Source-linked AI summary
Topology of a Smile: Persistent Homology in Dental Imaging
Leon Dahlmeier, Sara Kališnik, Albert Mehl, Bastian Rieck
TL;DR
CBCT scans contain valuable three-dimensional dental information, but analyzing and documenting them is labor-intensive. The paper combines persistent homology with support vector machines for tooth classification and diagnosis, achieving higher accuracy than a CNN trained on the same data. Its workflow uses relatively small datasets and few features, while the supplied limitation evidence only indicates that persistent homology has limitations.
Problem
CBCT analysis and documentation are labor-intensive, motivating automation of anatomical-structure classification and segmentation for dental diagnosis and treatment planning.
Method
The workflow extracts CBCT regions of interest using deep learning and classifies teeth and pathological findings with persistent homology and support vector machines.
Results
97.67% tooth-labeling accuracy and 96.77% diagnostic accuracy outperform a same-data CNN’s 70.27% and 86.67%, respectively.
Takeaways & Limitations
The workflow uses few features and small datasets, accommodates regions of interest of varying size, and is intended to reduce clinician workload and support more efficient diagnostics.
Takeaways & Limitations
Persistent homology is acknowledged as a powerful feature-extraction tool with limitations, but the supplied passage does not specify their nature.
Abstract
from arXiv · showhide
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.
1. Introduction
CBCT offers rich three-dimensional dental information but remains laborious to analyze and document, motivating automated tooth and pathology classification. The paper proposes persistent-homology-based automation and reports higher accuracy than a CNN baseline on both labeling and diagnostic tasks.
- CBCT supports implant, orthodontic, extraction, lesion-classification, monitoring, and treatment-control applications, but its three-dimensional visualization is laborious and time-consuming.
- Recent CBCT automation work has addressed tooth labeling, segmentation, and combined classification of teeth and bony anatomical structures.
- Convolutional architectures, including CNNs and UNet-like models, are common in existing CBCT classification and segmentation approaches.
- Persistent homology combined with support vector machines provides the paper’s topology-based procedure for classifying teeth and pathological findings in CBCT data.
- 97.67% tooth-labeling accuracy and 96.77% diagnostic accuracy exceed the same-data CNN baseline’s 70.27% and 86.67%, respectively.
2. Methods
The method represents CBCT tooth regions through cubical filtrations and persistent-homology descriptors, then vectorizes these descriptors for machine-learning classification. It combines multiple image representations, three-dimensional and two-dimensional views, and staged classification with cross-validation.
- Cubical filtrations: CBCT grayscale images are represented as cubical complexes, with lower-dimensional boundary cubes included for each image pixel.A one-parameter family preserves grayscale information that would be lost in a single-complex representation.
- Cubical filtrations: Sublevel set filtrations include the original, inverted, contrast, and inverted contrast images.Contrast transformations are motivated by the appearance of carious lesions relative to enamel, dentin, soft tissue, and air.
- Persistent homology: Persistent homology tracks connected components, loops, and voids as filtration features appear and disappear across scales.Persistence diagrams record feature birth and death times, with feature lifetime given by d_l − b_l.
- Vectorization: Persistent diagrams are vectorized using persistent statistics because diagrams are non-Euclidean, with birth and death summary statistics forming fixed-dimensional feature vectors.Persistent statistics performed best among the evaluated vectorization techniques.
- Feature construction: Each ROI combines the full three-dimensional volume with forty-one two-dimensional slices across coronal, sagittal, and axial directions, producing 996 persistence diagrams per ROI.The pipeline considers four image variants and persistence diagrams in every dimension up to the image or volume dimension.
- Study design: FDI labeling proceeds hierarchically from jaw to quadrant, tooth category, and final label, using staged datasets and 5-fold cross-validation.The initial datasets contain n = 555 labeling cases and n = 600 diagnostic cases; mirrored teeth increase samples for one classification step.
3. Results
The method achieves high accuracy for tooth labeling and diagnosis, with results reported across classification tables and compared against a CNN trained on the same data.
- Results: 97.67% average accuracy was achieved across all FDI tooth labels.Label scores ranged from 96.60% to 98.57%.
- Results: 96.77% average accuracy was achieved for diagnostic tasks.Diagnostic scores ranged from 88.41% to 98.17%.
- Results: The authors provide code for the reported implementation.The repository is identified in the paper as leon-dahlmeier/Topology-of-a-smile.
- Results: The classification results are summarized by quadrant, jaw, accuracy, AUC, and feature count.Table 1 covers quadrant differentiation and tooth classification in the upper and lower jaws.
- Results: The study compares its results with a CNN trained on the same dataset.The CNN configuration was adapted from a prior study while avoiding additional slices because of observed overfitting.
4. Conclusion
The paper presents an automated pipeline that extracts tooth regions from CBCT scans and classifies them using persistent homology, achieving high labeling and diagnostic accuracy with relatively modest data and feature requirements.
- 4. Conclusion: The pipeline extracts CBCT tooth regions with deep learning and performs classification via persistent homology.The workflow combines ROI extraction with topology-based classification.
- 4. Conclusion: 97.67% average accuracy was reached for tooth labeling, versus 70.27% for a CNN trained on the same data.These results were obtained on datasets comparable to those reported in the literature.
- 4. Conclusion: 96.77% average accuracy was reached for diagnostic tasks, versus 86.67% for the same-data CNN.The comparison reports the diagnostic accuracies for the proposed method and CNN, respectively.
- 4. Conclusion: The workflow uses small datasets and few features, enabling faster and less computationally demanding training.It also accommodates regions of interest with varying sizes.
- 4. Conclusion: Future work includes increasing the sample size and extending persistent homology to tooth detection itself.The proposed extension would eliminate the need for a separate segmentation step.
Appendix A. First Appendix
The appendix documents ablation studies and methodological decisions used to settle the normalization, tooth detection, slice selection, vectorization, SVM, and CNN configurations.
- Appendix A: The ablation studies examine normalization, tooth detection, slice locations, vectorization, SVM structure, and CNN choice.These experiments evaluate alternative methodological components before selecting the final approach.
- Appendix A: The initial configuration used the whole tooth voxel set and five two-dimensional slices in each anatomical direction.The filtration was then applied to these three-dimensional and slice-based inputs.
- Appendix A: Ablation scores should be interpreted relatively within each experiment rather than as absolute performance values.The appendix notes that the methodology described in the section is not always the final approach.
A.1. Normalization method:
The normalization study evaluates grayscale rescaling choices and finds that retaining the original grayscale values produces the highest classification accuracy, with a finite replacement for the infinite persistence feature enabling downstream processing.
- A.1. Normalization method: The images were tested with normalization applied either to the whole X-ray or only to the tooth region of interest.The grayscale values were rescaled to several candidate intervals.
- A.1. Normalization method: The tested normalization intervals included [0, 1], [0, 10, 000], and [0, 30, 000].The broader ranges were used to preserve more of the original grayscale variation.
- A.1. Normalization method: The highest classification accuracy was achieved without any normalization.This result is reported as the overall outcome of the normalization comparison.
- A.1. Normalization method: The single feature persisting until infinity was replaced by the image’s highest grayscale value plus one.This keeps the feature finite for vectorization and subsequent SVM processing while retaining the maximal grayscale value.
A.2. Tooth detection and impact on ROI:
The study uses segmentation-based regions of interest to create a fully automatic workflow, while comparing its performance with manually selected, voxel-precise regions. Segmentation-based results remain strong for both FDI labeling and diagnostics.
- A.2. Tooth detection and impact on ROI:: 97.67% average accuracy was achieved for FDI labeling with segmentation-based regions of interest.Scores ranged from 96.60% to 98.57% across labels.
- A.2. Tooth detection and impact on ROI:: 96.77% average accuracy was achieved for diagnostics using segmentation-based regions of interest.Diagnostic scores ranged from 88.41% to 98.17%.
- A.2. Tooth detection and impact on ROI:: 97.89% average FDI-labeling accuracy was obtained with manually selected regions of interest.The manually selected regions ensured voxel-level precision, with scores ranging from 97.31% to 98.55%.
A.3. Slice location:
The study evaluates how the positions of two-dimensional slices affect performance by fixing midpoint slices and varying the remaining slice locations. Results are reported in a heat map.
- A.3. Slice location:: Slice-location experiments fixed one midpoint slice in each dimension and varied the positions of four remaining slices.The inner slices were positioned relative to the midpoint, while the outer slices used separate outer parameters.
- A.3. Slice location:: The two slices nearest the midpoint were placed at (10 ± inner) · (dimension/20).The outermost slices were placed at (outer) · (dimension/20) and (20 −outer) · (dimension/20).
- A.3. Slice location:: Table 5 reports performance for the different two-dimensional slice locations using heat-map shading.
A.4. Vectorization method:
The vectorization study compares multiple methods for converting persistent-homology information into features. Statistical feature extraction produced the highest accuracy and was selected for subsequent experiments.
- A.4. Vectorization method:: Statistical feature extraction generated the highest accuracy among the compared vectorization methods.The comparison used code from Ali et al. (2023), with other method descriptions available in that reference.
- A.4. Vectorization method:: The selected statistical vectorization method was adopted for all subsequent experiments.
- A.4. Vectorization method:: Table 6 reports training and testing accuracy for the various vectorization methods.The table uses heat-map shading to display testing accuracy.
A.5. The SVM structure:
The study tunes the SVM kernel and examines feature choices to reduce overfitting and identify useful persistent-homology inputs. A linear kernel with C = 0.001 was selected for later iterations, while texture features did not improve test accuracy.
- A.5. The SVM structure:: A linear SVM kernel with C = 0.001 consistently performed best among polynomial, RBF, sigmoid, and linear kernels.The authors skipped further grid searches to combat overfitting.
- A.5. The SVM structure:: Texture analysis did not improve test accuracy.
- A.5. The SVM structure:: Feature-reduction experiments varied the use of three-dimensional images, slice orientations, and homology dimensions zero and one.The tests were designed to understand which features were most important and to combat overfitting.
- A.5. The SVM structure:: The final feature-selection procedure ranked features by linear-SVM weights and evaluated increasing subsets with 5-fold cross-validation.The linear SVM used C = 0.001.
- A.5. The SVM structure:: Table 7 reports train and test accuracy for experiments using fewer two-dimensional images.Heat-map shading indicates the reported accuracy scores.
A.6. The choice of CNN:
The study rejected proprietary commercial software as a CNN baseline because its larger training datasets and undisclosed methods prevent reproducible, comparable training. Instead, it selected a publicly available architecture trained exclusively on the study’s dataset for a fair comparison with the topological approach.
- Proprietary commercial software was excluded as a baseline because its larger datasets and undisclosed architectures and training procedures prevent comparable reproduction.
- The authors considered a pre-trained ResNet50 with an MLP, obtaining 82.88% for FDI labeling and 78.87% for diagnostics.ResNet50 was trained on a larger dataset and not specifically for teeth, complicating comparison.
- They selected the publicly available architecture from Esmaeilyfard et al. (2024) rather than relying on a proprietary black-box system.Public availability allowed the authors to implement and train the network themselves.
- The CNN was trained exclusively on the study’s dataset so both methods used the same training data for a fair comparison.