SEMIR: Topology-Preserving Graph Minors for Thin-Structure Segmentation

2026-06-22

AI Summary

This work addresses the fragmentation problem in segmenting fine structures—such as wires, cracks, and lane markings—caused by traditional pixel-wise representations that disrupt topological connectivity. To preserve structural continuity, the authors propose a topology-preserving, parameterized graph minor representation that compresses the input image into super-nodes via a boundary-aligned contraction criterion. This approach achieves substantial dimensionality reduction while rigorously maintaining the connectivity of fine structures. A lightweight graph neural network is then employed for classification, followed by bidirectional pixel-to-graph mapping to enable full-resolution inference. Evaluated on TTPLA, CrackSeg9k, and SkyScapes Lane datasets, the method matches or surpasses state-of-the-art domain-specific approaches in Dice, IoU, and Boundary F1 scores, while reducing mask fragmentation by at least 4.6×.

Abstract

Thin-structure segmentation--power lines, cracks, lane markings at 1-3 pixel width--requires preserving connectivity that standard representations preclude: patching severs continuous structures and conventional superpixels merge thin targets into background before classification. Topology-aware losses penalize connectivity breaks at the objective level but cannot recover what the representation has already destroyed. We propose SEMIR, a framework that replaces the pixel lattice with a parameterized graph minor whose contraction map preserves thin-structure connectivity under the contraction criterion. The minor collapses millions of pixels into tens or hundreds of boundary-aligned supernodes, enabling full-resolution inference without patching at scales demonstrated up to 21 MP in this paper; a lightweight GNN classifies the reduced graph and an exact map lifts predictions to pixel resolution. One pipeline--identical architecture, features, loss, and GNN hyperparameters across all dataset--matches or exceeds domain-specific baselines on TTPLA (power lines), CrackSeg9k (pavement cracks), and SkyScapes Lane (aerial markings) on Dice, IoU, and Boundary F1 while reducing mask fragmentation by at least 4.6x relative to SLIC at matched inference.

Problem

• thin-structure segmentation
• topology preservation
• graph minors
• connectivity
• superpixels

Innovation

• graph minor
• topology preservation
• thin-structure segmentation
• boundary-aligned supernodes
• lightweight GNN