Two-Sided Safe Screening for Scalable Tversky Optimization in Segmentation Decoding

Image segmentation is a fundamental task in computer vision. Segmentation networks typically output pixel- or voxel-level probabilities, whereas overlap measures evaluate discrete prediction masks. Metric-aware decoding uses these probabilities to optimize overlap measures, but exact optimization of the resulting decoding objective can be computationally demanding for large images and volumes. We study scalable decoding for a broad family of Tversky-type objectives, including Dice, intersection over union, and $F$-scores, under a plug-in expected linear-fractional (ELF) criterion defined by a ratio of expected confusion counts. We characterize the ranking-induced structure of its maximizers and derive a pair of complementary, closed-form safe-screening certificates: an upper-threshold certificate identifies coordinates that must be selected, whereas a data-adaptive lower-threshold certificate identifies coordinates that must be excluded before downstream exact optimization. Together, these two-sided certificates reduce the effective problem dimension while preserving a global optimizer of this criterion. We instantiate the screening rules in an efficient GPU implementation with a sorting based downstream backend. Experiments on synthetic probability maps and native medical volumes demonstrate substantial reductions in runtime and working memory at large scales.