What Survives Label Downsampling? Exact Region Survival for Coarse Segmentation Targets

Zhiyuan Zhang; Yukun Ou; San Tek Choi

cs.CVOct 29, 2026

What Survives Label Downsampling? Exact Region Survival for Coarse Segmentation Targets

Authors: Zhiyuan Zhang, Yukun Ou, San Tek Choi

Organizations: East China Jiaotong University · Imperial College London · University of Macau

Abstract

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.

Figures & tables

Target	Lost $\downarrow$	$\geq$ 1 cell $\downarrow$	Recon. $\uparrow$
Majority pooling	9,207	195	98.4
Strided (StarDist)	8,498	176	81.1
Nearest-exact (nnU-Net)	8,481	150	97.7
Max pooling	7,849	933	74.5
Greedy rescue	4,921	69	89.9
Maximal rescue	4,381	9	89.6

Table 1: Label-level evaluation on COCO-R at factor 8 (1,000 held-out images, 25,963 evaluated regions). Lost: evaluated regions missing from the target;

\geq

1 cell: lost regions of at least

f^{2}

pixels; Recon.: share (%) of the reachable regions ( Proposition 5 ) reconstructed at IoU

{}>0.5

by nearest upsampling. The lower bound ( Theorem 4 ) is 1,854. Keeping the small regions costs reconstruction quality ( Tab. S6 ). All factors and datasets: Tabs. S3 and S4 . Best in bold, second best underlined.

Figure 2: Regions lost against the lower bound, and loss by nucleus size. (a) Evaluated regions lost on COCO-R as a multiple of the lower bound of Theorem 4 . At factor 2, majority pooling loses 29 times the minimum and strided and nearest-exact sampling (which nearly coincide) 21 times; at factors 8 and 16 they lose 3.5 to 5 times, greedy rescue 2.6 to 5.7 times across factors, and MatchDown-P exactly the minimum. (b) BBBC038 at

f{=}8

, by region area (nuclei and their 4-connected pieces; bins labeled by their lower edge; dotted line: one cell): the share of regions lost by majority pooling and by MatchDown-P (38 pieces below a sixteenth of a cell, all certified; MatchDown-P loses no nucleus), and the share that is reachable, i.e . , whose IoU bound exceeds 0.5 ( Proposition 5 , shaded). Other datasets: Figs. S3 and S4 .

	BBBC038						BBBC039
	Affinity, $f{=}8$			Star-convex, $f{=}8$			Affinity, $f{=}16$			Star-convex, $f{=}16$			Star-convex, $f{=}8$
Target	CE $\downarrow$	F1 $\uparrow$	$\mathrm{Acc}_{50}$ $\uparrow$	CE $\downarrow$	F1 $\uparrow$	$\mathrm{Acc}_{50}$ $\uparrow$	CE $\downarrow$	F1 $\uparrow$	$\mathrm{Acc}_{50}$ $\uparrow$	CE $\downarrow$	F1 $\uparrow$	$\mathrm{Acc}_{50}$ $\uparrow$	CE $\downarrow$	F1 $\uparrow$	$\mathrm{Acc}_{50}$ $\uparrow$
Majority pooling	5.01	0.689	0.541	6.50	0.830	0.750	13.05	0.660	0.497	13.30	0.897	0.872	6.80	0.922	0.871
Cell center	3.91	0.696	0.558	5.78	0.841	0.770	10.43	0.698	0.539	11.57	0.922	0.855	5.51	0.926	0.871
Strided (StarDist)	4.10	0.440	0.270	4.84	0.809	0.728	8.70	0.080	0.070	5.62	0.888	0.799	4.29	0.915	0.847
MatchDown ∗ (ours)	3.69	0.673	0.530	4.10	0.854	0.770	3.77	0.591	0.425	3.35	0.904	0.827	2.90	0.932	0.873

Table 2: Main results with cross-validated thresholds: count error (CE, nuclei per image), F1 at IoU

{}>0.5

and

\mathrm{Acc}_{50}

of both heads on both datasets; BBBC038 (670 images) at factor 8, BBBC039 (197 images) at factor 16 and, for the star-convex head, also at factor 8; 9 seeds

\times

3 folds. ∗ MatchDown on BBBC038 and MatchDown-P on BBBC039 (on BBBC038 both lose no nucleus). Best of the targets shown in bold (ties share the mark), second underlined. Other targets: Tab. 3 ; details: Tabs. S10 , S12 , S14 and S15 .

Target	default	cross-validated
	Count err. $\downarrow$	$\Delta$ count err. $\downarrow$	$\Delta$ $\mathrm{Acc}_{50}$ $\uparrow$	F1 $\uparrow$
Majority pooling	5.93	ref.	ref.	0.689
Masked †	5.02	$-0.77$	$+0.000$	0.689
Greedy rescue	3.93	$-1.43$	$-0.010$	0.679
Soft labels	6.46	$-1.64$	$-0.082$	0.598
Full-res. loss	3.56	$-1.34$	$+0.018$	0.690

Table 3: Ablation on the affinity head , BBBC038 at factor 8; soft labels as in [ 1 ] . Count error at the default thresholds, then, with cross-validated thresholds, the differences from the majority model and F1 at IoU

{}>0.5

. † Masked: majority targets with the cells of the missing nuclei left out of the loss, from the second set of runs, differences against its majority model (in that set, MatchDown’s difference is

-1.34

). Intervals and further columns: Tabs. S10 and S11 ; the star-convex head: Tab. S12 . Best in bold, second best underlined.

Figure 3: Qualitative results on a held-out BBBC039 image at factor 16 ( $192{\times}320$ -pixel window, 59 nuclei; seed 0, default thresholds). (a) Affinity head: the image, two targets with their lost nuclei outlined, and the predictions of the models trained on them, with the nuclei that no predicted object covers by a fifth outlined. (b) Star-convex head: the same for the strided and MatchDown-P targets, with the nuclei that no prediction matches at IoU ${}>0.5$ outlined. More images: Fig. S10 .

Appendix figures & tables26 assets

Supplementary material from the paper’s appendix.

Appendix

Figure S1 : A worked example of survival as matching. (a) A $12{\times}12$ source at $f{=}4$ : seven regions on a background. (b) Its support graph. Bold edges are a maximum matching ( $\nu{=}7$ of 8 regions); regions 2, 3 and 4 share only cells c2 and c5, so one of them must be lost, and this Dulmage–Mendelsohn cluster certifies the single unavoidable loss ( Theorem 4 ). (c) Majority pooling keeps 2 of the 8 regions, the background and region 1. (d) MatchDown-P keeps 7 of 8 and loses only region 3, one of the three regions of the cluster certified in (b); the matching drawn in (b) loses region 4 instead, at the same survival.

Figure S2 : Spurious adjacencies forced by maximum survival. (a) A $4{\times}4$ source at $f{=}2$ : a connected background with single-pixel regions at three corners. (b) Majority pooling keeps one region and creates no spurious adjacency. (c) Of the eight supported $2{\times}2$ labelings, only this one keeps all four regions, and it creates the adjacencies $\{2,3\}$ and $\{2,4\}$ , which the source does not have.

Dataset	Image size	Images	Evaluated regions	Per image	Majority loss (%)	Use
COCO-A	up to $640{\times}640$	1,000	25,860	25.9	34.9	L
COCO-B	up to $640{\times}640$	1,000	25,909	25.9	34.7	L
COCO-R	up to $640{\times}640$	1,000	25,963	26.0	35.5	L
Cityscapes (6 cities)	$1024{\times}2048$	900	104,234	115.8	27.9	L
BBBC038 (stage 1)	varied ‡	670	29,668 / 29,461	44.3	8.8	L, T ( $f{=}8$ )
BBBC039	$520{\times}696$	197	23,615 nuclei	119.9	10.1 †	T, L ( $f{=}8$ –32)

Appendix

Table S1 : Datasets. Evaluated regions are the 4-connected components of instances and of stuff classes that a metric scores (not void or crowd); for the nucleus datasets the second number counts annotated nuclei, of which a few consist of several 4-connected pieces. COCO-A, COCO-B and COCO-R are disjoint random sets of COCO panoptic validation images; COCO-R was held out from all development. Majority loss: share of evaluated regions (COCO, Cityscapes) or nuclei (BBBC038, BBBC039) missing from the majority-pooling target at factor 8 ( † factor 16). ‡ From

256{\times}256

1040{\times}1388

pixels. Use: L, label-level evaluation (factors 2 to 16 unless stated); T, training; BSDS500 serves the repair-optimality and binary-topology comparisons ( Appendix D ).

	Affinity head	Star-convex head
Backbone	ResNet-18 (ImageNet weights) with a feature pyramid of 128 channels, laterals down to the target stride
Output stride	8 (BBBC038), 16 (BBBC039)	8 (BBBC038, also 4 and 2), 16 and 8 (BBBC039)
Outputs per cell	foreground, affinities to 4 of the 8 neighbors	object probability, center offset (2), 32 ray distances
Loss	BCE on foreground over all cells + BCE on affinities over valid cell pairs	BCE on probability + $0.2\times$ L1 on offsets + $0.2\times$ L1 on distances (assigned cells)
Optimizer	AdamW, learning rate $5{\times}10^{-4}$ , $\beta=(0.9,0.999)$ , weight decay $10^{-4}$
Schedule	500-iteration linear warm-up, then polynomial decay (power 0.9); 8,000 iterations

Appendix

Table S2 : Training and decoding settings. Every model of a seed and fold uses the same initialization, image crops and augmentations for all targets, so that differences between targets are paired.

	COCO-R (25,963 regions)				Cityscapes (104,234 regions)				BBBC038 (29,668 regions)
Method	$f{=}2$	4	8	16	$f{=}2$	4	8	16	$f{=}2$	4	8	16
Strided (StarDist)	17.6	26.5	32.7	40.1	8.7	15.1	24.0	38.3	0.42	0.95	6.2	26.4
Nearest (cell center)	17.6	26.8	32.8	40.2	8.7	15.0	24.0	38.1	0.42	0.69	5.3	26.2
Nearest-exact (nnU-Net)	17.9	26.9	32.7	40.1	8.6	15.0	24.0	38.1	0.41	0.78	5.2	26.0
Max pooling	12.9	21.4	30.2	41.6	9.8	17.5	28.2	41.6	0.23	0.43	1.3	7.4
Majority pooling	24.2	30.5	35.5	43.2	14.2	18.7	27.9	44.0	0.58	1.1	9.3	39.0

Appendix

Table S3 : Evaluated regions lost (%) by every method, dataset and factor. Lower bound: the minimum of Theorem 4 ; reachable: share of evaluated regions whose IoU bound exceeds 0.5 ( Proposition 5 ). MatchDown-P equals the lower bound in every column. At

f{=}2

the cell-center pixel is the first pixel of the cell, so nearest (cell center) equals strided. Majority pooling counts the most frequent region in each cell; the class-first variant picks the most frequent class, then its most frequent region. On COCO-A and COCO-B every entry is within one percentage point of COCO-R. Best in bold, second best underlined.

	Lost (%) $\downarrow$		$\geq$ 1 cell (per 1,000) $\downarrow$			Recon. (%) $\uparrow$			Void/crowd
Method	COCO-A	COCO-B	COCO-R	Cityscapes	BBBC038	COCO-R	Cityscapes	BBBC038	lost (%) $\downarrow$
Strided (StarDist)	32.2	32.1	6.8	26.6	12.2	81.1	69.1	59.8	93.3
Nearest (cell center)	32.2	32.1	6.2	27.7	4.4	97.8	96.0	96.7	–
Nearest-exact (nnU-Net)	32.3	32.0	5.8	27.4	5.3	97.7	95.9	96.7	93.3
Max pooling	29.5	30.0	35.9	76.8	1.6	74.5	64.6	60.3	97.8
Majority pooling	34.9	34.7	7.5	35.1	16.5	98.4	96.1	94.8	96.8

Appendix

Table S4 : Label-level evaluation at factor 8, further columns. Lost (%): evaluated regions lost on the two COCO development sets.

\geq

1 cell: lost regions of at least

f^{2}

pixels per 1,000 evaluated regions. Recon.: share of the reachable regions that the target reconstructs at IoU

{}>0.5

under nearest upsampling. Void/crowd lost: share of the 157,318 void and crowd components of COCO-R missing from the target; MatchDown and MatchDown-P lose the same total number of components (70,559) and differ only in which ones. –: not computed for this method. Best in bold, second best underlined.

Figure S3 : Loss by region area on COCO-R and Cityscapes at factor 8 (BBBC038 is Fig. 2 b). Per area bin, labeled by its lower edge: the share of evaluated regions each method loses, the share that is reachable (IoU bound above 0.5, shaded), and the share that the MatchDown-P target reconstructs at IoU

{}>0.5

. The dotted vertical line marks one cell.

Figure S4 : Every factor. (a) Evaluated regions lost on BBBC038 at factors 2 to 16, with the label pyramids built by repeated

2{\times}2

downsampling (dotted, open markers). Iterated majority pooling loses more than direct pooling to the same factor, and iterated MatchDown-P never loses fewer regions than direct MatchDown-P, which equals the lower bound at every factor. (b) Share of evaluated regions that are reachable (IoU bound above 0.5) on COCO-R, Cityscapes and BBBC038.

Figure S5 : Majority and MatchDown-P targets at factor 8 on three COCO-R images , at ranks 250, 500 and 749 of 1,000 by the per-image difference in lost evaluated regions. Left: the photograph with the region boundaries; middle and right: the majority-pooling and MatchDown-P targets drawn over it, void and crowd components in gray, each lost evaluated region outlined and ringed. (a) Image 308476, 7 evaluated regions, majority loses 1. (b) 292456, 25 regions, 5 against 1. (c) 319721, 22 regions, 10 against 0.

Figure S6 : Majority and MatchDown-P targets at factor 8 on three Cityscapes frames , chosen as in Fig. S5 (ranks 225, 450 and 674 of 900). Each row shows the $512{\times}1024$ -pixel window with the most regions lost by majority pooling; the left panel shows the semantic label map with the region boundaries. (a) Mönchengladbach 000000_000383, 57 evaluated regions in the window, majority loses 14 and MatchDown-P 2. (b) Mönchengladbach 000000_021104, 62 regions, 21 against 0. (c) Hamburg 000000_105464, 101 regions, 34 against 2.

Figure S7 : Majority and MatchDown-P targets at factor 8 on three BBBC038 images , chosen as in Fig. S5 (ranks 167, 334 and 502 of 670). (a) f0c9f135, 24 nuclei; neither target loses one, as on 27% of the images. (b) 136000dc, 34 nuclei, majority loses 2 and MatchDown-P 0. (c) d910b2b1, 24 nuclei, 4 against 0.

Method	PQ $\uparrow$	Lost (%) $\downarrow$	Spurious / img $\downarrow$
Majority, class first (void first)	93.54	24.0	0.76
Majority, class first (void last)	94.67	22.6	1.41
Majority pooling	93.51	24.2	0.59
Majority pooling (void last)	94.66	22.2	1.47
Majority pooling (ties to highest id)	94.59	20.8	1.72
One-hot bilinear + argmax	93.40	23.7	0.66

Appendix

Table S5 : Reconstruction quality and survival on COCO-R at factor 2 (1,000 images, 25,963 evaluated regions): reconstruction PQ over all 133 classes, evaluated regions lost, and spurious adjacencies among evaluated regions per image. “Void last” and “highest id” change only how ties are broken; the tie rule alone moves the PQ of majority pooling by 1.08 to 1.15 points. MatchDown’s PQ is 0.58 [0.48, 0.68] points (90% interval) below class-first majority. At

f{=}2

\kappa{=}1/8

and

2/8

give the MatchDown target. Best in bold, second best underlined.

	PQ $\uparrow$			Lost (%) $\downarrow$
Method	$f{=}2$	4	8	$f{=}4$
Nearest (cell center)	93.65	87.92	78.21	76.7
Majority pooling	93.81	88.58	78.86	86.7
One-hot bilinear + argmax	93.69	87.08	75.36	75.8
Smallest-region priority	92.51	86.50	77.30	79.1
Greedy rescue	93.28	85.31	71.33	19.3

Appendix

Table S6 : Reconstruction PQ on COCO-A (1,000 images, all 133 classes) at factors 2, 4 and 8, and the share of all components, void and crowd included, lost at factor 4. Smallest-region priority gives each cell the smallest region covering at least a quarter of it. Keeping more regions lowers PQ at factors 4 and 8, because many of the kept regions are not reachable ( Proposition 5 ). Best in bold, second best underlined.

Dataset	$\kappa$	Uncovered-region bound	Unweighted
Cityscapes ( $f{=}8$ )	$1/8$	0.5589	0.5627
	$2/8$	0.7254	0.7274
	$4/8$	0.9816	0.9816
COCO ( $f{=}8$ )	$1/8$	0.8280	0.8303
	$2/8$	0.9149	0.9159
	$4/8$	0.9988	0.9988

Appendix

Table S7 : Coverage threshold

\kappa

. Evaluated regions lost, as a fraction of those lost by class-first majority pooling on the same images. Uncovered-region bound: regions with no cell covered to

\kappa

and no fixed majority cell, which every

\kappa

-restricted labeling loses ( Sec. A.5 ). Unweighted: the unweighted construction on the thresholded support graph. The tiered construction, with the regions already kept by uncovered cells ranked last, attains the exact minimum of Theorem 9 on every image, checked against the minimum computed separately; on Cityscapes at

\kappa{=}1/8

that minimum is 0.5621.

Method	Relative time	Cityscapes frame
Majority pooling	1.0 $\times$	0.69 s
MatchDown	1.7–1.9 $\times$	1.29 s
$\kappa$ , no repair	2.0 $\times$	1.2 s
$\kappa$ , with repair	2.8–3.1 $\times$	2.0 s

Appendix

Table S8 : Run time on one core of an Intel Xeon Platinum 8468: median over 120 inputs at factor 4 (five repeats) relative to majority pooling, and a full

1024{\times}2048

Cityscapes frame at factor 8. Time grows about linearly with image size (log–log slopes 0.92 to 1.01). The target is built once before training; training and inference are unchanged.

$f$	Bound	Rescue	$\times$	MatchDown-P	$\geq$ 1 cell	Gap	Images (%)
8	0.025	0.182	7.2 $\times$	0.025	0	$+0.18$	13.2
16	0.271	0.885	3.3 $\times$	0.271	3	$+0.71$	32.5
24	0.648	3.231	5.0 $\times$	0.648	55	$+3.10$	86.3
32	1.266	7.948	6.3 $\times$	1.266	15	$+8.01$	98.5

Appendix

Table S9 : Where greedy rescue fails , BBBC039 at factors 8 to 32 (197 images, 23,615 nuclei), label level. Bound (the lower bound of Theorem 4 ), rescue and MatchDown-P: nuclei lost (%);

\times

: rescue’s loss as a multiple of the lower bound;

\geq

1 cell: nuclei of at least

f^{2}

pixels lost by rescue (MatchDown-P loses none); gap: oracle count-error difference, rescue minus MatchDown-P, per image; images: share of images on which rescue loses more nuclei than MatchDown-P. MatchDown-P never loses more nuclei than rescue on any image.

Target	Count err. $\downarrow$	cross-validated	equal FP	cross-validated	cross-validated	Detected (%) $\uparrow$
		$\Delta$ count err. $\downarrow$		$\Delta$ $\mathrm{Acc}_{50}$ $\uparrow$	$\Delta$ centroid F1 $\uparrow$
Majority pooling	5.93	ref.	ref.	ref.	ref.	31.4
Cell center †	4.64	$-1.01$ $[-1.34,-0.70]$	$-1.00$ $[-1.34,-0.70]$	$+0.022$ $[+0.015,+0.030]$	$+0.016$ $[+0.011,+0.021]$	–
Greedy rescue	3.93	$-1.43$ $[-2.46,-0.89]$	$-0.51$ $[-1.47,+0.23]$	$-0.010$ $[-0.016,-0.004]$	$+0.023$ $[+0.018,+0.028]$	53.0
Soft labels [ 1 ]	6.46	$-1.64$ $[-2.65,-1.10]$	$-1.38$ $[-2.40,-0.86]$	$-0.082$ $[-0.106,-0.056]$	$+0.019$ $[+0.013,+0.026]$	60.4
Full-res. loss	3.56	$-1.34$ $[-2.40,-0.75]$	$-0.57$ $[-1.56,+0.15]$	$+0.018$ $[+0.011,+0.025]$	$+0.028$ $[+0.024,+0.032]$	59.4

Appendix

Table S10 : Affinity head on BBBC038 at factor 8 (670 images, 29,461 nuclei; 9 seeds

\times

3 folds, held-out predictions). Count error at the default thresholds; then differences from the majority model with 95% confidence intervals, at cross-validated thresholds and at the equal-FP point (each model’s thresholds chosen so that its false positives per image do not exceed the majority model’s); detected: share (%) of the 2,587 nuclei missing from the majority target that the model detects, cross-validated. † From the second set of runs, whose majority model has a count error of 5.95 ( Tab. S11 ); its differences are taken against that model. Of the MatchDown model’s count-error reduction, 89% comes from nuclei that the majority model misses and the MatchDown model detects; the mean IoU bound of the 2,587 nuclei is 0.30 ( Sec. 4.5 ). Lost nuclei: Tab. S12 . Best in bold, second best underlined, in the count-error and detected columns.

Target	Lost (%)	Count err.	$\Delta$ count err.	$\Delta$ $\mathrm{Acc}_{50}$	$\mathrm{Acc}_{50}$
Majority pooling	8.8	5.95	ref.	ref.	0.543
Masked	8.8	5.02	$-0.93$ $[-1.17,-0.72]$	$+0.000$ $[-0.004,+0.005]$	0.543
Dilated	0	4.50	$-1.45$ $[-1.89,-1.03]$	$-0.234$ $[-0.249,-0.218]$	0.309
MatchDown	0	3.94	$-2.00$ $[-2.40,-1.63]$	$-0.012$ $[-0.017,-0.007]$	0.531

Appendix

Table S11 : How the target keeps nuclei , affinity head on BBBC038 at factor 8, default thresholds, from a second set of runs with the same protocol (so majority and MatchDown differ slightly from Tab. S10 ). Masked: majority targets with the cells of the missing nuclei excluded from the loss. Dilated: every cell a nucleus touches is labeled with it. Differences from majority with 95% confidence intervals. Best in bold (ties share the mark), second best underlined, in the lost, count-error and

\mathrm{Acc}_{50}

columns.

			Count err. $\downarrow$		$\mathrm{Acc}_{50}$ $\uparrow$		Missing nuclei
Factor	Target	Lost (%) $\downarrow$	default	cross-val.	default	cross-val.	matched $\uparrow$
$f{=}8$	Strided (StarDist)	5.6	8.08	4.84	0.664	0.728	0.241
	Nearest (cell center)	4.7	5.04	5.78	0.764	0.770	0.273
	Majority pooling	8.8	6.34	6.50	0.746	0.750	0.152
	Greedy rescue	0.35	5.14	4.77	0.765	0.772	0.331
	Dilated	0	14.47	10.47	0.732	0.767	0.399

Appendix

Table S12 : Star-convex head on BBBC038 (670 images, 29,461 nuclei; 9 seeds

\times

3 folds). Top: lost nuclei (%), count error and

\mathrm{Acc}_{50}

at the default and cross-validated thresholds, and the share of the 2,587 nuclei missing from the majority target that the model matches at IoU

{}>0.5

(cross-validated). Bottom: differences in

\mathrm{Acc}_{50}

with 95% confidence intervals. With default thresholds tuned for factor 8, the factor-2 strided model produces 27.7 false positives per image, and 5.7 with cross-validated thresholds. All models come from the second set of BBBC038 runs ( Appendix C ). Best in bold, second best underlined, over all nine models.

		Count err. $\downarrow$		$\mathrm{Acc}_{50}$ $\uparrow$
$f$	Target	$\geq 0.3$	$\geq 0.1$	$\geq 0.3$	$\geq 0.1$
8	Strided (StarDist)	4.84	4.02	0.728	0.751
	Nearest (cell center)	5.78	7.01	0.770	0.772
	Majority pooling	6.50	6.45	0.750	0.755
	Greedy rescue	4.77	4.27	0.772	0.775
	Dilated	10.47	11.70	0.767	0.774

Appendix

Table S13 : Sensitivity to the NMS search range , star-convex head on BBBC038: held-out count error and

\mathrm{Acc}_{50}

at thresholds cross-validated with NMS IoU in

\{0.3,0.4,0.5\}

(the range we report) or in

\{0.1,\dots,0.4\}

. The lower range raises the count error of several models, because on a few large images (up to

1040{\times}1388

pixels) the selected thresholds produce hundreds of objects; the

\mathrm{Acc}_{50}

difference between MatchDown and strided at factor 8 stays positive,

+0.019

[+0.012,+0.026]

Figure S8 : Where the count reduction of the affinity head comes from. (a) BBBC038,

f{=}8

, default thresholds: per-image count-error reduction of the MatchDown model over the majority model (mean over nine seeds) against the nuclei missing from the majority target (one image, at 126, is off the axis). (b) Every comparison of MatchDown with a baseline on both datasets and heads: the count-error reduction of the trained models against the difference between the targets themselves under oracle decoding (each target used as the prediction); letters name the baseline, followed for BBBC039 by the factor. Points on the diagonal recover the whole difference; the affinity head does so at factor 16 and recovers about half of it at factor 8. (c) Count error against

\mathrm{Acc}_{50}

of the majority and MatchDown models at every point of the

19{\times}19

threshold grid, with the default, cross-validated and equal-FP points marked (for majority the last two coincide). The MatchDown model has lower count error at every foreground threshold and lower

\mathrm{Acc}_{50}

at every threshold.

Figure S9 : Operating curves of the affinity head on BBBC038 at

f{=}8

(means over 670 images and nine seeds): count error (a) and

\mathrm{Acc}_{50}

(b) against the foreground threshold, at the default affinity threshold (thick) and at the other 18 affinity thresholds (thin, majority and MatchDown only), for five of the targets of Tab. S10 . Squares mark the cross-validated thresholds (mean over the 27 selections) and diamonds the equal-FP points; for majority the two coincide. MatchDown has the lower count error at every foreground threshold and the lower

\mathrm{Acc}_{50}

at every threshold.

Affinity head, factor 16
Target	Count err. $\downarrow$		$\mathrm{Acc}$ $\uparrow$	$\mathrm{Acc}_{50}$ $\uparrow$		Detected $\uparrow$	Matched $\uparrow$
	default	cross-val.		default	cross-val.
Majority pooling	15.86	13.05	0.105	0.472	0.497	0.034	0.037
Nearest (cell center)	14.23	10.43	0.116	0.523	0.539	0.133	0.038
MatchDown-P (ours)	3.95	3.77	0.094	0.418	0.425	0.300	0.104
Star-convex head, factor 16

Appendix

Table S14 : Trained models on BBBC039 (197 images, 23,615 nuclei; 9 seeds

\times

3 folds, held-out predictions). Count error and

\mathrm{Acc}_{50}

at the default and cross-validated thresholds;

\mathrm{Acc}

, detected and matched at the default thresholds. Detected: share of the nuclei missing from the majority target (2,382 at factor 16, 1,363 at factor 8) that the model detects ( Appendix B ); matched: share of the nuclei missing from the strided target (1,852 and 1,147) that the model matches at IoU

{}>0.5

. Differences with intervals: Tab. S15 . Best in bold, second best underlined, within each head and factor.

		$\Delta$ count error		$\Delta$ $\mathrm{Acc}_{50}$
Head	Target	default	cross-val.	default	cross-val.
Affinity, $f{=}16$	minus majority	$-11.90$ $[-12.96,-10.89]$	$-9.27$ $[-10.36,-8.24]$	$-0.054$ $[-0.058,-0.050]$	$-0.072$ $[-0.077,-0.067]$
	minus nearest	$-10.28$ $[-11.20,-9.40]$	$-6.66$ $[-7.53,-5.80]$	$-0.105$ $[-0.110,-0.100]$	$-0.115$ $[-0.121,-0.108]$
Star-convex, $f{=}16$	minus strided	$-4.05$ $[-4.99,-3.22]$	$-2.27$ $[-3.01,-1.58]$	$+0.014$ $[+0.008,+0.022]$	$+0.027$ $[+0.019,+0.037]$
	minus nearest	$-9.90$ $[-10.74,-9.11]$	$-8.22$ $[-9.16,-7.32]$	$-0.023$ $[-0.027,-0.018]$	$-0.028$ $[-0.034,-0.023]$
Star-convex, $f{=}8$	minus strided	$-1.66$ $[-2.24,-1.11]$	$-1.38$ $[-1.85,-0.92]$	$+0.021$ $[+0.016,+0.025]$	$+0.026$ $[+0.021,+0.031]$

Appendix

Table S15 : Differences between targets on BBBC039 (197 images; 9 seeds

\times

3 folds, held-out predictions), at the default and the cross-validated thresholds, with 95% confidence intervals from a bootstrap over seeds and images. Each row is MatchDown-P minus the named target; negative count-error differences favor MatchDown-P.

Figure S10 : Two more held-out BBBC039 images at factor 16 ( $320{\times}448$ -pixel windows holding 67 and 85 of the images’ 101 and 185 nuclei), as in Fig. 3 , with the models trained on nearest targets added: (a, c) the affinity head, (b, d) the star-convex head. On the first image the affinity models trained on majority, nearest and MatchDown-P targets predict 52, 60 and 99 objects for 101 nuclei.

							Detected $\uparrow$		Matched $\uparrow$
Head	Target	Count err. $\downarrow$	Signed	$\mathrm{Acc}$ $\uparrow$	$\mathrm{Acc}_{50}$ $\uparrow$	FP50 $\downarrow$	majority-missing	rescue-missing	strided-missing
Affinity	MatchDown-P (ours)	3.85	$-2.7$	0.094	0.418	48.1	0.300	0.308	0.104
	Greedy rescue	4.45	$-3.9$	0.101	0.449	43.4	0.289	0.262	0.104
	Soft labels [ 1 ]	15.36	$-15.4$	0.105	0.472	33.0	0.051	0.065	0.042
Star-convex	MatchDown-P (ours)	4.76	$-1.7$	0.634	0.827	10.7	0.491	0.350	0.301
	Greedy rescue	4.39	$-3.6$	0.648	0.841	8.4	0.482	0.281	0.316

Appendix

Table S16 : Greedy rescue and soft labels against MatchDown-P on BBBC039 at factor 16 (197 images; 9 seeds

\times

3 folds, held-out predictions, default thresholds; a separate set of runs with the BBBC039 protocol, in which the MatchDown-P models were trained again so that every difference is paired). Top: means; signed: mean predicted minus true count per image; FP50: false positives per image at IoU

{}>0.5

; detected: share of the nuclei missing from the majority target (2,382) or from the rescue target (209) that the model detects; matched: share of the 1,852 nuclei missing from the strided target matched at IoU

{}>0.5

. Bottom: differences, the named target minus MatchDown-P, with 95% confidence intervals, and the difference between the targets themselves under oracle decoding. Best in bold within each head. One MatchDown-P star-convex run over-counts by 22.7 nuclei per image and widens that interval; because of it, the retrained MatchDown-P models’ means differ from Tab. S14 (star-convex count error 4.76 here, 3.74 there; affinity 3.85 and 3.95).

Instance Segmentation

Instance segmentation identifies each object and assigns it a separate pixel-level mask in images or video.

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Jun 8, 2026

Maximum Matching Accuracy: An Instance Segmentation Evaluation Metric Utilizing Globally Optimal Matching

Reliable evaluation of instance segmentation models requires metrics that accurately and consistently reflect segmentation quality. However, the metrics most widely used in biological imaging carry fundamental mathematical weaknesses: hard Intersection-over-Union (IoU) thresholds that produce discontinuous, low sensitivity scoring; per-object normalization that distorts scores under object size variation; and greedy or one-to-many matching procedures that yield non-optimal, order-dependent correspondences. Together, these properties produce unintuitive and unreliable model rankings under common failure modes such as split cells, merged cells, and cell boundary imprecision. We propose Maximum Matching Accuracy (MMA), a threshold-free continuous metric that finds a globally optimal one-to-one matching between predicted and ground truth objects and aggregates total overlap using per-pixel normalization. We evaluate MMA against AP@50, PQ, SEG, and AJI across three experiments: synthetic failure cases, progressive corruption tests, and a model ranking comparison. MMA produces scores that are more stable, more sensitive, and more interpretable than existing alternatives, providing a principled foundation for fair instance segmentation benchmarking in biological cell imaging.

Kaden Stillwagon, Alexandra D. VandeLoo, Craig R. Forest

College of Computing, Georgia Institute of Technology, Atlanta, 30332, Georgia, United States · School of Materials Science and Engineering, Georgia Institute of Technology, Atlanta, 30332, Georgia, United States · Wallace H. Coulter Department of Biomedical Engineering, Georgia Institute of Technology, Atlanta, 30332, Georgia, United States +1

Instance Segmentation Microscopy Image Analysis

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Sep 23, 2026

Beyond Mean Foils: Auditing Worst-Foil Specificity in Frozen CLIP Region Explanations

A region can overlap a target object yet contribute more to another class. We test regions selected by Cluster-based Concept Importance (CCI) in frozen CLIP. Across COCO and VOC with two checkpoints, 41.08-64.78% of regions that pass overlap and mean-contrast checks fail against the strongest competing class. Removing competitors annotated in the image leaves 39.69-63.64% failing. We then test all eight candidate regions per image. An alternative passes the test for 6.25-7.84% of failures on COCO and 27.40-31.15% on VOC. Requiring it to preserve the original target-score drop within

ε= 0.02

reduces these rates to 0.16-0.98%. Available regions and target-drop tolerance constrain repair; relaxing the tolerance increases repair opportunities.

Kaixin Liu, Zhipeng Ye, Feng Jiang +2

Taizhou Institute of Science and Technology, Nanjing University of Science and Technology, Taizhou 225300, Jiangsu, China

Explainable Image Classification

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Sep 16, 2026

DISTA-Net++: Rethinking Infrared Small Target Unmixing Beyond Sub-Pixel Separation

Long-range infrared imaging frequently confronts dense target clusters whose diffraction-limited signatures merge into a single indistinguishable blob, concealing the number, sub-pixel positions, and radiant intensities of the underlying sources. While deep learning has advanced general object detection, resolving such Closely-Spaced Infrared Small Targets (CSIST) remains largely unexplored, owing to a systemic infrastructure void and a fundamental paradigm mismatch. The dominant formulation, which reduces unmixing to a blind, discrete sub-pixel separation, is inherently insufficient: without semantic guidance, the ill-posed inverse problem admits ambiguous solutions plagued by false and missed detections, while grid-based discretization locks predictions onto fixed lattice centers, chaining precision to prohibitively expensive grid refinement. We argue that CSIST unmixing should instead be informed and continuous. To ground this paradigm shift, we establish the first comprehensive open-source ecosystem for the field, comprising the large-scale CSIST-100K benchmark, a tailored metric suite, and the GrokCSO toolkit. Upon this foundation, we propose DISTA-Net++, which anchors a dynamic deep unfolding backbone with two synergistic mechanisms: a Count-Guided Prior that injects the global target count as an explicit semantic constraint to regularize the solution space, and a Continuous Coordinate Rectification that regresses off-grid offsets to decouple localization accuracy from grid resolution. Extensive experiments validate our paradigm: even under the most economical 3x division, DISTA-Net++ surpasses 7x-division state-of-the-art methods by 16.15% in CSO-mAP and 62.96% in count accuracy at merely one-sixth of their computation, demonstrating that unmixing precision need not be purchased with finer discretization. The complete ecosystem is available at https://github.com/GrokCV/GrokDet.

Mengze Xu, Zhu Liu, Weidong Sheng +4

VCIP, CS, Nankai University, Tianjin 300350, China · School of Software Technology, Dalian University of Technology, Dalian 116024, China · College of Electronic Science and Technology, National University of Defense Technology (NUDT), Changsha 410000, China

Infrared Small Target Detection

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Abstract

Instance Segmentation

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Maximum Matching Accuracy: An Instance Segmentation Evaluation Metric Utilizing Globally Optimal Matching

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