FILTR: Extracting Topological Features from Pretrained 3D Models

TL;DR

This paper introduces FILTR, a learnable framework that extracts topological features from pretrained 3D point cloud encoders, enabling data-driven persistence diagram prediction from raw point clouds.

Contribution

The paper presents FILTR, a novel transformer-based method that predicts persistence diagrams from frozen 3D encoders, and introduces DONUT, a synthetic benchmark for topological complexity.

Findings

Existing encoders retain limited global topological signals.

FILTR successfully predicts persistence diagrams from encoder features.

First data-driven method for extracting persistence diagrams from raw point clouds.

Abstract

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.