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Journal of Cranio-Maxillo-Facial Surgery xxx (2013) 1e7

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Journal of Cranio-Maxillo-Facial Surgery

journal homepage: www.jcmfs.com

Quantification of facial asymmetry by 2D analysis e A comparisonof recent approaches

Nina Franka Berlin a, Philipp Berssenbrügge a,*, Christoph Runte a, Kai Wermker b,Susanne Jung c, Johannes Kleinheinz c, Dieter Dirksen a

aDepartment of Prosthetic Dentistry and Biomaterials (Prof. Dr. Med. Dr. Med. Dent. Ludger Figgener), University of Münster, Albert-Schweitzer-Campus 1,Building W30, 48149 Münster, Germanyb Fachklinik Hornheide für Tumoren und Wiederherstellung an Gesicht und Haut, University of Münster, Dorbaumstr. 300, 48157 Münster, GermanycDepartment of Maxillofacial Surgery, University of Münster, Albert-Schweitzer-Campus 1, Building W30, 48149 Münster, Germany

a r t i c l e i n f o

Article history:Paper received 31 October 2012Accepted 17 July 2013

Keywords:ReviewFaceFacial asymmetry

* Corresponding author. Tel.: þ49 251 8343753; faxE-mail address: [email protected]

1010-5182/$ e see front matter � 2013 European Asshttp://dx.doi.org/10.1016/j.jcms.2013.07.033

Please cite this article in press as: Berlin NFJournal of Cranio-Maxillo-Facial Surgery (20

a b s t r a c t

Introduction: Symmetry has been found to play a crucial role in attractiveness assessment and so itsrestoration is an essential problem in oral maxillofacial surgery. This paper presents an overview ofrecent 2D asymmetry analysis techniques. These are techniques which are based on the evaluation oftwo-dimensional data, like photos. The aim of this paper is to find the most precise and practicaltechniques to investigate facial asymmetry.Materials and methods: For this purpose studies addressing symmetry investigations are collected andcategorized by the type of data they extract from the photos. The reference points on the facial surface,which are frequently used in these studies, are presented and calculation methods are described.Results: Three kinds of techniques using vertical or horizontal reference lines or centres of bilateralpoints appear to be most appropriate. Recommendations are made, which aspects should be taken intoaccount when calculating symmetry/asymmetry indices from photos. Advantages and disadvantages ofthe three selected methods are summarized in a table.Conclusions: Using one of the three recommended approaches denoted by FA, AI and z-score allowscalculating meaningful asymmetry values. The proper selection and identification of reference points iscrucial. For highest accuracy, a sufficient number of evenly distributed and reproducible reference pointsshould be used.

� 2013 European Association for Cranio-Maxillo-Facial Surgery. Published by Elsevier Ltd. All rightsreserved.

1. Introduction

For centuries a key to making concepts like beauty and attrac-tiveness measurable has been searched for (Koury and Epker,1992).Artists, like da Vinci, as well as physicians have dealt with thissubject. They have tried to combine single factors of attractive facesin norms or principles and thus understand them (Farkas et al.,2005; Bashour, 2006b; Edler et al., 2006; Mizumoto et al., 2009).Several theories, like the golden ratio as a basic principle ofharmonious shapes (Mizumoto et al., 2009), rules of harmoniousfacial proportions (Koury and Epker, 1992; Farkas et al., 2005; Hönnand Göz, 2007) or baby faceness as a factor of attractiveness infemale faces (Braun et al., 2001) have been investigated in thiscontext. Beyond that, it is known that potential rules for attractive

: þ49 251 8347182.(P. Berssenbrügge).

ociation for Cranio-Maxillo-Facial

, et al., Quantification of faci13), http://dx.doi.org/10.1016

faces are not universal but differ in different ethnic groups. Farkaset al. (2007) have researched this topic. Bashour (2006a) has triedto determine attractiveness objectively as the measurable corre-spondence of a face with a pattern (“phi mask”) postulated as beingideal. The pattern was created based on the golden ratio and othermathematical features like the Fibonacci sequence or logarithmicspirals.

Recently, there is growing evidence in the anthropologicalresearch that symmetry and averageness are important additionalkeys to the attractiveness of human faces (Enquist and Arak, 1994;Møller and Thornhill, 1998; Thornhill and Gangestad, 1999; Faureet al., 2002; Baudouin and Tiberghien, 2004; Farkas et al., 2005;Edler et al., 2006; Bashour, 2006b; Rhodes, 2006; Little and Jones,2006; Jones et al., 2007; Hönn and Göz, 2007; Zaidel andDeblieck, 2007; Springer et al., 2007; Komori et al., 2009). At thesame time, the question arises as to how the aspects of symmetryand averageness are related to each other and which of them ismore important (Hönn and Göz, 2007; Jones et al., 2007; Borelli and

Surgery. Published by Elsevier Ltd. All rights reserved.

al asymmetry by 2D analysis e A comparison of recent approaches,/j.jcms.2013.07.033

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Fig. 1. Some reference points frequently used: upper centre of the hair line tr, uppercentre of the eyebrow eup, inner corner of the eye en, outer corner of the eye ex,nasion n, upper corner of the ear aup, outermost point of the zygomatic arch zy, lowercorner of the ear ado, lateral margin of the nasal wing, outermost point an, lowermostpoint of the centre of the nose, subnasale sn, corner of the mouth ch, topmost centre ofthe upper lip lup, lowermost point of the lower lip ldo, centre of the lips st, outermostpoint of the angle of the mandible m, gnathion gn, pupil p.

N.F. Berlin et al. / Journal of Cranio-Maxillo-Facial Surgery xxx (2013) 1e72

Berneburg, 2010). Enquist and Arak (1994) were able to prove thatsymmetric abstract patterns are rated more attractive than asym-metric ones. They assumed that this preference in perception arisesas a by-product of the need to recognize objects irrespective of theirposition and orientation in the field of vision. Proofs have beenfound that symmetry occurring in different parts of the face hasvarying significance. Generally, its influence near the midline islarger, while in the marginal areas of very attractive faces minorasymmetric features can possibly even increase the aesthetics(Hönn and Göz, 2007; Springer et al., 2007; Borelli and Berneburg,2010). Naevi, known as “beauty marks” can have this effect.Perfectly symmetric faces are not perceived as maximally attractive(Zaidel and Deblieck, 2007).

In surgery, symmetry investigations make an importantcontribution to the planning of operations and evaluation ofdifferent surgical procedures (Bashour, 2006b). As reported in theliterature, such investigations are often linked with surgical pro-cedures concerning the correction of a cleft lip and palate (Stauberet al., 2008; Nkenke et al., 2006; Schwenzer-Zimmerer et al., 2008).Until now, 2D analysis techniques have been mainly used. Usuallyphotos are surveyed, and inmost cases points of the face in a frontalview are determined and their symmetry is investigated, often bymeans of a base line. Some authors additionally or exclusivelyutilize radiographs of the cranium without being able to analyseany external soft tissue. Newer approaches, evaluating 3D data, arenot mentioned in this paper because the measuring systems arestill not very common and the comparability of the differentmethods has still to be investigated.

A face specific symmetry/asymmetry value is calculated fromthe acquired data using different techniques. This can be used tocompare the symmetry characteristics of a face before and after anoperation andwith other faces. In this paper an overview is given oftechniques recently published and their applicability is discussed.To address the problem of some vague descriptions found in theliterature, the main relations are summarized concisely in unam-biguous mathematical formulas.

2. Materials and methods

2.1. Selection of the studies

In this paper, only studies addressing symmetry investigationsof human faces, which are available in the “PubMed” data base, aretaken into account. The primary goal of this work is to find 2Danalysis techniques which determine a face specific, objective andquantitative symmetry/asymmetry value based on soft-tissuelandmarks.

Terms used for the search in “PubMed” were: facial asymmetry,facial symmetry, analysis, soft-tissue analysis, 2D-analysis, 2D-measurements, photographs, diagnostic methods.

To be included, studies had to contain detailed descriptions ofthe techniques applied concerning the following aspects:

- selection of subjects (age, sex, number, state of health (healthy,pre-/postoperative, genetic disorders, other diseases), ethnicheritage

- usage of photos taken especially for the investigation or alreadyexisting ones or measurement directly at the subject

- investigation of the entire face or aspects of it, respectively- photography of the subjects: used camera, positioning of thecamera and the subjects, lighting conditions, camera settings,neutral facial expression

- image processing, image resolution, image size, documentedand considered reproduction scale, digital or analogueprocessing

Please cite this article in press as: Berlin NF, et al., Quantification of faciJournal of Cranio-Maxillo-Facial Surgery (2013), http://dx.doi.org/10.1016

- repetitions of the measurements in order to enhance the ac-curacy (on the same or different day)

- precise description and reproducible selection of facial refer-ence points

- comprehensible documentation of the calculations.

All publications only met these criteria partially, sometimeslacking crucial information necessary for the understanding. Not allauthors made calculations to obtain an objective symmetry value.However, these studies were included as well in order to find outtypically used face reference points and measuring techniques.

The publications date from 1994 to 2011 and include 11 to 1282subjects aged between >1 and 41.7 years.

3. Results

After presenting an illustration of the most commonly usedanatomical reference points the different concepts for a descriptionof facial symmetry aspects are explained. For each we describe howquantitative parameters for an evaluation of facial symmetry arecalculated.

3.1. Frequently used reference points

Fig. 1 shows an overview of the most frequently used referencepoints.

3.2. Usage of horizontal distances from a vertical reference line(median sagittal plane)

Onemethod described is tomeasure the distances from bilateralpoints to the reference plane. This is an analysis of the horizontalcomponent (Nakamura et al., 2001; Song et al., 2007; Little et al.,2008). A second technique determines the difference in height oflines which pass through bilateral points and are perpendicular to


N.F. Berlin et al. / Journal of Cranio-Maxillo-Facial Surgery xxx (2013) 1e7 3

the median sagittal line. This gives an analysis of the verticalcomponent. Fig. 2 illustrates these two approaches.

3.2.1. Calculation of a symmetry valueFor this purpose, Nakamura et al. (2001) introduced the

“asymmetry index” AI given as a percentage. A median sagittal lineis constructed and subsequently the distances of bilateral pointsfrom this line are measured. The asymmetry index is calculated asfollows:

AI ¼��dR � dLdR þ dL

��:

dR and dL denote the measured distances on the right side and onthe left side of the face, respectively. As this formula contains theratio of the difference of the distances to their sum, an over-weighting of large distances is avoided. A perfectly symmetric facewould result in AI¼ 0%. Increasing asymmetry means an increasingvalue of AI. Due to the absolute value, AI does not indicate in whichdirection single components of the face deviate from symmetry.Nakamura et al. (2001) have specified an individual AI for each pairof bilateral reference points. An overall face specific asymmetryindex has not been calculated by the authors although it couldeasily be done by averaging multiple AI.

3.3. Use of vertical distances from a horizontal reference line

A vertical asymmetry is defined by means of differing distancesof bilateral points from the bipupillary line, which serves as ahorizontal reference line (Altuc-Atac et al., 2008; Yamashita et al.,2009; Gosla-Reddy et al., 2011). Both techniques involving areference line (either vertical or horizontal) are also applied incombination (Baudouin and Tiberghien, 2004; Fong et al., 2010).Baudouin and Tiberghien use a coordinate system with the x-axis

Fig. 2. First, the median sagittal line, which passes through n and sn in this case, isconstructed. Then the differences in height and the distances from the vertical ofbilateral points can be measured.


being the bipupillary line and the y-axis being the median sagittalline. Its origin is located approximately at n as depicted in Fig. 3.

3.3.1. Calculation of a symmetry valueCalculations of a symmetry value obtained by using only a

horizontal reference line have not been published. However, thecombination of values obtained via the median sagittal line and ahorizontal reference line has been mentioned in literature.Baudouin and Tiberghien (2004) use a technique which involvessingle points (points lying more or less on the median sagittal line)as well as bilateral pairs of points. The symmetry index calculatedby Baudouin does not represent an absolute value, but rather arelative measure with respect to the group of faces under investi-gation. This technique takes into account vertical as well as hori-zontal symmetry by using signed x- and y-coordinates. Initially, foreach pair of values an individual symmetry value is calculated: Forbilateral points it is defined as the absolute value of the sum of theirx-coordinates (vertical component) or as the absolute value of thedifference between their y-coordinates (horizontal component).For single points, only the vertical symmetry can be specified as theabsolute value of the x-coordinate. The symmetry value of theentire face (named z-score) is then calculated as:

z� score ¼ 1n

Xn

i¼1

xi � xisi

:

Here, xi denotes the symmetry value of a single point or of a pair ofpoints for one direction calculated for an individual face, while xidenotes the average of this variable over the reference group and siits standard deviation. In this way, a partial z-score is calculated foreach measured variable of the regarded face. Subsequently, a totalface specific z-score is obtained by averaging over all variables of

Fig. 3. By constructing a horizontal reference line (passing through points rarelyaffected by asymmetries) as well as a vertical reference line, measurements in verticaland horizontal directions are possible. Fong et al. (2010) additionally use line segmentswhich can be measured on both sides and may be compared in the same way as thedistances. Moreover, they compare bilateral angles.



one face. The analogous calculations of an “overall vertical sym-metry” and an “overall horizontal symmetry” are described in(Baudouin and Tiberghien, 2004), too. As the z-score defines arelative symmetry value in comparison to a reference group, z-scorevalues <0 indicate a lower symmetry than the average, whilevalues >0 indicate a higher symmetry.

The AI described above (Section 3.2) could also be utilized in acombined investigation of vertical and horizontal asymmetry as ithas been done by Fong et al. (2010). However, neither this authornor others have applied the AI in this context.

3.4. Usage of distances without a reference line

For this method, bilateral points are connected by straight lines.The distance in the horizontal direction between the centres of twolines is then measured in pixels or millimetres (Fig. 4). This gives ameasure of the symmetry as described in (Grammar and Thornhill,1994; Rikowski and Grammar, 1999; Scheib et al., 1999; Penton-Voak et al., 2001).

3.4.1. Calculation of a symmetry valueThe centres mi of bilateral points (i.e. the absolute values of the

x-coordinates) on the left xli and on the right xri are calculated as:

mi ¼��xri � xli

2

��:

In the next step, the horizontal distances between the centresare determined. This obviates the need for the construction of amedian sagittal line. The sum of absolute values of all differences ofthe N centres mi provides the face specific asymmetry value:

FA ¼X

i; j ¼ 1;Nj < i

��mi �mj��

Fig. 4. Centres of bilateral points for a determination of symmetry without using areference line.


FA is the so-called overall facial asymmetry, which is the sum ofhorizontal differences between all centres. The central facialasymmetry (CFA), on the other hand, is the sum of horizontal dif-ferences only between neighbouring centres. In this case, multiplevalues per face are obtained. They allow analysis of the local sym-metry characteristics of the face (Grammar and Thornhill, 1994;Scheib et al., 1999).

Similar to the description above, the vertical symmetry can beinvestigated as well. The vertical deviations of correspondingpoints are measured in pixels or millimetres. The sum of thesevalues results in a variable, specifying the symmetry. Grammar andThornhill (1994) described this technique in detail. Scheib et al.(1999) use a similar method for a vertical analysis of symmetrybymeans of differences in height of reference points, but it remainsunclear whether or not a horizontal reference line has been used.

3.5. Usage of angles

Here, the angles between straight lines, each connecting tworeference points, are evaluated. In the case of an ideal symmetrythese lines would be parallel. This technique is applied using hor-izontal lines (Hwang et al., 2007; Song et al., 2007; Altuc-Atac et al.,2008; Yamashita et al., 2009; Yu et al., 2009) as well as vertical lines(Danel and Pawlowski, 2007; Yu et al., 2009; Fig. 5). In some cases,reference lines, such as the median sagittal line or the bipupillaryline are used. Vertical reference lines are used especially in order toinvestigate the midface and the lower face (Danel and Pawlowski,2007; Yu et al., 2009).

3.5.1. Calculation of a symmetry valueIn one paper the asymmetry is estimated as the sum of angles as

well. Both vertical and horizontal angles are included. Examplesare: the angle between the bipupillary line and the line connecting

Fig. 5. Investigation of the symmetry characteristics in the lower face using the me-dian sagittal line: The angle between the nearly vertical line through two points andthe vertical reference line is measured.


Fig. 6. The partial outline shown here is the most frequently used.


the corners of the mouth; the angle between a vertical referenceline and the line passing through the nasion and a second point,which in the ideally symmetric case would be located on the me-dian sagittal line. In the symmetric face the sum of angles equalszero.

Song et al. (2007) use only the first angle. The sign of the angledefines which side of the face is dominant. Yu et al. (2009) usemultiple angles, one horizontal and three vertical.

3.6. Area of the face in the frontal view

Area measurements of parts of both sides of the face (Legovi�cet al., 2001), of the lower face (Edler et al., 2001, 2002, 2003;Good et al., 2006) as well as of the nares (by using a photo takenfrom below) (Gosla-Reddy et al., 2011) have been published. Inorder to calculate the area, first the outline has to be determined. Asthe adjacent hair can interfere with measurement, the authorsEdler et al. (2001, 2002, 2003) and Good et al. (2006) restrict themeasurement to the lower face. In addition to the outline and thearea, the latter authors calculate the “compactness”, which is thesquared length of the outline divided by the area, the centre of areaand its distance from the median line. Using these variables allowsthem to make statements about symmetry.

3.6.1. Calculation of a symmetry valueThe method proposed by Legovi�c et al. (2001) does not require

the identification of any reference points except for those used forthe determination of a line of symmetry. Parts of the left and rightside of the face areas are calculated and compared using millimetrepaper on photos. Edler et al. (2001, 2002, 2003) and Good et al.(2006) use only a few reference points (point ado on both sides)and utilize the outline, the area, the compactness and the centre ofthe area as described above.

3.7. Other methods

In some reported cases parts of the outline of the face on bothsides are also utilized. For example, Altug-Atac et al. (2008) mea-sure the length of the outline between bilateral points (Fig. 6).

In several of the articles considered no face specific symmetryvalue is calculated and only single variables are analysed (Edleret al., 2001, 2002, 2003; Altug-Atac et al., 2008; Yamashita et al.,2009; Gosla-Reddy et al., 2011). Eskelsen et al. (2009) assign facesto the categories “symmetric” or “asymmetric”. Danel andPawlowski (2007) determine the facial symmetry characteristicsby just one single vertical angle in order to decide whether the leftor the right side of the face is dominant.

4. Discussion

The techniques chosen to measure the variables inevitablyresult in different methods to obtain a face specific, quantitativesymmetry value.

Techniques which only measure single angles or the outline, orcalculate the facial area cannot be recommended for an analysis of theentire face. However, they may be adequate for investigating partialaspects of facial symmetry. This is because thesemethods use too fewreference points or omit features inside the outline of the face.

When analysing the face without the use of a reference line, thetechnique of calculating the FA (overall facial asymmetry, see 3.4)seems most recommendable (Grammar and Thornhill, 1994;Rikowski and Grammar, 1999; Scheib et al., 1999; Penton-Voaket al., 2001). When multiple faces are to be compared, a repro-ducible alignment of the faces should be ensured. This is quitesimilar to the use of a reference line.


In contrast, when using a technique with one vertical referenceline, the calculation of several AI values (Nakamura et al., 2001) andsubsequent averaging seems appropriate to obtain a face specificasymmetry value. However, this approach has not been covered inliterature so far.

When using both a horizontal and a vertical reference line, atechnique similar to the calculation of the z-score (Baudouin andTiberghien, 2004) can be recommended, but instead of calcu-lating a relative symmetry value linked to a reference group, thesymmetry value should rather be defined in absolute terms like theAI in order to be more universal.

It is essential to choose from the measuring techniques intro-duced thosewhich are practical and precise. When taking photos ofthe subjects, a consistent image scale is essential. A comprehensivelist of instructions for clinical photography in cranio-maxillo-facialsurgery concerning illumination, views, technical advices andcommon mistakes is described and discussed in (Ettorre et al.,2006) and (Schaaf et al., 2006). Several independent examinersshould determine the reference points. This would simplify thedetection of mistakes and allow for a determination of statisticalaccuracy. Only accurately reproducible reference points should betaken into account. The points en, ex, p, ch can be identifiedunambiguously, while the location of the points zy, sn, lup, ldo, st,m,eup, tr, aup, ado has to be, at least partly, estimated. In general, notall athropometric landmarks are identifiable in clinical photo-grammetric techniques with high precision and reproducibility. Adetailed comparison of anthropometry with photogrammetry ismade by Han et al. (2010). All points covered by hair, hidden insome way or cut off from the image are difficult to reproduce. It iscrucial to find the optimal number of reference points. Using a largenumber of points increases accuracy but also leads to additionalexpenses. Points with a lower reproducibility can be omitted inorder to reduce their overall number. Similar to Fig. 1, the pointsshould be distributed evenly in the face and cover all areas relevant


Table 1Advantages and disadvantages of the most recommendable 2D analysis techniques of facial asymmetry.

Technique Short description Advantages Disadvantages

FA ¼ “overall facialasymmetry” as a sum

No use of a reference line; vertical andhorizontal symmetry characteristicscan be determined.

No errors related to theconstruction of referencelines; simple calculation.

No statement about which is thedominant half of the face; onlybilateral points usable; dependencyon the number of reference points.

AI ¼ “asymmetry index” in % Vertical reference line; individualsymmetry values for pairs of points;overall asymmetry index could becalculated by averaging; also applicablewith a horizontal reference line.

Clear results in %; simplecalculation.

Errors associated with the constructionof the reference line are possible; noprocedure to calculate an overallasymmetry index published; nostatement about which is thedominant half of the face; onlyapplicable with bilateral points.

z-score ¼ relative symmetry value incomparison to a reference group

Use of a horizontal and vertical referenceline; relative symmetry value with respectto a reference group.

Horizontal and verticalaspects are taken intoaccount; points lyingon the median sagittalline are included.

Relative values, only useful inconnection with the investigatedgroup; no statement about whichis the dominant half of the face.


for the symmetry characteristics, especially the nose, the eyes andthe mouth.

The construction of a reference linemay cause problems as well:When a line is defined that passes through two reference points,errors may occur if these points are not exactly placed on themedian in the case of a vertical reference line. The same mayhappen, if they are not placed at the same height in the case of ahorizontal reference line, which can occur in asymmetric faces.

According to the criteria mentioned above the techniquesregarded as recommendable are summarized in Table 1 along withthe advantages and disadvantages of each approach.

5. Conclusions

Three techniques denoted by FA, AI and z-score are recom-mended for determining an asymmetry value of the face from 2Dimages. For highest accuracy, an adequate number of evenlydistributed and reproducible reference points should be used,which cover all areas significant for symmetry (see Fig. 1). Severalindependent examiners should determine the reference points inorder to reduce the uncertainty of subjective identification.

For future work, a comparison of facial asymmetry analysistechniques based on 2D data with those based on 3D datawould bean interesting task. A further question that arises in this context is,what relations might exist between objective quantification offacial asymmetry and subjective perception.

Financial supportDeutsche Krebshilfe (German Cancer Aid).

Acknowledgement

The presented study has been carried out within the frame of aninterdisciplinary project in which the computer aided constructionof facial prostheses based on optically acquired data is investigated.Financial support by the Deutsche Krebshilfe (German Cancer Aid)is gratefully acknowledged.

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