Can Frozen Hyperspherical Features Guide the Selection of Pseudo Masks?

Xinge Guo; Fengyang Xiao; Dingming Zhang; Yuhan Chen; Rihan Zhang; Xingjian Li; Tianyang Wang; Chunming He

cs.CVSep 24, 2026

Can Frozen Hyperspherical Features Guide the Selection of Pseudo Masks?

Authors: Xinge Guo, Fengyang Xiao, Dingming Zhang, Yuhan Chen, Rihan Zhang, Xingjian Li, Tianyang Wang, Chunming He, +1 more

Organizations: Duke University · Carnegie Mellon University · University of Alabama at Birmingham

Abstract

Foundation segmenters such as SAM return several plausible masks for an unlabeled image, and a student trained on the wrong one inherits its errors. Choosing among them means querying a second large model or fitting a quality head to annotated masks. We show that a candidate can be judged by what it does to a frozen self-supervised backbone's features. Normalized DINOv2 patch features lie on a hypersphere, and a candidate mask splits that sphere in two. Based on this reading, we introduce SphereTrust, which scores each candidate by three properties of the split, the angular contrast between the two sides, the coverage of the foreground's appearance modes, and contact with the image frame, one for each of three common ways a mask fails, and ranks a pool in 0.55 s per image from the frozen features alone. On eight SAM and SAM3 candidate pools spanning camouflaged, salient, and dichotomous segmentation and camouflage under low light, SphereTrust exceeds the strongest evaluated external baseline on six pools by 1.7 to 9.3 percentage points in mean selected Dice. These comparisons include published selection rules and explicitly labeled adaptations of DSS and UCOD-MKD. On the two prompted camouflage pools, its mean selected Dice is within 0.1 percentage points of the candidate-derived DSS adaptation, with a lower catastrophic-error rate. Which cue carries the signal depends on the candidate pool. The same sphere also supports training. The leading candidates enter as a candidate set with their scores as priors, prototypes reorder them, and a cross-fitted second round completes the labels, raising weighted F by 4.5, 2.3, and 5.5 points over fixed-label training on the three MLLM anchor pools, with students competitive with published unsupervised methods on nineteen test sets.

Figures & tables

Figure 1: A mask as a partition of the sphere. Frozen DINOv2 patch directions under a correct mask, an omission, and leakage. The three measures respond differently to the two errors.

Figure 2: SPHERETRUST overview. (A) Frozen DINOv2 directions rank candidates by angular contrast, spherical coverage, and frame contact, where $\mathcal{F}$ is the patch feature matrix, distinct from $F$ of Eq. ( ). (B) A foreground posterior on the same sphere joins the ranking, the student chooses among the leading candidates as it learns, and a second round adds a completed mask from a cross fitted prediction (§ ). The select argmax box in (B) is Eq. ( ), $\arg\max_{k}[\pi_{ik}-\ell_{ik}/T]$ .

Figure 3: The three cues on real candidates. For one image per regime, the patch map coloured by the nearest foreground appearance mode and three candidates with their $F$ , $C$ , $E$ , and Dice.

each entry: sel-Dice $\uparrow$ / Top-1 $\uparrow$ / Dice $<$ .2 $\downarrow$
Selector	SAM3 alone	MLLM anchor $+$ SAM
	COD	COD	SOD	DIS
Random	.657/.096/.193	.678/.057/.170	.771/.045/.111	.576/.047/.204
SelfMask vote ( Shin et al., 2022 )	.821 /.124/ .062	.778 /.060/ .085	.887/.034/.024	.701/.060/ .086
SAQ ( Lin et al., 2024 )	.576/.109/.275	.676/.098/.184	.771/.163/.125	.606/.117/.187
Generator confidence ( Carion et al., 2025 )	.802/.145/.082	.728/.057/.135	.874/.033/.040	.636/.060/.179

Table 1: Unsupervised selection on prompted pools , the camouflage training pool SAM3 builds alone and the three training pools prompted from the MLLM anchor with SAM (Appendix Tab. ). Red , blue and grey mark the first, second and third value in each column among the evaluated external comparators, the published selection rules and the labeled adaptations, our row is shaded, and the rows below the rule, the size control and the oracle, stay unmarked.

$F$	$C$	$E$	COD	SOD	DIS
random candidate			.6780	.7709	.5762
oracle candidate			.8517	.9486	.8385
✓	✗	✗	.7663	.8789	.6351
✗	✓	✗	.6587	.8894	.6761
✗	✗	✓	.7490	.8269	.6108
✓	✓	✗	.7546	.9280	.7356

Table 2: Ranking and training ablations on the MLLM anchor pools. (a) Selected Dice for all seven combinations of the three ranking terms, with random and oracle selection as references. (b)

F^{w}_{\beta}

of the student, mean over the regime’s test sets and three seeds, with candidate set training (set), the sphere term in the round one order (

\Gamma_{1}

), the second round (R2), the completed mask (

U

), cross fitting (XF), and the sphere term in the second round score (

\Gamma_{2}

) on or off. Marks as in Tab. , reference rows stay unmarked, and Appendix Tab. adds the seed spreads.

Figure 4: Selected masks on the prompted pools. For two images of each pool, the SAM3 pool (S3) and the three MLLM anchor pools (ML), the ground truth and the candidate chosen by generator confidence (conf.), the candidate-derived adaptation of DSS (DSS), SAQ, UCOD-MKD-inspired filtering, and SPHERETRUST (ours) from one candidate list.

Panel of Figure 5 — Figure 5: Selection where it is hardest. Selected Dice on the four unprompted SAM pools of Appendix Tab. , where a selector must first find the target among decoys, for the two strongest evaluated external comparators, TokenCut and the candidate-derived adaptation of DSS, and SPHERETRUST, margins in points.

Camouflage COD10K, $n=2026$
Method	$S_{\alpha}$ $\uparrow$	$F^{w}_{\beta}$ $\uparrow$	$E_{\phi}$ $\uparrow$	MAE $\downarrow$
EReCu ( Jiang et al., 2026 ) †	.7221	.5628	.8185	.0613
FOUND ( Siméoni et al., 2023 ) †	.6783	.5056	.6475	.0841
TokenCut ( Wang et al., 2022b ) †	.6638	.4770	.7539	.1023
UCOD-DPL (DINOv2) ( Yan et al., 2025 ) †	.8340	.7630	.9160	.0310
UCOD-MKD (PVTv2) ( Chen et al., 2026 ) †	.8350	.7400	.9080	.0310

Table 3: Downstream comparison on one benchmark per condition, marks as in Tab. . Rows marked

\dagger

are transcribed, each camouflage method in its strongest published configuration (Appendix § ), other rows use our evaluator on released predictions or weights, and the Selfment rows are its published result and its released checkpoint under our evaluation. Selection only trains the same student on the fixed mask

\mathcal{R}

selects. The rank marks cover the published methods and our full method, leaving out that row and the last block, which prompts foundation models at test time.

Appendix figures & tables17 assets

Supplementary material from the paper’s appendix.

Appendix

	selection pool (Tab. )				training pool (Tab. )
regime	$n$	$k$	random	oracle	$n$	$k$	random	oracle
Camouflage	1979	10.2	.1319	.6770	3857	25.6	.6780	.8517
Salient	4993	10.7	.1697	.7878	4025	25.0	.7709	.9486
Dichotomous	465	11.3	.0992	.4856	2969	28.4	.5762	.8385
Low light	1932	9.4	.1307	.6028	direct camouflage evaluation

Appendix

Table 4: Selection pools and training pools.

k

is candidates per image, and random and oracle define the available selection gap. Selection uses unprompted generator output, training pools prompt the same generator from the MLLM anchor (the SAM3 pool is in Tabs. and ), and LL-COD reuses the degraded COD10K test set ( Fan et al., 2020 ) with the camouflage students.

Figure 9: Images with fewer than two eligible candidates after the plausibility filters, one per regime, with the ground truth and every proposal the generator returned.

Figure 10: How the cues respond to errors. Standardized responses of the three cues to controlled corruptions of the ground truth mask, grouped into wrong object, omission, leakage, and mixed errors.

pool family	datasets	images	candidates	$\Delta$ selected Dice [95% CI]
unprompted SAM macro	4	$6{,}340$	$64{,}962$	$-.0150\;[-.0192,-.0107]$
prompted SAM macro	3	$10{,}851$	$283{,}759$	$+.0206\;[+.0178,+.0235]$
non-SAM pool	4	$913$	$10{,}338$	$+.0045\;[+.0004,+.0089]$

Appendix

Table 5: Coverage and area on identical candidates.

\Delta

is selected mask Dice for

z(F)+z(C)-z(E)

minus that for

z(F)+z(\log a_{\mathrm{mask}})-z(E)

, with a

95\%

bootstrap interval.

each entry: sel-Dice $\uparrow$ / Top-1 $\uparrow$ / Dice $<$ .2 $\downarrow$
Selector	COD	SOD	DIS	LL
	COD10K	DUTS-TE	DIS-VD	LL-COD
Random	.132/.162/.821	.170/.129/.743	.099/.120/.824	.131/.183/.813
SelfMask vote ( Shin et al., 2022 )	.218/.221/.723	.348/.274/.534	.133/.110/.757	.203/.219/.731
SAQ ( Lin et al., 2024 )	.102/.133/.855	.141/.098/.777	.072/.067/.867	.082/.131/.876
SAM predicted IoU ( Kirillov et al., 2023 )	.256/.303/.693	.285/.264/.650	.096/.131/.843	.201/.271/.741

Appendix

Table 6: Unsupervised selection on unprompted SAM output , one fixed pool per regime. Marks are those of Tab. , and the rows below the rule are references and carry none. Appendix § states eligibility.

full method without
	COD		SOD		DIS
	$F^{w}_{\beta}$	$\Delta$ per seed	$F^{w}_{\beta}$	$\Delta$ per seed	$F^{w}_{\beta}$	$\Delta$ per seed
selection only (fixed rank one label)	.7513 $\pm$ .0004	$-4.3$ / $-4.6$ / $-4.6$	.8148 $\pm$ .0033	$-2.7$ / $-1.7$ / $-2.5$	.6048 $\pm$ .0018	$-5.7$ / $-5.4$ / $-5.3$
$+$ candidate set training (round one)	.7930 $\pm$ .0006	$-0.3$ / $-0.3$ / $-0.3$	.8232 $\pm$ .0031	$-1.3$ / $-1.0$ / $-2.0$	.6384 $\pm$ .0026	$-1.9$ / $-2.2$ / $-2.3$
$+$ second round (full method)	.7961 $\pm$ .0007		.8376 $\pm$ .0013		.6594 $\pm$ .0014
completed mask	.7941 $\pm$ .0002	$-0.1$ / $-0.2$ / $-0.3$	.8209 $\pm$ .0010	$-1.8$ / $-1.4$ / $-1.9$	.6434 $\pm$ .0010	$-1.6$ / $-1.6$ / $-1.6$

Appendix

Table 9: Ablation of the training method ,

F^{w}_{\beta}

on the MLLM anchor pools averaged over every test set of the regime, mean

\pm

population standard deviation over three seeds, the full method in red, and the paired difference of each row against the full method in points for seeds

0

1

2

. The seed varies the final student only. The fold split, the fold students, the out-of-fold maps

P_{i}

, the prototype fit and the round two candidate sets were produced once with seed

0

and are shared, so these spreads describe the last stage conditional on that cache rather than the end to end variance of the pipeline, which would be larger.

round one
	validation $F^{w}_{\beta}$				test regime mean $F^{w}_{\beta}$
configuration	COD	SOD	DIS	mean	COD	SOD	DIS
order by $\mathcal{R}$ , argmax rule	.7701	.9377	.7580	.8219	.7873	.8210	.6377
order by $\mathcal{R}$ , softmax weights	.7675	.9400	.7549	.8208	.7841	.8181	.6371
order by $\mathcal{R}+z(\Gamma)$ , argmax rule (chosen)	.7759	.9392	.7544	.8232	.7955	.8185	.6372
second round

Appendix

Table 10: Candidate configurations of the training stage. Validation

F^{w}_{\beta}

on the held out split of each training pool with its mean over the three, the number the choice read, and the test regime means of the same runs, single trainings with seed

0

on the nine tenths of each pool outside the validation split. The chosen configuration is in red.

	CAMO, $n=250$				CHAMELEON, $n=76$				NC4K, $n=4121$
Method	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$
EASE (DINO ViT-S/8) ( Du et al., 2025a ) †	.6530	.5630	.7370	.1660	.6760	.5500	.7650	.1050	.7280	.6330	.7900	.1080
EASE (DINOv2 ViT-L/14) ( Du et al., 2025a ) †	.7490	.6840	.8310	.0980	.8190	.7410	.8990	.0440	.8000	.7350	.8840	.0560
RISE (DINOv2 ViT-L/14) ( Du et al., 2025b ) †	.7340	.6100	.7870	.1090	.8220	.7200	.8840	.0500	.8050	.7050	.8680	.0610
RISE (SAM ViT-H masks) ( Du et al., 2025b ) †	.7600	.6510	.8070	.1020	.8230	.7330	.8820	.0550	.8250	.7360	.8740	.0560
DualUCOD (DINOv2) ( Liu et al., 2026 ) †	.7710	.7020	.8520	.0830	.8270	.7540	.9180	.0410	.8080	.7450	.8960	.0520

Appendix

Table 11: Downstream, camouflage. Rows marked

\dagger

are transcribed, EASE (DINO ViT-S/8), EReCu, FOUND, TokenCut, and UCOD-DPL (DINO ViT-S/8) from Table 1 of EReCu ( Jiang et al., 2026 ) , which reruns released code and copies EASE from its paper, the other EASE configurations from its Tables 1 and 2, and RISE, SdalsNet, DualUCOD, DSS, UCOD-DPL (DINOv2), UCOD-MKD, and Selfment (DINOv3-7B) from their papers, and Selfment, our evaluation is its released checkpoint under our evaluation. RISE uses SAM only to build its training masks, and SdalsNet reports max

F_{\beta}

and max

E_{\phi}

, so those entries stay empty. The rows below the last rule prompt SAM, HQ-SAM, or SAM2 at test time, DSS also an MLLM, and are listed for reference outside the marks. Other rows use our evaluator on released predictions.

	DUTS-TE			ECSSD			HKU-IS			DUT-OMRON			PASCAL-S
Method	MAE $\downarrow$	$F_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$	$F_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$	$F_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$	$F_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$	$F_{\beta}\uparrow$	$E_{\phi}\uparrow$
A2S-v3 ( Yuan et al., 2024 ) †	.0470	.8160	.9060	.0380	.9230	.9510	.0330	.9080	.9540	.0620	.7590	.8680	.0690	.8440	.8990
DCFD ( Lin et al., 2022 ) †	.0640	.7640	.8550	.0590	.8880	.9150	.0420	.8890	.9350	.0700	.7100	.8370	.0900	.7950	.8600
EDNS ( Zhang et al., 2020 ) †	.0650	.7350	.8470	.0680	.8720	.9060	.0460	.8740	.9330	.0760	.6820	.8210	.0970	.8010	.8460
STC ( Song et al., 2023 ) †	.0520	.8090	.8910	.0500	.9030	.9350	.0410	.8910	.9420	.0680	.7530	.8520	.0760	.8270	.8810
SelfMask ( Shin et al., 2022 ) †	.0630	.7140	.8480	.0580	.8560	.9200	.0530	.8190	.9150	.0780	.6680	.8150	.0870	.7740	.8560

Appendix

Table 12: Downstream, salient objects (DUTS-TE

5{,}019

images, ECSSD

1{,}000

, HKU-IS

4{,}447

, DUT-OMRON

5{,}168

, PASCAL-S

850

). Rows marked

\dagger

are transcribed, six methods from the comparison table of A2S-v3 ( Yuan et al., 2024 ) and the DUTS-TE row of CutLER from Table I of CSNet ( Guan et al., 2025 ) , each in its source’s convention. The

F_{\beta}

of that CutLER row, marked

\ddagger

, is at a fixed threshold of

0.5

and stays outside the adaptive-threshold ranking. Evaluated rows use the adaptive threshold

F_{\beta}

and the mean

E_{\phi}

, 3SD and UMNet from their released maps (UMNet’s release omits PASCAL-S), FOUND from its released weights (single mask setting with the bilateral solver), and CutLER as the union of its released detector’s instances at confidence

0.35

, which differs from CSNet’s CutLER row, so both are kept.

	DUTS-TE		ECSSD		HKU-IS		DUT-OMRON		PASCAL-S
Method	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$
3SD ( Yasarla et al., 2024 )	.8121	.6370	.8848	.7907	.8774	.7662	.7979	.6187	.8060	.6859
CutLER ( Wang et al., 2023 )	.6503	.5149	.7897	.7426	.7686	.7005	.6092	.4660	.7275	.6574
FOUND ( Siméoni et al., 2023 )	.8029	.7479	.8691	.8708	.7959	.7810	.7709	.6793	.8075	.7838
UMNet ( Wang et al., 2022c )	.8027	.7039	.8677	.8391	.8865	.8561	.8047	.6972	–	–
Selfment ( You et al., 2026 )	.7977	.5659	.8790	.7194	.8700	.6966	.7141	.4284	.8219	.6500

Appendix

Table 13: Downstream, salient objects, under

S_{\alpha}

and

F^{w}_{\beta}

. The evaluated rows of Tab. scored under the convention of Tab. in the same scoring run, red and blue marking the best and second best entry per column. Transcribed rows are left out since their sources report neither.

DIS-TE1 , $n=500$
Method	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$	mDice $\uparrow$
Selfment ( You et al., 2026 )	.7054	.3870	.6628	.1445	.5061
A2S-v3 ( Yuan et al., 2024 )	.6028	.4105	.6887	.1379	.4683
CSNet-crf ( Guan et al., 2025 )	.5828	.3625	.6645	.1171	.3996
SPHERETRUST , MLLM anchor	.7765	.6463	.8324	.0699	.6866
DIS-TE2 , $n=500$

Appendix

Table 14: Downstream, dichotomous segmentation , marks per column within each set.

	pool		student, mean of four COD sets
pool	oracle	selected	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$
MLLM anchor $+$ SAM	.858	.790	.8643	.7961	.9146	.0395
SAM3 alone	.895	.829	.8710	.8086	.9257	.0342

Appendix

Table 15: The rule across generators and anchors. (a) The camouflage training pool from the MLLM anchor with SAM and from SAM3 alone, pool oracle and selected Dice on the

2{,}770

COD10K-train images both pools contain, and the final student over four camouflage test sets and three seeds (Appendix § ). (b) Selection on a pool of

913

images from trained DPT-lite decoders (Appendix § ).

	COD			SOD			DIS
ranking rule	sel	fixed	full	sel	fixed	full	sel	fixed	full
SPHERETRUST	.787	.7526 $\pm$ .0004	.7971 $\pm$ .0009	.929	.8144 $\pm$ .0006	.8403 $\pm$ .0009	.771	.6047 $\pm$ .0013	.6597 $\pm$ .0010
size control	.763	.7287 $\pm$ .0009	.7958 $\pm$ .0005	.909	.8009 $\pm$ .0019	.8367 $\pm$ .0004	.755	.5842 $\pm$ .0009	.6571 $\pm$ .0008
adapted DSS	.788	.7624 $\pm$ .0011	.7953 $\pm$ .0016	.912	.7918 $\pm$ .0012	.8303 $\pm$ .0018	.720	.5464 $\pm$ .0032	.6529 $\pm$ .0011

Appendix

Table 16: One training procedure, three scoring rules , on the three MLLM anchor training pools. The three rules are SPHERETRUST

z(F)+z(C)-z(E)

, the size control

z(F)+z(\log a_{\mathrm{mask}})-z(E)

, and the candidate-derived adaptation of the DSS scoring rule. The selection columns report the mean Dice of each rule’s selected masks. Fixed and full report weighted

F

for fixed label training and the complete procedure, as means

\pm

population standard deviations across three final student seeds after averaging each seed’s results over the test sets of its regime. For the full procedure, these spreads describe final student variation conditional on the shared upstream fold students, prototype fit, and round two candidate cache of that rule. The student architecture, images, and schedule are matched, and the numerical score definitions are specified above. SPHERETRUST was retrained for this comparison. Red marks the highest observed mean, and paired per seed differences are reported for the full procedure in Tab. .

	COD			SOD			DIS
comparator	s0	s1	s2	s0	s1	s2	s0	s1	s2
size control	$+0.08$	$+0.10$	$+0.20$	$+0.20$	$+0.40$	$+0.48$	$+0.29$	$+0.29$	$+0.20$
adapted DSS	$+0.26$	$+0.19$	$+0.09$	$+1.13$	$+1.02$	$+0.88$	$+0.94$	$+0.66$	$+0.45$

Appendix

Table 17: Paired per seed differences under the complete procedure , SPHERETRUST minus the named rule on the same seed, in points of

F^{w}_{\beta}

. Every difference is positive, so the ordering of Tab. holds seed by seed as well as in the mean.

Selector	camouflage	salient		dichotomous
	PlantCamo	SOD300	MSRA-B	UHRSD
	$n{=}233$ , $k{=}34.7$	$219$ , $29.7$	$1932$ , $24.6$	$969$ , $26.8$
Random	.434	.555	.747	.676
SelfMask vote	.505	.611	.873	.789
SAQ	.433	.519	.769	.683
SAM predicted IoU	.474	.625	.856	.770

Appendix

Table 18: Unsupervised selection on the four further benchmarks , prompted pools,

n

eligible images,

k

candidates per image, selected Dice. Red and blue mark the highest and second highest point estimates among the evaluated external selectors and SPHERETRUST, below them the size control and the oracle.

camouflage students , PlantCamo-TE
student	$S_{\alpha}\uparrow$	$F^{w}_{\beta}\uparrow$	$E_{\phi}\uparrow$	MAE $\downarrow$
full method, MLLM anchor	.686	.515	.763	.097
full method, SAM3 pool	.621	.422	.682	.110
selection only, MLLM anchor	.681	.499	.755	.101
salient student , SOD300
full method	.765	.736	.797	.116

Appendix

Table 19: Students on the four further benchmarks , mean of three seeds (seed standard deviations at most

.016

), the full method against selection only.

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Apr 27, 2026cs.CV

Self-Supervised Representation Learning via Hyperspherical Density Shaping

Modern self-supervised representation learning methods often relies on empirical heuristics that are not theoretically grounded. In this study we propose HyDeS, a theoretically grounded method based on multi-view mutual information maximization within an hyperspherical space using Shannon differential entropy with a non-parametric von Mises-Fisher density estimator. We show that HyDeS bias the trained model towards focusing on foreground features of the images and perform well on segmentation tasks such as VOC PASCAL, while it lags in fine-grained classification. We provide a detailed analysis of the induced latent space geometry and learning dynamics, that can be used for designing other theoretically grounded self-supervised learning methods.

Esteban Rodríguez-Betancourt, Edgar Casasola-Murillo

Posgrado en Computación e Informática · Universidad de Costa Rica · Escuela de Ciencias de la Computación

Self-Supervised Representations Discriminative Congruence Transform Hyperbolic Space Mutual Information

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