Topology of a Smile: Persistent Homology in Dental Imaging

Leon Dahlmeier, Sara Kalisnik Hintz, Albert Mehl, Bastian Rieck
Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), PMLR 334(2):43-58, 2026.

Abstract

CBCT (Cone Beam Computed Tomography) scans provide detailed three-dimensional images, widely used in dentistry for diagnostic and treatment planning tasks. While invaluable, analyzing and documenting these scans is labor-intensive, prompting efforts to automate key steps like the classification and segmentation of anatomical structures to identify tooth types and associated pathologies. In this article, we propose an approach to automation that leverages persistent homology, a framework from topological data analysis that studies the shape of data by identifying features like connected components, holes, and voids across multiple scales. Persistent homology, together with a support vector machine, allows us to classify teeth in a CBCT scan and to perform diagnostics. Our method advances the state of the art, reaching average accuracy scores of 97.67% for tooth-labeling and 96.77% for diagnostic tasks, outperforming a CNN trained on the same data with accuracy of 70.27% and 86.67%, respectively.

Cite this Paper

BibTeX
@InProceedings{pmlr-v334-dahlmeier26a, title = {Topology of a Smile: Persistent Homology in Dental Imaging}, author = {Dahlmeier, Leon and Hintz, Sara Kalisnik and Mehl, Albert and Rieck, Bastian}, booktitle = {Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026)}, pages = {43--58}, year = {2026}, editor = {Berman, Eddie and Bernárdez, Guillermo and Chen, Samantha and Cloninger, Alex and Doster, Timothy and Emerson, Tegan and Grigsby, J. Elisenda and Kvinge, Henry and Lawrence, Hannah and Marrinan, Tim and Myers, Audun and Papillon, Mathilde and Tahmasebi, Behrooz and Telyatnikov, Lev and Walters, Robin and Weber, Melanie and Xie, YuQing and Yeats, Eric}, volume = {334}, number = {2}, series = {Proceedings of Machine Learning Research}, month = {18--20 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v334/main/assets/dahlmeier26a/dahlmeier26a.pdf}, url = {https://proceedings.mlr.press/v334/dahlmeier26a.html}, abstract = {CBCT (Cone Beam Computed Tomography) scans provide detailed three-dimensional images, widely used in dentistry for diagnostic and treatment planning tasks. While invaluable, analyzing and documenting these scans is labor-intensive, prompting efforts to automate key steps like the classification and segmentation of anatomical structures to identify tooth types and associated pathologies. In this article, we propose an approach to automation that leverages persistent homology, a framework from topological data analysis that studies the shape of data by identifying features like connected components, holes, and voids across multiple scales. Persistent homology, together with a support vector machine, allows us to classify teeth in a CBCT scan and to perform diagnostics. Our method advances the state of the art, reaching average accuracy scores of 97.67% for tooth-labeling and 96.77% for diagnostic tasks, outperforming a CNN trained on the same data with accuracy of 70.27% and 86.67%, respectively.} }
Endnote
%0 Conference Paper %T Topology of a Smile: Persistent Homology in Dental Imaging %A Leon Dahlmeier %A Sara Kalisnik Hintz %A Albert Mehl %A Bastian Rieck %B Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026) %C Proceedings of Machine Learning Research %D 2026 %E Eddie Berman %E Guillermo Bernárdez %E Samantha Chen %E Alex Cloninger %E Timothy Doster %E Tegan Emerson %E J. Elisenda Grigsby %E Henry Kvinge %E Hannah Lawrence %E Tim Marrinan %E Audun Myers %E Mathilde Papillon %E Behrooz Tahmasebi %E Lev Telyatnikov %E Robin Walters %E Melanie Weber %E YuQing Xie %E Eric Yeats %F pmlr-v334-dahlmeier26a %I PMLR %P 43--58 %U https://proceedings.mlr.press/v334/dahlmeier26a.html %V 334 %N 2 %X CBCT (Cone Beam Computed Tomography) scans provide detailed three-dimensional images, widely used in dentistry for diagnostic and treatment planning tasks. While invaluable, analyzing and documenting these scans is labor-intensive, prompting efforts to automate key steps like the classification and segmentation of anatomical structures to identify tooth types and associated pathologies. In this article, we propose an approach to automation that leverages persistent homology, a framework from topological data analysis that studies the shape of data by identifying features like connected components, holes, and voids across multiple scales. Persistent homology, together with a support vector machine, allows us to classify teeth in a CBCT scan and to perform diagnostics. Our method advances the state of the art, reaching average accuracy scores of 97.67% for tooth-labeling and 96.77% for diagnostic tasks, outperforming a CNN trained on the same data with accuracy of 70.27% and 86.67%, respectively.
APA
Dahlmeier, L., Hintz, S.K., Mehl, A. & Rieck, B.. (2026). Topology of a Smile: Persistent Homology in Dental Imaging. Proceedings of the 2nd Conference on Topology, Algebra, and Geometry in Data Science(TAG-DS 2026), in Proceedings of Machine Learning Research 334(2):43-58 Available from https://proceedings.mlr.press/v334/dahlmeier26a.html.

Related Material