Morphometric correlation between facial soft-tissue profile shape and skeletal pattern in children and adolescents

ORIGINAL ARTICLE

Morphometric correlation between facialsoft-tissue profile shape and skeletalpattern in children and adolescentsDemetrios J. HalazonetisAthens, Greece

Introduction: Prediction of soft-tissue outline shape from skeletal remains is useful in forensics andarchaeology. The inverse problem, the assessment of underlying skeletal relationships from the externalappearance, is pertinent in orthodontics. The purposes of this study were to assess the correlation betweencraniofacial shape and shape of the soft-tissue profile outline and to determine the extent to which it mightbe possible to predict the latter from the former. Methods: Lateral cephalograms from 170 consecutiveorthodontic patients were used, and 17 skeletal, 2 dental, and 22 soft-tissue landmarks were digitized andprocessed by using Procrustes superimposition and principal component analysis. The principal compo-nents of the skeletal and soft-tissue shapes were entered into the correlation analysis. Results: Significantcorrelations were found between the skeletal and the soft-tissue components. The use of 7 anterior skeletallandmarks (not including the nasal bone) resulted in a predictive power (coefficient of determination) of 38%of the variability of soft-tissue shape. This increased to almost 50% by adding nasal and incisor points butshowed only a slight further improvement by incorporating posterior skeletal landmarks. Conclusions:Anterior skeletal and dental landmarks can be used to predict soft-tissue profile shape with a 50% power in
children and adolescents. (Am J Orthod Dentofacial Orthop 2007;132:450-7)
Skeletal structures and overlying soft tissues of theface are intercorrelated both in form and func-tion. This relationship is of scientific interest in

many disciplines, including orthodontics, craniofacialsurgery, plastic and reconstructive surgery, and foren-sics. Forensic facial reconstruction (also called estima-tion or approximation) is perhaps the procedure that,most of all, assumes, and depends on, a strong interre-lationship between soft and hard tissues. Traditionally,the method of building the soft tissues has been byadding layers of clay or a similar material on thecraniofacial skeleton, by using, as a guide, values ofaverage thickness for various points of the face.1 Thus,facial estimation uses generic data (soft-tissue thick-ness), perhaps adjusted for age, race, and sex, to buildon a subject-specific foundation (the skull), with theimplied assumption that soft-tissue thickness is notrelated to the shape of the skeleton.

This last assumption is known to be false. Inforensics, Simpson and Henneberg2 reported that soft-tissue thickness is indeed related to various craniofacial

Assistant professor, Orthodontic Department, University of Athens DentalSchool, Athens, Greece.Reprint requests to: D. Halazonetis, 6 Menandrou St, Kifissia 145 61, Greece;e-mail, [email protected], August 2005; revised and accepted, October 2005.0889-5406/$32.00Copyright © 2007 by the American Association of Orthodontists.
doi:10.1016/j.ajodo.2005.10.033
450

skeletal dimensions. In orthodontics, similar results arecommonly accepted. Masseter muscle thickness andforce have been shown to be related to mandibularplane angle, anterior facial height, and facial width.3-6

Soft-tissue thickness has also been shown to differbetween persons with short and long faces.7 Therefore,it is not surprising that the accuracy of the traditionalforensic method of building up the soft tissues (directlyor with intervening muscles) might be lower thandesired.8,9 The guidelines for estimating soft-tissueparameters not only are too general, but also have notbeen sufficiently tested because they involve artistic (ie,subjective) interpretation.8,10

Data from studies relating craniofacial skeletalpattern to soft-tissue thickness could be used to increasethe accuracy of facial estimations. However, anothermethod would be to go directly from craniofacial shapeto soft-tissue shape without estimating thickness. Shape(skeletal and soft-tissue) could be described compre-hensively by using geometric morphometric meth-ods,11-13 thus circumventing the problems associatedwith conventional metric or angular measurements.14

Furthermore, this approach would correlate the 2shapes as a whole and might provide better resultsregarding the shape of the nose, which is notoriouslydifficult to predict,10 and the posture of the lips, which
tend to be incompetent more often in subjects with

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Halazonetis 451

large anterior facial height and hyperdivergent skeletalpattern.15,16

Apart from the obvious forensic applications, thecorrelation between hard- and soft-tissue shapes isparticularly interesting to orthodontists. In recent years,the emphasis in diagnosis and treatment planning hasshifted from the hard tissues to the soft tissues.17

Treatment decisions are being based more and more onfacial esthetics than on skeletal and dental relation-ships. This tendency is justified by the scientific rea-soning that hard tissues are not the sole determinants ofexternal form, but the trend might also be due tocultural pressures. Interestingly, this shift seems to haveoccurred, even though data regarding the extent of therelationship between skeletal and soft-tissue shapes arelimited.

The purposes of this investigation were to studythe shape of the soft-tissue outline in relation to theunderlying craniofacial pattern and to assess thestrength of the correlation between them. This ap-proach differs from previous research, in that the aimwas not to estimate the absolute position of soft-tissuelandmarks relative to the skeleton. Rather, it was toinfer the shape of the soft-tissue outline, without regardto its absolute size or position relative to the underlyingskeletal structures. Because a correlation between skel-etal and soft-tissue shapes is to be expected for purelybiological reasons, it was decided to determine thestrength of this correlation by using various subsets ofskeletal and dental structures. This would enable estab-lishment of the relative importance of each structureand determination of those that contribute most deci-sively to soft-tissue shape.

MATERIAL AND METHODS

The sample consisted of initial (pretreatment) ceph-alometric radiographs of 170 white patients of Greekethnic origin (82 male, 88 female), selected from alarger sample of consecutively treated patients from aprivate orthodontic office.18 The radiographs were se-lected irrespective of sex and type of malocclusion butfulfilling the following criteria: age from 7 to 17 years,radiographs of good quality that depicted a referenceruler on the cephalostat for exact measurement of themagnification factor, no congenital malformations orsyndromes, and lips in relaxed posture (not necessarilytouching), as evidenced by the absence of a strainedand flattened mentalis area. Descriptive statistics of thesample are given in Table I.

The radiographs were scanned at 150 dpi anddigitized on screen by using Viewbox 3 software(dHAL Software, Kifissia, Greece). To reduce the error
of point identification,19-21 all radiographs were digi-
tized twice, and the average of the 2 digitizations wasused. The following cephalometric points were used inthis study (Fig 1).

1. Seventeen skeletal landmarks. Of these, 16 wereanatomical cephalometric points: basion (Ba), sella(S), spheno-ethmoidale (Se), nasion (N), rhinion(Rh), porion (Po), orbitale (O), anterior nasal spine(ANS), A-point (A), posterior nasal spine (PNS),articulare (Ar), gonion (Go), antegonial notch (Ag),menton (Me), pogonion (Pg), and B-point (B). Theother skeletal landmark, Rh50%, was a constructedpoint, lying on the anterior outline of the nasal bonehalfway between N and Rh.

2. Two dental landmarks—the incisal edges of themost prominent maxillary and mandibular incisors(points U1 and L1).

3. Twenty-two soft-tissue landmarks. Of the soft-tissue landmarks, 12 were identified as lying atlocally extreme positions on the soft-tissue outline,

Table I. Age descriptive statistics (in years)

Male (n � 82) Female (n � 88)

Mean 11.59 11.91SD 1.68 1.80Range 7.34-16.07 7.86-16.68Median 11.52 11.89

Fig 1. The landmarks (squares) and constructed land-marks (circles) used in this investigation.

relative to the Frankfort horizontal plane: nasion=

American Journal of Orthodontics and Dentofacial OrthopedicsOctober 2007

452 Halazonetis

(N=), the most posterior point at the concavity at theroot of the nose; pronasale (Pr), the most anteriorpoint on the nose; subnasale (Sn), the most poste-rior-superior point where the columella meets theupper lip; A=-point (A=), the most posterior pointbetween the nose and the upper lip; labrale superior(Ls), the most anterior point of the upper lip;stomion superior (Ss), the most inferior point of theupper lip; stomion inferior (Si), the most superiorpoint of the lower lip; labrale inferior (Li), the mostanterior point of the lower lip; labiomental (Lm),the most posterior point on the concavity betweenthe lower lip and pogonion=; pogonion= (Pg=), themost anterior point of the chin; gnathion= (Gn=), themost anterior-inferior point of the chin; and men-ton= (Me=), the most inferior point of the chin,directly below the skeletal point Me. The other 10soft-tissue points (constructed landmarks) laybetween the extreme points at various distancesalong the soft-tissue outline. The distances werespecified as percentages of the total distance(along the curved outline) between the definingpoints; eg, N=-Pr-15% was defined as lying be-tween N= and Pr at a distance of 15% of the totaldistance between these points, starting from N=.With this notation, the 10 constructed landmarkswere N=-Pr-15%, N=-Pr-50%, N=-Pr-85%, Pr-Sn-50%, A=-Ls-50%, Ls-Ss-50%, Si-Li-50%, Li-Lm-30%, Li-Lm-80%, and Lm-Pg=-30%.

The x and y coordinates of all points were scaledaccording to the magnification of each radiograph tocorrespond to true life size. The skeletal and dentallandmarks were grouped to define 4 distinct areas (Fig 2):(1) posterior skeletal area, called P8, consisting of 8landmarks—Ba, S, Se, Po, PNS, Ar, Go, and Ag; (2)anterior skeletal area, called A7, consisting of 7 land-marks—N, Or, A, ANS, B, Pg, and Me; (3) nasal area,called N2, consisting of landmarks Rh50% and Rh; and(4) incisor area, called I2, consisting of points U1 and L1.

Morphometric methods, described below, were usedto assess skeletal and soft-tissue shapes. Nine shapes(collections of points) were defined. These included thesoft-tissue shape, comprising all 22 soft-tissue points and8 skeletodental shapes, as follows: (1) S:A7, comprisingpoints belonging to area A7; (2) S:A7�P8, comprisingpoints belonging to areas A7 and P8; (3) S:A7�I2,comprising points belonging to areas A7 and I2; (4)S:A7�N2, comprising points belonging to areas A7 andN2; (5) S:A7�P8�N2, comprising points belonging toareas A7, P8, and N2; (6) S:A7�P8�I2, comprisingpoints belonging to areas A7, P8, and I2; (7)
S:A7�N2�I2, comprising points belonging to areas A7,
N2, and I2; and (8) S:A7�P8�N2�I2, comprising allskeletal and dental landmarks.

The 9 shapes were processed separately. For each,the tracings were superimposed by using Procrustessuperimposition, which aims to achieve the best fit byminimizing the sum of the squared distances betweenall points.12 The average of the each shape was calcu-lated, and the residuals (differences in the x and ycoordinates) between each tracing and the average werecomputed for all points. Principal component analysis(PCA) was used on the residuals to extract the mostsignificant shape coefficients (principal components ofshape [PCs]).12,22 Procrustes superimposition and PCAwere performed by using Viewbox 3, and statisticaltests were run by using the StatsDirect software (Stats-Direct, Cheshire, United Kingdom).

RESULTS

Soft-tissue shape was described by 40 PCs. The 8most significant of these, accounting for approximately90% of the total shape variance, are shown in Table II. Agraphic depiction of the PCs is given in Figure 3, in whichwe can see the components of shape described by eachPC. The first 2 PCs seem to describe the overall convexityof the face and the proportions of upper and lower faceheight; they accounted for more than 50% of shape

Fig 2. Extents of shapes P8, A7, N2, and I2.

variance (Table II). The 8 PCs were used in subsequent


Halazonetis 453

analyses, and the rest were discarded because they de-scribed only a minor percentage of shape variance. Sim-ilarly, only the most significant coefficients of the other 8shapes were retained—those that cumulatively accountedfor approximately 90% of total shape variance (thisthreshold was an arbitrary decision).

For each of the 8 skeletodental shapes, thefollowing procedure was carried out. Multiple linearregressions between each soft-tissue PC (the depen-dent variable) and all PCs of the other shape (thepredictors) were calculated. The total variance ofsoft-tissue shape that could be predicted by eachskeletodental shape was calculated by multiplyingthe variance explained by each soft-tissue PC (TableII) with the corresponding coefficient of determina-tion (r2) of the multiple regression and adding theresults. This method was considered statisticallysound because the PCs are uncorrelated to eachother. Table III shows the results for shapeS:A7� N2� I2 as an example. Table IV shows theoverall results for all shapes studied. The highestpercentage of explained soft-tissue shape variancewas approximately 50%, achieved by using eitherS:A7�N2�I2 or S:A7�P8�N2�I2. The smallestskeletal shape (S:A7) could explain approximately38% of total soft-tissue shape variance.

Looking at the individual soft-tissue shape coeffi-cients, we can see that PC1 and PC2 were wellestimated; the coefficients of determination (r2) rangedfrom 55% to 77%. These coefficients describe theoverall shape of the face, and, therefore, these highcorrelations between skeletal and soft-tissue shapes arenot surprising. In contrast, PC3 and PC6 showed lowcorrelations, with r2 not exceeding 20%. Both of thesecoefficients seem to describe mainly the shape of thelower lip and the competency of the lips, as shown inFigure 3. Their low correlation to skeletal and dentalstructures might be explained on the premise that they

Table II. Percentage variance and cumulative varianceexplained by each of the 8 first soft-tissue PCs (totalnumber of PCs: 40)

Component % variance Cumulative variance

PC1 36.0% 36.0%PC2 18.4% 54.4%PC3 10.6% 65.0%PC4 7.0% 72.0%PC5 5.7% 77.7%PC6 4.9% 82.6%PC7 3.6% 86.2%PC8 2.8% 89.0%

describe lip posture, which can be neuromuscularly

controlled with little influence from teeth and osseousstructures. The remaining coefficients (PC4, PC5, PC7,and PC8) had moderate correlations: 17% to 44%.

To gain a visual impression of the power of thispredictive scheme, the regression equations related toshape S:A7�N2�I2 were used to derive estimates forthe first 8 PCs of the soft-tissue shape for all patients.With these estimates, patients were sorted in increasingorder of prediction success, with the sum of squareddifferences between actual and predicted PCs as thecriterion. Figure 4 shows the 3 best, the 3 worst, and the3 intermediate predictions.

DISCUSSION

The aim of this investigation was to assess therelationship between soft- and hard-tissue shapes. Al-though this is of interest to forensic science andarchaeology for developing more accurate facial esti-mation procedures, the extent of the hard- and soft-tissue interrelationship is also relevant in other disci-plines, such as orthodontics and craniofacial surgery. Inorthodontics, cephalometric skeletal and dental mea-surements have traditionally influenced treatment deci-sions to a large degree. However, the realization thatthe soft tissues might not follow the underlying struc-tures closely has shifted the focus of treatment planningtoward soft-tissue assessment, even though the extentof the soft- and hard-tissue interrelationship is largelyunknown.

The sample consisted of radiographs of childrenand adolescents between 7 and 17 years of age. Thisage group was selected because it encompasses a periodof intense growth and development of the craniofacialcomplex, when the interrelationship between hard- andsoft-tissue shapes should be particularly close, withoutthe added variability of the aging effects in adults.Lateral cephalometric radiographs are routinely takenat the start of orthodontic treatment, and no ethicalissues were present. Because the subjects were prospec-tive orthodontic patients, a wide range of craniofacialpatterns in the sample was ensured. This study was of2-dimensional data, focusing on the soft-tissue profileoutline with traditional cephalometric landmarks. Ex-tension to 3-dimensional data needs computed tomog-raphy images and is planned as a subsequent project.23

The sample was analyzed as a whole, withoutsubdividing into male and female groups. This wasdone for 2 reasons. First, forensic facial estimation ofchildren and adolescents is often performed withoutcertain knowledge of the subject’s sex because this isdifficult to assess reliably from the skeleton. Second,sexual dimorphism at these ages is small and probably
not clinically relevant. Although boys have thicker soft

e corr


454 Halazonetis

tissues than girls, especially after the pubertal growthspurt,24,25 the differences between the sexes are con-sidered small with questionable practical applica-tions.24 Also, differences in soft-tissue thickness do notnecessarily reflect differences in soft-tissue shape,which was found to be similar between the sexes.18 Ageeffects were not investigated, because this was a cross-sectional sample. Facial shape has been reported tochange with age, but the changes are small relative to

Fig 3. The first 8 principal components of shapshape. The left shape was constructed by sewhereas the right shape resulted by setting th

the overall variability of the sample.18 Subdivision of

this sample into younger and older groups, with 12years as the cutoff point, did not change the resultsappreciably. Although some correlation coefficientsshowed variations, the overall results—ie, the correla-tion between hard and soft tissues—was similar (resultsnot shown).

The methods that were used to study shape are basicmethods in morphometrics.11-13 The use of PCA per-mits the comprehensive description of shape with a few

middle shape in each group of 3 is the averageach component at 3 SD below the average,

esponding PC at 3 SD above the average.

e. Thetting e

parameters in contrast to other methods, such as Fourier


Halazonetis 455

analysis,26 in which many coefficients are necessary foraccurate representation. Furthermore, the shape de-scriptors used here did not require the lips to be incontact. This was a significant advantage because theshape of the lips could be studied at relaxed posture.Straining of the lips to achieve closure not only changesthe shape of the lips but also affects the chin area,because of constriction of the mentalis muscle. Anadded advantage was that the extent of lip openingcould be incorporated into the prediction scheme.Children with incompetent lips are frequently seen, andsometimes this is associated with mouth breathing,although this is still a debatable topic. In any case, anassociation between lip opening and craniofacial pat-tern (mainly hyperdivergency and increased anteriorfacial height) is generally accepted.16

The overall predictive power was approximately50% of the total soft-tissue shape variance. This num-ber should not be interpreted as implying that predic-tion results were equivalent to guesswork. Withoutpredictive information, the best that we can do is usethe average shape as our prediction. For any patient, theaverage can be a good or a bad approximation, andthere will be a difference between the average and thetrue soft-tissue shape. A predictive power of 50%means that we improve on the average by movingtoward the true shape 50% of the way.

The comparison of estimated and actual tracings(Fig 4) shows good approximation. Direct comparisonwith other studies is difficult because of differentassessment criteria, but these results seem decidedlybetter than those produced with the Fourier analysis.26

Stephan et al10 calculated regression equations forestimating the absolute horizontal and vertical position

Table III. Calculation of total variance of soft-tissueshape explained by area A7�N2�I2

Variance(% of total) r2 (%) Variance � r2 (%)

PC1 36.0 76.3 36.0 � 76.3 � 27.5PC2 18.4 74.0 18.4 � 74.0 � 13.6PC3 10.6 12.2 10.6 � 12.2 � 1.3PC4 7.0 35.5 7.0 � 35.5 � 2.5PC5 5.7 38.2 5.7 � 38.2 � 2.2PC6 4.9 14.5 4.9 � 14.5 � 0.7PC7 3.6 25.3 3.6 � 25.3 � 0.9PC8 2.8 25.4 2.8 � 25.4 � 0.7Total % variance 89.0 49.4

r2, Coefficient of determination of multiple regression of hard-tissuearea PCs (the first 9 most significant PCs were used) against each ofthe soft tissue PCs.

of Pr and reported r2 values of approximately 65%.

However, this number concerns the absolute position of1 point only and does not reflect nose shape.

Eight skeletodental areas were evaluated. Points onthe nasal bone and the incisors were assessed sepa-rately, because incorporation of these points was ex-pected to increase the predictive power significantly.The increase was about 4% to 5% for each of these andapproximately 10% if both areas N2 and I2 were added.These numbers might seem small, considering theamount of literature devoted to establishing clinical and

Fig 4. Examples of soft-tissue shape prediction. Toprow, the 3 patients with the least error between actualand predicted shape; middle row, the 3 patients withintermediate results; bottom row, the 3 worst fits. Solidline, actual profile; broken line, predicted profile.

cephalometric targets for the position of the incisors.

rked w


456 Halazonetis

Does this mean that posttreatment incisor position willhave little effect on the facial profile? If the profile isconsidered as a whole, then this is probably true, butthat does not mean that the incisors do not dictate theposition of the lips to a significant degree, only that thelips constitute a small part of the overall soft-tissueoutline. Correspondingly, the Rh points were expectedto provide much information on the shape of the nose,but, again, expectations fell short. Nose shape is noto-riously difficult to predict from skeletal structures.10

Inclusion of the posterior points (P8) did not con-tribute appreciably to the predictive power. Without theposterior points, the information regarding the diver-gence of the skeletal planes is lost, and this wasexpected to have a significant impact, but the dataproved otherwise. Perhaps much of the same informa-tion is present in the arrangement of the anterior points,reflected in the ratio of lower to upper facial heights orin the convexity of the face.

Apart from the usefulness in predicting soft-tissueshape, these results show the extent to which externalfacial form is dictated, on the one hand, by skeletal anddental structures and, on the other hand, by the softtissues themselves. Approximately 50% of the variabil-ity of soft-tissue shape was related to the hard tissues,leaving the other 50% to be attributed to soft-tissue–specific factors. A large part of facial shape variabilityis inherent in the soft tissues themselves, justifyingcurrent trends toward esthetics-based treatment. How-ever, the importance of the hard tissues should not beoverlooked.

CONCLUSIONS

Soft-tissue shape was correlated to skeletal shapeby a coefficient of determination (r2) of approximately50%. The anterior facial skeleton, including the nasal

Table IV. Multiple regression coefficients of determina

A7 A7�P8 A7�I2

Variance r2 Total r2 Total r2 Total

PC1 36.0 55.0 19.8 56.9 20.5 63.8 23.0PC2 18.4 64.3 11.8 68.5 12.6 66.7 12.3PC3 10.6 10.4 1.1 15.7 1.7 11.5 1.2PC4 7.0 30.8 2.2 18.1 1.3 32.2 2.3PC5 5.7 20.6 1.2 21.8 1.2 38.4 2.2PC6 4.9 5.3� 0.3 13.7 0.7 5.5� 0.3PC7 3.6 21.2 0.8 18.6 0.7 18.9 0.7PC8 2.8 24.1 0.7 25.0 0.7 18.5 0.5Total 89.0 37.8 39.3 42.4

All correlations were significant at the 5% level except for the 2 ma

bone, and the position of the central incisor edges were

sufficient to arrive at this predictive power. Posteriorskeletal landmarks did not add significant improve-ment.

REFERENCES

1. Prag J, Neave R. Making faces: using forensic and archaeolog-ical evidence. London: British Museum Press; 1997.

2. Simpson E, Henneberg M. Variation in soft-tissue thicknesses onthe human face and their relation to craniometric dimensions.Am J Phys Anthropol 2002;118:121-33.

3. Kiliaridis S, Kalebo P. Masseter muscle thickness measured byultrasonography and its relation to facial morphology. J Dent Res1991;70:1262-5.

4. Raadsheer MC, Kiliaridis S, Van Eijden TM, Van Ginkel FC,Prahl-Andersen B. Masseter muscle thickness in growing indi-viduals and its relation to facial morphology. Arch Oral Biol1996;41:323-32.

5. Kubota M, Nakano H, Sanjo I, Satoh K, Sanjo T, Kamegai T,et al. Maxillofacial morphology and masseter muscle thicknessin adults. Eur J Orthod 1998;20:535-42.

6. Benington PC, Gardener JE, Hunt NP. Masseter muscle volumemeasured using ultrasonography and its relationship with facialmorphology. Eur J Orthod 1999;21:659-70.

7. Blanchette ME, Nanda RS, Currier GF, Ghosh J, Nanda SK.A longitudinal cephalometric study of the soft tissue profile ofshort- and long-face syndromes from 7 to 17 years. Am J OrthodDentofacial Orthop 1996;109:116-31.

8. Stephan C, Henneberg M. Building faces from dry skulls: are theyrecognized above chance rates? J Forensic Sci 2001;46:432-40.

9. Stephan C. Do resemblance ratings measure the accuracy offacial approximations? J Forensic Sci 2002;47:239-43.

10. Stephan CN, Henneberg M, Sampson W. Predicting nose pro-jection and pronasale position in facial approximation: a test ofpublished methods and proposal of new guidelines. Am J PhysAnthropol 2003;122:240-50.

11. Bookstein FL. Morphometric tools for landmark data: Geometryand biology. Cambridge, United Kingdom: Cambridge Univer-sity Press;1991.

12. Dryden IL, Mardia KV. Statistical shape analysis. New York:John Wiley & Sons; 1998.

13. Mardia KV. Statistical shape analysis and its applications. In:

2) for each area and each soft-tissue PC

N2 A7�P8�N2 A7�P8�I2 A7�N2�I2A7�P8�

N2�I2

Total r2 Total r2 Total r2 Total r2 Total

24.2 67.4 24.3 64.1 23.1 76.3 27.5 77.5 27.913.0 72.7 13.4 69.5 12.8 74.0 13.6 73.6 13.51.1 16.7 1.8 18.2 1.9 12.2 1.3 20.0 2.11.7 20.8 1.5 30.9 2.2 35.5 2.5 34.8 2.41.0 23.4 1.3 42.4 2.4 38.2 2.2 43.7 2.50.4 10.5 0.5 14.4 0.7 14.5 0.7 20.2 1.01.0 22.4 0.8 19.1 0.7 25.3 0.9 24.2 0.90.8 28.8 0.8 24.6 0.7 25.4 0.7 27.6 0.8

43.2 44.3 44.5 49.4 51.1

ith an asterisk.

tion (r

A7�

r2

67.370.610.624.916.79.1

27.027.2

Chaplain MAJ, Singh GD, McLachlan JC, editors. On growth


Halazonetis 457

and form. Spatio-temporal pattern formation in biology. NewYork: John Wiley & Sons; 1999. p. 337-55.

14. Moyers RE, Bookstein FL. The inappropriateness of conven-tional cephalometrics. Am J Orthod 1979;75:599-617.

15. Fricke B, Gebert HJ, Grabowski R, Hasund A, Serg HG. Nasalairway, lip competence, and craniofacial morphology. EurJ Orthod 1993;15:297-304.

16. Trotman CA, McNamara JA Jr, Dibbets JM, van der Weele LT.Association of lip posture and the dimensions of the tonsils andsagittal airway with facial morphology. Angle Orthod 1997;67:425-32.

17. Sarver DM, Ackerman JL. Orthodontics about face: the re-emergence of the esthetic paradigm. Am J Orthod DentofacialOrthop 2000;117:575-6.

18. Halazonetis DJ. Morphometric evaluation of soft-tissue profileshape. Am J Orthod Dentofacial Orthop 2007;131:481-9.

19. Baumrind S, Frantz RC. The reliability of head film measure-ments. 1. Landmark identification. Am J Orthod 1971;60:
111-27.
20. Houston WJB. The analysis of errors in orthodontic measure-ments. Am J Orthod 1983;83:382-9.

21. Houston WJB, Maher RE, McElroy D, Sherriff M. Sources oferror in measurements from cephalometric radiographs. EurJ Orthod 1986;8:149-51.

22. Halazonetis DJ. Morphometrics for cephalometric diagnosis.Am J Orthod Dentofacial Orthop 2004;125:571-81.

23. De Greef S, Willems G. Three-dimensional cranio-facial recon-struction in forensic identification: latest progress and newtendencies in the 21st century. J Forensic Sci 2005;50:12-7.

24. Garlie TN, Saunders SR. Midline facial tissue thicknesses ofsubadults from a longitudinal radiographic study. J Forensic Sci1999;44:61-7.

25. Mamandras AH. Linear changes of the maxillary and mandibularlips. Am J Orthod Dentofacial Orthop 1988;94:405-10.

26. Rose AD, Woods MG, Clement JG, Thomas CDL. Lateral facialsoft-tissue prediction model: analysis using Fourier shape de-scriptors and traditional cephalometric methods. Am J Phys
Anthropol 2003;121:172-80.

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Morphometric correlation between facial soft-tissue profile shape and skeletal pattern in children and adolescents