Abstract
Evidence-based practice in oral and maxillofacial surgery would greatly benefit from an objective assessment of facial harmony or gestalt. Normal reference faces have previously been introduced, but they describe harmony in facial form as an average only and fail to report on harmonic variations found between non-dysmorphic faces. In this work, facial harmony, in all its complexity, is defined using a face-space, which describes all possible variations within a non-dysmorphic population; this was sampled here, based on 400 healthy subjects. Subsequently, dysmorphometrics, which involves the measurement of morphological abnormalities, is employed to construct the normal-equivalent within the given face-space of a presented dysmorphic face. The normal-equivalent can be seen as a synthetic identical but unaffected twin that is a patient-specific and population-based normal. It is used to extract objective scores of facial discordancy. This technique, along with a comparing approach, was used on healthy subjects to establish ranges of discordancy that are accepted to be normal, as well as on two patient examples before and after surgical intervention. The specificity of the presented normal-equivalent approach was confirmed by correctly attributing abnormality and providing regional depictions of the known dysmorphologies. Furthermore, it proved to be superior to the comparing approach.
Introduction
The means to evaluate facial gestalt and the harmony within it, in an objective manner, is important in evidence-based decision-making and for optimizing standards of care in oral and maxillofacial surgery. This requires quantitative assessments of facial form, a concept that encompasses size and shape independent from orientation and position, in combination with a useful definition of harmony: A harmonious form can be defined as a form that is considered to be within normal or typical variation. Facial discordancy is the lack of harmony and is best known in craniofacial disorders for which the surgical objective is to achieve normality. That is, the outcome of the intervention should be consistent with the facial form of the patient without any discordancy. This presents two challenges: defining normality or harmony in facial form and relating the dysmorphic face with respect to normality by identifying, localizing, and quantifying the discordancy.
This has in part been addressed by conventional facial anthropometrics comprising a variety of Euclidean distances, ratios, and angles between defined landmarks with established population-based normative datasets. These measures can, however, be an oversimplification of the three-dimensional (3D) facial complex when used in isolation and are difficult to interpret when used collectively. As an alternative, full 3D facial images were introduced as ‘archetypes’ for the diagnosis of syndromic faces and for the assessment of craniofacial disorders. In essence an archetype is a single ‘averaged’ face that is a representative or reference for a certain population, e.g. the average of a non-clinical population sample. However, the use of these archetypes is limited, as an average face rarely if ever resembles a typical face. There is a large variation in ‘normality’ with respect to facial form and this is why average faces do not look right and variations need to be accepted. The means to establish a patient-specific typical or normalized reference is more desirable. For example, consider the situation of identical twins, where one of the twins is unaffected whilst the other presents a craniofacial disorder ( Fig. 1 a and b). In such a setup, the unaffected twin can serve as a normalized reference for the affected twin. However, even in this useful (but very rare) situation, remaining differences of no interest are noted in both twins, influencing the assessment of harmony. For example, due to differences in self-esteem, the unaffected twin may live a healthier life, resulting in a lower body mass index (BMI) compared to the affected twin.
In this work a novel approach to assess 3D facial harmony in a patient-specific way is proposed. This approach uses a face-space instead of an archetype, in combination with the recently proposed technique of dysmorphometrics. In essence, a face-space is an expansion of archetypes, capturing the average facial form as well as differences and variations between facial forms in a given population. A face-space is used to establish the boundaries of what is normal in all its complexity. Thus, it captures all possible variations of facial harmony. The main strength of a face-space is the ability to construct new or synthetic faces within the range of harmonious facial variations. Subsequently, dysmorphometrics, which involves the measurement of morphological abnormalities, is employed to construct the ‘normal-equivalent’, which is a constructed face within the given face-space, of a presented dysmorphic face. In principle, the normal-equivalent is a synthetic identical but unaffected twin ( Fig. 1 c) that uses the ‘normal’ parts of the dysmorphic face to determine the ‘full normal’ face of the individual. As such it also compensates for facial differences of no interest due to differences in BMI, age, gender, ancestry, facial type, etc. Assessment of harmony is then simply obtained by comparing the dysmorphic face to its normal-equivalent. The overall degree (severity) and the extent (proportion) of the discordancy in the face are both scored using this approach. In this study, these scores were also recorded for healthy subjects to establish the range of discordancy expected in non-clinical faces. The proposed approach can be applied to a wide range of clinical abnormalities, without any modification. Pre- and postoperative 3D images of two clinical cases are used to illustrate the benefit of the technique compared to an archetype-based analysis.
Materials and methods
Participants
3D facial images of healthy young individuals between the ages of 5 and 25 years, of admixed self-reported ancestry, who had provided written informed consent, were made available from a library of facial scans comprising The Western Australian 3-Dimensional Facial Reference Range for Children and Adolescents. Distribution statistics for age and BMI can be found in Table 1 . Subjects completed a questionnaire on relevant health history and population affinity. Exclusion was made on the basis of self-reported prior surgery or the diagnosis of any condition impacting on the face. There was no exclusion based on facial type (short–long, Class I, II, and III profile, etc.). Subjects were instructed to display a neutral facial expression, in their natural head position, when scanned. The study cohort consisted of images of 400 individuals (210 females and 190 males). The precision and repeatability of the used 3dMDface™ (two pod) system was previously tested and validated by Aldridge et al. to be sub-millimetre.
| Age (years) | BMI | Normal-equivalent assessment | Archetype assessment | |||
|---|---|---|---|---|---|---|
| RMSE (mm) | RSD (%) | RMSE (mm) | RSD (%) | |||
| Mean | 16 | 21 | 0.91 | 10.6 | 4.00 | 16.30 |
| SD | 5.3 | 3.4 | 0.22 | 1.8 | 1.68 | 2.5 |
| First quartile | 11 | 18 | 0.75 | 9.5 | 2.84 | 14.5 |
| Median | 18 | 21 | 0.86 | 10.2 | 3.60 | 15.9 |
| Third quartile | 20 | 23 | 0.98 | 11.3 | 4.74 | 17.7 |
| Min | 5 | 15 | 0.52 | 7.3 | 1.51 | 11.2 |
| Max | 25 | 30 | 2.31 | 18.5 | 13.21 | 27.4 |
Two patient cases are presented for illustrative purposes: (1) a 19-year-old woman with right hemimandibular hypertrophy who presented with a discrepancy in the lower mandibular border and an occlusal cant. This was corrected with a lower border mandibular ostectomy in combination with a wedge Le Fort I osteotomy and a bilateral sagittal split mandibular osteotomy. The patient’s occlusion and skeletal symmetry were normalized. (2) A 19-year-old woman with a history of repaired unilateral cleft lip and palate who presented with severe maxillary hypoplasia, an occlusal cant, and a discrepancy in dental midlines. Maxillary distraction was performed to correct the occlusal cant and negative overjet prior to bimaxillary osteotomies to establish an optimal occlusal relationship. In both cases 3D images were taken preoperatively (within 6 weeks of the procedure) and postoperatively (at least 3 months after the procedure).
Anthropometric mask and mapping
An anthropometric mask (AM) was non-rigidly mapped onto the total of 404 3D images. The AM is essentially a template covering the facial area of interest, and the mapping thereof onto the facial images is a process equivalent to the indication of traditional anthropometric landmarks. This established homologous spatially dense (∼10,000) quasi-landmark configurations for all 3D images. Note that by homologous we mean that each quasi-landmark occupies the same position on the face relative to all other quasi-landmarks for all individuals. In other words, each quasi-landmark is a single measurement (∼10,000 measurements in total) in a specific anatomical location of the face and these measurements are made consistently on all 3D images. Therefore, image data from different individuals were standardized and could be analyzed in a spatially dense way. As shown in a previous work, this allows the quantification of the facial form and differences in facial form in a spatially dense and anatomically meaningful manner.
Face-space
A generalized Procrustes superimposition of all quasi-landmark configurations was performed to eliminate any position and orientation differences between all 3D images. Subsequently a principal component analysis (PCA), which is a typical technique for finding patterns in a complex dataset, was carried out on the quasi-landmark measurements to define the face-space. In PCA the major objective is to select a number of principal components (PC) that will express as much of the total variance in the data as possible. In our case, each PC captures a specific mode of facial variation (simplified examples: quasi-landmark differences between male and female faces or quasi-landmark differences in faces due to BMI, age, ancestry, etc., or quasi-landmark differences between facial types or profiles, etc.). The largest mode of variation within the dataset is extracted by the first PC, with subsequent PCs encoding decreasing portions of the remaining variation. The PCs corresponding to the last two percent of the variance observed in the complete dataset were deleted, since they typically correspond to insignificant variance due to random errors or artefacts arising from the scanning or imaging and mapping processes.
The result from PCA was a mathematical model of normality in all its complexity. It constituted an average facial form as well as variations between facial forms in a given population of 400 non-clinical faces. Furthermore, through various combinations of the PCs, different facial variations can be united into new and unseen synthetic faces. In other words, different facial aspects coded in the face-space can be combined into new and harmonious faces. For technical details on face-spaces and their ability to generate synthetic faces we refer the reader to the work of Blanz and Vetter, as well as a previous work.
Dysmorphometrics and the normal-equivalent
Assessment of a face with or without dysmorphology was performed using an appropriate dysmorphometric technique. Dysmorphometrics identifies abnormal morphology, given what is normal. Dysmorphometrics has been similarly applied in previous studies to measure changes in facial shape due to surgical intervention and asymmetry in facial shape in the presence of abnormalities. For technical details we refer the reader to the published work on dysmorphometics.
In this scenario, dysmorphometrics involves a robust superimposition of the face-space, representing what is normal, onto the face under assessment. It establishes a synthetic face of the given face in terms of harmonious facial variation only. In other words, it uses the ‘normal’ parts of a face to determine a synthetic ‘full normal’ face or identical but unaffected twin of the individual. The superimposition eliminates position, orientation, and, more importantly, harmonious facial differences between the given face and the average face of the face-space. Elimination of harmonious facial variation thus allows the average face of the face-space to actually change or navigate throughout the face-space in order to compensate for form differences of no interest (including differences in BMI, age, gender, ancestry, facial type, etc.) thereby constructing a patient-specific but population-based reference. As a consequence this patient-specific normal encompasses equivalent overall and even localized form characteristics; hence the term normal-equivalent. Simultaneously, during the dysmorphometric superimposition, each of the 10,000 quasi-landmark measurements on the face under assessment obtains a discordancy value, reflecting the recognition of such a quasi-landmark being discordant (value closer to 1) or not (value closer to 0). This allows the separation of the ‘normal’ from ‘abnormal’ parts of the face.
Comparative archetypes
A comparative archetype approach was also developed. In contrast to the normal-equivalent, here the average of the face-space was not allowed to change, whilst the same detection of discordant quasi-landmark measurements was employed from dysmorphometrics. The average was corrected for age and gender using techniques developed previously. These techniques allow the use of the face-space to explicitly create synthetic averages of a certain age and gender value. Subsequently, the face under assessment was compared to the corrected average in the same way it was compared to the normal-equivalent, as explained in the next section.
Scoring, analysis, and visualization
Remaining differences between corresponding quasi-landmarks on the face under assessment and its normal-equivalent or archetype are used to provide numerical and visual feedback as a distance map. A distance map encodes for the distances between corresponding quasi-landmarks on both faces, and is visualized using colours, representing different levels of magnitude, onto the original facial image. It allows for the visual localization of facial regions that are different. This distance map is summarized by a root mean squared error (RMSE), which incorporates both the variance and average of the discordancy as an error in mm. This output reflects the overall degree (magnitude but not the direction) of discordancy found in an individual. The dysmorphometric discordancy values (between 0 and 1) of all the 10,000 quasi-landmark measurements are summarized by their average. This reflects overall relative significant discordancy (RSD) in an individual and can be used to quantify the extent or the proportion of the face being discordant. A high RMSE in combination with a low RSD implies a very localized but severe discordancy. A low RMSE in combination with a high RSD implies a less severe discordancy but affecting a larger part of the face. Other combinations of these two scores are possible, and the two of them together provide more insight than those reported for each alone.
It was expected that some degree of discordancy would be present in non-clinical or normal faces due to the fact that every individual is unique and that some discordancy, if present, is not considered abnormal nor does it affect the individual’s psychosocial functioning. Furthermore, some additional discordancy was expected as a consequence of random errors of scanning and mapping artefacts. Therefore, in order to establish the range of discordancy that is accepted to be ‘normal’, discordancy as described here was computed for each of the 400 healthy individuals in the study cohort. Every face was assessed in turn, whilst using the remaining faces to construct the face-space. Distributions of overall RMSE and RSD scores were computed as a means of reference for patient assessment outcomes enabling them to be expressed as z -scores. Such a score is a standard score and indicates by how many standard deviations an observation is above or below the mean. As such it allows the expression of a patient’s assessment of discordancy relative to the normal ranges of discordancy. Clinically, an absolute value of a z -score (| z -score| is the non-negative value of the z -score without regard to its sign) between 0 and 1 indicates normal or certainly acceptable discordancy. A | z -score| between 1 and 2 indicates an acceptable but borderline discordancy close to the outer ranges of normal discordancy. A | z -score| higher than 2 indicates abnormal discordancy. This was done for both the normal-equivalent and archetype strategies.
Materials and methods
Participants
3D facial images of healthy young individuals between the ages of 5 and 25 years, of admixed self-reported ancestry, who had provided written informed consent, were made available from a library of facial scans comprising The Western Australian 3-Dimensional Facial Reference Range for Children and Adolescents. Distribution statistics for age and BMI can be found in Table 1 . Subjects completed a questionnaire on relevant health history and population affinity. Exclusion was made on the basis of self-reported prior surgery or the diagnosis of any condition impacting on the face. There was no exclusion based on facial type (short–long, Class I, II, and III profile, etc.). Subjects were instructed to display a neutral facial expression, in their natural head position, when scanned. The study cohort consisted of images of 400 individuals (210 females and 190 males). The precision and repeatability of the used 3dMDface™ (two pod) system was previously tested and validated by Aldridge et al. to be sub-millimetre.
| Age (years) | BMI | Normal-equivalent assessment | Archetype assessment | |||
|---|---|---|---|---|---|---|
| RMSE (mm) | RSD (%) | RMSE (mm) | RSD (%) | |||
| Mean | 16 | 21 | 0.91 | 10.6 | 4.00 | 16.30 |
| SD | 5.3 | 3.4 | 0.22 | 1.8 | 1.68 | 2.5 |
| First quartile | 11 | 18 | 0.75 | 9.5 | 2.84 | 14.5 |
| Median | 18 | 21 | 0.86 | 10.2 | 3.60 | 15.9 |
| Third quartile | 20 | 23 | 0.98 | 11.3 | 4.74 | 17.7 |
| Min | 5 | 15 | 0.52 | 7.3 | 1.51 | 11.2 |
| Max | 25 | 30 | 2.31 | 18.5 | 13.21 | 27.4 |
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