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

Abstract

Topological correctness is crucial for tubular structures such as blood vessels, nerve fibers, and road networks. Existing topology-preserving methods rely on domain-specific ground truth, which is costly and rarely transfers across domains. When deployed to a new domain without annotations, a key question arises: how can we detect topological anomalies without ground-truth supervision? We reframe this as topological anomaly detection, a structured visual reasoning task requiring a model to locate and classify topological errors in predicted segmentation masks. Vision-Language Models (VLMs) are natural candidates; however, we find that state-of-the-art VLMs perform nearly at random, lacking the fine-grained, topology-aware perception needed to identify sparse connectivity errors in dense structures. To bridge this gap, we develop an automated data-curation pipeline that synthesizes diverse topological anomalies with verifiable annotations across progressively difficult levels, thereby constructing the first large-scale, multi-domain benchmark for this task. We then introduce Topo-R1, a framework that endows VLMs with topology-aware perception via two-stage training: supervised fine-tuning followed by reinforcement learning with Group Relative Policy Optimization (GRPO). Central to our approach is a topology-aware composite reward that integrates type-aware Hungarian matching for structured error classification, spatial localization scoring, and a centerline Dice (clDice) reward that directly penalizes connectivity disruptions, thereby jointly incentivizing semantic precision and structural fidelity. Extensive experiments demonstrate that Topo-R1 establishes a new paradigm for annotation-free topological quality assessment, consistently outperforming general-purpose VLMs and supervised baselines across all evaluation protocols.

Figures (6)

• Figure 1: Intuition of the framework. (a) A segmentation mask can achieve a high pixel-wise Dice score (0.91) yet contain critical topological errors, such as broken or spurious connections, that are visible only upon close structural inspection. (b) State-of-the-art VLMs, including GPT-5.2 and Gemini-2.5-Flash, fail to detect these topological anomalies (near-zero Detection F1@0.5). (c) Topo-R1 successfully detects and classifies the topological error with structured, typed bounding-box outputs.
• Figure 2: The performance of state-of-the-art VLMs and our Topo-R1 on the topological anomaly detection task.
• Figure 3: Overview of the automatic data curation pipeline.
• Figure 4: Qualitative results of topological anomaly detection on 0- and 1-topological errors. Topo-R1 demonstrates superior capability in the localization and classification of diverse topological errors.
• Figure 5: IoU-to-score mapping $\phi$ for different reward designs.