the boundary vertces ) search for the vertces wthn dstance σ 6 to the boundary vertces; 3) set the salency of all these vertces to zero. The fourth step s feature pont extracton. The salency map at each scale s processed such that each salency value s set to zero unless t s larger than the salency of 85% of ts neghborng vertces. The fnal salency map for the surface model s then obtaned by addng the salency map at all sx scales followed by a normalzaton process. Fnally, a vertex whose salency value s a local maxmum and larger than 60% of the global maxmum s detected as a salent pont. As shown n Fg. 6, edge ponts are detected as feature ponts by the exstng [3-5]. Usually, more feature ponts requre more computatonal tme n fndng correspondence at the next stage. The edge ponts are not feature ponts of tooth shape. The feature ponts detected by ths wth edge effect removal are shown n Fg. 6. Later, we compare the number of extracted ponts and the total tme n matchng genune samples and mposter samples. It s about sx tmes faster usng feature pont detecton algorthm n ths n matchng one PM sample to ts genune AM sample. The results are shown n Experment III n the next secton. Fg. 6 Feature ponts on dental meshes exstng ths Correspondence Let P and Q be the feature ponts extracted from the PM dental surface and the AM dental surface respectvely. For each feature pont p P' and q Q', the respectve salency value S( p ) and Sq ( ) were already calculated n the feature pont detecton stage. The followng trplet-constran algorthm s presented to fnd the best transformatons. Ths step s to fnd three feature ponts both n PM and AM samples wth smlar salency values and smlar relatve postons n Eucldean space for correspondence. For any feature pont p P', select the salent ponts q as potental correspondence f S( p) S( q), where ε s threshold value and set to be 0.1 n our tests. Therefore, a set of potental correspondences for each feature pont are determned and desgnated as (C(p 1 ),, C(p n )). For each par of feature ponts (p, p j ), choose any q C( p ), q C( p ) and set the pont par (q, q j ) j j whch mnmzes the dstance root mean squared (drms) error defned n equaton 1 n n drms ( P', Q') ( p p j q q j ) (4) n 1 j 1 as the assocated correspondence par, resultng n a set E of two-pont correspondences. E s then sorted n order of ascendng drms error. Any e E whose drms error s larger than a threshold drms s dscarded. For each two-pont correspondence e E, add another potental correspondence par (p k, q k ) whch mnmzes the drms error. In ths way, a set E3 of trplet-pont correspondence s formed. E3 s then sorted n order of ascendng drms error. Any e E3 whose drms error s larger than a threshold drms s dscarded. For each trplet-pont correspondence n E3, a rotaton and translaton matrx can be obtaned by Sngular Value 4

5 Decomposton (SVD) method and the correspondng coordnate root mean square (crms) error s then computed usng equaton 1 n crms ( P, Q) mn Rp t q. (5) Rt, n 1 Fnally, E3 s sorted n order of crms error. The frst trplet-pont correspondence n E3 correspondng to mnmal crms error s taken as the best trplet-pont correspondence. Fg. 7 shows the correspondence n genune samples. We compare the exstng [6] wth ths n Experment IV n the next secton. We show more robust characterstcs of ths regardng pose nvarant. Fg. 7 Trplet-pont correspondence n genune samples Fne Matchng Wth the estmated ntal poston by feature ponts correspondence, the fne comparsons are acheved by utlzng teratve closest pont (ICP) algorthm whch was frst developed by Besel and Mckay [7], Chen and Medon[8]. The results of genune matchng and mposter matchng of samples n Fg.8. The comparson shows that genune samples requre less teratons and the matchng error s much smaller. Fg. 8 Fne matchng of samples n Fg 8. genune samples mposter samples 3. Expermental Results Towards an automatc 3D dental dentfcaton system development, an automatc segmentaton method for PM samples are also expected. In our prelmnary study, t s nterestng to nvestgate the dentfcaton accuracy f all the process are automated. Therefore, two experements are desgned. Experment I Identfcaton process wth human nteracton n PM segmentaton Expermental results show fully correct prorty rankng accuracy based on matchng of 7 manually segmented PM samples to a database of 100 AM samples. At rank 1, 100% accuracy was acheved. The retreval performance curve, as shown n Fg. 9, s often used to evaluate the accuracy of the experment. The x axs represents the rank of retreved subjects. Identfcaton of 7 PM samples from 100 AM samples, each PM sample has 100 possble ranks. The y axs ndcates the cumulated number of correct retrevals at each rank. Experment II Fully automated dentfcaton process wthout human nteracton In Experment I, the PM segmentaton s the only manual part of the whole dentfcaton process. In Experment II, the same 7 PM samples are segmented usng the same PCA-plane segmentaton method for AM samples, namely a porton of gum has not been exactly segmented and attached to the teeth. Undoubtedly, the gum and plaster porton wll brng errors but the dentfcaton process becomes fully automated. We try to test dentfcaton accuracy under a rough segmentaton condton. The results are shown n Fg. 9. Fve out of seven acheved rank-1 accuracy(5/7=71.4%); 6 out of 7 acheved rank- accuracy (6/7=85.7%) and at rank 4, 100% accuracy was acheved. Experment III Feature pont extracton algorthms comparson We compare the number of extracted ponts and the computatonal tme n matchng two samples between the exstng algorthm and ths by usng the same computer. The ntal postons of the two samples are the same. We test both genune samples and mposter samples. The results are shown n Table 1. All the calculatons n ths paper nclude tme (second) for model mportng, vsualzaton. By usng ths, the computatonal total tme for matchng one par samples s reduced to 1/6~1/5 (139/=6.3;151/9=5.). Experment VI Correspondence algorthms comparson regardng pose nvarant characterstc We compare the smlar exstng greedy algorthm [6] wth ths. We show that ours s more robust to pose varatons. The results are shown n Table. The rotaton varaton s desgned to smulate the possble real rotatons n scannng. There s a base plane (almost a parallel plane to the prncpal plane we calculated n Fg.4) the plaster s placed on ths plane wth the teeth sde facng the scanner. Therefore, most rotaton varaton s around the normal to ths plane. Subsequently, we ncreased 30 degree every tme untl 360 degree rotaton. And we also test the mposter samples. Results show that ths always gave the correct 5

6 matchng whle the exstng [6] faled n most cases. The reason s the prevous s developed for general shapes, such as anmal shapes whch have vsual salent ponts at ear tps, mouths, claws, nose tps, falng n correspondng dental mesh wth hghly smlar convex and concave, saddle ponts. We have run further experments to show that our trplet-constrant algorthm s ndeed robust: we njected destructve noses, and our algorthm was stll able to correctly locate the correspondng ponts, even when sgnfcant nose was added. Due to page lmtaton, we are unable to gve further detals. Ths Exstng [6] Ths Rotaton 60 degree Exstng [6] Rotaton 90 degree Ths Fg.9 Comparsons of dentfcaton accuracy between a user-nterventon process (Experment I) and a fully automated process (Experment II) Exstng [6] Rotaton 180 degree Table 1 Feature extracton algorthms comparson (Experment III) Number of ponts Total tme (second) Genune Exstng AM I samples PM I 103 [3-5] Ths AM I 48 Imposter samples Exstng [3-5] PM I 30 AM II PM I 103 Ths AM II 74 9 PM I 30 Table -Experment VI Correspondence algorthms comparson Rotaton 30 degree Exstng [6] Ths 4. Conclusons and Future Work A novel pose nvarant 3D dental bometrcs frame has been proposed n ths paper. As best as we know, our s the frst attempt at 3D dental bometrcs; all exstng s use only D mages. A feature pont extracton algorthm and a trplet-correspondence algorthm are developed for pose estmaton of dental meshes. Expermental results show that the developed algorthms are faster and more robust than the exstng ones for pose estmaton. We also facltate the dentfcaton process by usng 3D dental features drectly, avodng tedous sngle tooth segmentaton and contour extracton processes. We dscover that the dscrmnablty of these dental features s enough to provde potental denttes. 100% rank-1 accuracy s acheved wth user nteracton n segmentaton by retrevng 7 subjects from 100 subjects. In addton, 6

7 71.4% rank-1 accuracy s acheved n fully automated dentfcaton process. The sngle subject retreval tme has also been sgnfcant reduced compare to that usng D dentfcaton frame. There s no 3D dental bometrcs benchmark database and the D database s not publcly avalable[9]. Although the comparsons to D are not based on the same dataset, our prelmnary s to provde a new vson nto dental bometrcs by usng 3D dentfcaton frame whch ams to overcome lmtatons n prevous D whle facltatng the whole dentfcaton process. The retreval effcency, accuracy and capablty have shown the feasblty of the proposed 3D frame. However, there are some lmtatons. The data used n ths are dental plasters whch only contan the tooth crown shapes. Thus the tooth root and dental (tooth fllngs) are not avalable whch are also useful for dental dentfcaton. The samples sze s stll small. Therefore, our future could nclude 1) sample acquston from Computed Tomography (CT) or Magnetc Resonance Imagng (MRI) mages; ) further testng on a larger database; and ) other effcent geometrc nvarant features extracton and correspondence algorthms development. 5. References [1] D.R. Senn, P.G. Stmson, Forensc Dentstry, Second Edton ed., CRC Press, Taylor& Francs Group, 010. [] Dental records beat DNA n tsunam IDs, New Scentsts, 516:1 (005). [3] R.M. Lorton L, Frdeman R, The computer-asssted postmortem dentfcaton (CAPMI) system: a computer-based dentfcaton program., Journal of Forensc Scence, (1988) [4] M. J, WnID3 dental dentfcaton system, n, 006. [5] H. Chen, A.K. Jan, Automatc Forensc Dental Identfcaton Handbook of Bometrcs (008) [6] A.K. Jan, H. Chen, Matchng of dental X-ray mages for human dentfcaton, Pattern Recognton, 37 (004) [7] H. Chen, A.K. Jan, Tooth contour extracton for matchng dental radographs, n: ICPR 004. Proceedngs of the 17th Internatonal Conference on Pattern Recognton, 004, pp [8] M.H. Mahoor, M. Abdel-Mottaleb, Automatc classfcaton of teeth n btewng dental mages, n: ICIP '04. Internatonal Conference on Image Processng, 004, pp [9] P.L. Ln, Y.H. La, P.W. Huang, An effectve classfcaton and numberng system for dental btewng radographs usng teeth regon and contour nformaton, Pattern Recognton, 43 (010) [10] O. Nomr, M. Abdel-Mottaleb, Fuson of matchng algorthms for human dentfcaton usng dental X-ray radographs, IEEE Transactons on Informaton Forenscs and Securty, 3 (008) [11] O. Nomr, M. Abdel-Mottaleb, Herarchcal contour matchng for dental X-ray radographs, Pattern Recognton, 41 (008) [1] H. Chen, A.K. Jan, Dental Bometrcs: Algnment and Matchng of Dental Radographs, IEEE Transactons on Pattern Analyss and Machne Intellgence, 7 (005) [13] L. Xaoguang, A.K. Jan, Deformaton Modelng for Robust 3D Face Matchng, Pattern Analyss and Machne Intellgence, IEEE Transactons on, 30 (008) [14] C. Hu, B. Bhanu, Effcent Recognton of Hghly Smlar 3D Objects n Range Images, Pattern Analyss and Machne Intellgence, IEEE Transactons on, 31 (009) [15] S. Tohnak, A.J.H. Mehnert, M. Mahoney, S. Crozer, Syntheszng Dental Radographs for Human Identfcaton, J. Dent. Res., 86 (007) [16] D. Maraj, S.D. Wolthusen, C. Busch, Teeth Segmentaton and Feature Extracton for Odontologcal Bometrcs, n: Intellgent Informaton Hdng and Multmeda Sgnal Processng (IIH-MSP), 010 Sxth Internatonal Conference on, 010, pp [17] H. Chen, AUTOMATIC FORENSIC IDENTIFICATION BASED ON DENTAL RADIOGRAPHS, n: Department of Computer Scence and Engneerng, PhD Thess, Mchgan State Unversty, 007. [18] W.J. Schroeder, J.A. Zarge, W.E. Lorensen, Decmaton of trangle meshes, SIGGRAPH Comput. Graph., 6 (199) [19] T. Kondo, S.H. Ong, K.W.C. Foong, Tooth segmentaton of dental study models usng range mages, Medcal Imagng, IEEE Transactons on, 3 (004) [0] T. Kronfeld, D. Brunner, G. Brunnett, Snake-based segmentaton of teeth from vrtual dental casts, Computer-Aded Desgn and Applcatons, 7 (010) [1] L. Itt, C. Koch, E. Nebur, A model of salency-based vsual attenton for rapd scene analyss, IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 0 (1998) [] D.G. Lowe, Dstnctve mage features from scale-nvarant keyponts, Internatonal Journal of Computer Vson, 60 (004) [3] C. Lee, A. Varshney, D. Jacobs, Mesh salency, n: SIGGRAPH '05: ACM SIGGRAPH 005 Papers, ACM, 005, pp [4] Y.-S. Lu, M. Lu, D. Khara, K. Raman, Salent crtcal ponts for meshes, n: SPM 007: ACM Symposum on Sold and Physcal Modelng, June 4, June 6, 007, Assocaton for Computng Machnery, Bejng, Chna, 007, pp [5] U. Castellan, M. Crstan, S. Fanton, V. Murno, Sparse ponts matchng by combnng 3D mesh salency wth statstcal descrptors, n, Blackwell Publshng Ltd, 9600 Garsngton Road, Oxford, OX4 XG, Unted Kngdom, 008, pp [6] N. Gelfand, N.J. Mtra, L.J. Gubas, H. Pottmann, Robust global regstraton, n: Proceedngs of the thrd Eurographcs symposum on Geometry processng, Eurographcs Assocaton, Venna, Austra, 005, pp [7] P.J. Besl, A Method for Regstraton of 3-D Shapes, IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, 14, NO. (199) [8] M. Chen, Object modelng by regstraton of multple range mages, 1991 IEEE Internatonal Conference on Robotcs and Automaton, Proceedngs.,, vol.3 (199) [9] CJIS dvson-adis, dgtzed radographc mages (database), (August 00). 7