Biogeneric tooth: a new mathematical representation for tooth morphology in lower first molars

A mathematical representation of tooth morphology may help to improve and automate restorative computer-aided design processes, virtual dental education, and parametric morphology. However, to date, no quantitative formulation has been identified for the description of dental features. The aim of this study was to establish and to validate a mathematical process for describing the morphology of first lower molars. Stone replicas of 170 caries-free first lower molars from young patients were measured three-dimensionally with a resolution of about 100,000 points. First, the average tooth was computed, which captures the common features of the molar's surface quantitatively. For this, the crucial step was to establish a dense point-to-point correspondence between all teeth. The algorithm did not involve any prior knowledge about teeth. In a second step, principal component analysis was carried out. Repeated for 3 different reference teeth, the procedure yielded average teeth that were nearly independent of the reference (less than +/- 40 microm). Additionally, the results indicate that only a few principal components determine a high percentage of the three-dimensional shape variability of first lower molars (e.g. the first five principal components describe 52% of the total variance, the first 10 principal components 72% and the first 20 principal components 83%). With the novel approach presented in this paper, surfaces of teeth can be described efficiently in terms of only a few parameters. This mathematical representation is called the 'biogeneric tooth'.