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

Segmenting small and sparse structures in large-scale images is fundamentally constrained by voxel-level, lattice-bound computation and extreme class imbalance -- dense, full-resolution inference scales poorly and forces most pipelines to rely on fixed regionization or downsampling, coupling computational cost to image resolution and attenuating boundary evidence precisely where minority structures are most informative. We introduce SEMIR (Semantic Minor-Induced Representation Learning), a representation framework that decouples inference from the native grid by learning a task-adapted, topology-preserving latent graph representation with exact decoding. SEMIR transforms the underlying grid graph into a compact, boundary-aligned graph minor through parameterized edge contraction, node deletion, and edge deletion, while preserving an exact lifting map from minor predictions to lattice labels. Minor construction is formalized as a few-shot structure learning problem that replaces hand-tuned preprocessing with a boundary-alignment objective: minor parameters are learned by maximizing agreement between predicted boundary elements and target-specific semantic edges under a boundary Dice criterion, and the induced minor is annotated with scale- and rotation-robust geometric and intensity descriptors and supports efficient region-level inference via message passing on a graph neural network (GNN) with relational edge features. We benchmark SEMIR on three tumor segmentation datasets -- BraTS 2021, KiTS23, and LiTS -- where targets exhibit high structural variability and distributional uncertainty. SEMIR yields consistent improvements in minority-structure Dice at practical runtime. More broadly, SEMIR establishes a framework for learning task-adapted, topology-preserving latent representations with exact decoding for high-resolution structured visual data.

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.

Accurate segmentation of thin, tortuous anatomical structures, such as retinal vessels, cerebral vasculature, and facial wrinkles, remains challenging due to low contrast, frequent discontinuities, and severe class imbalance. Although recent convolutional and Transformer-based models have improved performance, they often yield fragmented predictions and fail to recover fine branches. We propose CSWinUNETR, a general-purpose backbone for 2D and 3D thin-structure segmentation. It employs cross-shaped stripe self-attention to model long-range principal-axis context and incorporates cyclic shifts to enhance information exchange across stripes. To better preserve fine-grained details, we further introduce a detail-enhanced multi-scale self-attention module that aggregates contextual features from multi-resolution representations. In addition, we propose sparse-control dynamic snake convolution, which reconstructs reliable dense curvilinear kernels from sparsely predicted control points to better follow tortuous geometry. Extensive experiments on four benchmarks across ophthalmology, neurovascular imaging, and dermatology demonstrate that CSWinUNETR consistently outperforms state-of-the-art methods without task-specific post-processing or topology-aware losses. The code is available at https://github.com/labhai/CSWinUNETR.