ErrorRoute: Budgeted Utility-Aware Resolution Routingfor 3D Medical Image Segmentation

Three-dimensional medical image segmentation is unusually heterogeneous in its computational needs: large homogeneous organ interiors are often resolved at coarse scale, whereas small organs, lesions, thin vessels, and ambiguous boundaries benefit from native-resolution processing. Yet modern 3D segmentation networks allocate nearly uniform computation across the entire volume. Existing dynamic-resolution or coarse-to fine methods reduce cost, but typically route regions using hand-crafted image complexity, prediction confidence, or a fixed crop, none of which directly estimates whether spending additional computation on a region will improve the segmentation. We introduce ERRORROUTE, a budgeted inference framework that learns the marginal refinement utility of candidate 3D blocks. A coarse branch first predicts global low-resolution semantics. During training, we estimate for each candidate block the loss reduction achievable by native resolution refinement and supervise a utility estimator to predict this gain before refinement. A differentiable budgeted selector then allocates a fixed compute budget to blocks with the highest expected utility per unit cost, while unselected regions remain on the efficient global path. Selected blocks are refined locally and merged through residual cross-scale fusion. Across six 3D CT/MRI benchmarks, ERRORROUTE achieves a mean Dice of 90.5% at 128 GFLOPs, improving the accuracy-compute frontier over dense 3D baselines and fixed coarse-to-fine systems. At a 30% routing budget, the learned utility estimator recovers 83% of the blocks selected by an oracle router, with the largest allocation concentrated on lesions, small structures, and complex boundaries. These results suggest that efficient medical segmentation benefits from learning where additional computation is useful, rather than merely where the model is uncertain.