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

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

arXiv:2610.07883v1cs.CV

TL;DR

For point maps, cross-run variance can reflect unobserved similarity-gauge changes as well as prediction instability, making it difficult to interpret as uncertainty. ReVar3R aligns frozen-model predictions before computing per-point variance. Across three backbones and six datasets, it improves ranking over built-in confidence in most conditions, while retaining limits in bias detection and cross-domain calibration.

  • Problem

    Point-map outputs can vary in similarity gauge across runs, so native-frame perturbation variance confounds prediction instability with coordinate-frame variation.

    Source: §3.2 · p. 3

  • Method

    ReVar3R registers perturbed frozen-model predictions to a common similarity frame before computing per-point variance, with calibration and fusion optional.

    Source: §1 · p. 2, §4 · p. 4, §4.3 · p. 5

  • Results

    15 of 18 conditions: ReVar3R lowers AUSE below built-in confidence across VGGT, π3, and MASt3R on six datasets.

    Source: §1 · p. 2

  • Takeaways & Limitations

    ReVar3R improves multi-view point filtering, but its ranking does not detect stable systematic bias.

    Source: §1 · p. 2

    ReVar3R does not detect stable systematic error, transfer magnitude calibration across domains, or improve novel-view synthesis; multiple passes add roughly an order of magnitude in latency.

    Source: §1 · p. 2, §7 · p. 8

Abstract

from arXiv · show

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, {\pi}3, 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.

1 Introduction

Feed-forward 3D models produce point maps without a fixed coordinate frame, making run-to-run variation an unreliable uncertainty signal unless gauge changes are separated from geometric error. ReVar3R aligns predictions before estimating variance and improves ranking over built-in confidence in most evaluated conditions, while retaining clear limits.

1 Introduction

  • ReVar3R registers perturbed predictions to a common Sim(3) frame before computing per-point variance, without modifying or retraining the frozen model.Held-out calibration and rank-space fusion are optional.Source: §1 · p. 2

1. A closed form exposes gauge contamination in black-box perturbation ensembles

  • Run-to-run similarity-gauge variation adds an error-independent variance term that grows with scene extent and can make naive variance rank position rather than error.Simulation reproduces the effect, and all 30 tested real VGGT view-sets exhibit the predicted ∥xp∥2 signature.Source: §1 · pp. 1–2

2. One output-side estimator applies across frozen point-map backbones

  • One output-side estimator applies without adaptation to any backbone that emits point maps.A global Sim(3) correction accounts for 65% of the empirical gain, followed by default per-view frame stabilization.Source: §1 · p. 2

3. Ablations isolate alignment as the source of the ranking gain

  • 15 of 18 conditions: ReVar3R lowers AUSE below built-in confidence across VGGT, π3, and MASt3R on six datasets.Ablations separate the supervision of each evaluation stage.Source: §1 · p. 2

4. The improved ranking has a defined use and boundary

  • ReVar3R improves multi-view point filtering, but does not detect stable systematic bias, transfer magnitude calibration across domains, or improve novel-view synthesis.Compared with a trained head, the result is a trade-off rather than a uniform ranking.Source: §1 · p. 2

2 Related Work

Related work spans feed-forward point-map reconstruction, uncertainty estimation, and gauge alignment. The unresolved issue is how to interpret cross-run variance for frozen predictors whose outputs have similarity-gauge freedom.

Feed-forward 3D reconstruction

  • Point-map systems emit geometry in a network-selected frame, so similarity-gauge freedom is a setting-wide concern rather than a property of one backbone.View-order equivariance does not remove the global frame freedom.Source: §2 · p. 2

Uncertainty estimation

  • Perturbation uncertainty works for fixed-coordinate outputs, but point maps leave cross-run variance confounded by global similarity freedom.AUSE evaluates ranking against an oracle ordering, while calibration measures score-to-error scaling.Source: §2 · p. 2

Uncertainty for feed-forward 3D models

  • Trust3R trains an evidential head on labelled 3D data, whereas ReVar3R uses equivalent-input responses from an unchanged checkpoint in exchange for additional inference passes.The methods address the same reliability question under different access and cost assumptions.Source: §2 · p. 3

Gauge freedom and alignment

  • Classical gauge remedies presume access to estimator parameters or a Jacobian, which a frozen feed-forward predictor does not expose.The paper claims no novelty for the underlying principle of gauge alignment.Source: §2 · p. 3
  • Evaluation-time alignment does not fix raw-frame variance accumulated across ensemble runs; the missing remedy is to register runs before computing variance.Trust3R’s evaluator aligns images for scoring but accumulates cross-pass variance in raw predicted frames.Source: §2 · p. 3

3 Problem: Perturbation Variance in Gauge-Ambiguous 3D

The section formalizes why perturbation variance for point maps can mix prediction instability with unobserved changes in the output frame. Its decomposition identifies an error-independent gauge term that can dominate the desired signal in large scenes.

3.1 Setup and notation

  • The objective is to rank pixels by geometric error using only a frozen model’s outputs, with AUSE comparing the ranking to an oracle ordering.Prediction error is computed after gauge-free alignment to ground truth, so a global frame offset is not itself an error.Source: §3 · p. 3, §3.1 · p. 3

3.2 Why a direct variance is not well defined

  • Because point-map geometry is defined only up to a global similarity transform, native-frame variance mixes predictive instability with error-independent gauge variation.Scale and rotation displace points in proportion to their distance from the origin.Source: §3.2 · p. 3

3.3 Gauge contamination of the variance

  • Under the small-perturbation gauge model, cross-run covariance separates into true spread and an additive gauge-contamination term.The model assumes small, mutually independent gauge variables and predictive noise.Source: §3.3 · pp. 3–4
  • Scale and rotation contamination grows with squared distance and can make variance rank position rather than error, while translation adds a position-independent offset.Centring removes only the translation offset; the model covers a global frame varying across runs, not residual view-dependent motion.Source: §3.3 · p. 4

4 Gauge-Aware Perturbation Uncertainty

ReVar3R removes similarity-gauge variation at the output level by aligning perturbed predictions before estimating their spread. Its core is aligned variance; calibration and fusion are optional additions.

4 Gauge-Aware Perturbation Uncertainty

  • ReVar3R aligns each perturbed run to a shared frame, aggregates aligned spread, and can optionally calibrate and fuse the resulting scores.Output alignment is the conceptual contribution; aggregation, calibration, and fusion are standard operations.Source: §4 · p. 4

4.1 Alignment before variance

  • The gauge-aligned variance is the trace of per-point sample covariance after mapping runs into a reference run’s frame.Internal registration uses prediction-derived correspondences; ground-truth validity is reserved for evaluation.Source: §4.1 · p. 4

4.2 Robust similarity alignment

  • Robust registration initializes a closed-form Sim(3) fit, then trims the worst 10% of correspondences over five Cauchy-estimator rounds.Trimming is intended to prevent unstable or high-error regions from pulling the fit toward themselves.Source: §4.2 · p. 4
  • The fit uses finite prediction-valid correspondences without confidence thresholds or manual masks, and is insensitive to tested trimming, scale, and near-planar settings.It uses a fixed-seed subsample of at most 8,000 correspondences and applies the fit to every point.Source: §4.2 · pp. 4–5

4.3 Aggregation, calibration, and fusion

  • The core score is the trace of aligned covariance; optional isotonic calibration maps scores to error magnitude, while rank-space fusion weights signals using held-out inverse-AUSE2.The held-out split separates label-free ranking from fusion and magnitude calibration.Source: §4.3 · p. 5

5 Experimental Setup

The evaluation compares three frozen point-map backbones across six datasets using gauge-free error alignment, multiple uncertainty baselines, and view-set-level statistical testing.

Models and datasets

  • The six datasets cover in-distribution, wide-baseline outdoor, training-overlap, indoor RGB-D, and driving regimes across overlapping five-view sets.Ground-truth point maps are resized to model resolution; Trust3R comparisons cover TUM, KITTI, and ETH3D among its four reported benchmarks.Source: §5 · p. 5

Metrics

  • AUSE is the primary ranking metric; Spearman, AURG, and regression ECE provide complementary ranking and magnitude-calibration measures.Per-point error is Euclidean distance to ground truth after robust similarity alignment, separate from the estimator’s internal registration.Source: §5 · p. 6

Baselines

  • Training-free baselines include built-in confidence and input-noise ensembles with and without the same registration path used by ReVar3R.Trust3R is evaluated on frozen MASt3R at matched 224 px resolution and identical point sets.Source: §5 · p. 6

Protocol and statistics

  • ReVar3R uses five passes for each of two perturbation families, sharing a reference prediction for nine total model evaluations.AUSE differences are tested over view-sets with paired Wilcoxon tests; correlated view-sets within scenes can make the test anticonservative when scene counts are small.Source: §5 · p. 6
  • Training-free estimators share predictions, alignment conventions, and scoring code, while stochastic results average five seeds against deterministic single-pass references.Trust3R uses its own refined point map, scored on the same valid pixels and identical view-sets.Source: §5 · p. 6

6 Results

The experiments validate gauge contamination, test alignment and fusion, compare ReVar3R with built-in and trained uncertainty estimates, and assess point filtering.

6.1 Controlled validation of gauge contamination

  • Unaligned AUSE rose from 0.007 to 0.47 as gauge increased, while aligned AUSE stayed ≈0.008; real VGGT showed the predicted distance signature in 30/30 view-sets.The real-view-set median Spearman correlation for the signature was +0.59.Source: §6.1 · p. 6

6.2 Alignment removes the dominant nuisance

  • Alignment lowers mean AUSE by 0.165 for VGGT, 0.131 for MASt3R, and 0.105 for π3, with larger benefit in-distribution than under shift.AUSE falls from 0.543 without alignment to 0.392 with Sim(3); global correction accounts for 65% of the default alignment gain, and the fixed-run, medoid, and random references perform indistinguishably.Source: §6.2 · pp. 6–7

6.3 Comparison with built-in confidence

  • ReVar3R lowers AUSE most where built-in confidence is weak, including VGGT on KITTI (0.401 →0.237, −41%), but loses in three conditions.The exceptions are π3 and MASt3R on BlendedMVS and π3 on ETH3D, where built-in confidence is comparatively strong.Source: §6.3 · p. 7

6.4 Behaviour under distribution shift

  • On KITTI, ReVar3R AUSE is 0.216 against 0.359 for built-in confidence; on ETH3D, its 0.667 is worse than built-in’s 0.585.In simulation, unaligned AUSE degrades as injected gauge grows, while aligned variance stays near oracle quality.Source: §6.4 · p. 7, Figure 2 · p. 7

6.3 Comparison with built-in confidence

  • 15 of 18 conditions favor ReVar3R over built-in confidence, with the label-free core winning 11/18 and held-out-weight fusion reaching 14/18.Label-free equal-weight fusion wins 12/18; including built-in confidence reaches 15/18.Source: §6.3 · p. 7, Figure 3 · p. 8

6.5 Relation to a trained uncertainty head

  • ReVar3R is favored by median AUSE on three of five Trust3R datasets, while the trained head calibrates magnitude better throughout.The head leads on TUM, and 7-Scenes is nearly tied at 0.272 versus 0.271.Source: §6.5 · p. 8

6.6 Downstream utility

  • At 50% point removal, ReVar3R closes 43% of the built-in-to-oracle gap on 7-Scenes, 57% on DTU, and 30% on KITTI.It beats built-in, input-noise, and random removal on every dataset.Source: §6.6 · p. 8

7 Discussion and Limitations

ReVar3R measures perturbation instability rather than geometric correctness, and its calibration and downstream benefits have defined limits.

Limitations

  • Stable systematic errors can have low variance when perturbations agree on the same wrong geometry; calibration requires labels and transfers poorly across domains.Multiple passes add roughly an order of magnitude in latency, and the analysis idealizes the estimated gauge.Source: §7 · p. 8

Broader implication

  • Camera-centre uncertainty shows the predicted distance inflation, but centre-error Spearman supports only three of six conditions, leaving pose instability a weak error ranker in some settings.The proposed extension to shape codes and radiance fields is framed for outputs defined up to a global similarity or world frame.Source: §7 · p. 8

8 Conclusion

The conclusion presents align-before-variance as a training-free approach that improves uncertainty ranking in most evaluated conditions, with explicit limits on what it measures.

8 Conclusion

  • ReVar3R applies align-before-variance to frozen-model outputs without added parameters or retraining, improving ranking over built-in confidence in most conditions and in point filtering.It measures procedural reliability rather than geometric error and does not detect stable systematic bias or transfer calibration across domains.Source: §8 · pp. 8–9

Reproducibility statement

  • The reproducibility statement identifies the estimator specification, checkpoints, datasets, perturbation settings, statistical protocol, and supporting appendices.The appendices include the gauge-term derivation and Monte Carlo check, Trust3R comparison protocol, seed stability, and per-condition values.Source: Reproducibility statement · p. 9

AI use statement

  • The authors report that AI assisted with drafting and prose polishing under author supervision, while authors developed the research and verified the reported results.The authors state that AI did not originate ideas or hypotheses, derive proofs, or produce reported results.Source: AI use statement · p. 9

Supplementary Material

Table 1 organizes the paper’s notation by the roles its symbols serve.

Supplementary Material

  • Table 1 groups symbols by model and perturbation ensemble.These are two of the table’s five stated categories.Source: Table 1 · p. 12
  • Gauge and estimator are separate notation categories.The table groups symbols by model, perturbation ensemble, gauge, estimator, and evaluation.Source: Table 1 · p. 12, A Notation · p. 12
  • Metric notation is grouped under evaluation.The table’s stated categories include evaluation.Source: Table 1 · p. 12, A Notation · p. 12

B Gauge Mechanism and Verification

The section tests the predicted distance-growing gauge contamination in point maps and camera poses, then evaluates alignment and estimator components. It reports that the effect is present in real scenes, while pose-ranking gains and component benefits vary by setting.

B Gauge Mechanism and Verification

  • In the synthetic test, scale and rotation create persistent distance-scaled contamination, while translation adds a position-independent offset that does not reorder points.The scale-and-rotation contamination persists as the number of samples increases.Source: B Gauge Mechanism and Verification · p. 13, Table 2 · p. 13
  • The gauge contribution rises with point distance in all 30 real VGGT view-sets, with median Spearman correlation +0.59 against |x_p|^2.The pooled binned curve rises monotonically; the test spans six datasets and eight scenes.Source: B Gauge Mechanism and Verification · p. 13, Figure 4 · p. 14
  • Across 18 backbone–dataset conditions, the fitted distance-dependent coefficient is positive in 16, with median R2 = 0.74.The two exceptions show no detectable distance dependence, rather than a contrary trend.Source: B Gauge Mechanism and Verification · p. 14

B.1 Second Modality: SE(3) Camera Poses

  • Centre alignment lowers pose-error AUSE in all six conditions, but outlier-robust centre Spearman improves in only three.VGGT on 7-Scenes and ETH3D remains a weak negative ranker; rotation AUSE improves in four of six conditions.Source: Table 3 · p. 15, §B.1 · p. 15

C Estimator Components and Alignment

  • Alignment dominates in-distribution, held-out learned fusion helps in every shifted condition, and naive equal fusion is unreliable.After alignment, photometric and input-noise perturbations differ only marginally in average best-configuration AUSE; under shift, input noise is marginally stronger.Source: C Estimator Components and Alignment · p. 15, Figure 5 · p. 17
  • Robust Umeyama alignment reduces AUSE on every backbone averaged over six datasets, with reductions of 0.165, 0.131, and 0.105 on VGGT, MASt3R, and π3, respectively.It reduces AUSE in 15/18 conditions individually and is at least as good as plain Umeyama on every backbone.Source: C Estimator Components and Alignment · p. 15
  • 11/18 conditions favor the label-free core over built-in confidence, versus 15/18 for the full fusion that also admits built-in confidence.The core uses aligned single-family variance without fusion; the full fusion includes held-out inputs.Source: C Estimator Components and Alignment · p. 16, Table 5 · p. 16, Figure 5 · p. 17
  • Trace variance is the strongest aligned-spread aggregator; median spread is weaker by mean AUSE +0.068, while the largest eigenvalue is weaker by +0.006.Median spread is weaker in 16/18 conditions and the largest eigenvalue in 15/18, though the latter is close to a tie.Source: C Estimator Components and Alignment · p. 17, Table 6 · p. 17

C.1 Alignment Ablations: Reference, Group, and Scope

Alignment ablations identify the similarity group and per-view registration—not reference choice—as key design choices. The section compares ranking across datasets, a trained head, and point filtering.

C.1 Alignment Ablations: Reference, Group, and Scope

  • Similarity alignment performs best, reference choice is immaterial, and per-view scope beats scene-level scope across the alignment ablations.Expanding the alignment group helps most when adding rotation and scale; translation helps least. Per-view alignment also stabilizes residual view-dependent frame variation.Source: §C.1 · p. 17, Table 7 · p. 18
  • Aligned input-noise uncertainty beats built-in AUSE in all 9 conditions, versus 5 without alignment, and closely matches aligned photometric jitter.The comparison uses the same pass budget, registration, aggregation, and scoring path.Source: §C.1 · p. 19, Table 8 · p. 19

D.1 Per-Condition Results

  • ReVar3R improves Spearman in 8 of 12 conditions, ties in one, and regresses in three conditions where built-in ranking is comparatively strong.The regressions are π3/BlendedMVS (0.59 → 0.48), MASt3R/ETH3D (0.27 → 0.22), and MASt3R/BlendedMVS (0.50 → 0.35).Source: §D.1 · p. 19, Table 9 · p. 19

D.2 Competitor-Benchmark Results (TUM, KITTI)

  • The full estimator beats built-in AUSE in all 6 TUM and KITTI conditions; the core wins 3/6, and KITTI Spearman reaches +0.67 for the core and +0.77 for the full estimator.Built-in confidence reaches +0.30–+0.53 Spearman on KITTI.Source: §D.2 · pp. 19–20, Table 10 · p. 20

D.3 Comparison with a Trained Uncertainty Head

  • The larger-sample scene-blocked analysis finds a significant ReVar3R advantage over Trust3R only on DTU; other datasets are reported as effect sizes or cannot be tested.View-sets from the same scene are correlated, so the analysis uses one view-set per scene where possible.Source: §D.3 · p. 20, Table 11 · p. 21
  • The trained head calibrates magnitude better throughout, while ReVar3R is favored by per-view-set median AUSE on DTU, ETH3D, and KITTI.On DTU, ReVar3R has lower per-view-set AUSE on all 30 scans: median 0.228 versus 0.459, with a scene-level sign-flip test of p = 1.9 × 10−9.Source: §D.3 · p. 20, Table 11 · p. 21

D.4 Frozen-Feature Probe

  • The frozen-feature probe has worse AUSE than ReVar3R on all three tested datasets, but higher Spearman on DTU: 0.56 versus 0.46.The probe predicts per-point error from frozen VGGT features.Source: §D.4 · pp. 21–22, Table 13 · p. 22

D.5 Downstream Utility

  • ReVar3R-ranked point removal retains lower-error geometry than built-in confidence, input-noise, or random removal, closing 30–57% of the built-in-to-oracle gap at 50% removal.The KITTI Trust3R comparison uses its own refined point map and a different zero-removal error, so its curve shape—not its offset—is comparable.Source: Figure 7 · p. 22

D.6 Negative Results: Systematic Bias, Calibration Transfer, NVS

The negative results delimit where uncertainty rankings and calibration are useful, while additional analyses describe sample-count, shift, cost, and alignment boundaries.

D.6 Negative Results: Systematic Bias, Calibration Transfer, NVS

  • Variance misses stable systematic bias, magnitude calibration does not transfer across domains, and uncertainty-guided initialization does not improve novel-view synthesis.For stable bias, the variance ranking falls from Spearman +0.39 at biased fraction f = 0 to −0.67 at f = 0.6; under shift, top-decile-error AUROC is 0.53 on ETH3D.Source: §D.6 · pp. 22–23

D.7 Sample-Count Sweep

  • At N=5, the in-distribution sweep captures a median 85% of the improvement available at N=8, while shifted ETH3D AUSE is largely insensitive to sample count.The in-distribution spread is 40–99%; MASt3R on DTU is still improving at N=8.Source: §D.7 · p. 23, Figure 10 · p. 24

D.8 Distribution-Shift Breakdown

  • On 24 ETH3D view-sets spanning nine scenes, the trained head has the lowest AUSE and best calibration, while ReVar3R leads on neither; far-shift KITTI reverses the ordering.The larger ETH3D sample supersedes an earlier, more favorable ten-view-set result.Source: §D.8 · p. 24, Table 14 · p. 24

D.10 Additional Qualitative Results

  • On VGGT, the full estimator has lower pooled AUSE than built-in confidence on all three shown datasets; the core beats unaligned variance on 7-Scenes and DTU, but not ETH3D.The full estimator ranks error better in 9/10 view-sets on 7-Scenes, 10/10 on DTU, and 5/10 on ETH3D.Source: §D.10 · pp. 24–25, Figure 11 · p. 25

D.9 Cost and Efficiency

  • ReVar3R uses roughly ten-fold more inference passes than the single-pass trained head, but adds no training or parameters and has comparable peak memory.Its output-only design transfers to another backbone or resolution without a new training stage.Source: §D.9 · p. 24, Table 15 · p. 25

E.1 Scope of the Analysis and Design Choices

  • The analysis models one global similarity frame varying across runs, while practical alignment leaves residual error; robust alignment limits its empirical effect, but no formal bound is provided.The procedure is interpreted as global gauge removal followed by per-view frame stabilization, not as attributing all improvement to the single-transform model.Source: §E.1 · pp. 25–26, Table 17 · p. 26

E.2 Robustness of the Robust Alignment

Across five seeds, the fused estimator’s comparison with built-in confidence is stable; the alignment ranking also persists across robust-fit settings and near-degenerate geometry. The internal fit does not use ground-truth validity, and restricting it to evaluation-valid pixels improves pooled AUSE.

E.2 Robustness of the Robust Alignment

  • Restricting the internal fit to evaluation-valid pixels improves pooled AUSE by −0.010 on 7-Scenes, −0.006 on DTU, and −0.088 on KITTI (0.417 → 0.330).The reported estimator uses only prediction-valid, finite correspondences, so these results indicate that ground-truth validity does not account for its gains.Source: §E.2 · p. 26
  • Changing the trimmed fraction from 0 to 30% keeps Spearman in [0.98, 0.99] and AUSE in [0.007, 0.011]; scaling Cauchy width from 0.25–4× its default changes neither past the third decimal.In the controlled synthetic harness, all three sweeps preserve the ranking of known σtrue.Source: §E.2 · p. 26
  • With depth extent shrunk to 1.5% of lateral extent, the near-planar scene still preserves ranking (ρ≈0.99), as lateral point spread keeps the fit well determined.The depth-direction similarity fit is ill-conditioned, but that degeneracy does not propagate to the estimate.Source: §E.2 · p. 27

E.3 Seed Stability and Determinism

  • 15 of 18 conditions beat built-in confidence in every seed, with no condition changing sign; the result is identical under both view-set protocols.The three losses are always MASt3R and π3 on BlendedMVS and π3 on ETH3D.Source: §E.3 · p. 27

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