Structured Subset-Relative Decision Fields for Medical Image Segmentation from Scarce Scribbles

Scribble annotations reduce the labeling cost of medical image segmentation, yet when only a few samples are scribble-annotated, models still struggle to learn reliable anatomical semantics from such scarce supervision. Task-specific priors can provide additional inductive guidance beyond direct label supervision, while they often encode higher-order structures, such as region-level organization, semantic relations, and spatial and geometric regularities, which are not readily accommodated by conventional pixel-level supervision. To address this issue, we propose SRDF, an anatomy- and geometry-aware structured representation framework. It formulates multiclass predictions as subset-relative decision fields with locally calibrated distances, yielding differentiable structured objects that jointly encode region semantics and local boundary geometry. Building on SRDF, we further design anatomical-structure and boundary-geometry constraints, allowing anatomical priors and local image evidence to constrain region organization and boundary localization, respectively, at semantic scopes aligned with the corresponding priors, thereby providing structural and geometric guidance for learning under scarce scribble supervision. Experiments on ACDC and Prostate show that the proposed method outperforms existing methods under few-shot scribble supervision.