Landmark-free geometric methods in biological shape analysis

In this paper, we propose a new approach for computing a distance between two shapes embedded in three-dimensional space. We take as input a pair of triangulated genus zero surfaces that are topologically equivalent to spheres with no holes or handles, and construct a discrete conformal map f between the surfaces. The conformal map is chosen to minimize a symmetric deformation energy E(sd)(f) which we introduce. This measures the distance of f from an isometry, i.e. a non-distorting correspondence. We show that the energy of the minimizing map gives a well-behaved metric on the space of genus zero surfaces. In contrast to most methods in this field, our approach does not rely on any assignment of landmarks on the two surfaces. We illustrate applications of our approach to geometric morphometrics using three datasets representing the bones and teeth of primates. Experiments on these datasets show that our approach performs remarkably well both in shape recognition and in identifying evolutionary patterns, with success rates similar to, and in some cases better than, those obtained by expert observers

Second premolar agenesis is associated with mandibular form : a geometric morphometric analysis of mandibular cross-sections

The aim of this study was to compare mandibular form (i.e., size and shape) between patients with agenesis of the lower second premolar (P2) and a control group with no agenesis. Three hypotheses were tested: (H1) agenesis causes a change in mandibular morphology because of inadequate alveolar ridge development in the area of the missing tooth (mandibular plasticity); (H2) agenesis is caused by spatial limitations within the mandible (dental plasticity); and (H3) common genetic/ epigenetic factors cause agenesis and affect mandibular form (pleiotropy). A geometric morphometric analysis was applied to cross-sectional images of computed tomography (CT) scans of three matched groups (n = 50 each): (1) regularly erupted P2; (2) agenesis of P2 and the primary second molar in situ; and (3) agenesis of P2 and the primary second molar missing for 43 months. Cross-sections of the three areas of interest (first premolar, P2, first molar) were digitized with 23 landmarks and superimposed by a generalized Procrustes analysis. On average, the mandibular cross-sections were narrower and shorter in patients with P2 agenesis compared with that in the control group. Both agenesis groups featured a pronounced submandibular fossa. These differences extended at least one tooth beyond the agenesis-affected region. Taken together with the large interindividual variation that resulted in massively overlapping group distributions, these findings support genetic and/or epigenetic pleiotropy (H3) as the most likely origin of the observed covariation between mandibular form and odontogenesis. Clinically, reduced dimensions and greater variability of mandibular form, as well as a pronounced submandibular fossa, should be expected during the treatment planning of patients with P2 agenesis