Abstract
Three-dimensional (3D) shape analysis of anatomical structures is currently based either on the analysis of distances or angles between landmarks or on the computation of metric parameters which characterize the deformation of landmark configurations. However, significant differences which are not related to the normal inter-individual variation are not only metrical but also "structural". For example, in prognathism, it is a whole subset of landmarks which protrudes relative to another subset, in a correlated way. Such a deformation is not directly emphasized by the variation of the landmark coordinates and this suggests the need for additional 3D morphometric tools. We propose to model the 3D landmark configurations by using the oriented matroid theory, a combinatorial mathematical structure which was developed over the past forty years. Oriented matroids allow one to model the relative positions of points in 3D without taking into account the distances between them. It is then possible to characterize some geometrical properties as the convexity or the alignment of subsets of landmarks and to detect structural changes as the crossing of a landmark through the plane defined by three others. We applied this new method on sets of 133 3D cranial landmarks collected on 43 individuals presenting with varying types of coronal craniosynostosis. We computed the oriented matroid-based models and introduced a new discrete distance between two individuals. The matrix of all the distances allows differentiation among the craniosynostosis variant groups. We will also show how it could be used to compare extant and fossil skulls as STS5.