Learning Task-Conditioned Utilities for Topological Errors in Thin-Structure Segmentation

Topological errors with similar overlap can have different functional consequences, and the same gap, spur, or bridge can have different utility across tasks. Existing topology-aware losses encode structure but usually fix the relative cost of error types. We formulate topology supervision as learning a task-conditioned utility over a finite, interpretable edit signature, with held-out functional outcomes separated from the segmentation-training objective. TOPOUTILITY represents gaps, false bridges, spurs, loops, endpoint displacement, and branch mismatch, and defines diagnostics for utility identifiability, ranking stability, grouping stability, and extractor stability before weights are frozen or cross-fitted. On DRIVE, it reaches 0.86 pairwise agreement, 0.83 severity correlation, 7.2% downstream path failure, and 0.858 clDice at 21.5 ms; fixed graph-edit costs reach 0.78, 0.74, 10.9%, and 0.847 at 36.7 ms. These reported aggregates validate held-out predictive utility and its downstream association; the full identification diagnostics remain separate evidence requirements.