Self-Supervised Automatic Abutment Design (SSA3D)

• The paper introduces a dual-branch framework that integrates masked-patch reconstruction and regression to achieve state-of-the-art accuracy in dental abutment design.
• The methodology transforms intraoral scan meshes with 32,000 faces into standardized patch embeddings processed via self-supervised and text-conditioned transformer modules.
• Results demonstrate significant improvements with up to 41.41% IoU for abutment height and a 60% reduction in training time compared to conventional SSL methods.

The Self-supervised Assisted Automatic Abutment Design Framework (SS$A^3$D) is an advanced system for the automated parameterization of dental implant abutments using intraoral scan data and clinical metadata. SS$A^3$D integrates a dual-branch architecture with a shared transformer-based encoder operating in a self-supervised auxiliary regime, employs text-conditioned clinical prompts for targeted guidance, and achieves state-of-the-art results for automatic abutment design with significantly reduced computational overhead and improved accuracy relative to conventional SSL and both point- and mesh-based alternatives (Zheng et al., 12 Dec 2025).

1. Data Pipeline and Mesh Representation

SS$A^3$D processes individual intraoral scan meshes containing 32,000 triangular faces. Each mesh is remeshed using MAPS (as implemented in SubdivNet), standardizing the mesh to %%%%3%%%% faces with uniform topology. The mesh is subdivided into $f_n$ patches, each containing 45 vertices. For each face, a 13-dimensional feature vector is extracted:

• Area,
• 3 face normals,
• 3 internal angles,
• Coordinates of the face centroid $(x, y, z)$,
• Inner product between face and vertex normals.

Patches aggregate the per-face vectors into raw patch features of $\mathbb{R}^{45\times 13}$, which are transformed via a multi-layer perceptron $$\mathrm{MLP}_p:\mathbb{R}^{45\times 13}\to\mathbb{R}^d$$ to produce patch embeddings $X=\{x_i\}_{i=1}^{f_n}\in\mathbb{R}^{f_n\times d}$. Positional encodings are constructed from 3D patch centroids projected to $\mathbb{R}^d$.

2. Dual-Branch Architecture and Feature Sharing

A shared transformer encoder $E$ with 12 blocks processes the patch embeddings. The architecture bifurcates into two branches:

• Reconstruction Branch: Receives masked patch embeddings $X_e \in \mathbb{R}^{(1-r)f_n\times d}$, with a masking ratio $r=0.5$. The encoder outputs latent features $Z_e$, which are decoded by a 6-block transformer decoder $D_r$. Mask tokens are used for missing patches. The decoder outputs:
  • Vertex-head: linear projection for per-patch vertex coordinate prediction.
  • Feature-head: linear projection for face feature vector recovery.
• Regression Branch: Processes the complete patch embeddings $X \in \mathbb{R}^{f_n\times d}$ through the shared encoder, yielding mesh features $F_e$. The branch then incorporates clinical metadata via the Text-Conditioned Prompt (TCP) module before regressing abutment parameters through a three-stage MLP.

The shared encoder enforces direct structural feature transfer between the self-supervised and supervised tasks.

3. Mathematical Formulation and Optimization Objectives

Let $X\in\mathbb{R}^{f_n\times d}$ denote the complete patch embeddings. For each training sample:

• Reconstruction Loss:
  • The Chamfer-$L_2$ loss between predicted ($V_p$) and ground-truth ($G_q$) masked-patch vertex sets:

  $$L_{\mathrm{CD}}(V_p, G_q) = \frac{1}{|V_p|}\sum_{p\in V_p}\min_{q\in G_q}\|p-q\|_2^2 + \frac{1}{|G_q|}\sum_{q\in G_q}\min_{p\in V_p}\|q-p\|_2^2$$ - The mean squared error for per-mask patch feature vectors:

  $$L_{\mathrm{MSE}} = \frac{1}{|M|} \sum_{i\in M} \| \hat f_i - f_i \|_2^2$$ - The combined reconstruction loss:

  $$\mathcal{L}_{\mathrm{rec}} = L_{\mathrm{CD}} + \eta L_{\mathrm{MSE}},\quad \eta=1$$

• Regression Loss:
  • Target is $p\in\mathbb{R}^3$ (transgingival, diameter, height), predicted as $\hat p$.
  • Smooth-$L_1$ loss (Huber):

  $$L_{l1}(x, y) = \begin{cases} 0.5(x-y)^2/\delta, & |x-y|<\delta \ |x-y| - 0.5\delta, & \text{otherwise} \end{cases},\quad \delta=1\,\mathrm{mm}$$ - Mean squared error:

  $$L_{\mathrm{MSE}}^*(x, y) = \frac{1}{N}\sum_{i=1}^N (x_i - y_i)^2$$ - Total regression loss:

  $$\mathcal{L}_{\mathrm{reg}} = L_{l1}(\hat p, p) + L_{\mathrm{MSE}}^*(\hat p, p)$$

• Unified End-to-End Training Objective:

  $$\mathcal{L}_{\mathrm{total}} = \varsigma\mathcal{L}_{\mathrm{rec}} + \mathcal{L}_{\mathrm{reg}},\quad \varsigma=0.1$$

Weight sharing ensures that features acquired for the reconstruction task benefit downstream regression.

4. Text-Conditioned Prompt Module for Clinical Context

The TCP module integrates clinical metadata—implant location ($L$), system ($S$), and series ($R$)—as a templated string, $$X_t = \langle L\rangle\,\langle S\rangle\,\langle R\rangle$$. The string is embedded using a CLIP-based text encoder $T$ to yield $\mathcal{F}_t=T(X_t)\in\mathbb{R}^{1\times c}$, which is mapped linearly to $\mathbb{R}^d$.

A cross-attention fusion mechanism is employed:

• Mesh features $F_e$ serve as queries $Q$, text features as $K=V=\mathcal{F}_{pj}$.
• Attention weights:

$$A = \mathrm{softmax}\left(\frac{F_e\,\mathcal{F}_{pj}^T}{\sqrt d}\right)\in\mathbb{R}^{f_n\times 1}$$

yielding the cross-attended features,

$$\mathcal{F}_{ca} = A\,\mathcal{F}_{pj}\in\mathbb{R}^{f_n\times d}$$

• Global max- and mean-pooling are applied:

$$\mathcal{F}_{\mathrm{max}} = \mathrm{MaxPool}(\mathcal{F}_{ca}),\quad \mathcal{F}_{\mathrm{mean}} = \mathrm{MeanPool}(\mathcal{F}_{ca})$$

The concatenated result is linearly projected:

$$\mathcal{F}_o = W_o[\mathcal{F}_{\mathrm{max}}\oplus\mathcal{F}_{\mathrm{mean}}]\in\mathbb{R}^d$$

$\mathcal{F}_o$ is used in the regression branch to guide the prediction of abutment parameters, ensuring focus on clinically relevant aspects.

5. Training Procedure and Computational Efficiency

SS$A^3$D employs single-stage joint training (the SSAT paradigm), optimizing both reconstruction and regression losses simultaneously. Traditional SSL frameworks require sequential pre-training (300 epochs) and fine-tuning (100 epochs), totaling approximately 7.7 hours per mesh dataset on GPU hardware. SS$A^3$D's joint training (400 epochs) completes in 3.1 hours, resulting in an approximately 50% reduction in total GPU hours. The single-stage protocol eliminates the need for model freezing, conversion, or staged optimization, simplifying the pipeline and reducing wall-clock time (Zheng et al., 12 Dec 2025).

6. Output Parameterization and CAD Integration

The output is a 3-dimensional vector $p=[p_1,p_2,p_3]$, denoting:

• $p_1$: Transgingival height (mm)
• $p_2$: Diameter (mm)
• $p_3$: Gingival-mandibular distance (height, mm)

These scalars are directly ingested by standard CAD systems using cylindrical and conical primitives to reconstruct the physical abutment. SS$A^3$D does not include additional kinematic or geometric constraint modules.

7. Empirical Performance Evaluation

Quantitative comparison against traditional SSL + fine-tuning and state-of-the-art (SOTA) alternatives (point and mesh-based), as well as ablation studies, is summarized below.

Training Time and Accuracy

Paradigm	Transgingival IoU (%)	Diameter IoU (%)	Height IoU (%)	Training Time (h)
SSL+FT	29.75	70.05	32.77	7.7
SSAT (SS$A^3$D)	30.58	70.69	41.41	3.1

SS$A^3$D achieves higher accuracy on all abutment parameters, with a particularly pronounced gain for height (from 32.77% to 41.41% IoU), alongside a $\sim 60\%$ reduction in training time.

SOTA Comparison

Input	Method	Transgingival IoU (%)	Diameter IoU (%)	Height IoU (%)
Point	PointNet	28.61	46.18	22.81
	PointNet++	29.14	63.26	24.29
	PointFormer	29.37	63.89	19.91
	PointMAE	29.14	58.57	17.76
	PointMamba	28.85	59.72	14.67
	PointFEMAE	30.15	62.82	15.60
Mesh	MeshMAE	29.55	62.86	17.29
Mesh	SS$A^3$D	30.58	70.69	41.41

SS$A^3$D outperforms all compared methods, with the most substantial relative improvement in height estimation.

Ablation Study: Reconstruction Branch and TCP

Reconstruction	TCP	Trans. IoU (%)	Diam. IoU (%)	Height IoU (%)
–	–	29.24	69.99	31.94
✓	–	29.85	62.94	20.86
✓	✓	30.58	70.69	41.41

These results indicate that both the reconstruction branch and the TCP module are critical—especially for the height parameter, where the TCP module in particular yields substantial performance improvements.

Conclusion

SS$A^3$D introduces a dual-branch transformer architecture for abutment parameter regression with direct feature transfer from a masked-patch reconstruction task and a clinical text-guided prompt to constrain predictions. The architecture enables single-stage, joint optimization, which reduces training time by nearly half and achieves superior accuracy across all key abutment parameters compared to state-of-the-art point and mesh-based models. SS$A^3$D’s clinical context integration via the TCP module is particularly impactful for anatomically challenging abutment dimensions (Zheng et al., 12 Dec 2025).