Topo-R1: Detecting Topological Anomalies via Vision-Language Models

TL;DR

This paper evaluates vision-language models' ability to perceive topological anomalies in tubular structures, finds current models lacking, and introduces a new benchmark and Topo-R1 method that significantly improve topological understanding.

Contribution

It creates the first large-scale benchmark for topological anomaly detection in segmentation masks and proposes Topo-R1, a reinforcement learning approach that enhances topological perception.

Findings

Current VLMs perform nearly at random on topological tasks.

The benchmark enables systematic evaluation of topological perception.

Topo-R1 outperforms general-purpose VLMs and matches supervised methods.

Abstract

Topology is critical in tubular structures such as blood vessels, nerve fibers, and road networks, where connectivity and loop structure govern downstream functional analysis. Vision-Language Models (VLMs) are promising candidates for understanding such structures, given their reasoning and grounding capabilities. To probe their topological perception, we systematically evaluate leading closed- and open-source VLMs on localizing and classifying four canonical topological anomalies (broken/spurious connections, missing/extra branches) in tubular-network segmentation masks. They perform nearly at random, indicating that topology-aware perception is largely absent from current general-purpose VLMs. As no existing resource pairs segmentation masks with localized anomaly annotations, we build an automated, multi-domain data-curation pipeline that synthesizes diverse topological perturbations with verifiable Betti-number annotations across graduated difficulty levels, yielding the first systematic benchmark with a large-scale training set and held-out in-distribution (ID) and out-of-distribution (OOD) test suites. Building on this benchmark, we introduce Topo-R1, centered on a topology-aware composite reward that jointly scores localization, classification, and skeleton-level structural fidelity. Supervised fine-tuning cold-starts schema-compliant outputs, and Group Relative Policy Optimization (GRPO) then optimizes the policy against this reward, steering predictions toward topologically meaningful structure rather than superficial pixel overlap. Extensive experiments show that Topo-R1 substantially outperforms general-purpose VLMs and matches or exceeds supervised baselines across ID, OOD, and real-segmentation-output protocols, establishing a strong foundation for VLM-based topological understanding of structured visual data.