Feed-forward models regress dense 3D point trajectories directly from monocular video, yet the residual after global alignment is substantial and lacks a structural explanation. Measured on dynamic query points across models and datasets, the error concentrates along the view direction, while the scale correction each motion group requires differs. The predicted displacement direction nevertheless supports reliable grouping, with a median angle far below the 90° random baseline. The systematic part of the residual is therefore a family of radial degrees of freedom per motion group, along directions 2D observations cannot constrain. We call it group-wise view inconsistency. We present GAUGE (Group-wise Adaptive Unsupervised Gauge Estimation), a training-free and model-agnostic post-hoc module. It recovers motion groups from direction consistency and spatial connectivity, then estimates a per-frame radial scale and group-level translation from 1% to 5% metric anchors, four degrees of freedom per group and frame. On dynamic query points of eight trackers, including D4RT, 4RC and SM4RT, our correction lowers endpoint error by 15.1% to 62.6% over the uncorrected predictions, while spending the same anchors on gradient fine-tuning improves the same models by only -1.1% to 15.2%. Code is publicly available at https://github.com/HCPLab-SYSU/GAUGE.
Figures & tables
Figure 1: Per-group radial scale ambiguity. (a) RGB frame. (b) The prediction appears accurate in the camera view, but (c) seen from the side, it exposes a systematic depth bias along the view direction; (d) grouping recovers this bias as per-group radial scales, and (e) GAUGE removes it.
Figure 2: Error structure. Values in Tables A3 and A13 .
Parameterization
DOF ( T frames)
EPE ↓
No correction
0
0.1812 / 0.1930
Single global scale
1
0.1835 / 0.1927
Per-group Sim(3)
7
0.1528 / 0.1983
GAUGE (ours)
T+3
0.1269 / 0.1597
Table 1: Parameterization comparison under the same grouping and anchors (D4RT).
Figure 3: Pipeline of GAUGE. Any tracker that outputs trajectories and visibility can plug in without retraining. The three blocks in GAUGE show main steps of correction.
Model
Method
PointOdyssey
EPE–Sim(3)
EPE ↓
APD ↑
AJ ↑
Correction
Base
0.1812 / 0.1930
0.6877 / 0.6654
0.1038 / 0.3358
—
D4RT
+GAUGE
0.1269 / 0.1597 ( +29.9 / +17.3 )
0.7648 / 0.7015 ( +11.2 / +5.4 )
0.1214 / 0.3320 ( +17.0 / -1.1)
+15.7 / -2.8
Base
0.1421 / 0.2471
0.7334 / 0.6127
0.0711 / 0.2603
—
4RC
+GAUGE
0.1035 / 0.1470 ( +27.2 / +40.5 )
0.7832 / 0.7332 ( +6.8 / +19.7 )
0.0892 / 0.3172 ( +25.5 / +21.9 )
-29.6 / +12.8
Base
0.1451 / 0.0778
0.7322 / 0.8792
0.1164 / 0.4478
—
Table 2: Main results on PointOdyssey. The Sim(3) column is the seven-degree-of-freedom fit under the same grouping and anchors. Cell values are DQS / Full; improvements (%) are in parentheses.
EPE ↓
APD ↑
AJ ↑
Model
Base
+Ours
Impr. (%)
Base
+Ours
Impr. (%)
Base
+Ours
Impr. (%)
D4RT
0.1345
0.0838
+37.7
0.7783
0.8650
+11.1
0.0180
0.0207
+15.0
4RC
0.1531
0.1154
+24.6
0.7359
0.7970
+8.3
0.0128
0.0144
+12.5
V-DPM
0.1087
0.0758
+30.3
0.8082
0.8491
+5.1
0.0587
0.0646
+10.1
SM4RT
0.1256
0.0930
+26.0
0.7838
0.8331
+6.3
0.0154
0.0160
+3.9
TAPIP3D
0.0915
0.0623
+31.9
0.8351
0.8523
+2.1
0.0403
0.0452
+12.2
Table 3: WorldTrack results averaged over the four subsets under DQS. Averages are unweighted over the evaluated subsets; per-subset values are in Table A1 .
Figure 4: Qualitative comparison on two scenes. Query points are colored by signed depth error. Without grouping the errors scatter ahead of and behind the surface, while D4RT + GAUGE concentrates them better.
Figure 8
Grouping
EPE ↓
APD ↑
AJ ↑
Oracle instance
0.1334 / 0.1159
0.7518 / 0.7717
0.1260 / 0.3913
Direction KNN only
0.1274 / 0.1606
0.7692 / 0.7006
0.1210 / 0.3328
Spatial merge only
0.1271 / 0.1602
0.7693 / 0.6992
0.1213 / 0.3322
Full (Ours)
0.1269 / 0.1597
0.7648 / 0.7015
0.1214 / 0.3320
Table 4: Ablation studies (D4RT) under the camera-center parameterization; the 4RC version is in Appendix Table A10 .
Anchor source
Median error (cm)
Radial fraction
Δ EPE
Ground truth
0
—
29.9%
Visual SLAM keyframes
8.57
0.49
20.6%
Single-frame depth
8.50
1
10.1%
Sparse LiDAR returns
0.81
1
29.2%
Table 5: Effect of anchor source on the gain (D4RT).
Figure 11
Appendix figures & tables17 assets
Supplementary material from the paper’s appendix.
Appendix
Model
Method
ADT
PO
PStudio
DS
EPE ↓
APD ↑
AJ ↑
EPE ↓
APD ↑
AJ ↑
EPE ↓
APD ↑
AJ ↑
EPE ↓
APD ↑
AJ ↑
DQS protocol
D4RT
Base
0.1516
0.7462
0.0398
0.1770
0.7191
0.0187
0.1092
0.8141
0.0094
0.1000
0.8338
0.0039
+Ours
0.1142
0.8025
0.0450
0.1001
0.8152
0.0216
0.0526
0.9482
0.0120
0.0681
0.8941
0.0043
Impr. (%)
+24.7
+7.5
+13.1
+43.4
+13.4
+15.5
+51.8
+16.5
+27.7
+31.9
+7.2
+10.3
4RC
Base
0.2350
0.6687
0.0218
0.1587
0.6944
0.0161
0.1269
0.7955
0.0089
0.0917
0.7850
0.0043
Appendix
Table A1: Per-subset WorldTrack results under the DQS and Full protocols, in the world coordinate frame. ADT and PStudio provide no depth ground truth, so the three depth-dependent models are marked with a dash. Improvements are computed from the ratio of the absolute values in this table. Table 3 in the main text reports the averages over the subsets under DQS.
Model
Status
EPE ↓
APD ↑
AJ ↑
Δ EPE (%)
D4RT
base
0.1812 / 0.1930
0.6877 / 0.6654
0.1038 / 0.3358
—
+TTO
0.1720 / 0.1685
0.7090 / 0.6933
0.1057 / 0.3380
5.1 / 12.7
+Ours
0.1269 / 0.1597
0.7648 / 0.7015
0.1214 / 0.3320
29.9 / 17.3
4RC
base
0.1421 / 0.2471
0.7334 / 0.6127
0.0711 / 0.2603
—
+TTO
0.1419 / 0.2436
0.7358 / 0.6153
0.0863 / 0.2611
0.1 / 1.4
+Ours
0.1035 / 0.1470
0.7832 / 0.7332
0.0892 / 0.3172
27.2 / 40.5
Appendix
Table A2: Comparison with test-time optimization. Three metrics and the relative change in endpoint error for five models under three settings, base, +TTO and +Ours.
Model
Radial energy (%)
Flow direction error ( ∘ )
Between-group scale variance (%)
D4RT
77.7 / 74.8
24.0 / 19.8
62.9 / 74.4
4RC
67.3 / 89.4
38.4 / 31.4
73.7 / 72.2
V-DPM
73.2 / 73.0
35.5 / 37.9
47.6 / 69.7
SM4RT
62.3 / 80.2
64.1 / 62.9
47.9 / 68.1
TAPIP3D
67.9 / 37.9
7.4 / 87.7
59.7 / 15.1
SpatialTrackerV2
37.6 / 44.7
87.8 / 67.0
26.7 / 30.4
Appendix
Table A3: Error structure of the eight trackers. The isotropic baseline of radial energy is 50% and the random baseline of flow direction error is about 90∘ .
Noise σ (cm)
EPE ↓
APD ↑
AJ ↑
Δ EPE vs. clean (%)
base
0.1812 / 0.1930
0.6877 / 0.6654
0.1038 / 0.3358
—
0 (clean)
0.1269 / 0.1597
0.7648 / 0.7015
0.1214 / 0.3320
0.0000 / 0.0000
1
0.1277 / 0.1598
0.7645 / 0.7040
0.1216 / 0.3313
-0.6524 / -0.1072
5
0.1386 / 0.1722
0.7502 / 0.6944
0.1210 / 0.3234
-9.2242 / -7.8694
10
0.1549 / 0.1994
0.7248 / 0.6634
0.1198 / 0.3122
-22.0386 / -24.9011
20
0.2241 / 0.2634
0.6565 / 0.6033
0.1107 / 0.2872
-76.5662 / -64.9686
Appendix
Table A4: Robustness to anchor noise (D4RT). The correction problem is re-solved after applying isotropic Gaussian noise of standard deviation σ to the ground-truth anchor positions; the base row is the uncorrected baseline and σ=0 is the noiseless anchor.
Model
Protocol
1%
2%
5%
10%
20%
50%
100%
D4RT
DQS
0.1399
0.1371
0.1269
0.1312
0.1216
0.1167
0.1289
Full
0.1704
0.1702
0.1597
0.1495
0.1326
0.1300
0.1363
4RC
DQS
0.1048
0.1124
0.1035
0.1004
0.1177
0.1052
0.1095
Full
0.1591
0.1510
0.1470
0.1347
0.1467
0.1253
0.1257
V-DPM
DQS
0.1217
0.0981
0.1086
0.1000
0.1014
0.1115
0.1150
Full
0.0669
0.0641
0.0619
0.0626
0.0595
0.0611
0.0566
Appendix
Table A5: Anchor budget. Endpoint error at each budget level; Appendix Figure A3 plots this curve for D4RT.
Model
Grouping
EPE ↓
APD ↑
AJ ↑
D4RT
Oracle instance
0.1334 / 0.1159
0.7518 / 0.7717
0.1260 / 0.3913
Unsupervised (Ours)
0.1269 / 0.1597
0.7648 / 0.7015
0.1214 / 0.3320
4RC
Oracle instance
0.1091 / 0.1216
0.7655 / 0.7435
0.0777 / 0.3213
Unsupervised (Ours)
0.1035 / 0.1470
0.7832 / 0.7332
0.0892 / 0.3172
V-DPM
Oracle instance
0.1194 / 0.0549
0.7871 / 0.9071
0.1043 / 0.4674
Unsupervised (Ours)
0.1086 / 0.0619
0.8091 / 0.9077
0.1164 / 0.4634
Appendix
Table A6: Unsupervised grouping versus oracle instance grouping. On PointOdyssey, the three metrics of the eight trackers when the correction switches from oracle instances to the unsupervised motion grouping of this paper; the Unsupervised row is the result of applying GAUGE in Table 2 of the main text. Instance labels are used only in the Oracle instance row.
Model
Δ EPE (%)
Resampling std (%)
Paired bootstrap 95% CI (%)
D4RT
28.70
1.0
[18.2, 39.3]
4RC
19.7
3.8
[16.8, 40.2]
V-DPM
18.6
2.4
[8.0, 28.8]
SM4RT
20.4
8.3
[5.4, 36.2]
TAPIP3D
31.2
1.2
[17.4, 45.8]
SpatialTrackerV2
9.4
3.2
[-3.1, 20.8]
Appendix
Table A7: Resampling dispersion. These values use a different estimator from the improvement in Table 2 of the main text and are not directly comparable.
Model
P25 (%)
P50 (%)
P75 (%)
Seq. with gain (%)
D4RT
19.3
31.0
41.7
92.3
4RC
-16.9
36.6
50.8
66.7
V-DPM
-3.6
18.4
37.5
53.8
SM4RT
-3.9
22.7
38.4
66.7
DELTA
43.8
60.2
65.2
100.0
TAPIP3D
8.7
28.6
65.0
91.7
Appendix
Table A8: Distribution of per-sequence endpoint error improvement. The quantiles use a different estimator from the improvement in Table 2 of the main text and are not directly comparable.
Median wall (s)
P95 wall (s)
Median CPU (s)
Peak RSS (MiB)
Extra RSS (MiB)
0.490 / 2.601
3.181 / 35.183
0.490 / 2.600
594.109 / 769.656
0.742 / 29.688
Appendix
Table A9: Post-processing cost. Timings in seconds per sequence, from a single core whose frequency scales dynamically between 1.50 and 3.71 GHz; each cell gives DQS / Full. No GPU, autograd or optimizer is used.
Grouping Method
EPE ↓
APD ↑
AJ ↑
No grouping (global)
0.1370 / 0.2427
0.7511 / 0.6217
0.0716 / 0.2651
Oracle instance
0.1091 / 0.1216
0.7655 / 0.7435
0.0777 / 0.3213
Full (Ours)
0.1035 / 0.1470
0.7832 / 0.7332
0.0892 / 0.3172
Appendix
Table A10: Ablations repeated on 4RC. Configurations are taken from Table 4 in the main text. The two forms that scale about an in-group anchor were not repeated on 4RC, and the single-form-on-all-groups and pure-translation rows report endpoint error only. In (c), AE is the average per-anchor efficiency accumulated to that budget, defined as in Table A5 .
Configuration
EPE ↓
APD ↑
AJ ↑
TAPIP3D (GT depth input)
0.1548
0.7600
0.1560
TAPIP3D (GT depth input) + Ours
0.0966
0.8365
0.1576
TAPIP3D (predicted depth input)
1.6705
0.0565
0.0319
TAPIP3D (predicted depth) + Ours
0.6949
0.3639
0.0651
Appendix
Table A11: Depth input versus post-hoc correction. Three metrics of TAPIP3D before and after correction under two input conditions, ground-truth depth and predicted depth; DQS only.
Model
Predicted-motion gain %
GT-motion gain %
Δ (pp)
Jaccard
D4RT
30.5
30.5
-0.01
0.7
4RC
16.5
37.6
-21.11
0.59
V-DPM
23.6
29.4
-5.88
0.71
SM4RT
83.4
24.6
58.82
0.16
SpatialTrackerV2
30.4
36.1
-5.69
0.35
TAPIP3D
34.5
38.3
-3.80
0.61
Appendix
Table A12: Screening control with ground-truth motion magnitude. Gain in endpoint error after redoing the dynamic query screening with ground-truth motion magnitude in place of the predicted value; Δ is the predicted-motion gain minus the ground-truth one and Jaccard is the overlap of the two selected point sets. These gains are computed on motion-screened point sets and are not comparable with the DQS improvement in Table 2 of the main text.
Model
Protocol
Observed
Null mean
Null p95
Excess over p95
D4RT
DQS
62.94
12.39
30.97
28.24
Full
74.36
11.03
12.38
51.09
4RC
DQS
73.65
12.81
24.09
48.54
Full
72.17
4.52
12.8
60.92
V-DPM
DQS
47.64
16.83
32.52
24.05
Full
69.67
4.42
7.17
47.95
Appendix
Table A13: Null hypothesis test. The tested statistic is the between-group scale variance, that is, the between-group difference in per-point optimal radial scale that unsupervised grouping can explain; the definition is given in Appendix A.3 . The null model keeps the size of each group unchanged and randomly permutes the point-to-group labels, one hundred times per sequence.
Figure A1: Failure prediction. Relative endpoint error improvement against between-group scale variance, one point per model, split and protocol. The gray line is the least-squares fit over the 58 points and the band its 95% confidence interval.
Figure A2: Heatmap of relative endpoint error improvement.
Model
Protocol
Baseline
GAUGE 5%
Ceiling
D4RT
DQS
0.1812
0.1269
0.1167
Full
0.1930
0.1597
0.1300
4RC
DQS
0.1421
0.1035
0.1004
Full
0.2471
0.1470
0.1203
V-DPM
DQS
0.1451
0.1086
0.0994
Full
0.0778
0.0619
0.0566
Appendix
Table A14: Error budget. The upper bound from fitting radial scale and translation per group and per frame on all ground-truth points, against what GAUGE achieves with 5% anchors.
Figure A3: Anchor budget of D4RT. (a) Endpoint error and (b) average accumulated per-anchor efficiency.
We introduce Point4D, a feed-forward model for 4D reconstruction of long-range video sequences. Point4D is able to reliably infer dense per-point 3D trajectories across multi-hundred-frame videos, unlike existing 4D methods that are limited to short input windows of at most a few dozen frames. A key innovation that enables this is our flexible 3D query-based motion decoder that decouples trajectory prediction from image-plane visibility. The predicted 3D endpoints are then directly re-queried in the next chunk without re-projection or matching. Furthermore, we show that extracting and reusing a visual descriptor from an arbitrary frame where the point is visible leads to better performance than relying solely on the source patch. Overall, Point4D achieves state-of-the-art performance across diverse long-video tracking benchmarks spanning over 200 frames and largely outperforms previous feed-forward 4D method. Project page: https://point-4d.github.io
Dynamic scene reconstruction from monocular video remains a fundamental challenge in computer vision. Existing feed-forward methods predict 3D Gaussians pixel-wise for each frame, suffering from duplicated Gaussians and view-dependent biases that hinder effective learning of scene motion. We present C4G, a feed-forward 4D reconstruction framework built upon a compact set of timestamp-conditioned learnable Gaussian query tokens. Each token aggregates corresponding features across the full temporal context and decodes a 3D Gaussian whose position is modulated by the target timestamp, enabling globally coherent motion modeling without per-scene optimization. To capture fine-grained details, we further introduce a video diffusion model-based rendering enhancement module. Since our framework effectively aggregates features into Gaussians, we extend this capability to feature lifting, producing a 4D feature field that supports point tracking and dynamic scene understanding. C4G achieves strong novel-view synthesis performance using significantly fewer Gaussians and without requiring camera poses, while exhibiting stronger motion modeling and robustness to large temporal gaps.
Recent feed-forward 3D gaussian splatting methods have made dramatic progress on individual aspects of 3D scene reconstruction, but no existing method jointly addresses dynamic content, multi-view input, and unknown camera poses in a single feed-forward pass. Methods that handle dynamics either require accurate camera poses or accept only monocular input; pose-free multi-view methods address only static scenes; and per-scene optimization methods bridge some of these gaps but at minutes-to-hours cost per scene. We introduce NoPo4D, the first feed-forward system that addresses this empty quadrant. Building on a pretrained geometry backbone and recent 4D Gaussian frameworks, NoPo4D introduces a velocity decomposition that splits Gaussian motion into per-pixel image-plane shifts and depth changes, allowing direct supervision from pseudo ground-truth optical flow on the 2D component. This sidesteps both the differentiable rendering that couples prior posed methods to pose accuracy and the 3D motion ground truth that prior pose-free methods require. The system is rounded out by a bidirectional motion encoder for cross-view and cross-frame feature aggregation, and view-dependent opacity that mitigates cross-view and cross-timestep Gaussian misalignments. On four multi-view dynamic benchmarks, NoPo4D consistently outperforms prior feed-forward baselines, and with an optional post-optimization stage surpasses per-scene optimization methods, while running orders of magnitude faster.