从3D点云模型中提取拓扑特征，实现高效数据驱动的图谱生成。
FILTR: Extracting Topological Features from Pretrained 3D Models
- 设计FILTR框架，将拓扑图生成视为集合预测任务。
- 在可控复杂度数据集上验证，可有效还原点云的拓扑结构。
- 首次实现无需手动设计即可从原始点云提取持久性图谱。
近期预训练3D点云编码器（如Point-BERT、Point-MAE）取得了显著进展，其性能通常在几何或语义任务上评估。与此同时，拓扑描述符被证明能有效总结形状的多尺度结构。本文探讨了能否从3D编码器产生的特征中提取拓扑信息。为此，我们首先提出DONUT——一个具有受控拓扑复杂度的合成基准，并设计FILTR（Filtration Transformer），一种可学习框架，直接从冻结编码器中预测持久性图谱。FILTR采用Transformer解码器，将图谱生成视为集合预测任务。在DONUT上的分析表明，现有编码器仅保留有限的全局拓扑信号，但FILTR成功利用这些特征逼近持久性图谱。本方法首次实现了通过高效可学习前馈机制，从原始点云中数据驱动地提取持久性图谱。
原文摘要 · Abstract (English)
Recent advances in pretraining 3D point cloud encoders (e.g., Point-BERT, Point-MAE) have produced powerful models, whose abilities are typically evaluated on geometric or semantic tasks. At the same time, topological descriptors have been shown to provide informative summaries of a shape's multiscale structure. In this paper we pose the question whether topological information can be derived from features produced by 3D encoders. To address this question, we first introduce DONUT, a synthetic benchmark with controlled topological complexity, and propose FILTR (Filtration Transformer), a learnable framework to predict persistence diagrams directly from frozen encoders. FILTR adapts a transformer decoder to treat diagram generation as a set prediction task. Our analysis on DONUT reveals that existing encoders retain only limited global topological signals, yet FILTR successfully leverages information produced by these encoders to approximate persistence diagrams. Our approach enables, for the first time, data-driven extraction of persistence diagrams from raw point clouds through an efficient learnable feed-forward mechanism.
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