SEMIR: Semantic Minor-Induced Representation Learning on Graphs for Visual Segmentation

Segmenting small and sparse structures in large-scale images is fundamentally constrained by pixel-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 inference space. 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 optimization problem that replaces hand-tuned preprocessing with a boundary-alignment objective: minor parameters are learned by maximizing agreement between predicted boundary elements and class-agnostic 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—BraTS2021, KiTS2023, and LiTS2017—where targets exhibit high structural variability and distributional uncertainty, providing a stringent testbed for structure-adaptive inference. SEMIR yields consistent improvements in minority-structure Dice at practical runtime, positioning minor-induced representations as a principled alternative to pixel-centric segmentation in challenging, high-variability visual domains.