TRACE: Topology-Aware Reconnection via Prediction-Adaptive Connectivity Enforcement for Thin-Structure Segmentation

Segmenting slender curvilinear structures such as retinal vessels, cracks, and roads demands topological correctness, as even a single-pixel discontinuity can fragment a continuous network and invalidate downstream analysis. Under standard binary-mask supervision, models optimized for pixel-level overlap frequently produce topologically broken predictions. We trace this to a fundamental mismatch: pixel-wise losses distribute gradients uniformly, yet connectivity hinges on a sparse set of bottleneck pixels. These pixels are vastly outnumbered by thick structures and background, rendering their aggregate gradient contribution negligible. We term this phenomenon topological gradient starvation (TGS). To address it, we propose Widest-Path Reachability Fields (WPRF), a differentiable Max-Min reachability objective that redirects gradient flow to connectivity bottlenecks. The module is plug-and-play, backbone-agnostic, and incurs no inference overhead. WPRF implements a differentiable Max-Min objective via dynamic programming on a domain-restricted graph, coupled with a bottleneck-aware observation term that balances gradient contributions across varying structures. Compared to prior topology-aware losses that rely on post-hoc skeletonization or homology computation, WPRF directly optimizes end-to-end reachability via differentiable Max-Min algebra, enabling gradient flow to concentrate on connectivity bottlenecks without auxiliary structures. We introduce OMVIS, a new oral microvessel segmentation dataset. Experiments across nine architectures and six datasets validate the bottleneck-focused gradient routing mechanism. WPRF improves 87% of experiments with fixed hyperparameters and achieves clDice gains of 7.2 percentage points on structurally fragile datasets.

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.

Accurate segmentation of thin curvilinear structures is vital for various real-world applications, from vessel analysis to road extraction. Yet their intricate geometry makes even minor pixel-wise errors enough to break the global topology, and this structural fragility turns severe domain shifts into catastrophic failures. The difficulty is most acute under cross-modality gaps, where the imaging process itself differs fundamentally between source and target. While test-time adaptation (TTA) offers a practical source-free remedy, existing methods adapt feature statistics and confidence, neither of which constrains connectivity, and thus degrade under such extreme gaps. To address this, we propose Skeleton-Guided Progressive Test-Time Adaptation (SGP-TTA). Progressive Batch Normalization (ProgBN) shifts normalization from frozen source statistics toward current target estimates under a sample-count schedule, so that the source-target balance follows the stage of adaptation rather than a fixed coefficient. Consensus Skeleton Recall (CSR) then derives a structural target from geometrically aligned multi-view predictions and updates only the BN affine parameters to preserve connected structures. Extensive experiments show that SGP-TTA consistently outperforms existing TTA methods in topological connectivity, with the largest margins under cross-modality shift. The project page is available at https://boa-jang.github.io/SGP-TTA.