Tooth morphometry using quasi-conformal theory.

• A shape classification model based on quasi-conformal theory is proposed. • The surface geometry, anatomical landmarks and curvature differences of the shapes are all taken into account in our proposed method. • The classification accuracy for teeth with respect to ancestry and gender is significantly improved by our proposed method. Shape analysis is important in anthropology, bioarchaeology and forensic science for interpreting useful information from human remains. In particular, teeth are morphologically stable and hence well-suited for shape analysis. In this work, we propose a framework for tooth morphometry using quasi-conformal theory. Landmark-matching Teichmüller maps are used for establishing a 1-1 correspondence between tooth surfaces with prescribed anatomical landmarks. Then, a quasi-conformal statistical shape analysis model based on the Teichmüller mapping results is proposed for building a tooth classification scheme. We deploy our framework on a dataset of human premolars to analyze the tooth shape variation among genders and ancestries. Experimental results show that our method achieves much higher classification accuracy with respect to both gender and ancestry when compared to the existing methods. Furthermore, our model reveals the underlying tooth shape difference between different genders and ancestries in terms of the local geometric distortion and curvatures. In particular, our experiment suggests that the shape difference between genders is mostly captured by the conformal distortion but not the curvatures, while that between ancestries is captured by both of them. [ABSTRACT FROM AUTHOR]