  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 Teichm\"uller 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
Teichm\"uller 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.
