Segmentation networks that predict at an output stride are trained against label maps downsampled by strided sampling, nearest-neighbor resampling or majority pooling. These methods label each coarse grid cell on its own, so a region that wins no cell is absent from the target and receives no positive label. We present MatchDown, which builds the coarse target from a minimum-cost matching between regions and the grid cells they occupy. It keeps as many regions as any one-region-per-cell target can, certifies how many losses are unavoidable, and with priority tiers (MatchDown-P) keeps every evaluated region (a region that a metric scores) of at least one cell's area. On COCO, Cityscapes and BBBC038 at factors 2 to 16, MatchDown-P loses exactly the minimum number of regions, whereas the downsampling used by StarDist, nnU-Net and connectomics pyramids loses four to five times as many on COCO at factor 8. Keeping a region in the target and reconstructing its shape are different problems: we show that no region lost by majority pooling can be reconstructed above IoU 0.5 by upsampling any coarse target, yet on BBBC038 a star-convex head trained on MatchDown targets segments 35% of the nuclei that majority pooling loses above IoU 0.5, against 15% when trained on majority targets and 24% on StarDist's strided target. On two nucleus datasets, with thresholds cross-validated for count error, this head has instance accuracy at IoU 0.5 (Acc50) 2.6 to 4.2 points above the strided target and at most 2.8 points below cell-center sampling, and a lower count error than the strided and cell-center targets on BBBC039. On BBBC039, an affinity head, which outputs one label per cell, lowers count error relative to majority targets by 9.3 nuclei per image at 7.2 points lower Acc50. MatchDown runs once, before training, in place of the label-downsampling step.

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