Initial results of multilevel principal components analysis of facial shape

Traditionally, active shape models (ASMs) do not make a distinction between groups in the subject population and they rely on methods such as (single-level) principal components analysis (PCA). Multilevel principal components analysis (PCA) allows one to model between-group effects and within-group effects explicitly. Three dimensional (3D) laser scans were taken from 240 subjects (38 Croatian female, 35 Croatian male, 40 English female, 40 English male, 23 Welsh female, 27 Welsh male, 23 Finnish female, and 24 Finnish male) and 21 landmark points were created subsequently for each scan. After Procrustes transformation, eigenvalues from mPCA and from single-level PCA based on these points were examined. mPCA indicated that the first two eigenvalues of largest magnitude related to within-groups components, but that the next largest eigenvalue related to between-groups components. Eigenvalues from single-level PCA always had a larger magnitude than either within-group or between-group eigenvectors at equivalent eigenvalue number. An examination of the first mode of variation indicated possible mixing of between-group and within-group effects in single-level PCA. Component scores for mPCA indicated clustering with country and gender for the between-groups components (as ex-pected), but not for the within-group terms (also as expected). Clustering of component scores for single-level PCA was harder to resolve. In conclusion, mPCA is viable method of forming shape models that offers distinct advantages over single-level PCA when groups occur naturally in the subject population

What’s in a Smile? Initial results of multilevel principal components analysis of facial shape and image texture

Multilevel principal components analysis (mPCA) has previously been shown to provide a simple and straightforward method of forming point distribution models that can be used in (active) shape models. Here we extend the mPCA approach to model image texture as well as shape. As a test case, we consider a set of (2D frontal) facial images from a group of 80 Finnish subjects (34 male; 46 female) with two different facial expressions (smiling and neutral) per subject. Shape (in terms of landmark points) and image texture are considered separately in this initial analysis. Three-level models are constructed that contain levels for biological sex, “within-subject” variation (i.e., facial expression), and “between-subject” variation (i.e., all other sources of variation). By considering eigenvalues, we find that the order of importance as sources of variation for facial shape is: facial expression (47.5%), between-subject variations (45.1%), and then biological sex (7.4%). By contrast, the order for image texture is: between-subject variations (55.5%), facial expression (37.1%), and then biological sex (7.4%). The major modes for the facial expression level of the mPCA models clearly reflect changes in increased mouth size and increased prominence of cheeks during smiling for both shape and texture. Even subtle effects such as changes to eyes and nose shape during smile are seen clearly. The major mode for the biological sex level of the mPCA models similarly relates clearly to changes between male and female. Model fits yield “scores” for each principal component that show strong clustering for both shape and texture by biological sex and facial expression at appropriate levels of the model. We conclude that mPCA correctly decomposes sources of variation due to biological sex and facial expression (etc.) and that it provides a reliable method of forming models of both shape and image texture

Multilevel models of age-related changes in facial shape in adolescents

Here we study the effects of age on facial shape in adolescents by using a method called multilevel principal components analysis (mPCA). An associated multilevel multivariate probability distribution is derived and expressions for the (conditional) probability of age-group membership are presented. This formalism is explored via Monte Carlo (MC) simulated data in the first dataset; where age is taken to increase the overall scale of a three-dimensional facial shape represented by 21 landmark points and all other “subjective” variations are related to the width of the face. Eigenvalue plots make sense and modes of variation correctly identify these two main factors at appropriate levels of the mPCA model. Component scores for both single-level PCA and mPCA show a strong trend with age. Conditional probabilities are shown to predict membership by age group and the Pearson correlation coefficient between actual and predicted group membership is r = 0.99. The effects of outliers added to the MC training data are reduced by the use of robust covariance matrix estimation and robust averaging of matrices. These methods are applied to another dataset containing 12 GPA-scaled (3D) landmark points for 195 shapes from 27 white, male schoolchildren aged 11 to 16 years old. 21% of variation in the shapes for this dataset was accounted for by age. Mode 1 at level 1 (age) via mPCA appears to capture an increase in face height with age, which is consistent with reported pubertal changes in children. Component scores for both single-level PCA and mPCA again show a distinct trend with age. Conditional probabilities are again shown to reflect membership by age group and the Pearson correlation coefficient is given by r = 0.63 in this case. These analyses are an excellent first test of the ability of multilevel statistical methods to model age-related changes in facial shape in adolescents

Initial Investigations of the cranial size and shape of adult Eurasian otters (Lutra lutra) in Great Britain

Three-dimensional (3D) surface scans were carried out in order to determine the shapes of the upper sections of (skeletal) crania of adult Eurasian otters (Lutra lutra) from Great Britain. Landmark points were placed on these shapes using a graphical user interface (GUI) and distance measurements (i.e., the length, height, and width of the crania) were found by using the landmark points. Male otters had significantly larger skulls than females (P < 0.001). Differences in size also occurred by geographical area in Great Britain (P < 0.05). Multilevel Principal Components Analysis (mPCA) indicated that sex and geographical area explained 31.1% and 9.6% of shape variation in “unscaled” shape data and that they explained 17.2% and 9.7% of variation in “scaled” data. The first mode of variation at level 1 (sex) correctly reflected size changes between males and females for “unscaled” shape data. Modes at level 2 (geographical area) also showed possible changes in size and shape. Clustering by sex and geographical area was observed in standardized component scores. Such clustering in a cranial shape by geographical area might reflect genetic differences in otter populations in Great Britain, although other potentially confounding factors (e.g., population age-structure, diet, etc.) might also drive regional differences. This work provides a successful first test of the effectiveness of 3D surface scans and multivariate methods, such as mPCA, to study the cranial morphology of otters

What's in a smile? Initial analyses of dynamic changes in facial shape and appearance

Single-level principal component analysis (PCA) and multi-level PCA (mPCA) methods are applied here to a set of (2D frontal) facial images from a group of 80 Finnish subjects (34 male; 46 female) with two different facial expressions (smiling and neutral) per subject. Inspection of eigenvalues gives insight into the importance of different factors affecting shapes, including: biological sex, facial expression (neutral versus smiling), and all other variations. Biological sex and facial expression are shown to be reflected in those components at appropriate levels of the mPCA model. Dynamic 3D shape data for all phases of a smile made up a second dataset sampled from 60 adult British subjects (31 male; 29 female). Modes of variation reflected the act of smiling at the correct level of the mPCA model. Seven phases of the dynamic smiles are identified: rest pre-smile, onset 1 (acceleration), onset 2 (deceleration), apex, offset 1 (acceleration), offset 2 (deceleration), and rest post-smile. A clear cycle is observed in standardized scores at an appropriate level for mPCA and in single-level PCA. mPCA can be used to study static shapes and images, as well as dynamic changes in shape. It gave us much insight into the question “what’s in a smile?

Multilevel analysis of the influence of maternal smoking and alcohol consumption on the facial shape of English adolescents

This cross-sectional study aims to assess the influence of maternal smoking and alcohol consumption during pregnancy on the facial shape of non-syndromic English adolescents and demonstrate the potential benefits of using multilevel principal component analysis (mPCA). A cohort of 3755 non-syndromic 15-year-olds from the Avon Longitudinal Study of Parents and Children (ALSPAC), England, were included. Maternal smoking and alcohol consumption during the 1st and 2nd trimesters of pregnancy were determined via questionnaire at 18 weeks gestation. 21 facial landmarks, used as a proxy for the main facial features, were manually plotted onto 3D facial scans of the participants. The effect of maternal smoking and maternal alcohol consumption (average 1–2 glasses per week) was minimal, with 0.66% and 0.48% of the variation in the 21 landmarks of non-syndromic offspring explained, respectively. This study provides a further example of mPCA being used effectively as a descriptive analysis in facial shape research. This is the first example of mPCA being extended to four levels to assess the influence of environmental factors. Further work on the influence of high/low levels of smoking and alcohol and providing inferential evidence is required

Facial genetics: A brief overview

Historically, craniofacial genetic research has understandably focused on identifying the causes of craniofacial anomalies and it has only been within the last 10 years, that there has been a drive to detail the biological basis of normal-range facial variation. This initiative has been facilitated by the availability of low-cost hi-resolution three-dimensional systems which have the ability to capture the facial details of thousands of individuals quickly and accurately. Simultaneous advances in genotyping technology have enabled the exploration of genetic influences on facial phenotypes, both in the present day and across human history. There are several important reasons for exploring the genetics of normal-range variation in facial morphology.     - Disentangling the environmental factors and relative parental biological contributions to heritable traits can help to answer the age-old question "why we look the way that we do?"     - Understanding the etiology of craniofacial anomalies; e.g., unaffected family members of individuals with non-syndromic cleft lip/palate (nsCL/P) have been shown to differ in terms of normal-range facial variation to the general population suggesting an etiological link between facial morphology and nsCL/P.     - Many factors such as ancestry, sex, eye/hair color as well as distinctive facial features (such as, shape of the chin, cheeks, eyes, forehead, lips, and nose) can be identified or estimated using an individual's genetic data, with potential applications in healthcare and forensics.     - Improved understanding of historical selection and adaptation relating to facial phenotypes, for example, skin pigmentation and geographical latitude.     - Highlighting what is known about shared facial traits, medical conditions and genes

Facial Genetics: A Brief Overview

Historically, craniofacial genetic research has understandably focused on identifying the causes of craniofacial anomalies and it has only been within the last 10 years, that there has been a drive to detail the biological basis of normal-range facial variation. This initiative has been facilitated by the availability of low-cost hi-resolution three-dimensional systems which have the ability to capture the facial details of thousands of individuals quickly and accurately. Simultaneous advances in genotyping technology have enabled the exploration of genetic influences on facial phenotypes, both in the present day and across human history. There are several important reasons for exploring the genetics of normal-range variation in facial morphology.     - Disentangling the environmental factors and relative parental biological contributions to heritable traits can help to answer the age-old question "why we look the way that we do?"     - Understanding the etiology of craniofacial anomalies; e.g., unaffected family members of individuals with non-syndromic cleft lip/palate (nsCL/P) have been shown to differ in terms of normal-range facial variation to the general population suggesting an etiological link between facial morphology and nsCL/P.     - Many factors such as ancestry, sex, eye/hair color as well as distinctive facial features (such as, shape of the chin, cheeks, eyes, forehead, lips, and nose) can be identified or estimated using an individual's genetic data, with potential applications in healthcare and forensics.     - Improved understanding of historical selection and adaptation relating to facial phenotypes, for example, skin pigmentation and geographical latitude.     - Highlighting what is known about shared facial traits, medical conditions and genes