Statistical Shape Model–based Refinement of Dental Surface Geometries for Digital Manufacturing Workflows

Technical Summary: Statistical Shape Model–based Refinement of Dental Surface Geometries for Digital Manufacturing Workflows

Problem Statement
Digital manufacturing workflows in dentistry rely on accurate, anatomically consistent 3D tooth models derived from heterogeneous acquisition modalities, such as Cone-Beam Computed Tomography (CBCT) and intraoral scanners. However, preliminary tooth segmentations often contain incomplete, ambiguous, or geometrically inconsistent regions, particularly at interdental contacts and occlusal superpositions. These defects arise from imaging artifacts (e.g., beam hardening, partial-volume effects), scanning occlusions, and limitations in automated segmentation algorithms. When propagated into downstream CAD/CAM processes, these inaccuracies compromise the design of patient-specific devices (e.g., surgical guides), affect occlusal relationships, and reduce manufacturing reliability. While deep learning-based segmentation methods have improved accuracy, they often struggle with posterior teeth where interproximal contacts create anatomically ambiguous regions, and they lack explicit mechanisms to enforce global anatomical plausibility on imperfect inputs.

Methodology
The authors propose a fully automated, anatomy-aware refinement pipeline based on an Enhanced Statistical Shape Model (eSSM). This framework operates as a post-processing stage for preliminary tooth reconstructions, regardless of their origin (CBCT or intraoral scan).

1. Enhanced Statistical Shape Model (eSSM):

   • The core of the method is a classical Statistical Shape Model (SSM) trained on a population of complete tooth segmentations (specifically adult maxillary first molars derived from CBCT).
   • Unlike standard SSMs, the eSSM is semantically enriched. It encodes additional anatomical and functional information directly into the mean shape representation via extra columns:
     • Lateral face identification: Binary labels distinguishing regions adjacent to neighboring teeth (prone to contact ambiguity) from other regions.
     • Semantic segmentation: Labels for specific anatomical regions (occlusal, mesial, roots).
     • Tooth class: Encoding to select the appropriate model for specific tooth types.
   • The model captures population-level variability using Principal Component Analysis (PCA), constraining shape parameters to ensure anatomical plausibility (typically within ±3 standard deviations).

2. Reliability Assessment and Region Identification:

   • The pipeline identifies "reliable" versus "unreliable" regions on the input target model ($s_0$).
   • Unreliable regions are flagged based on two criteria:
     • Semantic priors: Points corresponding to lateral faces (adjacent to neighbors) are marked as potentially unreliable.
     • Geometric consistency: The angular deviation between surface normals of the input model and the normals predicted by the statistical model is calculated. Points exceeding a threshold ($\theta_{th} = 20^\circ$) are classified as unreliable.
   • Reliable regions are preserved to maintain fidelity to the observed data.

3. Iterative Shape Completion (MAP Estimation):

   • The reconstruction is formulated as a Maximum A Posteriori (MAP) estimation problem.
   • The algorithm iteratively fits the eSSM to the subset of reliable points ($\mathcal{R}$) while inferring the geometry of unreliable/missing regions through global statistical deformation.
   • The process minimizes the error between the observed reliable points and the model prediction, regularized by the statistical prior.
   • At each iteration, the reliability set is updated based on the deviation between the reconstructed shape and the input, allowing the algorithm to progressively refine the boundary between observed and inferred geometry until convergence.

4. Partial-Shape Conditioning:

   • For intraoral scans (which lack subgingival data), the pipeline performs a coarse alignment and uses a k-nearest neighbors approach to select observed crown points. These points condition the initial fit, allowing the eSSM to infer the complete tooth morphology (including roots) based on population priors while respecting the observed crown geometry.

Key Contributions

• Anatomy-Aware Refinement: The introduction of a pipeline that explicitly distinguishes between reliable and ambiguous surface regions, preserving high-fidelity observed data while statistically completing uncertain areas.
• Semantic Enrichment of SSMs: The development of an eSSM that integrates vertex-level semantic labels (lateral faces, anatomical regions) to guide the refinement process and enable automatic partitioning of the final model for downstream applications.
• Modality Independence: A framework that accepts preliminary reconstructions from any acquisition modality (CBCT or intraoral scan) and segmentation strategy, provided a discrete surface or point cloud representation is available.
• Global Consistency: A shift from local geometric interpolation (common in CAD-based methods) to a global shape estimation problem that enforces anatomical coherence across the entire tooth structure.

Results
The method was evaluated on a test set of 10 adult maxillary first molars (5 from CBCT, 5 from intraoral scans), none of which were part of the training set (16 samples).

• Qualitative Performance: The pipeline successfully produced complete, smooth, and anatomically plausible tooth models. Visual inspection confirmed that reliable regions were preserved with minimal deviation, while ambiguous regions (interdental contacts, occluded areas) were reconstructed smoothly without local artifacts.
• Quantitative Metrics: Point-wise deviation analysis showed that reliable regions exhibited expected low deviations, whereas larger deviations were localized to the reconstructed ambiguous regions. The maximum deviations were approximately +0.67/-0.62 mm for CBCT-derived targets and +0.53/-0.83 mm for intraoral scan-derived targets.
• Model Quality: The constructed eSSM demonstrated stable Generalization Ability ($G \approx 0.56$ mm), Specificity, and Compactness, indicating the model effectively captures the variability of the training population despite the limited dataset size.

Significance and Claims
The paper positions this work as a proof-of-concept for a refinement strategy within digital dental manufacturing workflows. The authors claim that the primary value of the method is not the recovery of an exact, unobservable ground truth, but the generation of anatomically consistent and structurally coherent geometries suitable for downstream CAD/CAM tasks.

• Manufacturing Utility: The refined models are directly suitable for designing surgical guides and restorative devices, reducing the need for manual intervention and improving the robustness of digital workflows.
• Handling Uncertainty: The method effectively mitigates the impact of acquisition artifacts and segmentation inaccuracies by leveraging population-based priors to fill gaps where data is missing or ambiguous.
• Limitations and Scope: The authors modestly note that the current validation is limited to a single tooth class (maxillary first molar) and a specific dataset size. They acknowledge that a direct quantitative validation against ground truth is impossible in clinical scenarios due to the unobservability of true morphology in contact regions. Future work is identified as necessary to extend the framework to other tooth classes, automate initialization, and perform systematic sensitivity analyses on missing data patterns.