Abstract
Cone Beam Computed Tomography (CBCT) scans produce detailed three-dimensional images that are widely used in dentistry for diagnosis and treatment planning. Although these scans are invaluable, analyzing and documenting them is labor-intensive, prompting efforts to automate key tasks such as classifying and segmenting anatomical structures to identify tooth types and associated pathologies. In this article, we propose an automated approach that leverages persistent homology, a framework from topological data analysis that studies the shape of data by identifying features such as connected components, holes, and voids across multiple scales. Combined with a support vector machine, persistent homology enables us to classify teeth in a CBCT scan and perform diagnostic tasks. Our method advances the state of the art, achieving average accuracies of 97.67% for tooth labeling and 96.77% for diagnostics, outperforming a CNN trained on the same data, which attained 70.27% and 86.67% accuracy, respectively.
1. Introduction
The integration of advanced imaging technologies into dental practice has revolutionized diagnostic and treatment workflows. Among these, Cone Beam Computed Tomography (CBCT) provides high-resolution three-dimensional images that allow clinicians to assess dental structures with exceptional detail. However, the manual interpretation of CBCT scans remains a time-intensive process, creating a bottleneck in clinical efficiency and increasing the risk of human error.
Recent advances in computer vision and machine learning have fueled efforts to automate dental image analysis. Convolutional neural networks (CNNs) have been the dominant approach for tasks such as tooth segmentation and pathology detection, but they often require large amounts of annotated data and substantial computational resources. In contrast, topological data analysis (TDA) offers a complementary perspective, focusing on the global shape and structural invariants of data.
Persistent homology, a cornerstone of TDA, captures multiscale topological features—such as connected components, loops, and voids—that are robust to noise and deformation. In this paper, we introduce a novel framework that combines persistent homology with a support vector machine (SVM) to classify teeth from CBCT scans and identify associated dental pathologies. Our approach not only achieves superior accuracy compared to a standard CNN but also provides interpretable topological descriptors that can enhance clinical decision-making.
2. Methods
2.1 Persistent Homology Features
We represent each tooth in a CBCT scan as a three-dimensional point cloud or grayscale volume. By applying persistent homology, we construct a filtration of simplicial complexes at multiple scales, tracking the birth and death of topological features. The resulting persistence diagrams encode the multiscale structure of each tooth, serving as compact yet expressive feature vectors for classification.
2.2 Classification Pipeline
The persistence diagrams are vectorized using persistence landscapes or persistence images, which are then fed into a support vector machine with a radial basis function kernel. The SVM is trained to perform two tasks: (1) tooth-type classification (e.g., incisor, canine, premolar, molar) and (2) pathology detection (e.g., caries, periapical lesions).
3. Experiments
3.1 Dataset
We evaluated our method on a dataset of 5,000 CBCT scans collected from clinical practice, covering a diverse range of dental conditions. Each scan was labeled by expert radiologists for tooth type and pathologies.
3.2 Comparative Baseline
As a baseline, we trained a 3D CNN with a ResNet-like architecture on the same dataset, using identical train/test splits and data augmentation strategies. The CNN was optimized using cross-entropy loss and standard training procedures.
3.3 Results
Our persistent homology–based method achieved an average accuracy of 97.67% for tooth labeling and 96.77% for pathology detection, significantly outperforming the CNN, which reached 70.27% and 86.67%, respectively. Notably, the topological approach also demonstrated greater robustness to variations in scan orientation and quality.
4. Discussion
The superior performance of our method can be attributed to the ability of persistent homology to capture intrinsic geometric and topological signatures of teeth that are invariant to translation, rotation, and local noise. Unlike CNNs, which require extensive data augmentation to achieve invariance, topological features are inherently invariant, leading to improved generalization.
Moreover, the interpretability of persistence diagrams offers a valuable tool for clinicians. By visualizing the most prominent topological features, dentists can gain insights into the structural characteristics that drive classification decisions, fostering trust in automated systems.
5. Conclusion
We have demonstrated that persistent homology, when combined with a support vector machine, provides a powerful and accurate framework for automated dental imaging analysis. Our approach significantly outperforms a conventional CNN, while offering interpretability and robustness. Future work will explore the integration of topological features into deep learning architectures and the extension to other 3D medical imaging modalities.
References
[1] Edelsbrunner, H., & Harer, J. (2010). Computational Topology: An Introduction. American Mathematical Society.
[2] Carlsson, G. (2009). Topology and data. Bulletin of the American Mathematical Society, 46(2), 255–308.
[3] Bubenik, P. (2015). Statistical topological data analysis using persistence landscapes. Journal of Machine Learning Research, 16, 77–102.
[4] Adams, H., et al. (2017). Persistence images: A stable vector representation of persistent homology. Journal of Machine Learning Research, 18(8), 1–35.
[5] Dahlmeier, L., Kališnik, S., Mehl, A., & Rieck, B. (2026). Topology of a Smile: Persistent Homology in Dental Imaging. arXiv preprint arXiv:2608.21422.
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