Retrieval-Augmented Tooth Completion

• The paper introduces a retrieval-augmented approach that employs prototype memory banks and statistical shape dictionaries to enhance the reconstruction of missing dental structures.
• The methodology integrates deep encoder–decoder models with sparse coding to fuse external prior knowledge, resulting in anatomically faithful and robust 3D reconstructions.
• Empirical evaluations demonstrate lower Chamfer Distance errors and millimeter-level prediction accuracy compared to traditional methods, confirming its superior performance.

A retrieval-augmented framework for tooth completion refers to a class of computational methods for reconstructing missing or occluded dental structures by leveraging structured retrieval mechanisms built atop encoder–decoder or statistical dictionary architectures. These frameworks explicitly integrate external sources—such as learnable memory banks or shape dictionaries—retrieved and fused into the completion pipeline to supply strong structural priors, improve inference robustness, and facilitate detailed 3D dental reconstructions. This approach contrasts with conventional encoder–decoder models that rely exclusively on the observed partial input and learned feature representations, which are often biased or unstable in regions lacking geometric information.

1. Architectural Foundations and Key Frameworks

Retrieval-augmented tooth completion has been instantiated in both deep learning and statistical modeling paradigms, each introducing retrieval modules at critical stages of the completion workflow.

Encoder–Decoder with Prototype Memory

In the memory-guided point cloud completion model for dental reconstruction, two independent encoders are employed: one processes the partial dental point cloud $\mathcal{P}_{pi}$, and the other encodes the ground-truth tooth $\mathcal{P}_{gt}$. The fully-encoded global descriptor is then passed through a folding-based decoder to produce the completed 3D structure. A learnable prototype memory bank $\mathcal{M}$ of $K$ prototypes (with prototype dimension $d$, e.g., $K=51$, $d=256$) is integrated into the pipeline. During inference, the partial input descriptor $\mathcal{F}_{pi}$ retrieves its nearest prototype from $\mathcal{M}$ (measured by $\ell_2$ distance), which is subsequently fused with the query via confidence-gated weighting before decoding (Sun et al., 3 Dec 2025).

Retrieval-Augmented Sparse Representation

Alternatively, in the context of mesh-based implant planning, a retrieval-augmented sparse-coding framework constructs tooth-type statistical shape dictionaries from healthy population data. After estimating strict pointwise correspondence, the adjacent existing teeth are encoded via sparse linear combinations over these dictionaries. The learned coefficients are directly transferred to the dictionaries for missing tooth types, enabling simultaneous completion of position and morphology for arbitrary missing-tooth patterns (Ma et al., 2023).

2. Prototype Memory and Dictionary Mechanisms

The retrieval modules in state-of-the-art dental completion can be categorized as prototype memories (deep feature space) or statistical shape dictionaries (geometric feature space):

Module Type	Representation	Retrieval Strategy
Prototype Memory	Latent (feature)	Nearest-prototype search
Shape Dictionary	Geometric (point set)	Sparse coding

The memory bank $\mathcal{M}$ in (Sun et al., 3 Dec 2025) self-organizes via VQ-style objectives and alignment losses, evolving to represent reusable, canonical modes of the healthy tooth manifold without explicit tooth-position labels. The statistical dictionaries $D_i$ in (Ma et al., 2023) are constructed per tooth type, with strict anatomical correspondence across population subjects to capture representative positional and morphological variability.

3. Retrieval and Fusion Mechanisms

Retrieval mechanisms play a dual role: mitigating information loss due to large missing regions and regularizing inference toward plausible anatomic variation.

• Prototype-based Fusion: The nearest prototype $F_m^i$ for a partial feature $\mathcal{F}_{pi}$ is fused with the query using a confidence-gated mechanism:

$$\mathcal{F}' = \alpha\,m + (1-\alpha)\,\mathcal{F},$$

with scalar gate $\alpha$ computed by a learned sigmoid over concatenated features $[\mathcal{F}; m]$.

• Sparse Representation and Application: Given adjacent-tooth features, a sparse coefficient vector $c$ is learned by solving

$$\min_{c} \|D_{\text{adj}}c - A_{\text{adj}}\|_2^2 + \lambda\|c\|_1,$$

then applied to the missing-tooth dictionary:

$\widehat{x}^{(i)} = D_{M_i} \cdot c.$

This methodology exploits cross-subject regularities to estimate missing geometry even when relevant local context is absent (Ma et al., 2023).

4. Optimization Objectives and Training Strategy

Retrieval-augmented deep learning frameworks employ a combination of structural and feature-level supervision. In (Sun et al., 3 Dec 2025):

• Chamfer Distance Loss ($\mathcal{L}_{cd}$): Drives reconstruction accuracy.
• Prototype Commitment Loss ($\mathcal{L}_{mem}$): Ensures prototype usage by aligning features and prototypes in a VQ-style scheme.
• Feature Alignment Loss ($\mathcal{L}_{align}$): Encourages matching between partial and ground-truth encodings.

The total loss is

$$\mathcal{L} = \mathcal{L}_{cd} + \lambda_{mem}\,\mathcal{L}_{mem} + \lambda_{align}\,\mathcal{L}_{align}.$$

Prototypes are optimized end-to-end, automatically organizing into clusters covering high-density shape regions.

In sparse-representation-based pipelines, LASSO regularization controls solution sparsity, and iterative alignment-refinement enhances accuracy via repeated correspondence updates (Ma et al., 2023).

5. Empirical Evaluation and Performance Benchmarks

Both deep prototype-memory and dictionary-based sparse-coding frameworks demonstrate efficacy across challenging dental completion benchmarks.

• On Teeth3DS, the memory-guided folding network (Mem4Teeth) achieved Chamfer Distance $1.56\times10^{-4}$, outperforming SVDFormer (1.85), PoinTr (2.43), and legacy folding/pointer networks (5.61/3.76) (Sun et al., 3 Dec 2025). Qualitative analysis reveals more anatomically faithful completions: sharper cusp formation, continuous occlusal ridges, and realistic interproximal morphology.
• In mesh-based completion, average single-missing-tooth prediction error was $1.04\,\text{mm}$ (min $0.88$, max $1.26$ by tooth type) with errors rising gently to $1.33\,\text{mm}$ in 14-way multi-tooth completions. No directly comparable 3D baselines yielded full-shape predictions at this level of precision (Ma et al., 2023).

6. Practical Integration and Limitations

Retrieval-augmented modules are compatible with standard encoder–decoder completion backbones and statistical pipelines, introducing minimal computational overhead. Memory banks typically require $O(Kd)$ computation per query with $K<128$, and decoder/loss terms are unmodified (Sun et al., 3 Dec 2025). Dictionary-based approaches can be fully automated post-dictionary construction (Ma et al., 2023).

Principal limitations include dependence on robust segmentation, correspondence, and labeling. For prototype memories, the absence of explicit positional supervision introduces potential ambiguity in cases with extreme anatomical variation. Sparse-coding solutions may degrade for wide edentulous gaps due to insufficient adjacent-tooth context. Both paradigms are best validated on healthy adult populations; unseen pathological variation may constrain generalizability.

7. Extensions and Prospects

Future research directions include augmentation of prototype/dictionary banks with pathological data, integration of bone quality and soft-tissue priors, and fusion with deep autoencoders to directly map observed context to completed geometry. Patient-specific conditional modeling—incorporating demographic or functional priors—may further personalize reconstructions. Efforts to bridge deep prototype-memory mechanisms and classical statistical dictionaries suggest a convergent path toward unified, retrieval-augmented completion platforms with enhanced anatomical fidelity and robustness across diverse dental reconstructions (Sun et al., 3 Dec 2025, Ma et al., 2023).