Research Article Automatic Tooth Segmentation of Dental Mesh …downloads.hindawi.com/journals/bmri/2015/187173.pdf · 2019-07-31 · Research Article Automatic Tooth Segmentation

Research ArticleAutomatic Tooth Segmentation of Dental Mesh Based onHarmonic Fields

Sheng-hui Liao1 Shi-jian Liu1 Bei-ji Zou1 Xi Ding2 Ye Liang3 and Jun-hui Huang4

1School of Information Science and Engineering Central South University Changsha 410083 China2Department of Stomatology First Affiliated Hospital of Wenzhou Medical University Wenzhou 325000 China3Department of Stomatology Xiangya Hospital of Central South University Changsha 410008 China4Xiangya Stomatological Hospital of Central South University Changsha 410008 China

Correspondence should be addressed to Bei-ji Zou bjzouvip163com

Received 27 September 2014 Accepted 6 January 2015

Academic Editor Ilker Ercan

Copyright copy 2015 Sheng-hui Liao et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

An important preprocess in computer-aided orthodontics is to segment teeth from the dental models accurately which shouldinvolve manual interactions as few as possible But fully automatic partition of all teeth is not a trivial task since teeth occur indifferent shapes and their arrangements vary substantially from one individual to anotherThe difficulty is exacerbated when severeteeth malocclusion and crowding problems occur which is a common occurrence in clinical cases Most published methods inthis area either are inaccurate or require lots of manual interactions Motivated by the state-of-the-art general mesh segmentationmethods that adopted the theory of harmonic field to detect partition boundaries this paper proposes a novel dental-targetedsegmentation framework for dental meshes With a specially designed weighting scheme and a strategy of a priori knowledgeto guide the assignment of harmonic constraints this method can identify teeth partition boundaries effectively Extensiveexperiments and quantitative analysis demonstrate that the proposed method is able to partition high-quality teeth automaticallywith robustness and efficiency

1 Introduction

In recent years much effort has been spent in developingcomputerized systems for clinical and research applicationsin dentistry Most computerized algorithms for orthodonticdiagnostic and treatment require 3D dental mesh modelswhich are often needed to extract move and rearrangeteeth for simulation of the treatment outcome Thus teethsegmentation is an important step in many automatedand semiautomated computer-based dental software pack-ages

However tooth segmentation on dental meshes remainsa difficult task [1] Dental meshes from patients often haveteeth crowding problems when adjacent teeth aremisalignedthus making the interstices between them irregular anddifficult to distinguish Various tooth shapes make outliningtooth contours difficult Artifacts resulting from scanning or

model-making errors on commonly obtained clinical meshesmake teeth segmentation more challenging

General mesh segmentation approaches are not directlysuited for segmenting dental meshes because they lackadjustments to handle complex tooth shapes and teetharrangements Other segmentation approaches proposed tohandle dentalmeshes have shortcomings such as being eitherlabor-intensive or not sufficiently accurate [2] Althoughseveral commercial products in this field are available suchas ldquo3Shaperdquo their user interactions are intensive and signifi-cantly influence the accuracy of results

Many tooth segmentation methods prefer to use surfacecurvature when identifying potential tooth boundaries asthey follow the most widely cited mesh segmentation cri-terion the minima rule which states that human percep-tion usually divides a surface into parts along the concavediscontinuity of the tangent plane [3 4] However surface

Hindawi Publishing CorporationBioMed Research InternationalVolume 2015 Article ID 187173 10 pageshttpdxdoiorg1011552015187173

2 BioMed Research International

curvature estimation is typically error-prone for real-worldnoisy models for example curvature distribution on clinicaldental models is generally complicated and irregular (seeSection 2 for further description)

This paper aims to develop an automatic and robustmethod for segmentation of digital dental models Motivatedby state-of-the-art general interactive mesh segmentationmethods [5ndash8] we developed a convenient and efficient den-tal segmentation framework which identifies tooth bound-aries by a dental-targeted harmonic field This approach hasthree major benefits

(1) The dental-targeted harmonic field is robust to vari-ous tooth shapes complex malocclusion and crowd-ing problems and is insensitive to noise with mini-mum parameter considerations

(2) The dental-targeted harmonic field can guaranteeclosed tooth boundary extraction from dental meshunlike curvature-based methods needing complexconnectivity and morphologic operations in mostcases

(3) The whole dental segmentation procedure is auto-matic which requires no user interaction to generateteeth with accurate and high-quality cutting bound-aries

2 Related Work

This paper focuses on dental mesh segmentation We intro-duce general mesh segmentation methods before dentalspecific methods The theory of harmonic field will be givenat the end of the section

21 General SegmentationMethod Numerousmesh segmen-tation approaches have been proposed in computer graphicsSome of these algorithms are automated like clustering[9] random walk [10] shape diameter function [11] fittingprimitives [12] and fast marching watershed [13] Most ofthese methods aim to partition different regions based onsimilarity measures [14] but defining a semantic subarea oftooth with various shapes remains a challenging task andnone of these methods is directly suitable for our specificapplication

Recently sketch-based interactive mesh segmentationmethods have become very popular [5ndash8] Most of thesemethods employ harmonic field theory and similar userinterfaces but they are different in computational weightingscheme and constraint styles Interested readers should referto literature such as surveys of comparisons between thesesketch-based methods [15] These methods have good per-formance in general mesh segmentation but require time-consuming and error-prone user interaction when dealingwith special and complicated tooth shapes and arrange-ments Furthermore they cannot produce high-quality cut-ting boundaries in cases where no obvious concave regionsare near the location of interaction

While our method also employs the harmonic fieldfor segmentation it fully exploits the dental characteristics

(see Section 33) which makes the proposed method smartaccurate and more robust in tooth partition

22 Dental-Targeted Segmentation Method A large groupof dental segmentation approaches prefer to use surfacecurvature to identify tooth boundaries The typical routinecan be summarized as follows

(1) Curvature estimation principal curvatures includingminimum principal curvature [16ndash19] and mean principalcurvature [1] are used to measure the surface property quan-titatively (2) Teeth-part rough locating though not alwaysnecessary this is a plane-estimating technique based on PCAthat produces a cutting plane to separate gingiva and teethpart introduced in previous works [1 20] We also involvethis step in our framework but the method we used is moreconvenient and effective (see Section 32) (3) Thresholdinga curvature threshold value is inevitably needed to separatepotential tooth boundary regions from the rest when usingcurvature fields for boundary identificationThat value can beobtained either interactively such as when using an intuitiveslider [16] or by taking a result of an experiential equationor even plugging in a constant preset number [19 20] Infact a global threshold value used in this mandatory step isone of the major drawbacks it can significantly influence thisentire solution because the thresholding generally cannotappropriately distinguish target objects from the rest of theregion leading to either over- or undersegmentation (4)Potential boundary region refining because the curvaturefield introduces lots of useless features in tooth crown regionsand is sensitive to noise in identifying tooth boundarymethods [1 17 19] using a morphologic operation willfurther refine the region obtained by thresholding For somecomplicated dentalmodels however (eg in cases of adjacentteeth crowding when the interstices in between are irregularand difficult to distinguish) the potential tooth boundaryregion may still be incomplete even after morphologic oper-ation (5) Boundary locating and refining as proposed inprevious works [1 16 17 19] a skeleton operation is usedto extract boundaries from potential regions However teethwith such boundaries are unacceptable for precise clinicaltreatment planning Refinements should be carried out tomake sure the boundary of each tooth is both smooth andprecise [1] More seriously the extracted boundaries couldbe incomplete (eg opened) so special refinement shouldbe taken to close the opened boundaries before attemptingsmooth and precise operations All such proceduresmake theentire framework tedious and complicated

Kondo et al introduced a fully automatic algorithm tosegment tooth from dental models using two range images[20] However they used a rectangular inspection spoketo cut the model which will introduce inaccurate cuts forsevere malocclusions Kronfeld et al proposed a snake-basedapproach that starts with an initial contour on the gingiva andevolves through a feature attraction field [21] The cusps ofeach tooth are then selected to start a local tooth contour andevolve until each tooth bottom is reached The approach isautomatic but may not produce good results when the modelhas boundary noises that interrupt a feature field defined bythe curvature information

BioMed Research International 3

As another option interactive dental partition meth-ods [22 23] allow users to select several boundary pointsinteractively for segmentation Geodesics are then generallyused to connect two adjacent control points The interactivepartition procedures are intuitive and capable of segmentingcomplicated dental models but the shortcomings are alsoquite obvious for example users would have to rotate ortranslate multiple times to carefully specify particular markpoints to generate one accurate tooth boundary Such tediousand time-consuming experiences certainly are undesirableand impracticable for clinical application

Recently Zou et al proposed an interactive tooth parti-tion method based on harmonic field [24] The method hasgreat flexibilities which benefit from their specially designeduser interfaces But the employed harmonic field is onlyldquotooth-targetrdquo in other words only one tooth could be identi-fied manually one time and the whole dental mesh has to beprocessed multiple times to finish the whole segmentationIn contrast our novel segmentation framework is able tosegment all teeth only once under a uniform harmonic fieldautomatically which greatly improves the partition efficiency

23 Harmonic Field In mathematics a harmonic field on 3Dmesh 119872 = (119881 119864 119865) is a scalar field attached to each meshvertex and satisfies ΔΦ = 0 where119881 119864 and 119865 denote vertexedge and face set of 119872 respectively The symbol Δ is theLaplacian operator subject to particular Dirichlet boundaryconstraint conditions For example 0 and 1 are used asminimum and maximum constraints in most harmonic fieldcomputations The standard definition of Laplacian operatoron a piecewise linear mesh119872 is the operator

ΔΦ119894= sum

(119894119895)isin119864

119908119894119895(Φ119894minus Φ119895) (1)

where 119908119894119895is a scalar weight assigned to the edge 119864

119894119895 This

Poisson equation ΔΦ = 0 can be solved by the least-squaressense which leads to

119860Φ = 119887

119860 = [119871

119862]

119887 = [0

1198871015840]

(2)

where 119871 is the Laplacian matrix given by

119871119894119895=

sum

119896isin1198731(119894)

119908119894119896 if 119894 = 119895

minus119908119894119895 if (119894 119895) isin 119864

0 otherwise

(3)

where 1198731(119894) is the 1-ring neighbor set of vertex 119894 119862 and

1198871015840 are matrix and vector respectively standing for theconstraints in the harmonic field Different weighting schemeand constraints will lead to a different kind of harmonic fieldFor example let 120572

119894119895and 120573

119894119895denote angles opposite to 119864

119894119895

respectively the standard cotangent-weighting scheme willbe given by

119908119894119895=

cot120572119894119895+ cot120573

119894119895

2 (4)

leading to a smooth transiting harmonic field suited toapplications like mesh deformation [25] and direction fielddesign [26] However the standard weighting scheme cannotidentify the local shape variation this drawback makes it nolonger suitable for segmentation purposes

Our method utilizes a novel dental-targeted weight-ing scheme which preserves the nice property of classiccotangent-weighting schemewhile having the ability to sensethe concave feature for each tooth boundary A specialconstraint assigning strategy is also proposed accordingly

3 Materials and Methods

Since human teeth occur in different shapes and theirarrangements vary substantially from one individual toanother careful selection of test datasets is necessary intooth segmentation studies We evaluate 60 sets of dentalmodels including both low and up jaw of varying complexityand precision For instance teeth on some of the dentalmeshes have severe malocclusion and crowding problemwhile others may be absent from the jaw These datasetswere accumulated in the years between 2010 and 2014 atXiangya Hospital of Central South University and the FirstAffiliated Hospital of Wenzhou Medical University frompatients who need medical treatments such as orthodonticsor dental implantation These models are acquired by a3D dental scanner or intraoral scanner with accuracy of001mmndash01mm Each of the dental meshes is guaranteedto be manifold and nondegenerate as preprocessed by thesoftware supplied by the scanner manufacturers

These dental mesh models are taken as input of theproposed framework as demonstrated in Figure 1 and theoutput results are segmented individual teeth

As illustrated in the block diagram teeth anatomicalfeature points and the occlusal plane employed as the priorknowledge of following computation are firstly identified(Section 31) Secondly a rough locating procedure for teethparts is performed and a cut plane is found to automaticallyremove the gingival region of the dental model (Section 32)Then dental-targeted constraint points can be initialized toprepare for the harmonic field calculation Once a harmonicfield is generated an optimal isoloop for each tooth can beextracted as a tooth boundary (Section 33)

31 Dental Features Identification We use a priori knowledgeof feature points on human teeth and occlusal plane inour method The feature points consist of cusps on thecanines premolars and molars and point to the end of theincisal edge on incisors Identification of these points andthe occlusal plane is a fundamental dental process A robustcomputer-aided automatic identificationmethod [27] is usedin our framework to identify them as demonstrated by whitespheres and a blue plane in Figure 2


Start

Boundary extraction

Dental features identification

Automatic cutting of gingiva

Constraint points initialization

Harmonic field computing

End

Output

Input

Figure 1 Block diagram of our proposed framework

(a)

(b)

Figure 2 Automatically identified features of a dental model Top row from left to right indicates anatomical feature points onmolar incisorcanine and premolar bottom row illustrates the occlusal plane


(a)

10

(b) (c)

Figure 3 Steps of gingiva cutting Images from left to right illustrate (a) the inappropriate cutting when multiple intersection loops areacquired (b) the acquisition of only one intersection loop (c) the desirable cutting attained when the variance energy stops decreasing

The inspection spoke-based strategy [20] is then em-ployed to automatically separate these teeth feature pointsinto different groups This approach first fits a curve of thetooth-based dental arch and then detects inspection spokesalong the dental arch Instead of using the inspection spokesto do tooth segmentation which may lead to unsatisfactorycut results we utilize them to separate those feature pointsinto different groups (each group corresponding to onetooth)

In addition these feature point groups are arranged inorder along the direction of the dental arch And we furtherclassify them into two bigger point sets that is one featurepoints set Ω

1 consisting of groups with odd indexes of

1 3 5 and the other set Ω2 consisting of alternating

groups with even indexes of 2 4 6 These two featurepoint sets will be employed as part of constraints in thecomputation of the dental-targeted harmonic field

32 Automatic Cutting of Gingiva We seek a cutting plane toroughly separate the teeth parts from the gingiva region toaccelerate following harmonic field computation The basicidea is similar to earlier methods [1] but we have made itmore efficient Initially the plane is located at the positionof the occlusal plane and then moved iteratively towards thebottom of the dental model along the normal direction Thedistance moved in each step is a small constant value 119889 (wenoticed that 119889 = 1mm meets the requirement of almost alldental models in our experiments) During the movementeach plane 119875

119894(1 le 119894 le 119873 119873 is the count of move steps)

will intersect with dental mesh and generate one or moreintersecting loops

At the beginning a multiple-loop intersection will bedetected as shown in Figure 3(a) which implies that the planeis intersecting with the teeth parts or outliers The iteration iscontinued until only one-loop intersection is acquired as thefirst meaningful loop shown in Figure 3(b) Afterwards for

each119875119894 the variance energy ofminimumprincipal curvature

120601119894 is used to evaluate the intersection

120601119894=

1

119899 minus 1

119899

sum

119896=1

(119888min119896 minus 119888minavg)2

(5)

where 119899 is the number of mesh points on the intersectionloop 119888min119896 denotes the minimum principal curvature ofpoint 119896 and 119888minavg indicates the average minimum principalcurvature of all points

When all one-loop intersections are found their corre-sponding variance energies are linearly mapped to axes 01 The results are shown as colors ranging from red to bluein Figure 3(b) The normalized variance energy of each 119875

119894

is utilized to select the best cutting plane because we noticethat the energy is high at the teeth parts (larger than 05generally) and decreases towards the gingiva region Basedon this observation we select the cutting plane by checkingthe normalized variance which is less than 05 in eachstep until it stops decreasing In the extreme situation themovement stops when there is no intersection of the planewith the dental model in this case we use the last one-loopintersection plane as the cutting plane

Finally useless dental parts (eg the transparent gingivaregion in Figure 3(c)) are clipped out using the cutting planeIn addition the mesh points on the loop are recorded as partof constraints in the following harmonic field computation(see Section 33)

Procedures described in this section are valuable for high-precision dental meshes because large percentages of uselessmesh can be removed to relieve the burden of harmonic fieldcomputation Although general mesh decimation processescan be also used to reduce complexity of mesh along withthe global decimation quality of teeth surfaces will receivedamage as well

33 Harmonic Field Calculation We adopted the basic ideaof utilizing harmonic field for tooth boundary identification


(a) (b)

Figure 4Harmonic fields under different weighting schemesThe images demonstrate harmonic field under (a) the special weighting schemeand (b) cotangent-weighting scheme respectively

[24] which makes use of a special weighting scheme givenby

119908lowast

119894119895=

120574119894119895(cot120572119894119895+ cot120573

119894119895)

2 (6)

The properties of this kind of harmonic field can besummarized as follows which is the reason we chose it forthe tooth partition

(i) Smoothness As a method derived from classic cotangent-weighting scheme the harmonic field successfully inheritsthe smooth transition propertyThat is the transitions of ver-tex scalars from minimum to maximum Dirichlet boundaryvalues are stable and smooth in both concave and nonconcaveregions

(ii) Shape-Awareness The harmonic field has strong aware-ness of concave creases and seams Therefore the uniformlysampled isolines which are dense at concave regions cannaturally form the candidates of partition boundaries

Figure 4 demonstrates differences between two harmonicfields by mapping field scalars whose values range from 0 to1 and the colors range from red to blue Figure 4(a) showsthe harmonic field using the special weighting scheme whileFigure 4(b) shows the harmonic field with the same con-straints but uses the standard cotangent-weighting schemeUniformly sampled isolines on mesh are also extracted andcolored to indicate field variance

Our new dental-targeted segmentation framework isdifferent from previous tooth-targeted study [24] in twomajor aspects The first one is that the constraints of den-tal harmonic field are automatically identified as proposedabove And the second one is our special designed assignmentof constraints for dental teeth segmentation as introduced inthe following which is the key to segment all teeth only onceunder a uniform harmonic field computation automatically

For Dirichlet constraints of the dental-targeted harmonicfield there are two major considerations (1) the method forchoosing constraint points on dentalmeshes and (2) the valueof constraint points assigned in harmonic field computation

For the first issue we choose constraint points by takinga priori knowledge of human teeth into consideration Inother words the teeth feature points setsΩ

1andΩ

2 and the

mesh points set Ω3 on the gingiva cutting plane are used as

constraintsFor the second issue the maximum and minimum

constraint values 1 and 0 are assigned to the teeth featurepoints sets Ω

1and Ω

2 separately That is feature points on

the same tooth will have the same constraint value either 0 or1 but feature points on the neighbor teeth will have differentconstraint value either 1 or 0 as demonstrated by red and bluespheres in Figure 5(a) respectively

In addition a middle constraint value of 05 is assignedto the mesh points set Ω

3 on the gingiva cutting plane (as

green contour and points depicted in Figure 5(a))As demonstrated by Figures 5(b) and 5(c) the resulting

harmonic field using our assignment strategy of a prioriknowledge guided constraints has much better distinguish-ing tooth partition patterns for all teeth compared to onewithout suchmiddle constraint value which is a conventionalcase in many other harmonic field-based methods

According to the constraints assignment entities ofmatrix 119862 and vector 1198871015840 introduced above can be set solving(2) Specifically if we denote points assigned with constraintvalues 0 05 and 1 by 119901min 119901mid and 119901max on mesh 119872respectively and put them into a list 119878 then 119888

119894119895isin 119862 (1 le 119894 le

119899 1 le 119895 le 119898) and 119887119894isin 1198871015840 (1 le 119894 le 119899) can be given by the

following equations respectively

119888119894119895=

119908 for (119894 119895) | 119872 (119901119894) = 119895

0 otherwise(7)

119887119894=

119908 for 119894 | Type (119901119894) = 119901max

05119908 for 119894 | Type (119901119894) = 119901mid

0 for 119894 | Type (119901119894) = 119901min

(8)

where 119908 is a large constant value (1000 in our experiments)119899 and119898 denote number of vertexes in 119878 and119872 respectivelyand 119901

119894(0 le 119894 le 119899 minus 1) is an element of 119878 whose index is 119894


(a) (b)

(c)

Figure 5 Assignment of constraint points on dental mesh for harmonic field computation (a) Constraints assigned in our proposedmethod(b) Resulting harmonic fieldwith intersecting contourmesh points as constraints (c) Resulting fieldwithout intersecting contourmesh pointsas constraints

119872(119901119894) denotes the index of 119901

119894in 119872 Type(119901

119894) and returns

the type of 119901119894

Modern sparse Cholesky factorization and modificationsoftware package [28 29] are used to solve the linear system(ie (2)) efficiently which results in the dental-targetedharmonic field showed in Figure 5(b)

With our objective almost accomplished all that is left tosample and uniformly extract is a number of isolines from theharmonic field as shown by colored loops in Figure 6(a) andselect optimal isoloops as the tooth boundaries (eg whiteloops in Figures 6(b) and 6(c)) Andweuse the voting strategyproposed in previous work [5] to automatically select the bestisoloop

4 Experiments and Results

We have tested our approach on 60 dental mesh models (lowand up jaw) of varying complexityThedatasets included laserscans of plaster models obtained from different commercial

scanners Our approach was performed with reasonableaccuracy on almost all of these models Figure 7 illustrates12 of these dental models some of which show teeth withsevere crowding problems while others may be absent fromthe jaw For each of the 12 models in Figure 7 three imagesare used to illustrate states during the partition namely (1)the input original mesh (2) the clipped dental mesh attachedwith dental-targeted harmonic field and (3) the segmentednonteeth part (colored with red) and individual teeth (withother colors) as output

To provide a ldquoground truthrdquo dental segmentation bench-mark for quantitative evaluation we asked two dentistseach with the necessary training and sufficient practice timeto identify the boundary of each tooth manually on allexperimental models For each tooth all marked contoursfrom the two dentists were averaged to produce a groundtruth The boundaries of our segmented teeth were thencompared with the ground truth results usingmean errors asshown in Figure 8 The average mean error of our approach


(a) (b) (c)

Figure 6 Tooth boundaries identification (a) isoloops evenly extracted from generated harmonic field (b and c) two perspectives of theextracted optimal isoloops as the tooth boundaries

Figure 7 The segmentation results of our approach on various dental meshes with crowding problems

within the 60 models is about 01mm which was approvedby the dentists

We also recorded the time consumed by our approachon different scales of dental models (measured with a

number of mesh points and faces) during experiments asshown in Figure 9 including the time for (a) dental basecutting (b) harmonic field precomputing (c) harmonic fieldupdating (d) boundary extraction and (e) total time for


0002004006008

01012014

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59

Figure 8 The mean errors of our tooth segmentation resultscompared to manually labeled ground truth of all 60 models Thehorizontal axis denotes 60 cases in our experiments and the verticalaxis denotes the mean errors correspondingly

0

1

2

3

4

5

6

7

8

Time (a)Time (b)Time (c)

Time (d)Time (e)

65468

130944

76566

153092

73679

147354

28398

56792

26127

52206

26710

53420

44624

89164

35414

70775

73844

147684

87297

174590

83338

166672

70762

141520

Figure 9 Time statistics of our dental mesh segmentation Thetiming is recorded in seconds for (a) dental base cutting (b)harmonic field precomputing (c) harmonic field updating (d)boundary extraction and (e) total time of dental segmentation Thehorizontal axis illustrates different mesh model scales by numberof mesh points and faces The vertical axis illustrates the timeconsumption for procedures in the segmentation framework

dental segmentation All experiments were carried out on acommon PC with Intel Core Quad-Core Processor 267GHzwith 4GBmemoryThe total segmentation time of one dentalmodel in our experiments is usually less than 7 seconds Bycontrast the popular commercial software ldquo3Shaperdquo oftentakes manyminutes of interaction to segment one model theaccompanying method [1] often takes 1 or 2 minutes

5 Conclusions

For this paper we studied the fundamental problem ofautomatically segmenting teeth in dental mesh models intoindividual tooth objects With a specially designed weightingscheme and a strategy of a priori knowledge to guide the

assignment of constraints we built a novel dental-targetedharmonic field which is able to segment all teeth only onceunder a uniform harmonic field computation automaticallyThis harmonic field is robust to various tooth shapes complexmalocclusion and crowding problems and can guaranteeclosed tooth boundary extraction from dental mesh unlikecurvature-based methods needing complex connectivity andmorphologic operations in most cases

Extensive experiments and quantitative analysis demon-strated the effectiveness of the method in terms of accuracyrobustness and efficiency We plan to integrate this conve-nient dental segmenting algorithm in a computer-aided 3D-orthodontic system that is suitable for deployment in clinicalsettings

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Authorsrsquo Contribution

Sheng-hui Liao and Shi-jian Liu are co-first authors theycontributed equally to the work

Acknowledgments

This study was supported by the National Natural ScienceFoundation of China (no 60903136 no 61173122 and no81000461) the Doctoral Fund of Ministry of Educationof China (no 20130162130001) and the Cultivate StrategicEmerging Industries Special Foundation of Changsha City(no K1406035 11)

References

[1] K Wu L Chen J Li and Y Zhou ldquoTooth segmentation ondental meshes using morphologic skeletonrdquo Computers andGraphics vol 38 no 1 pp 199ndash211 2014

[2] L Fan L Liu and K Liu ldquoPaint mesh cuttingrdquo ComputerGraphics Forum vol 30 no 2 pp 603ndash611 2011

[3] Y Lee S Lee A Shamir D Cohen-Or and H-P Seidel ldquoMeshscissoring withminima rule and part saliencerdquoComputer AidedGeometric Design vol 22 no 5 pp 444ndash465 2005

[4] Z Ji L Liu and Z Chen ldquoEasy mesh cuttingrdquo in ComputerGraphics Forum vol 25 pp 283ndash291 Blackwell London UK2006

[5] Y Zheng C-L Tai and O K-C Au ldquoDot scissor a single-click interface for mesh segmentationrdquo IEEE Transactions onVisualization and Computer Graphics vol 18 no 8 pp 1304ndash1312 2012

[6] M Meng L Fan and L Liu ldquoICutter a direct cut-out tool for3D shapesrdquo Computer Animation and Virtual Worlds vol 22no 4 pp 335ndash342 2011

[7] Y Zheng and C-L Tai ldquoMesh decomposition with cross-boundary brushesrdquoComputer Graphics Forum vol 29 no 2 pp527ndash535 2010

[8] O Kin-Chung Au Y Zheng M Chen P Xu and C-LTai ldquoMesh segmentation with concavity-aware fieldsrdquo IEEE


Transactions on Visualization and Computer Graphics vol 18no 7 pp 1125ndash1134 2012

[9] S Katz and A Tal ldquoHierarchical mesh decomposition usingfuzzy clustering and cutsrdquo ACM Transactions on Graphics vol22 no 3 pp 954ndash961 2003

[10] Y-K Lai S-M Hu R R Martin and P L Rosin ldquoRapidand effective segmentation of 3D models using random walksrdquoComputer Aided Geometric Design vol 26 no 6 pp 665ndash6792009

[11] L Shapira A Shamir andD Cohen-Or ldquoConsistentmesh part-itioning and skeletonisation using the shape diameter functionrdquoVisual Computer vol 24 no 4 pp 249ndash259 2008

[12] M Attene B Falcidieno andM Spagnuolo ldquoHierarchicalmeshsegmentation based on fitting primitivesrdquoVisual Computer vol22 no 3 pp 181ndash193 2006

[13] A F Koschan ldquoPerception-based 3D triangle mesh segmenta-tion using fast marching watershedsrdquo in Proceedingsof the IEEEComputer Society Conference on Computer Vision and PatternRecognition vol 2 pp II-27ndashII-32 IEEE June 2003

[14] A Shamir ldquoA survey on mesh segmentation techniquesrdquo Com-puter Graphics Forum vol 27 no 6 pp 1539ndash1556 2008

[15] L Fan M Meng and L Liu ldquoSketch-based mesh cutting acomparative studyrdquo Graphical Models vol 74 no 6 pp 292ndash301 2012

[16] Y Kumar R Janardan B Larson and J Moon ldquoImproved seg-mentation of teeth in dental modelsrdquo Computer-Aided Designand Applications vol 8 no 2 pp 211ndash224 2011

[17] T Yuan W Liao N Dai X Cheng and Q Yu ldquoSingle-tooth modeling for 3D dental modelrdquo International Journal ofBiomedical Imaging vol 2010 Article ID 535329 14 pages 2010

[18] Z Li X Ning and Z B Wang ldquoA fast segmentation methodfor STL teeth modelrdquo in Proceedings of the IEEEICME Interna-tional Conference on Complex Medical Engineering (CME rsquo07)pp 163ndash166 IEEE May 2007

[19] M Zhao L Ma W Tan and D Nie ldquoInteractive tooth seg-mentation of dental modelsrdquo in Proceedings of the 27th AnnualInternational Conference on Engineering inMedicine andBiologySociety (IEEE-EMBS rsquo05) pp 654ndash657 IEEE Shanghai ChinaJanuary 2006

[20] T Kondo S H Ong and K W C Foong ldquoTooth segmentationof dental study models using range imagesrdquo IEEE Transactionson Medical Imaging vol 23 no 3 pp 350ndash362 2004

[21] T Kronfeld D Brunner and G Brunnett ldquoSnake-based seg-mentation of teeth from virtual dental castsrdquo Computer-AidedDesign and Applications vol 7 no 2 pp 221ndash233 2010

[22] Y Q Ma and Z K Li ldquoComputer aided orthodontics treatmentby virtual segmentation and adjustmentrdquo in Proceedings of theInternational Conference on Image Analysis and Signal Pro-cessing pp 336ndash339 IEEE 2010

[23] C Sinthanayothin and WTharanont ldquoOrthodontics treatmentsimulation by teeth segmentation and setuprdquo in Proceedingsof the 5th International Conference on Electrical Engineer-ingElectronics Computer Telecommunications and InformationTechnology vol 1 pp 81ndash84 IEEE May 2008

[24] B-J Zou S-J Liu S-H Liao XDing andY Liang ldquoInteractivetooth partition of dental mesh base on tooth-target harmonicfieldrdquo Computers in Biology and Medicine vol 56 pp 132ndash1442014

[25] M-F Li S-H Liao and R-F Tong ldquoFacial hexahedral meshtransferring by volumetric mapping based on harmonic fieldsrdquoComputers amp Graphics vol 35 no 1 pp 92ndash98 2011

[26] S-H Liao B-J Zou J-P Geng J-XWang andX Ding ldquoPhys-ical modeling with orthotropic material based on harmonicfieldsrdquo Computer Methods and Programs in Biomedicine vol108 no 2 pp 536ndash547 2012

[27] Y Kumar R Janardan and B Larson ldquoAutomatic featureidentification in dental meshesrdquo Computer-Aided Design andApplications vol 9 no 6 pp 747ndash769 2012

[28] Y Chen T A DavisWW Hager and S Rajamanickam ldquoAlgo-rithm 887 CHOLMOD supernodal sparse Cholesky factoriza-tion and updatedowndaterdquo ACM Transactions on Mathemati-cal Software vol 35 no 3 article 22 2008

[29] T A Davis User Guide for CHOLMOD A Sparse Cholesky Fac-torization and Modification Package Department of ComputerInformation Science and Engineering University of FloridaGainesville Fla USA 2014

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Evolutionary BiologyInternational Journal of



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ArchaeaHindawi Publishing Corporationhttpwwwhindawicom Volume 2014


Genetics Research International


Advances in

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curvature estimation is typically error-prone for real-worldnoisy models for example curvature distribution on clinicaldental models is generally complicated and irregular (seeSection 2 for further description)

This paper aims to develop an automatic and robustmethod for segmentation of digital dental models Motivatedby state-of-the-art general interactive mesh segmentationmethods [5ndash8] we developed a convenient and efficient den-tal segmentation framework which identifies tooth bound-aries by a dental-targeted harmonic field This approach hasthree major benefits

(1) The dental-targeted harmonic field is robust to vari-ous tooth shapes complex malocclusion and crowd-ing problems and is insensitive to noise with mini-mum parameter considerations

(2) The dental-targeted harmonic field can guaranteeclosed tooth boundary extraction from dental meshunlike curvature-based methods needing complexconnectivity and morphologic operations in mostcases

(3) The whole dental segmentation procedure is auto-matic which requires no user interaction to generateteeth with accurate and high-quality cutting bound-aries

2 Related Work

This paper focuses on dental mesh segmentation We intro-duce general mesh segmentation methods before dentalspecific methods The theory of harmonic field will be givenat the end of the section

21 General SegmentationMethod Numerousmesh segmen-tation approaches have been proposed in computer graphicsSome of these algorithms are automated like clustering[9] random walk [10] shape diameter function [11] fittingprimitives [12] and fast marching watershed [13] Most ofthese methods aim to partition different regions based onsimilarity measures [14] but defining a semantic subarea oftooth with various shapes remains a challenging task andnone of these methods is directly suitable for our specificapplication

Recently sketch-based interactive mesh segmentationmethods have become very popular [5ndash8] Most of thesemethods employ harmonic field theory and similar userinterfaces but they are different in computational weightingscheme and constraint styles Interested readers should referto literature such as surveys of comparisons between thesesketch-based methods [15] These methods have good per-formance in general mesh segmentation but require time-consuming and error-prone user interaction when dealingwith special and complicated tooth shapes and arrange-ments Furthermore they cannot produce high-quality cut-ting boundaries in cases where no obvious concave regionsare near the location of interaction

While our method also employs the harmonic fieldfor segmentation it fully exploits the dental characteristics

(see Section 33) which makes the proposed method smartaccurate and more robust in tooth partition

22 Dental-Targeted Segmentation Method A large groupof dental segmentation approaches prefer to use surfacecurvature to identify tooth boundaries The typical routinecan be summarized as follows

(1) Curvature estimation principal curvatures includingminimum principal curvature [16ndash19] and mean principalcurvature [1] are used to measure the surface property quan-titatively (2) Teeth-part rough locating though not alwaysnecessary this is a plane-estimating technique based on PCAthat produces a cutting plane to separate gingiva and teethpart introduced in previous works [1 20] We also involvethis step in our framework but the method we used is moreconvenient and effective (see Section 32) (3) Thresholdinga curvature threshold value is inevitably needed to separatepotential tooth boundary regions from the rest when usingcurvature fields for boundary identificationThat value can beobtained either interactively such as when using an intuitiveslider [16] or by taking a result of an experiential equationor even plugging in a constant preset number [19 20] Infact a global threshold value used in this mandatory step isone of the major drawbacks it can significantly influence thisentire solution because the thresholding generally cannotappropriately distinguish target objects from the rest of theregion leading to either over- or undersegmentation (4)Potential boundary region refining because the curvaturefield introduces lots of useless features in tooth crown regionsand is sensitive to noise in identifying tooth boundarymethods [1 17 19] using a morphologic operation willfurther refine the region obtained by thresholding For somecomplicated dentalmodels however (eg in cases of adjacentteeth crowding when the interstices in between are irregularand difficult to distinguish) the potential tooth boundaryregion may still be incomplete even after morphologic oper-ation (5) Boundary locating and refining as proposed inprevious works [1 16 17 19] a skeleton operation is usedto extract boundaries from potential regions However teethwith such boundaries are unacceptable for precise clinicaltreatment planning Refinements should be carried out tomake sure the boundary of each tooth is both smooth andprecise [1] More seriously the extracted boundaries couldbe incomplete (eg opened) so special refinement shouldbe taken to close the opened boundaries before attemptingsmooth and precise operations All such proceduresmake theentire framework tedious and complicated

Kondo et al introduced a fully automatic algorithm tosegment tooth from dental models using two range images[20] However they used a rectangular inspection spoketo cut the model which will introduce inaccurate cuts forsevere malocclusions Kronfeld et al proposed a snake-basedapproach that starts with an initial contour on the gingiva andevolves through a feature attraction field [21] The cusps ofeach tooth are then selected to start a local tooth contour andevolve until each tooth bottom is reached The approach isautomatic but may not produce good results when the modelhas boundary noises that interrupt a feature field defined bythe curvature information





ΔΦ119894= sum

(119894119895)isin119864

119908119894119895(Φ119894minus Φ119895) (1)


119894119895 This


119860Φ = 119887

119860 = [119871

119862]

119887 = [0

1198871015840]

(2)


119871119894119895=

sum

119896isin1198731(119894)

119908119894119896 if 119894 = 119895

minus119908119894119895 if (119894 119895) isin 119864

0 otherwise

(3)



119894119895and 120573


119894119895


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cot120572119894119895+ cot120573

119894119895

2 (4)









Start

Boundary extraction





End

Output

Input


(a)

(b)



(a)

10

(b) (c)













120601119894=

1

119899 minus 1

119899

sum

119896=1

(119888min119896 minus 119888minavg)2

(5)



119894






(a) (b)



119908lowast

119894119895=

120574119894119895(cot120572119894119895+ cot120573

119894119895)

2 (6)








1andΩ

2 and the




1and Ω








119894119895isin 119862 (1 le 119894 le



119888119894119895=

119908 for (119894 119895) | 119872 (119901119894) = 119895

0 otherwise(7)

119887119894=

119908 for 119894 | Type (119901119894) = 119901max

05119908 for 119894 | Type (119901119894) = 119901mid

0 for 119894 | Type (119901119894) = 119901min

(8)




(a) (b)

(c)



119894in 119872 Type(119901

119894) and returns

the type of 119901119894








(a) (b) (c)







0002004006008

01012014

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59


0

1

2

3

4

5

6

7

8


Time (d)Time (e)

65468

130944

76566

153092

73679

147354

28398

56792

26127

52206

26710

53420

44624

89164

35414

70775

73844

147684

87297

174590

83338

166672

70762

141520



5 Conclusions








Acknowledgments


References







































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology





ΔΦ119894= sum

(119894119895)isin119864

119908119894119895(Φ119894minus Φ119895) (1)


119894119895 This


119860Φ = 119887

119860 = [119871

119862]

119887 = [0

1198871015840]

(2)


119871119894119895=

sum

119896isin1198731(119894)

119908119894119896 if 119894 = 119895

minus119908119894119895 if (119894 119895) isin 119864

0 otherwise

(3)



119894119895and 120573


119894119895


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cot120572119894119895+ cot120573

119894119895

2 (4)









Start

Boundary extraction





End

Output

Input


(a)

(b)



(a)

10

(b) (c)













120601119894=

1

119899 minus 1

119899

sum

119896=1

(119888min119896 minus 119888minavg)2

(5)



119894






(a) (b)



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119894119895=

120574119894119895(cot120572119894119895+ cot120573

119894119895)

2 (6)








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2 and the




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119894119895isin 119862 (1 le 119894 le



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05119908 for 119894 | Type (119901119894) = 119901mid

0 for 119894 | Type (119901119894) = 119901min

(8)




(a) (b)

(c)



119894in 119872 Type(119901

119894) and returns

the type of 119901119894








(a) (b) (c)







0002004006008

01012014

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59


0

1

2

3

4

5

6

7

8


Time (d)Time (e)

65468

130944

76566

153092

73679

147354

28398

56792

26127

52206

26710

53420

44624

89164

35414

70775

73844

147684

87297

174590

83338

166672

70762

141520



5 Conclusions








Acknowledgments


References







































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


Start

Boundary extraction





End

Output

Input


(a)

(b)



(a)

10

(b) (c)













120601119894=

1

119899 minus 1

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sum

119896=1

(119888min119896 minus 119888minavg)2

(5)



119894






(a) (b)



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2 (6)








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119908 for 119894 | Type (119901119894) = 119901max

05119908 for 119894 | Type (119901119894) = 119901mid

0 for 119894 | Type (119901119894) = 119901min

(8)




(a) (b)

(c)



119894in 119872 Type(119901

119894) and returns

the type of 119901119894








(a) (b) (c)







0002004006008

01012014

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59


0

1

2

3

4

5

6

7

8


Time (d)Time (e)

65468

130944

76566

153092

73679

147354

28398

56792

26127

52206

26710

53420

44624

89164

35414

70775

73844

147684

87297

174590

83338

166672

70762

141520



5 Conclusions








Acknowledgments


References







































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a)

10

(b) (c)













120601119894=

1

119899 minus 1

119899

sum

119896=1

(119888min119896 minus 119888minavg)2

(5)



119894






(a) (b)



119908lowast

119894119895=

120574119894119895(cot120572119894119895+ cot120573

119894119895)

2 (6)








1andΩ

2 and the




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119894119895isin 119862 (1 le 119894 le



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119908 for 119894 | Type (119901119894) = 119901max

05119908 for 119894 | Type (119901119894) = 119901mid

0 for 119894 | Type (119901119894) = 119901min

(8)




(a) (b)

(c)



119894in 119872 Type(119901

119894) and returns

the type of 119901119894








(a) (b) (c)







0002004006008

01012014

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59


0

1

2

3

4

5

6

7

8


Time (d)Time (e)

65468

130944

76566

153092

73679

147354

28398

56792

26127

52206

26710

53420

44624

89164

35414

70775

73844

147684

87297

174590

83338

166672

70762

141520



5 Conclusions








Acknowledgments


References







































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a) (b)



119908lowast

119894119895=

120574119894119895(cot120572119894119895+ cot120573

119894119895)

2 (6)








1andΩ

2 and the




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119908 for 119894 | Type (119901119894) = 119901max

05119908 for 119894 | Type (119901119894) = 119901mid

0 for 119894 | Type (119901119894) = 119901min

(8)




(a) (b)

(c)



119894in 119872 Type(119901

119894) and returns

the type of 119901119894








(a) (b) (c)







0002004006008

01012014

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59


0

1

2

3

4

5

6

7

8


Time (d)Time (e)

65468

130944

76566

153092

73679

147354

28398

56792

26127

52206

26710

53420

44624

89164

35414

70775

73844

147684

87297

174590

83338

166672

70762

141520



5 Conclusions








Acknowledgments


References







































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a) (b)

(c)



119894in 119872 Type(119901

119894) and returns

the type of 119901119894








(a) (b) (c)







0002004006008

01012014

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59


0

1

2

3

4

5

6

7

8


Time (d)Time (e)

65468

130944

76566

153092

73679

147354

28398

56792

26127

52206

26710

53420

44624

89164

35414

70775

73844

147684

87297

174590

83338

166672

70762

141520



5 Conclusions








Acknowledgments


References







































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


(a) (b) (c)







0002004006008

01012014

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59


0

1

2

3

4

5

6

7

8


Time (d)Time (e)

65468

130944

76566

153092

73679

147354

28398

56792

26127

52206

26710

53420

44624

89164

35414

70775

73844

147684

87297

174590

83338

166672

70762

141520



5 Conclusions








Acknowledgments


References







































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology


0002004006008

01012014

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59


0

1

2

3

4

5

6

7

8


Time (d)Time (e)

65468

130944

76566

153092

73679

147354

28398

56792

26127

52206

26710

53420

44624

89164

35414

70775

73844

147684

87297

174590

83338

166672

70762

141520



5 Conclusions








Acknowledgments


References







































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology































Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology








Volume 2014

Zoology






















Advances in

Virolog y



Volume 2014




Enzyme Research



Microbiology

Documents

Research Article Automatic Tooth Segmentation of Dental Mesh …downloads.hindawi.com/journals/bmri/2015/187173.pdf · 2019-07-31 · Research Article Automatic Tooth Segmentation