# Tooth morphometry using quasi-conformal theory

arXiv: https://arxiv.org/abs/1901.01651 · HTML: https://mlsanity.com/paper/1901.01651/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Jan 2019.

## Built on by (most cited first, 6 of 6)

- [Topology-Preserving 3D Image Segmentation Based On Hyperelastic Regularization](https://mlsanity.com/paper/2103.16768/) (2021)
- [A unifying framework for n-dimensional quasi-conformal mappings](https://mlsanity.com/paper/2110.10437/) (2021)
- [A Deep Learning Framework for Diffeomorphic Mapping Problems via Quasi-conformal Geometry applied to Imaging](https://mlsanity.com/paper/2110.10580/) (2021)
- [Automatic Landmark Detection and Registration of Brain Cortical Surfaces via Quasi-Conformal Geometry and Convolutional Neural Networks](https://mlsanity.com/paper/2208.07010/) (2022)
- [Adaptive area-preserving parameterization of open and closed anatomical surfaces](https://mlsanity.com/paper/2111.04265/) (2021)
- [Variational Geometry-aware Neural Network based Method for Solving High-dimensional Diffeomorphic Mapping Problems](https://mlsanity.com/paper/2511.01911/) (2025)

## Abstract (arXiv)

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.