Dysmorphometrics: the modelling of morphological abnormalities

A theoretical concept, called dysmorphometrics, is introduced augmenting current geometric morphometrics with a focus on identifying and modelling form abnormalities. Dysmorphometrics applies the paradigm of detecting form differences as outliers compared to an appropriate norm. To achieve this, the likelihood formulation of landmark superimpositions is extended with outlier processes explicitly introducing a latent variable coding for abnormalities. A tractable solution to this augmented superimposition problem is obtained using Expectation-Maximization. The topography of detected abnormalities is encoded in a dysmorphogram.We demonstrate the use of dysmorphometrics to measure abrupt changes in time, asymmetry and discordancy in a set of human faces presenting with facial abnormalities.The results clearly illustrate the unique power to reveal unusual form differences given only normative data with clear applications in both biomedical practice & research.Morphometrics involves the measurement of morphology based on quantitative descriptions [1]. Different definitions of form exist but the most commonly adopted is that form is defined as size and shape independent of position and orientation [2]. Morphometric methods are designed to measure form and variations in form and have been extensively used in evolutionary, developmental and systematic biology. In those contexts, they provide information on phylogenetic relationships and the evolutionary development of organisms [3]. They also allow for taxonomic discrimination of sampled populations to test whether these were drawn from different (sub)species or not [4]. However, in biomedical contexts unusual from instances such as abnormalities [5] are often encountered and of interest. For example abnormalities may include deformations in form due to congenital malformation and/or environmental constraints as well as abrupt changes in form associated with traumatic injuries and surgical interventions. The occurrence of a