用谱方法生成牙齿形状,数据少也能稳定建模。
Deep Spectral Models for Robust Dental Shape Generation

- 在谱域构建牙齿几何的紧凑表示,通过同步谱嵌入保持一致性。
- 重建和生成性能优于或媲美传统方法,且参数更少。
- 适合小样本医疗数据,尤其适用于不同诊所的牙齿建模。
准确建模牙冠形态对诊断、正畸规划和计算机辅助修复设计至关重要。然而,可用于训练此类模型的数据集通常规模有限。我们提出 ToothForge,一种基于深度谱生成框架,从紧凑的内在表示中建模牙冠几何。通过在谱域操作,ToothForge 利用同步谱嵌入学习三维牙齿形状的潜在流形,确保不同拓扑连接样本间的建模一致性。谱同步缓解了拉普拉斯-贝尔特拉米特征基的不稳定性,并在低维空间实现高效学习。该框架通过鲁棒性分析、消融实验及与基于 PCA 的统计形状模型和点基生成框架的对比评估。结果表明,同步谱建模在重建与生成性能上达到或超过空间方法水平,同时保持紧凑性和几何可解释性。紧凑的同步系数与低维学习空间使该框架特别适用于小样本医疗数据,如牙科领域,并适用于现实中难以保证跨诊所形状拓扑一致性的实际场景。
原文摘要 · Abstract (English)
Accurate modeling of dental crown morphology is fundamental for diagnosis, orthodontic planning, and computer-aided restoration design. However, datasets suitable for training such models are typically limited in size. We present ToothForge, a deep spectral generative framework that models dental crown geometries from compact, intrinsic representations. By operating in the spectral domain, ToothForge learns a latent manifold of 3D tooth shapes through synchronized spectral embeddings, ensuring consistent modeling across samples with varying connectivity. Spectral synchronization mitigates the instability of Laplace-Beltrami eigenbases and enables efficient learning in a low-dimensional space. The framework is thoroughly evaluated through robustness analysis, ablation studies, and benchmarking against PCA-based statistical shape models and point-based generative frameworks. Results show that synchronized spectral modeling achieves reconstruction and generative performance comparable to or exceeding spatial approaches, while maintaining compactness and geometric interpretability. Together, the compact synchronized coefficients and low-dimensional learning space make the framework particularly suitable for limited datasets, as often encountered in dental and medical domains, and applicable in real-world scenarios where guaranteeing consistent connectivity across shapes from various clinics is unrealistic.
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