GEPAR3D: Geometry Prior-Assisted Learning for 3D Tooth Segmentation

1Sano Centre for Computational Medicine, 2Jagiellonian University, 3Jagiellonian University Medical College, 4Warsaw University of Technology, 5Research Institute IDEAS, 6Harvard Medical School
Accepted for MICCAI 2025 Daejeon, Republic of Korea
Hausdorff distance heat map
Segmenting the root apices (the tips of roots) is critical to assess root resorption accurately because the apical region is where much of the initial and most clinically significant loss of tissue occurs; without precise delineation of the apex, volumetric measures of resorption will be biased, underestimating damage. However existing methods struggle to segment them accurately due to their small size and complex morphology. The heatmap above shows the surface Hausdorff Distance (HD) between ground truth and predicted segmentation for three methods: GEPAR3D (ours), ToothSeg, and SGANET. The HD is a measure of the maximum distance between the surfaces of the two segmentations, with lower values indicating better accuracy. The heatmap highlights that GEPAR3D achieves significantly lower HD values at the root apices compared to the other methods, demonstrating its superior ability to capture these fine structures accurately. Surface Hausdorff Distance heatmaps overlaid on GT labels (green = low, purple = high) highlight apex deviations. GEPAR3D shows superior root sensitivity versus tooth-specific baselines. Missing teeth are shown in gray.

Abstract

Tooth segmentation in Cone-Beam Computed Tomography (CBCT) remains challenging, especially for fine structures like root apices, which is critical for assessing root resorption in orthodontics. We introduce GEPAR3D, a novel approach that unifies instance detection and multi-class segmentation into a single step tailored to improve root segmentation. Our method integrates a Statistical Shape Model of dentition as a geometric prior, capturing anatomical context and morphological consistency without enforcing restrictive adjacency constraints. We leverage a deep watershed method, modeling each tooth as a continuous 3D energy basin encoding voxel distances to boundaries. This instance-aware representation ensures accurate segmentation of narrow, complex root apices. Trained on publicly available CBCT scans from a single center, our method is evaluated on external test sets from two in-house and two public medical centers. GEPAR3D achieves the highest overall segmentation performance, averaging a Dice Similarity Coefficient (DSC) of 95.0% (+2.8% over the second-best method) and increasing recall to 95.2% (+9.5%) across all test sets. Qualitative analyses demonstrated substantial improvements in root segmentation quality, indicating significant potential for more accurate root resorption assessment and enhanced clinical decision-making in orthodontics.

3D Segmentation Results

GEPAR3D
SGANet
ToothSeg
Center A

(Rotate volumes: Left mouse button; Move volumes: Shift + Left mouse button; Load scan: click bullet.)

Interactive side-by-side 3D renderings of sample segmentations (top row) and corresponding 3D surface Hausdorff distance heatmaps overlaid on ground-truth (GT) labels (bottom row). Heatmaps use green to indicate low error and purple to indicate high error (>2.0 mm), highlighting apex deviations. GEPAR3D demonstrates improved root sensitivity compared to tooth-specific baselines. Missing teeth are rendered in gray.

Method

GEPAR3D method overview
An overview of GEPAR3D, which unifies instance detection and multi-class segmentation for precise tooth root segmentation. (a) Crops the region of interest (ROI) during inference. (b) Simultaneously performs multi-class segmentation and instance regression. (c) Regularizes segmentation loss Lseg with a geometric prior from an SSM of normal dentition by Kim et al. (2023). (d) Uses instance regression task LEDT to generate energy maps for the Deep Watershed Algorithm. (e) Captures complex root apex geometries via Energy Direction loss Ldir. Finally, (f) assigns each detected instance a class via majority voting based on segmentation outputs.

GEPAR3D is an encoder-decoder model with dual decoders for multi-class segmentation and instance regression. The segmentation branch classifies 32 tooth categories with Statistical Shape Model (SSM)-based regularization, while the regression branch models instances as energy basins guided by energy descent, where we adapt Deep Watershed method for 3D. Each detected instance receives class votes from the multi-class segmentation branch, and the final instance segmentation is obtained via a voting scheme. The SSM is built from a representative patient cohort, this 3D atlas encodes anatomical knowledge. By processing the SSM, we extract inter-tooth distances for morphologically guided segmentation, capturing anatomical context and morphological consistency without enforcing restrictive adjacency constraints. This integration of geometric priors and instance-aware representation ensures accurate segmentation of narrow, complex root apices.

resorption
Index for quantitative assessment of apical root resorption (1: irregular root contour; 2: resorption < 2 mm of the original root length; 3: resorption 2 mm to 1/3 of the original root length; 4: resorption > 1/3 of the original root length). Malmgren et al. (1982) developed this index to classify the severity of root resorption based on radiographic appearance.

Geometry Prior - Wasserstein Loss

Wasserstein optimal transport weights
Intermediate step in the computation of the Wasserstein loss, where penalties are assigned to each class based on the Wasserstein distance from a designated reference tooth. A 3D heatmap visualization, overlaid on the segmentation GT label, is shown for two different reference teeth (indicated by arrows and gray overlays). The highest misclassification penalties correspond to teeth that are both morphologically dissimilar and spatially distant from the reference.
Wasserstein matrix weights
Geometrical Wasserstein Distance (GWD) loss - Wasserstein matrix based on geometrical and morphological priors. The colormap displays penalty values normalized to 1, with red indicating the highest penalty. In addition to the main diagonal, perpendicular valleys of low penalties can be observed. They correspond to directly adjacent teeth in the opposite arch or are located symmetrically within the same dental arch. The former are larger due to greater morphological differences.

Morphology Aware Deep Watershed 3D

direction map
Energy direction and energy map sections reveal rapid angular transitions in the vector field around anatomically intricate regions. This is especially pronounced at the root apices, where fine, tapering structures curve sharply and diverge from neighboring bone. The directional vector field exhibits high angular gradients in these areas, reflecting the need for fine-grained vector guidance to avoid root-level in- GEPAR3D: Geometry Prior-Assisted Learning for 3D Tooth Segmentation 23 stance fusion. Similarly, the bite area, specifically in the z component representing superior-inferior direction, shows abrupt vector shifts due to the vertical overlap of opposing arches in occlusion. These steep gradients are critical for disambiguating closely apposed crowns from opposing jaws, enabling accurate watershed ridge formation along occlusal interfaces. This capacity to encode fast angular variation is essential for resolving complex 3D topologies in tight anatomical configurations.
energy map
Energy map in the axial (xy) plane. A representative slice from the 3D scan is shown, selected near the contact points where adjacent tooth crowns exhibit close anatomical proximity. This region, characterized by broad interproximal contact and parallel axial walls, presents a challenging condition for separating anatomically congruent and tangentially aligned teeth. The energy map highlights the GEPAR3D ability to resolve individual instances despite the absence of clear interproximal gaps or distinct morphological transitions between adjacent crowns.

Qualitative Results

Hausdorff heatmap roots
More qualitative comparisons of GEPAR3D with Surface Hausdorff Distance heatmaps overlaid on GT labels highlight apex deviations (green = low, purple = high error). GEPAR3D shows superior root sensitivity versus tooth-specific baselines. Missing teeth are shown in gray.
dental notation color map
The Universal Numbering System, also called the American System. Tooth number 1 is the maxillary right third molar, with the count progressing along the upper arch to the left side. The numbering then resumes at the mandibular left third molar, number 17, continuing along the lower teeth to the right side.
Hausdorff heatmap roots
Qualitative comparisons of segmentation on external test sets. We present the raw 32-class segmentation results.

BibTeX

@InProceedings{Szczepanski2025MICCAI_GEPAR3D,
        author = { Szczepański, Tomasz and Płotka, Szymon and Grzeszczyk, Michal K. and Adamowicz, Arleta and Fudalej, Piotr and Korzeniowski, Przemysław and Trzciński, Tomasz and Sitek, Arkadiusz},
        title = { { GEPAR3D: Geometry Prior-Assisted Learning for 3D Tooth Segmentation } },
        booktitle = {proceedings of Medical Image Computing and Computer Assisted Intervention -- MICCAI 2025},
        year = {2025},
        publisher = {Springer Nature Switzerland},
        volume = {LNCS 15961},
        month = {September},
        page = {216 -- 226}
}
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