On the measurement and analysis of asymmetry with applications to facial modelling

An innovative analysis of nasolabial dynamics of surgically managed adult patients with unilateral cleft lip and palate using 3D facial motion capture

AIM

To compare dynamic nasolabial movement between end-of-treatment cleft and a matched non-cleft group in adult patients.

MATERIALS AND METHODS

Thirteen treated adult participants with unilateral cleft lip and palate had images taken using a facial motion capture system performing a maximum smile. Seventeen landmarks were automatically tracked. For each landmark pair, on either side of the midline, changes in the x, y, and z directions were used to analyze the magnitude of displacement and path of motion. An asymmetry score was developed at rest, mid-smile, and maximum smile to assess the shape of the mouth and/or nose.

RESULTS

At maximum smile, displacement of right and left cheilion was clinically and statistically (p < 0.05) less in the cleft group. The lip asymmetry score was greater (p < 0.05) at each time point in the cleft group using the clinical midline. Using Procrustes superimposition, the differences were significant (p < 0.05) only at rest and mid-smile. The alar bases were displaced significantly less (p < 0.05) in the z direction in the cleft group. The asymmetry score of the alar base was significantly higher using the clinical midline than using Procrustes superimposition in patients with cleft conditions (p < 0.001). In the cleft group, at maximum smile, the right and left cristae philter moved significantly less (p < 0.05) in the x and z directions.

CONCLUSIONS

There was an increase in asymmetry score of the corners of the mouth and alar bases from rest to maximum smile. The lips were similar in shape but oriented differently in the faces of patients with cleft conditions than in individuals without those conditions.

Bowman A. Functional data analysis and visualisation of three-dimensional surface shape

The advent of high-resolution imaging has made data on surface shape widespread. Methods for the analysis of shape based on landmarks are well established but high-resolution data require a functional approach. The starting point is a systematic and consistent description of each surface shape and a method for creating this is described. Three innovative forms of analysis are then introduced. The first uses surface integration to address issues of registration, principal component analysis and the measurement of asymmetry, all in functional form. Computational issues are handled through discrete approximations to integrals, based in this case on appropriate surface area weighted sums. The second innovation is to focus on sub-spaces where interesting behaviour such as group differences are exhibited, rather than on individual principal components. The third innovation concerns the comparison of individual shapes with a relevant control set, where the concept of a normal range is extended to the highly multivariate setting of surface shape. This has particularly strong applications to medical contexts where the assessment of individual patients is very important. All of these ideas are developed and illustrated in the important context of human facial shape, with a strong emphasis on the effective visual communication of effects of interest.

Epistasis regulates the developmental stability of the mouse craniofacial shape

Fluctuating asymmetry is a classic concept linked to organismal development. It has traditionally been used as a measure of developmental instability, which is the inability of an organism to buffer environmental fluctuations during development. Developmental stability has a genetic component that influences the final phenotype of the organism and can lead to congenital disorders. According to alternative hypotheses, this genetic component might be either the result of additive genetic effects or a by-product of developmental gene networks. Here we present a genome-wide association study of the genetic architecture of fluctuating asymmetry of the skull shape in mice. Geometric morphometric methods were applied to quantify fluctuating asymmetry: we estimated fluctuating asymmetry as Mahalanobis distances to the mean asymmetry, correcting first for genetic directional asymmetry. We applied the marginal epistasis test to study epistasis among genomic regions. Results showed no evidence of additive effects but several interacting regions significantly associated with fluctuating asymmetry. Among the candidate genes overlapping these interacting regions we found an over-representation of genes involved in craniofacial development. A gene network is likely to be associated with skull developmental stability, and genes originally described as buffering genes (e.g., Hspa2) might occupy central positions within these networks, where regulatory elements may also play an important role. Our results constitute an important step in the exploration of the molecular roots of developmental stability and the first empirical evidence about its genetic architecture.

Fluctuating asymmetry of dynamic smiles in normal individuals

The aim of this study was to quantify the fluctuating dynamic facial asymmetry during smiling in a group of 'normal' adults, using three-dimensional (3D) motion facial capture technology. Fifty-four male and 54 female volunteers were recruited. Each subject was imaged using a passive markerless 3D motion capture system (DI4D). Eighteen landmarks were tracked through the 3D capture sequence. A facial asymmetry score was calculated based on either a clinically derived midline or Procrustes alignment; scores were based on the Euclidean distance between landmark pairs. Facial asymmetry scores were determined at three time points: rest, median, and maximum frame. Based on the clinically derived midline and on Procrustes alignment, the differences between male and female volunteers, as well as those at the three different time points, were not clinically significant. However, throughout a smile, facial and lip asymmetry scores increased over the duration of the smile. Fluctuating facial asymmetry exists within individuals, as well as between individuals. Procrustes superimposition and the clinically derived midline produced similar asymmetry scores and both are valid for symmetrical faces. However, with facial asymmetry, Procrustes superimposition may not be a valid measure, and the use of the clinically derived midline may be more appropriate, although this requires further investigation.

Assessing the outcome of orthognathic surgery by three-dimensional soft tissue analysis

Studies of orthognathic surgery often focus on pre-surgical versus post-surgical changes in facial shape. In contrast, this study provides an innovative comparison between post-surgical and control shape. Forty orthognathic surgery patients were included, who underwent three different types of surgical correction: Le Fort I maxillary advancement, bilateral sagittal split mandibular advancement, and bimaxillary advancement surgery. Control facial images were captured from volunteers from local communities in Glasgow, with patterns of age, sex, and ethnic background that matched those of the surgical patients. Facial models were fitted and Procrustes registration and principal components analysis used to allow quantitative analysis, including the comparison of group mean shape and mean asymmetry. The primary characteristic of the difference in shape was found to be residual mandibular prognathism in the group of female patients who underwent Le Fort I maxillary advancement. Individual cases were assessed against this type of shape difference, using a quantitative scale to aid clinical audit. Analysis of the combined surgical groups provided strong evidence that surgery reduces asymmetry in some parts of the face such as the upper lip region. No evidence was found that mean asymmetry in post-surgical patients is greater than that in controls.

Using three-dimensional average facial meshes to determine nasolabial soft tissue deformity in adult UCLP patients

BACKGROUND AND PURPOSE

There is limited literature discussing the residual nasolabial deformity of adult patients prior to undergoing orthognathic surgery. The purpose of this study is to determine the site and severity of the residual nasolabial soft tissue deformity between adult unilateral cleft lip and palate (UCLP) patients and a non-cleft reference group, prior to orthognathic surgery.

MATERIAL AND METHODS

Sixteen adult male UCLP patients, who all received primary lip and palate surgery according to a standardised Hong Kong protocol were recruited for this study. Facial images of each individual were captured using three-dimensional (3D) stereophotogrammetry and compared to a previous published Hong Kong non-cleft reference group of 48 male adults. Using two-sample t-tests differences in linear and angular measurements and asymmetry scores were evaluated between the two groups. In addition a "conformed" average UCLP facial template was superimposed and compared to conformed average non-cleft reference group facial template. Reproducibility of the measurements were assessed using Students paired t-tests and coefficients of reliability.

MAIN FINDINGS

Significant differences in linear and angular measurements and asymmetry scores were observed between the two groups (p < 0.05). Adult UCLP patients showed significantly narrower nostril floor widths, longer columella length on the unaffected side, a wider nose, shorter cutaneous lip height, shorter upper lip length and shorter philtrum length. Prior to orthognathic surgery adult UCLP patients showed significantly more facial asymmetry. Superimposition of the average facial meshes clearly showed the site and severity of the deficiency in the x, y and z-directions.

CONCLUSIONS

Many of the nasolabial characteristics reported to be present in children following primary UCLP repair continue into adulthood. The detrimental soft tissue effects of orthognathic surgery for UCLP patients may be different to non-cleft individuals; and as such the site and severity of the residual deformity should be assessed prior to surgery.

The definitions of three-dimensional landmarks on the human face: an interdisciplinary view

The analysis of shape is a key part of anatomical research and in the large majority of cases landmarks provide a standard starting point. However, while the technology of image capture has developed rapidly and in particular three‐dimensional imaging is widely available, the definitions of anatomical landmarks remain rooted in their two‐dimensional origins. In the important case of the human face, standard definitions often require careful orientation of the subject. This paper considers the definitions of facial landmarks from an interdisciplinary perspective, including biological and clinical motivations, issues associated with imaging and subsequent analysis, and the mathematical definition of surface shape using differential geometry. This last perspective provides a route to definitions of landmarks based on surface curvature, often making use of ridge and valley curves, which is genuinely three‐dimensional and is independent of orientation. Specific definitions based on curvature are proposed. These are evaluated, along with traditional definitions, in a study that uses a hierarchical (random effects) model to estimate the error variation that is present at several different levels within the image capture process. The estimates of variation at these different levels are of interest in their own right but, in addition, evidence is provided that variation is reduced at the observer level when the new landmark definitions are used.

Three-dimensional assessment of facial appearance following surgical repair of unilateral cleft lip and palate

BACKGROUND AND OBJECTIVE

Objective assessment of postsurgical facial asymmetry can be difficult, but three-dimensional (3D) imaging techniques have made this possible. The objective of this study was to assess residual asymmetry in surgically repaired unilateral cleft lip (UCL) and unilateral cleft lip and palate (UCLP) patients and to compare this with noncleft controls.

DESIGN

Retrospective multicohort comparative study.

PATIENTS AND METHODS

Fifty-one 10-year-old children with surgically managed UCLP and 44 children with UCL were compared with a control group of 68 ten-year-olds. The 3D facial models at rest and with maximum smile were created using a 3D imaging system. Asymmetry scores were produced using both anatomical landmarks and a novel method of facial curve analysis.

RESULTS

Asymmetry for the whole face was significantly higher in both cleft groups compared with controls (P < .001). UCLP asymmetry was higher than UCL (P < .001). In cleft patients, the upper lip and nasal rim were the most asymmetric (P < .001 to .05). Control subjects also displayed a degree of facial asymmetry. Maximum smile did not significantly affect the symmetry of the whole face, but it increased asymmetry of the vermillion border and nasal rim in all three groups (P < .001).

CONCLUSIONS

Despite surgical intervention at an early age, asymmetry remains significant in cleft patients at 10 years of age. Three-dimensional imaging is a noninvasive objective assessment tool that identifies specific areas of the face responsible for asymmetry. Facial curve analysis describes the face more comprehensively and characterizes soft tissue contours.

Psychological status as a function of residual scarring and facial asymmetry after surgical repair of cleft lip and palate

Objective : Objective measure of scarring and three-dimensional (3D) facial asymmetry after surgical correction of unilateral cleft lip (UCL) and unilateral cleft lip (UCLP). It was hypothesized that the degree of scarring or asymmetry would be correlated with poorer psychological function. Design : In a cross-sectional design, children underwent 3D imaging of the face and completed standardized assessments of self-esteem, depression, and state and trait anxiety. Parents rated children's adjustment with a standard scale. Setting : Glasgow Dental School, School of Medicine, College of Medical, Veterinary and Life Sciences. Patients : Fifty-one children aged 10 years with UCLP and 43 with UCL were recruited from the cohort treated with the surgical protocol of the CLEFTSIS managed clinical network in Scotland. Methods : Objective assessment to determine the luminance and redness of the scar and facial asymmetry. Depression, anxiety, and a self-esteem assessment battery were used for the psychological analysis. Results : Cleft cases showed superior psychological adjustment when compared with normative data. Prevalence of depression matched the population norm. The visibility of the scar (luminance ratio) was significantly correlated with lower self-esteem and higher trait anxiety in UCLP children (P  =  .004). Similar but nonsignificant trends were seen in the UCL group. Parental ratings of poorer adjustment also correlated with greater luminance of the scar. Conclusions : The objectively defined degree of postoperative cleft scarring was associated with subclinical symptoms of anxiety, depression, and low self-esteem.

Surface shape analysis with an application to brain surface asymmetry in schizophrenia

Some methods for the statistical analysis of surface shapes and asymmetry are introduced. We focus on a case study where magnetic resonance images of the brain are available from groups of 30 schizophrenia patients and 38 controls, and we investigate large-scale brain surface shape differences. Key aspects of shape analysis are to remove nuisance transformations by registration and to identify which parts of one object correspond with the parts of another object. We introduce maximum likelihood and Bayesian methods for registering brain images and providing large-scale correspondences of the brain surfaces. Brain surface size-and-shape analysis is considered using random field theory, and also dimension reduction is carried out using principal and independent components analysis. Some small but significant differences are observed between the the patient and control groups. We then investigate a particular type of asymmetry called torque. Differences in asymmetry are observed between the control and patient groups, which add strength to other observations in the literature. Further investigations of the midline plane location in the 2 groups and the fitting of nonplanar curved midlines are also considered.