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arxiv: 2605.26519 · v2 · pith:AK2S2SDOnew · submitted 2026-05-26 · 💻 cs.CV

R³: 3D Reconstruction via Relative Regression

Congrong Xu , Huachen Gao , Xingyu Chen , Yuliang Xiu , Jun Gao , Anpei Chen This is my paper

Pith reviewed 2026-06-29 17:53 UTC · model grok-4.3

classification 💻 cs.CV
keywords 3D reconstructionrelative regressionpose estimationstreaming reconstructionfeed-forward modelscomputer visiondepth estimation
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The pith

R³ uses relative regression via a lightweight MLP to predict confidence-weighted constraints, removing the global coordinate frame bottleneck for long-context and streaming 3D reconstruction.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that existing feed-forward geometry models are limited by their assumption of a global coordinate frame, which creates problems with arbitrary origins and growing translation magnitudes in extended sequences. It proposes relative regression as the fix, where an MLP outputs relative constraints each weighted by a predicted . These confidences then serve as the single mechanism for both weighting training losses and aggregating poses at inference time. The result supports full offline reconstruction as well as causal streaming with bounded memory. A sympathetic reader cares because this directly targets the scalability barrier that prevents current models from handling realistic long videos or live capture.

Core claim

R³ employs relative regression. We employ a lightweight MLP to predict confidence-weighted relative constraints. These confidences serve as a unified anchor: weighting losses during training and guiding pose aggregation during inference. R³ supports both full-context offline reconstruction and causal, bounded-memory streaming.

What carries the argument

Confidence-weighted relative constraints output by a lightweight MLP, acting as the single anchor for loss weighting in training and pose aggregation in inference.

If this is right

  • Full-context offline reconstruction becomes possible without global-frame constraints.
  • Causal streaming reconstruction runs with bounded memory and no need to maintain an arbitrary temporal origin.
  • Translation magnitudes no longer grow unbounded, avoiding the scaling issues that appear in long sequences.
  • The same predicted confidences improve training stability and inference aggregation in both modes.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The bounded-memory streaming mode opens the door to real-time applications such as live AR or robot navigation where memory must stay fixed.
  • Relative regression may transfer to other sequential geometry tasks like video-based SLAM where global frames produce similar drift.
  • Direct comparisons of cumulative error on hour-long sequences would test whether the unified anchor fully eliminates the accumulation problem.

Load-bearing premise

The MLP can produce relative constraints and confidences accurate enough to prevent error accumulation or drift when used for streaming inference over long sequences.

What would settle it

Measuring large pose drift or reconstruction collapse on extended streaming video sequences when the relative mechanism is applied would show the central claim does not hold.

Figures

Figures reproduced from arXiv: 2605.26519 by Anpei Chen, Congrong Xu, Huachen Gao, Jun Gao, Xingyu Chen, Yuliang Xiu.

Figure 1
Figure 1. Figure 1: Consistent, scalable, and efficient streaming geometry via relative pose regression. R3 reconstructs camera poses and dense geometry from unbounded video streams via feed-forward relative pose regression. It maintains local consistency, scales to ultra-long sequences with bounded memory, and runs at 20+ FPS with 372M parameters. the model to emphasize reliable pairs. This enables any registered frame to se… view at source ↗
Figure 2
Figure 2. Figure 2: Three feed-forward pose paradigms, viewed as pose graphs. Edges denote supervised pairwise pose terms; arrowheads encode directional supervision. (a) VGGT [64] fixes the world frame to the first camera and supervises only edges from this anchor to every other camera. (b) π 3 [69] regresses absolute poses in a model-chosen world frame and supervises every unordered pair with uniform weight. (c) R3 drops the… view at source ↗
Figure 3
Figure 3. Figure 3: Overview of R3 . A causal geometry backbone extracts a single camera token from each frame. A lightweight pairwise pose head then predicts directed relative-pose edges from token pairs, along with separate rotation and translation confidences. These confidence-weighted edges are fused into a coherent trajectory, enabling streaming inference with a bounded active keyframe bank. As contrasted in [PITH_FULL_… view at source ↗
Figure 5
Figure 5. Figure 5: Long streaming comparison. Qualitative in-the-wild results show that R3 maintains more consistent trajectories and point-map alignments over hundreds of frames than baselines [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: Pose accuracy scaling on long sequences. We plot ATE for ScanNet [14] and TUM￾dynamics [56] as the number of input frames increases. While several streaming baselines exhibit cumulative drift or trigger out-of-memory (OOM) failures, R3 maintains stable trajectory estimation. We further test pose-only trajectory accuracy on a subset of DL3DV-Benchmark [35] (304–439 frames), which contains wider camera basel… view at source ↗
Figure 6
Figure 6. Figure 6: Reconstruction gallery. Qualitative reconstruction results from R3 in streaming mode across diverse indoor and outdoor scenes. The reconstructed point clouds remain geometrically coherent and visually consistent across varied scene layouts, object scales, and camera trajectories, demonstrating R3 ’s ability to maintain stable scene structure during online reconstruction of long sequences. 16 [PITH_FULL_IM… view at source ↗
Figure 7
Figure 7. Figure 7: reports inference FPS and GPU memory usage under the same 7-Scenes protocol used in Sec. 4.3. Global-regression baselines (e.g., StreamVGGT) either hit OOM or slow sharply as N grows; R3 replaces this O(N2 ) growth with a bounded memory increase and a gentler FPS decline, consistent with the bounded keyframe bank. 200 400 600 800 1000 Number of Input Views 5 10 15 20 F P S ↑ OOM OOM OOM R 3 TTT3R CUT3R Poi… view at source ↗
Figure 8
Figure 8. Figure 8: Learned confidence behaves as pair reliability. Across all pairs from the first 20 ScanNet scenes, pairs are grouped into equal-mass confidence quantile bins; the x-axis is the bin center. The solid line shows the per-bin mean pose error and the shaded band shows the within-bin dispersion, so each polyline reports the average error and spread within that confidence quantile interval. Higher predicted confi… view at source ↗
Figure 9
Figure 9. Figure 9: Bird’s-eye view of a long streaming sequence. Without reset, the trajectory eventually drifts [PITH_FULL_IMAGE:figures/full_fig_p023_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Causal streaming reconstructions. Distant viewpoints, occlusions, and long sequences can [PITH_FULL_IMAGE:figures/full_fig_p023_10.png] view at source ↗
read the original abstract

Recent feed-forward geometry foundation models have demonstrated impressive generalization by recovering depth and poses in a single forward pass. However, these models are typically constrained by a global coordinate frame assumption. This dependency becomes a significant bottleneck for long-context and streaming reconstruction, as it forces the network to maintain an arbitrary temporal origin and handle translation magnitudes that grow unbounded over time. Our solution, which we call $R^3$, employs relative regression. We employ a lightweight MLP to predict confidence-weighted relative constraints. These confidences serve as a unified anchor: weighting losses during training and guiding pose aggregation during inference. $R^3$ supports both full-context offline reconstruction and causal, bounded-memory streaming. Our evaluation in both offline and streaming settings validates the effectiveness of our relative mechanism. Project page: https://kevinxu02.github.io/r3-site

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 0 minor

Summary. The paper proposes $R^3$, a feed-forward 3D reconstruction method that replaces global coordinate frame regression with relative regression. A lightweight MLP predicts confidence-weighted relative constraints; these confidences weight the training losses and, at inference, guide pose aggregation. The method is claimed to support both full-context offline reconstruction and causal streaming reconstruction with bounded memory. Evaluation in both regimes is said to validate the relative mechanism.

Significance. If the confidence-weighted aggregation demonstrably bounds drift, the unified-anchor design would be a practical contribution to long-sequence and streaming reconstruction, removing the need to regress unbounded translations. The idea of reusing the same predicted confidences for both loss weighting and inference-time aggregation is a clean architectural choice.

major comments (1)
  1. [Abstract] Abstract: the central claim that the MLP-predicted confidences prevent unbounded error growth during causal streaming aggregation is load-bearing, yet the text supplies neither the aggregation equations, a drift bound, nor an ablation isolating the confidence mechanism; without these the effectiveness statement cannot be evaluated.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback. We address the single major comment below and will incorporate the requested clarifications in the revised manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that the MLP-predicted confidences prevent unbounded error growth during causal streaming aggregation is load-bearing, yet the text supplies neither the aggregation equations, a drift bound, nor an ablation isolating the confidence mechanism; without these the effectiveness statement cannot be evaluated.

    Authors: We agree that the abstract's claim about bounded error growth in causal streaming would be stronger with explicit technical support. The current manuscript describes the relative regression and the dual use of MLP-predicted confidences for loss weighting and pose aggregation, but does not present the aggregation equations, a drift analysis, or a dedicated ablation in the main text or appendix. In the revision we will (1) add the aggregation equations and a simple drift bound to Section 3, (2) include an ablation isolating the confidence weights in the streaming setting in Section 4, and (3) revise the abstract to reference these additions rather than stating the effectiveness claim without support. These changes directly address the concern. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The abstract and description present R³ as employing relative regression via a lightweight MLP for confidence-weighted constraints that act as a unified anchor, but contain no equations, derivations, self-citations, or fitted parameters renamed as predictions. No load-bearing step reduces to its own inputs by construction. The method is described at a conceptual level with evaluation claimed to validate it, making the derivation self-contained against external benchmarks with no circularity indicators.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only abstract available; no free parameters, axioms, or invented entities can be identified from the given text.

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