Revar3r: gauge-aware perturbation uncertainty for feed-forward 3d reconstruction

Sammam Mahdi; Fariha Binta Salim; Rakin Bin Rabbani; Aniqua Nusrat Zereen

cs.CVOct 6, 2026

Revar3r: gauge-aware perturbation uncertainty for feed-forward 3d reconstruction

Authors: Sammam Mahdi, Fariha Binta Salim, Rakin Bin Rabbani, Aniqua Nusrat Zereen

Organizations: BRAC University · Mahidol University

Abstract

A correctly reconstructed distant point appears uncertain even when a frozen 3D model processes equivalent inputs because its output frame rotates fractionally. This exposes a weakness of trainingfree perturbation uncertainty: when outputs contain an unobserved symmetry, run-to-run variation potentially reflects symmetry rather than error. Existing alternatives have trade-offs: built-in confidence is outperformed in most evaluated conditions, while trained evidential heads require modelspecific supervision. For point maps, this research derives a closed-form, error-independent variance term that grows with scene extent and potentially overwhelms the desired signal. Simulation reproduces the effect; all 30 real VGGT view-sets tested exhibit its predicted $\|x_p\|^2$ signature. ReVar3R robustly registers predictions to a common similarity frame before computing per-point variance, without retraining or modifying the frozen model. Optional calibration and fusion use a held-out split. Across VGGT, π3, and MASt3R on six datasets, the same estimator on every backbone lowers AUSE below built-in confidence in 15 of 18 conditions. The staged evaluation yields 11 of 18 wins for the label-free core, 12/18 for label-free equal-weight fusion, 14/18 with held-out weights, and 15/18 when the built-in signal is included. Against a trained evidential head, the result is a trade-off: the head calibrates magnitude better and leads in its training domain, whereas ReVar3R transfers across backbones without adaptation. Its ranking improves point filtering, but it does not detect stable systematic bias, aid novel-view synthesis, or transfer calibration across domains.

Figures & tables

Figure 1: ReVar3R pipeline. Alignment precedes per-point variance.

Figure 2: Gauge contamination in simulation. (a) A growing injected

\mathrm{Sim}(3)

gauge degrades unaligned perturbation variance (AUSE

\downarrow

); gauge-aligned variance stays near oracle quality. (b) At a fixed gauge, the degradation grows with the scene’s distance from the origin, the lever arm in the

\|x\|^{2}

term of Eq. ( 3 ).

Figure 3: Main comparison over six datasets. AUSE improvement (built-in $-$ ReVar3R) per backbone and dataset; blue is a gain and red a loss, darker is larger. Positive cells ( 15 of 18 ) are conditions where ReVar3R lowers AUSE.

Appendix figures & tables25 assets

Supplementary material from the paper’s appendix.

Appendix

Model and geometry
Symbol	Meaning
$f$	frozen feed-forward 3D model (weights never modified)
$V$	number of input views
$H,\,W$	height and width of each per-view point map
$X\in\mathbb{R}^{V\times H\times W\times 3}$	per-view point maps emitted by $f$
$p,\;v$	pixel (correspondence) index; view index

Appendix

Table 1: Notation. Definitions used throughout the paper, grouped by model, perturbation ensemble, gauge, estimator, and metric.

Sweep	setting	$\boldsymbol{\rho_{\text{unaligned}}}$	$\boldsymbol{\rho_{\text{aligned}}}$	AUSE ${}_{\text{un}}$	AUSE ${}_{\text{al}}$
gauge mag.	$0.0$	0.991	0.990	0.007	0.008
	$0.01$	0.936	0.989	0.033	0.008
	$0.03$	0.774	0.989	0.117	0.008
	$0.10$	0.395	0.990	0.469	0.007
distance	$D{=}0$	0.962	0.989	0.020	0.008
	$D{=}20$	0.852	0.989	0.090	0.008

Appendix

Table 2: Synthetic gauge contamination. Spearman against true uncertainty and AUSE show that aligned estimates remain invariant while unaligned estimates degrade with gauge magnitude and scene distance. Component rows use magnitude

0.05

; the

N

-sweep reports unaligned Spearman and shows persistent contamination.

Figure 4: The gauge term grows with distance within real scenes. After per-view-set normalization and pooling over

30

view-sets from six datasets (eight scenes in all),

U_{\mathrm{unaligned}}-U_{\mathrm{aligned}}

rises monotonically with point distance

|x_{p}|

. Its rank correlation with

|x_{p}|^{2}

is positive in

30/30

view-sets (median

+0.59

), matching the

\|x_{p}\|^{2}

term in Eq. ( 3 ).

Backbone	Dataset	naive	align	naive	align	naive	align	naive
		Centre AUSE		Centre Spearman		Rot. AUSE		$\boldsymbol{\rho(\\|c\\|^{2})}$
$\pi^{3}$	7-Scenes	0.217	0.175	0.276	0.351	0.299	0.314	$0.38^{\ast}$
$\pi^{3}$	DTU	0.210	0.119	$-0.006$	0.521	0.156	0.088	$0.15$
$\pi^{3}$	ETH3D	0.534	0.519	0.157	0.007	0.401	0.445	$0.07$
VGGT	7-Scenes	0.556	0.461	$-0.297$	$-0.301$	0.322	0.291	$0.70^{\ast}$
VGGT	DTU	0.083	0.048	0.121	0.386	0.355	0.305	$0.66^{\ast}$

Appendix

Table 3: The gauge confound transfers to SE(3) camera poses, but ranking gains are mixed. Naive and gauge-aligned pose uncertainty rank pose error over all cameras pooled per condition (AUSE lower is better; Spearman higher is better). Bold marks the better AUSE. Centre alignment lowers AUSE in all six conditions, whereas outlier-robust centre Spearman improves in three (both DTU and

\pi^{3}

/7-Scenes); VGGT/7-Scenes and VGGT/ETH3D remain weak negative rankers. The final column measures Eq. ( 3 )’s

\|c\|^{2}

signature through the rank correlation between naive centre uncertainty and squared camera-centre magnitude, which is strong where the frame moves.

Level	What it adds	Labels
Core	aligned single-family variance (a ranking)	none
$+$ fusion	rank-space fusion of families with the built-in confidence	held-out split
$+$ calibration	isotonic map from score to error magnitude (ECE)	held-out split

Appendix

Table 4: The three levels of ReVar3R. The training-free core produces the AUSE/Spearman ranking. Fusion and calibration use a small held-out labelled split; neither changes a single family’s ranking, and calibration alone changes only magnitude. This separation distinguishes ranking from calibration in the Trust3R comparison (Section 6.5 ).

Figure 5: Component decomposition. Mean AUSE reduction (positive

=

improvement) and, in parentheses, the share of conditions each component helps, split into in-distribution and shifted conditions. Alignment supplies the largest in-distribution gain, held-out learned fusion is the most consistent component, and equal fusion exhibits occasional degradation under shift. The fifth group isolates admitting built-in confidence as a fusion input: it is of the same order as the fusion step itself, which is why the label-free core (

11/18

) is reported alongside the fused

15/18

Model	Dataset	built-in	unaligned	core (train-free)	full (fused)
VGGT	7-Scenes	0.712	0.655	0.536	0.491
VGGT	DTU	0.248	0.313	0.236	0.171
VGGT	ETH3D	0.740	0.520	0.578	0.635
VGGT	BlendedMVS	0.786	0.597	0.276	0.407
$\pi^{3}$	7-Scenes	0.517	0.541	0.439	0.363
$\pi^{3}$	DTU	0.273	0.660	0.276	0.220

Appendix

Table 5: Training-free core vs. built-in. Decomposition of the gain (AUSE

\downarrow

) across the four original datasets (twelve conditions): built-in confidence; unaligned single-family perturbation variance; the training-free core ReVar3R estimator (robust-aligned single-family variance, no fusion, no built-in confidence); and the full held-out fusion. The training-free core beats built-in in

8/12

here and

11/18

with the competitor benchmarks (Table 10 ), versus

5/18

for unaligned perturbation. The gain comes from alignment, not fusion with the baseline.

Aggregator	ID	OOD	overall
Trace variance (used)	0.359	0.464	0.394
Median absolute deviation	0.440	0.507	0.462
Largest eigenvalue	0.365	0.468	0.399

Appendix

Table 6: Aggregation statistic (full grid). Mean AUSE over

3

models

\times

6

datasets for three aligned-photometric aggregators; lower is better. Trace variance is strongest, median spread is clearly weaker, and the largest eigenvalue is marginally weaker. The trace column reproduces the rung-7 core values of Table 5 on the four original datasets; TUM and KITTI are recomputed here over ten view-sets rather than the eight used in Table 10 .

		AUSE
axis	variant	all	ID	OOD	Spearman	helps
group	none	0.543	0.526	0.578	$+0.20$	$3/18$
	translation	0.500	0.459	0.581	$+0.27$	$8/18$
	rigid $\mathrm{SE}(3)$	0.460	0.420	0.539	$+0.31$	$7/18$
	similarity $\mathrm{Sim}(3)$	0.392	0.347	0.483	$\mathbf{+0.36}$	$\mathbf{11/18}$
reference	run $0$	0.392	0.347	0.483	$+0.36$	$11/18$

Appendix

Table 7: Alignment ablations: group, reference, and scope. Photometric-core means over

18

conditions (AUSE

\downarrow

, Spearman

\uparrow

). Similarity alignment performs best, reference choices are indistinguishable, and per-view scope beats scene-level scope. “helps” counts conditions beating built-in AUSE; similarity/run-0/per-view is the default core and appears identically in all three blocks. This ablation uses the first

8

view-sets in every condition, whereas Table 5 uses

10

for the four original datasets (TUM and KITTI have eight in both). With the larger sample, unaligned variance beats built-in confidence in

5/18

conditions rather than

3/18

\pi^{3}

on ETH3D and VGGT on BlendedMVS change sign.

Figure 6: Alignment removes the dominant nuisance. For each backbone (group) and dataset (colour), AUSE

\downarrow

of photometric perturbation variance without alignment (hollow circle) and of the same runs after gauge alignment (filled circle, the ReVar3R core); each arrow runs from unaligned to aligned, so an arrow sloping down is a reduction. The pair of one condition is offset horizontally so the arrow stays readable where the effect is small. The labels under the groups give the mean reduction over the six datasets (VGGT

0.165

, MASt3R

0.131

\pi^{3}

0.105

). Alignment lowers AUSE in

15

of the

18

conditions; the exceptions are ETH3D for VGGT and

\pi^{3}

, and BlendedMVS for

\pi^{3}

, the last by

0.009

. Table 5 lists the values for the four original datasets.

			input-noise		photometric
Model	Dataset	built-in	unaligned	aligned	aligned
MASt3R	DTU	0.463	0.491	0.358	0.343
MASt3R	ETH3D	0.570	0.568	0.540	0.576
MASt3R	7-Scenes	0.587	0.494	0.374	0.389
$\pi^{3}$	DTU	0.273	0.613	0.272	0.269
$\pi^{3}$	ETH3D	0.528	0.490	0.453	0.481

Appendix

Table 8: Aligned sampling baseline at matched budget. AUSE

\downarrow

for the input-noise ensemble with and without gauge alignment, beside aligned photometric jitter, all scored identically. Bold marks the best of the three uncertainty estimators per row. Same pass budget, registration and scoring throughout, so the columns differ only in whether the ensemble is aligned and in which perturbation generates it.

		AUSE $\downarrow$		Spearman $\uparrow$
Model	Dataset	built-in	ReVar3R	built-in	ReVar3R
VGGT	7-Scenes	0.712	0.491	0.06	0.32
VGGT	DTU	0.248	0.171	0.31	0.44
VGGT	ETH3D	0.740	0.635	$-0.11$	0.13
VGGT	BlendedMVS	0.786	0.407	$-0.16$	0.43
$\pi^{3}$	7-Scenes	0.517	0.363	0.36	0.48

Appendix

Table 9: Per-condition results at native resolution. AUSE (

\downarrow

) and Spearman (

\uparrow

) compare built-in confidence with full ReVar3R. Improvements concentrate where built-in ranking is weak; regressions occur where it is already comparatively strong.

Dataset	Model	built-in	unaligned	core (train-free)	full (fused)
TUM	VGGT	0.296 / +0.48	0.819 / $-$ 0.01	0.446 / +0.39	0.199 / +0.51
TUM	$\pi^{3}$	0.273 / +0.25	0.286 / +0.65	0.212 / +0.51	0.198 / +0.46
TUM	MASt3R	0.226 / +0.63	0.433 / +0.24	0.270 / +0.44	0.182 / +0.56
KITTI	VGGT	0.401 / +0.30	0.592 / +0.32	0.432 / +0.58	0.237 / +0.62
KITTI	$\pi^{3}$	0.385 / +0.45	0.451 / +0.53	0.337 / +0.64	0.273 / +0.74
KITTI	MASt3R	0.346 / +0.53	0.477 / +0.45	0.313 / +0.67	0.215 / +0.77

Appendix

Table 10: Competitor benchmarks (TUM, KITTI). AUSE

\downarrow

/ Spearman

\uparrow

for built-in confidence, unaligned single-family perturbation, the training-free core (aligned single-family variance), and the full fused estimator. Full ReVar3R beats built-in AUSE in

6/6

conditions; the core wins in

3/6

(

\pi^{3}

on both benchmarks and MASt3R/KITTI).

		7-Scenes	TUM	ETH3D	DTU	KITTI
sets		23	12	24	30	12
scenes		7	2	9	30	1
pooled AUSE $\downarrow$	built-in	0.535	0.232	0.585	0.557	0.359
	ReVar3R	0.293	0.188	0.667	0.403	0.216
	Trust3R	0.268	0.119	0.477	0.637	0.319
per-set median AUSE $\downarrow$	ReVar3R	0.272	0.148	0.471	0.228	0.209

Appendix

Table 11: ReVar3R vs. a trained evidential head (Trust3R). Frozen MASt3R at

224

px on identical point sets and all available view-sets. AUSE

\downarrow

, Spearman

\uparrow

; Trust3R uses its paper-default epistemic readout and ReVar3R entries are means over five seeds. “scenes” counts the independent scenes available for inference.

	AURC $\downarrow$				AUSE $\downarrow$ (unnormalized)
	built-in	ReVar3R	input	Trust3R	built-in	ReVar3R	input	Trust3R
Dataset			noise				noise
7-Scenes	0.249	0.189	0.224	0.179	0.127	0.068	0.102	0.067
TUM	0.079	0.082	0.101	0.067	0.027	0.030	0.050	0.019
ETH3D	3.812	3.535	3.408	3.513	2.114	1.837	1.710	1.834
DTU	34.95	25.93	33.20	33.59	16.83	7.81	15.08	17.87

Appendix

Table 12: Trust3R’s metric definition, recomputed on the present point sets. Risk-coverage AURC

\downarrow

and unnormalized AUSE

\downarrow

, both in scene units, so methods are comparable within a row but values are not comparable across datasets. Ten view-sets per dataset (eight for TUM and KITTI), seed

0

, Trust3R total readout, and an exact sort-based curve in place of their log-binned estimator; it is a cross-check on the metric definition, not a reproduction of their protocol.

Signal	7-Scenes	DTU	ETH3D
Built-in conf.	0.702 / 0.09	0.402 / 0.24	0.754 / $-0.09$
Learned probe (frozen features)	0.791 / 0.09	0.245 / 0.56	0.644 / 0.14
ReVar3R (aligned perturbation)	0.546 / 0.29	0.170 / 0.46	0.510 / 0.15

Appendix

Table 13: Frozen-feature probe on VGGT. AUSE

\downarrow

/ Spearman

\uparrow

for built-in confidence, a learned probe, and ReVar3R. ReVar3R has lower AUSE throughout, while the probe has higher Spearman on DTU.

Figure 7: Better ranking yields better geometry. Mean error of kept points

\downarrow

vs. removal fraction. Dropping the points ReVar3R ranks most-uncertain retains lower-error geometry than built-in confidence, a naive input-noise ensemble, or random removal, closing

30

–

57\%

of the built-in-to-oracle gap at

50\%

removal. All panels use frozen MASt3R: (a) and (b) the

224

px protocol with ten view-sets, (c) the native-resolution KITTI run with eight, where the

224

px Trust3R checkpoint does not apply. Trust3R filters its own refined point map and starts from a different zero-removal error (DTU

31.7

vs.

35.0

), so read its shape, not its offset.

Figure 8: Calibration improves within domain. Raw versus isotonic-calibrated ECE (

\downarrow

) from a within-domain calibration split. Raw perturbation scores are poorly scaled, with DTU and ETH3D saturated; a small held-out isotonic map corrects ECE for ReVar3R and the trained head. On 7-Scenes, Trust3R’s native standard deviation is already calibrated.

Figure 9: Calibration does not transfer across domains. ECE ( $\downarrow$ ) for an isotonic map fit on the row domain and evaluated on the column domain, for ReVar3R (left) and Trust3R (right). Both methods calibrate well on the diagonal and poorly off it; neither transfers magnitude calibration across domains.

Figure 10: Sample-count sweep. AUSE (

\downarrow

) versus perturbed passes

N

for each backbone and dataset; shading gives standard deviation across view-sets, and the dashed line marks the

N{=}5

default. In-distribution AUSE flattens by

N{=}5

, while shifted ETH3D is nearly flat throughout.

Method	AUSE $\downarrow$	Spearman $\uparrow$	ECE $\downarrow$
oracle (bound)	0.000	1.00	$-$
built-in conf.	0.585	0.31	$-$	best ranking
random removal	0.743	0.00	$-$	reference
input-noise ensemble	0.766	$-0.31$	$-$	worse than random
Trust3R (trained)	0.475	0.25	0.10	best AUSE and calibration
ReVar3R	0.667	0.13	0.38	neither

Appendix

Table 14: Distribution-shift breakdown on ETH3D with frozen MASt3R at

224

px, over

24

view-sets spanning nine scenes. Bold marks the best non-oracle value per column.

Method	Training	Params	Passes	Peak mem.	Latency
Built-in conf.	none	$0$	$0$ (free)	${\leq}2.91$ GB	${\sim}0.92$ s/pair
Input-noise ensemble	none	$0$	${\sim}5$	${\sim}$ base	subset of $9$ s/set
ReVar3R	none	$0$	${\sim}10$ – $11$	$2.91$ GB	$9.09$ s/set ( ${\sim}9.9\times$ )
Trust3R	$10$ ep. / $150$ k pairs	$40.4$ M	$1$	$3.37$ GB	$0.919$ s/pair

Appendix

Table 15: Cost and efficiency on the shared backbone. ReVar3R adds no parameters or training and uses comparable peak memory, but requires multiple passes and roughly an order of magnitude more latency than the single-pass trained head. Latency is wall-clock time on one

16

GB GPU.

Figure 11: Qualitative uncertainty maps from VGGT (seed 0), one typical view-set per dataset (median within-set AUSE gap between built-in confidence and the full estimator). Columns: input, ground-truth error, built-in confidence as uncertainty, unaligned photometric variance, and ReVar3R: the core (the same runs, gauge-aligned) and the full estimator (held-out rank fusion with view-order variance and built-in confidence). Each map shows every pixel’s percentile rank within the view among pixels with ground truth, from low (dark) to high (light) on the scale at the right; grey pixels have no ground truth. The number under each map is that view’s own AUSE.

Model	Dataset	built-in	ReVar3R	wins
MASt3R	BlendedMVS	0.282	$0.349\,{\pm}\,0.011$	0/5
MASt3R	DTU	0.463	$0.330\,{\pm}\,0.012$	5/5
MASt3R	ETH3D	0.570	$0.556\,{\pm}\,0.005$	5/5
MASt3R	KITTI	0.358	$0.240\,{\pm}\,0.007$	5/5
MASt3R	7-Scenes	0.587	$0.353\,{\pm}\,0.005$	5/5
MASt3R	TUM	0.231	$0.172\,{\pm}\,0.004$	5/5

Appendix

Table 16: Full estimator over five seeds. Per-condition AUSE

\downarrow

of the fused estimator, mean

\pm

standard deviation over five seeds, against built-in confidence; “wins” counts the seeds in which ReVar3R is lower.

trim drop	$\rho$ / AUSE	Cauchy $\times$	$\rho$ / AUSE	depth ext.	$\rho$ / AUSE
$0\%$	$0.98/0.011$	$0.25$	$0.99/0.008$	$2.0$	$0.99/0.008$
$5\%$	$0.99/0.008$	$0.5$	$0.99/0.007$	$1.0$	$0.99/0.008$
$10\%$	$0.99/0.008$	$1.0$	$0.99/0.008$	$0.3$	$0.99/0.008$
$20\%$	$0.99/0.007$	$2.0$	$0.99/0.008$	$0.1$	$0.99/0.008$
$30\%$	$0.99/0.007$	$4.0$	$0.99/0.008$	$0.03$	$0.99/0.008$

Appendix

Table 17: Alignment robustness in simulation. Aligned-estimator Spearman

\uparrow

/ AUSE

\downarrow

against known

\sigma_{\mathrm{true}}

remains stable across trimming-fraction, Cauchy-scale, and near-planar sweeps. The default drops

10\%

and sets Cauchy scale to the median residual.

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