Teeth Localization Accuracy in Dental Imaging

• TLA is defined as the precision measurement of computational methods in dental imaging that pinpoint tooth positions using metrics like mean Euclidean distance and IoU.
• Advances in deep learning and segmentation–landmarking pipelines, including transformer architectures, have reduced errors to sub-millimeter levels.
• Standardized benchmarks and open challenges drive reproducible improvements while highlighting challenges in handling incomplete scans and anatomical variability.

Teeth Localization Accuracy (TLA) quantifies the precision with which computational methods determine the positions or extents of teeth or dental landmarks in medical and dental imaging. TLA is of foundational importance for automated orthodontic analysis, prosthetic planning, digital workflow integration, and large-scale population studies. Its precise mathematical definition and operational use vary with application domain, anatomical target (instance, part, landmark), and input modality (2D radiograph, 3D intraoral scan, volumetric CBCT). TLA measures have undergone rapid development alongside the adoption of deep learning, transforming from pixel-based heuristics to rigidly defined, clinically interpretable quantitative metrics.

1. Accuracy Metrics: Mathematical Definitions of TLA

The core principle underlying all TLA metrics is the quantification of geometric concordance between predicted and ground-truth tooth positions, which may be centroidal coordinates, full masks, or surface landmarks. Two families of definitions dominate:

• Point-based accuracy (landmark regression):
  • Mean Euclidean distance between $N$ predicted $\{p_i\}$ and true $\{g_i\}$ 3D landmark coordinates:

  $$\text{TLA}_\text{mean} = \frac{1}{N}\sum_{i=1}^N \|p_i - g_i\|_2$$

  Standard deviation and RMSE are often reported (Ben-Hamadou et al., 9 Dec 2025, Wu et al., 2021). - Thresholded localization rate:

  $$\text{TLA}(r) = \frac{1}{N}\sum_{i=1}^N \mathbf{1}\bigl[\|p_i - g_i\|_2 < r\bigr]$$

  where $r$ (mm) matches clinical tolerances (Hadzic et al., 2023, Wei et al., 2021).

• Overlap-based accuracy (mask/region):

  • Mean Intersection-over-Union (IoU) per tooth:

  $$\text{TLA}_\text{IoU} = \frac{1}{C}\sum_{c=1}^C \frac{|S_c^\text{pred} \cap S_c^\text{gt}|}{|S_c^\text{pred} \cup S_c^\text{gt}|}$$

  Frequently, $\tau$-thresholded TLA is also used:

  $$\text{TLA}_\tau = \frac{1}{C} \sum_{c=1}^C \mathbf{1}\bigl[\text{IoU}(c) \geq \tau\bigr]$$

  with typical $\tau=0.5$ (Liang et al., 2021, Zou et al., 2024, Lu et al., 12 Dec 2025).

• Normalized centroid error (instance/centroid detection):

  • Scale-invariant definition, such as

  $$d_i = \frac{\|c_i^\text{pred} - c_i^\text{gt}\|_2}{r_i}$$

  TLA is then the mean normalized error, with a lower value reflecting better localization (Ben-Hamadou et al., 2023).

In all definitions, missing teeth/landmarks are generally masked or predicted as "null," and cross-jaw anatomical structure is implicitly incorporated in assignment-based matching protocols.

2. TLA in Automated 3D Mesh and Point Cloud Pipelines

Modern dental landmarking and segmentation research employs deep neural networks operating directly on 3D intraoral scans or extracted dental meshes. The most prominent pipeline architecture is the two-stage segmentation–landmarking paradigm, as in TS-MDL (Wu et al., 2021):

1. Stage 1: Instance Segmentation (e.g., iMeshSegNet, 3DTeethSAM)

   • Segmentation partitions the mesh into tooth regions with high Dice (0.964 ± 0.054) or T-mIoU (91.90%) (Wu et al., 2021, Lu et al., 12 Dec 2025).
   • Post-processing includes graph-cut refinement or SVM-based label upsampling.
2. Stage 2: Landmark Localization
   • Each tooth’s ROI is localized.
   • Regression networks (PointNet-Reg, Point Transformer, etc.) predict a heatmap per anatomical landmark, and the cell with maximal response is selected.
   • Landmark MAE of 0.597 mm (TS-MDL) or mean success rates (TLA(1 mm) ≈ 87%) are typical (Wu et al., 2021, Rodríguez-Ortega et al., 22 Jan 2025, Wei et al., 2021).

Advances:

• Dense field encoding, multi-scale and local/global feature aggregation, and transformer backbone architectures substantially reduce median and mean localization errors (e.g., 0.37 mm and SRₚ(0.6 mm)=86.3% (Wei et al., 2021)).
• Complete end-to-end solutions, such as CHaRNet, eliminate explicit segmentation and handle missing teeth via conditioned heatmap regression, reducing complexity while maintaining high mean success rate (MSR = 82–87%) (Rodríguez-Ortega et al., 22 Jan 2025).

Failure Modes:

• Outlier cases include incomplete mesh scans (missing posterior teeth), extreme crowding or malocclusion, and rare anatomy.

3. TLA in 2D Radiograph and CBCT Applications

In 2D imaging—panoramic X-ray and CBCT—TLA is measured for tooth centroid, bounding box, or full-mask localization, often with additional accuracy constraints:

• Point regression: Directly regressing the 32 anatomical tooth center-points on panoramic X-ray with mean squared error loss, then refined by distance regularization and patch-wise offset networks. Final mean IoU (mIoU) of 0.84 for bounding boxes, identification precision=0.997, recall=0.972 (Chung et al., 2020).
• Mask-based TLA: On 2D panoramic or per-slice views, mean per-tooth IoU (0.847 ± 0.071) is reported; for wisdom teeth, localization accuracy is lower (0.705 ± 0.056). A threshold of IoU ≥ 0.5 (τ=0.5) yields TLA₀.₅ ≈ 0.94 (Liang et al., 2021).
• 3D volumetric CBCT: Using explicit heatmap regression on isotropic volumes, landmark TLA(6 mm)=97.3% is achieved with a spatial configuration network; stricter thresholds (2–4 mm) produce correspondingly lower rates, reflecting the geometric uncertainty in clinical annotations (Hadzic et al., 2023).

Integration of spatial configuration priors and local appearance models is essential for robustness to anatomical variation and artifact.

4. TLA Evaluation Protocols in Community Benchmarks and Challenges

Public challenges—3DTeethLand (Ben-Hamadou et al., 9 Dec 2025), 3DTeethSeg (Ben-Hamadou et al., 2023), and Teeth3DS (Lu et al., 12 Dec 2025)—provide standardized datasets and evaluation metrics, greatly facilitating reproducibility and inter-method comparison.

• Landmark benchmarks: TLA is assessed via mean Euclidean distance, mAP/mAR over 0–3 mm radii, and per-class AP, directly reflecting clinical detectability. In 3DTeethLand, sub-millimeter to millimeter mean errors are typical for the best methods (Radboud, ChohoTech groups), while contact points (mesial/distal) remain most challenging.
• Segmentation/instance benchmarks: Mean per-tooth IoU (T-mIoU) is used as the primary TLA, with leaderboards showing state-of-the-art at ~92% (3DTeethSAM) and top teams separated by small fractions (see table below) (Lu et al., 12 Dec 2025, Ben-Hamadou et al., 2023).

Method	Primary TLA Metric	Value
3DTeethSAM	T-mIoU (mean IoU/inst.)	91.90%
TS-MDL (stage 2)	Landmark MAE (mm)	0.597 ± 0.761
CHaRNet	MEDE (mm)	0.51 (normal)
3DTeethSeg top	exp(–TLA)	0.9924

Correct identification rates and normalized centroid distances are also used (TIR, dᵢ/rᵢ), especially in segmentation-centric tasks.

5. Clinical Interpretation, Limitations, and Significance

TLA metrics are tightly coupled to clinical relevance:

• Mean localization error well below 1 mm (TS-MDL MAE=0.6 mm, Dense Landmark MAE=0.37 mm) meets or exceeds American Board of Orthodontics tolerances (0.5 mm).
• Sub-millimeter precision simplifies manual effort for practitioners and enables fully automated analysis pipelines (Wu et al., 2021, Wei et al., 2021).
• Datasets may underrepresent extreme variation; TLA scores on outlier cases (multiple missing or highly rotated teeth, poor scan quality) are degraded, prompting explicit reporting of both mean error and success rates at varying thresholds.
• Performance on posterior/wisdom teeth is consistently worse due to both anatomical variability and frequent incomplete capture (e.g., T-mIoU=83.3% for 3DTeethSAM on T₈/₁₆) (Lu et al., 12 Dec 2025).

6. Algorithmic Interventions and Future Directions for Maximizing TLA

Key determinants of high TLA include:

• Segmentation–localization joint optimization: Ceiling analyses show further improvements in TLA require refining heatmap regression/localization more than segmentation per se (Wu et al., 2021).
• Data diversity and augmentation: Larger, more varied datasets, including artifacts, missing teeth, and greater ethnic/age representation, are critical to improving generalizability (Ben-Hamadou et al., 9 Dec 2025).
• Architectural developments: Inclusion of spatial priors (anthropic priors, arch curves), multi-scale aggregation, and cross-gating mechanisms reduces error, especially in challenging settings (Teeth-SEG: permutation upscaling boosts mean IoU from 0.72→0.90 and TLA(0.5) from 0.75→0.92) (Zou et al., 2024).
• Hybrid modalities: Incorporation of 2D projections or multi-view fusion with 3D point/regression networks may resolve ambiguities in occluded or atypical geometries (Ben-Hamadou et al., 9 Dec 2025).
• Open benchmarks: Community challenges anchor reproducible and rapid progress via standardization and leaderboard-based evaluation (Ben-Hamadou et al., 9 Dec 2025, Ben-Hamadou et al., 2023, Lu et al., 12 Dec 2025).

A plausible implication is that future gains in TLA will depend not only on improvements at the model/architecture level but also on systematic expansion of training data, advanced loss functions matching clinical targets, and algorithmic support for rare or ambiguous configurations.

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References

• (Wu et al., 2021) Two-Stage Mesh Deep Learning for Automated Tooth Segmentation and Landmark Localization on 3D Intraoral Scans
• (Ben-Hamadou et al., 9 Dec 2025) Detecting Dental Landmarks from Intraoral 3D Scans: the 3DTeethLand challenge
• (Lu et al., 12 Dec 2025) 3DTeethSAM: Taming SAM2 for 3D Teeth Segmentation
• (Wei et al., 2021) Dense Representative Tooth Landmark/axis Detection Network on 3D Model
• (Rodríguez-Ortega et al., 22 Jan 2025) CHaRNet: Conditioned Heatmap Regression for Robust Dental Landmark Localization
• (Ben-Hamadou et al., 2023) 3DTeethSeg'22: 3D Teeth Scan Segmentation and Labeling Challenge
• (Liang et al., 2021) X2Teeth: 3D Teeth Reconstruction from a Single Panoramic Radiograph
• (Chung et al., 2020) Individual Tooth Detection and Identification from Dental Panoramic X-Ray Images via Point-wise Localization and Distance Regularization
• (Hadzic et al., 2023) Teeth Localization and Lesion Segmentation in CBCT Images using SpatialConfiguration-Net and U-Net
• (Ma et al., 2023) Accurate 3D Prediction of Missing Teeth in Diverse Patterns for Precise Dental Implant Planning
• (Zou et al., 2024) Teeth-SEG: An Efficient Instance Segmentation Framework for Orthodontic Treatment based on Anthropic Prior Knowledge
• (Kubík et al., 15 Apr 2025) Leveraging Point Transformers for Detecting Anatomical Landmarks in Digital Dentistry