For dysmorphic syndromes with known genetic causes, molecular analysis is the appropriate route of investigation in order to confirm a diagnosis. Even then, there are situations where a clinical examination may suggest multiple possibilities for a diagnosis or none at all. How might 3D models of face shape help to distinguish between different syndromic facial phenotypes? In general, single linear anthropometric facial measures are unlikely to discriminate well between controls and a syndrome or between different syndromes. Multiple measurements, following normalisation, can be combined to determine a craniofacial index of dysmorphology and hence give an average profile for each syndrome against which an individual can be compared.20
Combining measures provides a richer description of the dysmorphology, but the loss of the associated 3D geometry ultimately limits their potential. For example, philtrum length and inner canthal separation might be useful discriminators in isolation or in tandem. It is likely, however, that greater discrimination is achievable using the local geometry, that is, relative 3D juxtaposition, of the landmarks affording these two measurements (left and right inner canthi, subnasale and labiale superius).
Landmarks annotating 3D face surfaces (fig 1B) and derived anthropometric measurements found no significant difference in facial asymmetry between controls and syndrome‐affected individuals.21
No firm conclusions about specific syndromes were able to be drawn because the 30 syndrome‐affected subjects were of mixed ethnicity and affected by one of 18 different conditions. Landmark‐based analyses have established strong discriminating features in a series of elegant studies of male–female and control–schizophrenia face shape differences.22,23
These morphometric studies employ a statistical analysis technique, principal component analysis (PCA), in order to transform the number of variables corresponding to the landmark positions to a much smaller number of important principal components or modes of shape variation. For example, 24 3D landmarks result in 72 parameter values being recorded for each face. The use of PCA can reveal as few as three modes explaining discriminating face shape differences.24
The application of a similar PCA‐based approach to sets of face surfaces made up of tens of thousands of densely corresponded points, rather than a sparse set of landmarks, gives rise to a similar set of modes of face shape variation. The surface of each face can be reconstructed using a linear weighted sum of the PCA modes. The term dense surface model (DSM) has been coined for such a model of 3D face shape.13
A range of other shape modelling techniques are described elsewhere.12,23,24
It is possible to compute the proportion of face shape variation covered by a single DSM mode, and typically the modes are ordered in terms of increasing coverage. By far the greatest amount of variation, often over 80%, captures variation in overall size of the face (fig 3, mode 1, 79.3%). Subsequent modes may correspond to oval/round face shape variation (fig 3, mode 2, 5.3%) or differences in ear and mandible position (fig 3, mode 3, 2.3%). Depending on the mix of faces, the amount of coverage varies and additional shape complexities will be involved. For a DSM for a mixed collection of faces, for example 187 controls and 69 individuals with Williams syndrome, the first, or dominant mode, still reflects face size and correlates highly with age. Separate regressions of mode 1 against age, for the control and Williams syndrome subgroups, enable a quantitative comparison of facial growth (fig 4) that can also be visualised as a diagnostic aid (fig 5). The colour‐distance codings in fig 2 are computed with mode 1 set to 0 in the appropriate DSM and thus emphasise mean shape rather than shape and size differences.
Figure 3Dense surface model (DSM) of face variation for a group of controls. The first three modes of face shape variation in a DSM generated for 187 controls. In each row, the mean is flanked by its morph to −2 and +2 standard (more ...)
Figure 4Mode 1 versus age for DSM of control and Williams syndrome groups. Scatter plot of mode 1 versus age for a mixed DSM of 69 individuals with Williams syndrome and 187 controls. Regression lines, included for each subgroup, demonstrate (more ...)
The later modes resulting from the PCA, those corresponding to extremely small amounts of shape variation, can be ignored and typically only those leading modes covering in total 95–99% are included in a DSM. Frequently, only 50–100 modes are required to cover 99% of shape variation in a set of faces. Thus a face can be represented by an ordered sequence of 50 or so numbers. This is a huge data compaction, reducing the representation of a face surface from as many as 75
000 parameters (25
000 3D points each with x
ordinates) down to 50 or so DSM mode values. The average surface of a set of faces is then represented by the sequence of average values of the different DSM modes. A simple and intuitively appealing way to compare an individual face with two sets of faces is to calculate how close, in terms of the 50 or so mode values, that face surface is to the average face surfaces of each set. Whichever of the average faces is closest determines the classification of the individual. This so‐called closest mean classification algorithm has achieved control–syndrome discrimination rates of between 85% and 95% for Cornelia de Lange,16
Noonan, Smith‐Magenis, velocardiofacial and Williams syndromes. By considering face patches it is also possible to identify regions of the face that are the most discriminating.14,15
Discrimination rates for syndrome–syndrome comparisons are typically a few percentage points lower.