A Straight Line Is Not a Camera Pose: Auditing Short-Clip Pose Benchmarks

Xinyi Shi

cs.CVOct 31, 2026

A Straight Line Is Not a Camera Pose: Auditing Short-Clip Pose Benchmarks

Authors: Xinyi Shi

Organizations: Duke University

Abstract

The absolute trajectory error (ATE) is the standard measure of camera-motion accuracy, from SLAM to feed-forward 3D reconstruction. On the common Sintel protocol, an image-free constant-velocity line has a lower mean ATE than 10 of 11 recent models re-run with official code and than 85 of 110 published methods. On Lightspeed it beats 5 of 9 models and 10 of 11 published methods, while on TUM, ScanNet, DyCheck and ADT every model beats it. Two properties of ATE's alignment explain this. First, it maps any moving constant-velocity prediction onto the line that best fits the true path, so the line scores the path's regression residual. A residual signal-to-noise ratio (SNR) criterion tells when moving a prediction towards its constant-velocity fit lowers ATE. With the alignment's first-order refit, it accounts for the outcome of all but one of 4010 model-clip evaluations, including all 504 on three benchmarks registered before any model ran. The true path's straightness flags Sintel and Lightspeed. Second, the alignment ignores where cameras look: rotating a trajectory by 30 degrees against its orientations leaves ATE unchanged yet worsens the static-point reprojection of every model on Sintel, TUM and ScanNet, and the line reprojects worst on Sintel by geometric mean. Fitting the alignment's rotation to the predicted orientations gives pose-anchored ATE (PA-ATE), a one-function change at about ATE's cost (37 vs. 34 $μ$ s per clip, and 61 vs. 66 $μ$ s with the rotation error). It is never below ATE and, as we prove, equals the translational relative pose error over all frame pairs divided by $\sqrt{2}$ when the orientations agree. It ranks every image-free reference below every model on Sintel, follows the reprojection error where ATE does not, and largely preserves the models' order. Its rotation error also exposes Lightspeed ground-truth orientations that the images contradict.

Figures & tables

	Sintel (14 clips)					TUM	ScanNet
Method	ATE	half	cl.	PA-ATE	RPE r	ATE	ATE
$\pi^{3}$	0.082	0.081	5	0.131	0.284	0.015	0.030
Line (no img.)	0.092	–	–	0.540	0.964	0.148	0.232
DA3-Giant	0.112	0.092	7	0.163	0.347	0.012	0.032
$\pi^{3}$ X	0.113	0.097	5	0.171	0.265	0.011	0.030
DA3-Base	0.133	0.103	11	0.193	0.936	0.029	0.059

Table 1: Rows: the 11 models we re-ran with their official code, ordered by Sintel ATE, and the image-free constant-velocity line; below, five methods added later ( † ). Columns: errors under the official protocol, lower is better, on Sintel, TUM (8 clips) and ScanNet (94). More in the appendix. Half: ATE after half straightening. Cl.: Sintel clips (of 14) on which half straightening lowers the ATE. PA-ATE: pose-anchored ATE ( Sec. 6 ); for the line, constant orientation and the one camera-axis direction, of six, with the lowest mean. Our CUT3R values (0.211; ScanNet 0.097) are close to the published 0.213 and 0.099 [ 74 ] . † Added after the main analysis, official environments, not in Tabs. 2 , 4 and 5 ; published values [ 86 , 6 , 15 , 77 , 81 , 85 , 48 ] in the appendix.

Figure 2: Published Sintel ATE values admitted by our inclusion rule (appendix), one per method paper (its best variant), by the method’s first arXiv date; open markers: 29 later re-evaluations. No admitted value in the window published before July 2025 lies below the line (MegaSaM’s open marker is a Dec 2025 re-evaluation; MONA, excluded by inference from LEAP-VO’s code, would be the only such value; appendix). Offline and streaming: feed-forward models; other: optimisation-based and SLAM/VO methods. Red: the line, 0.0915.

			models gaining			median
Benchmark	clips	$R^{2}_{\text{line}}$	predicted	observed	ratio	SNR
Sintel (official)	14	0.99	10	11	0.78	0.86
TUM (official)	8	0.51	0	0	2.65	6.1
ScanNet (official)	94	0.67	0	0	2.25	5.7
Bonn, full	5	0.36	0	0	1.45	2.7
Wild-SLAM, full	10	0.23	0	0	6.66	27

Table 2: Half straightening (

\alpha=0.5

in Eq. 1 ) on eight benchmarks (rows): five for the 11 models and, below, three registered before 9 models ran on them ( Sec. 4.3 ).

R^{2}_{\text{line}}

: median over clips, from ground truth. Models gaining: of the 11 (below: of the 9), those whose mean ATE decreases. Predicted: by Eq. 5 from each pair’s

S

N

and

c

before straightening. Observed: after it (clip-bootstrap 95% interval on Sintel 5–11). Ratio: median over models of ATE after / before. SNR: median over model–clip pairs of the residual SNR ( Eq. 4 ). Bonn: camera poses via its calibration.

Figure 3: Effect of half straightening ( Eq. 1 ) against residual SNR ( Eq. 4 ), for every development pair and every pair of the three benchmarks registered later (outlined markers, Sec. 4.3 ). The SNR is divided by the threshold of Eq. 5 with each pair’s measured

c

, so the threshold is at 1 (dashed). Below the horizontal line, straightening lowers the ATE.

				correct (%)
Set	pairs	SNR	gain	$R^{2}_{\text{line}}$	error	$c=0$	criterion	+refit
Development	1056	7.4	20	84	88	94	95	99.9
Held-out	792	2.6	38	61	62	90	98	100
ScanNet	1034	5.7	5	94	94	95	97	100
Added methods	624	4.5	14	89	84	90	97	100
PA-ATE	352	3.3	32	80	77	92	97	100

Table 3: Every test of the straightening criterion, per model–clip pair. Rows: the development pairs, the KITTI and 7-Scenes windows registered before any model ran (per setting in the appendix), the registered ScanNet test, methods added later, the criterion applied to PA-ATE on Sintel, TUM and Wild-SLAM, and three benchmarks registered before any model ran on them, with 9 models ( Sec. 4.3 ). SNR: median residual SNR ( Eq. 4 ). Gain: % of pairs whose ATE falls under half straightening. Correct: % of pairs whose outcome after refitting is given by a threshold, fitted on the development pairs, on the true path’s straightness alone or on the model’s error

N

(divided by the true centres’ RMS distance from their mean) alone, and by Eq. 5 with

c=0

(threshold

\sqrt{3}

) or the measured

c

(criterion), and by the criterion with the refit’s first-order term (+refit, appendix). Added methods: MonST3R and the four later methods of Tab. 1 , LASER and AnyCam in two configurations each (appendix).

	Sintel (14 clips)			TUM (8)			ScanNet (94)
Score	rank	rot.	str.	rank	rot.	str.	rank	rot.	str.
ATE	2	0	10	12	0	0	12	0	0
PA-ATE	12	11	6	12	11	0	12	11	0
reprojection error	11	11	3	12	11	0	12	11	0

Table 4: Rows: three scores, with arithmetic means over clips as in the protocol. PA-ATE: pose-anchored ATE ( Sec. 6 ). Reprojection error: of static points, pairs 5 frames apart. Columns: three tests on each benchmark. Rank: the image-free line’s rank among itself and the 11 models (of 12, 12 is last). Rot.: of the 11 models, those whose score worsens when their centres are rotated by 30 ∘ about their centroid and the

y

-axis of the world frame, orientations kept. Str.: of the 11 models, those whose score improves when their positions are replaced by their constant-velocity fit (

\alpha=1

). Under geometric means the line ranks 4th by ATE but last under both other scores on Sintel, and none of the 11 models reprojects better when straightened (TUM and ScanNet unchanged). Ranges over 26 settings of gap, filter and scale (4 on ScanNet) in the appendix.

Figure 4: ATE against static-point reprojection error (geometric means over clips). Filled: each model; open: its prediction with the centres rotated by 30 ∘ against its orientations (same ATE). The line has a low ATE on Sintel but reprojects worst of all unmodified predictions on both (arithmetic means in the appendix).

Score	rotation	form	alone	+rot.	$>$ ref	flips	$\tau_{\text{ref}}$
	detects	ATE’s	µs per clip
ATE (positions)	$\times$	$\checkmark$	34	66	1	22	.54
ATE’s rotation error	$\checkmark$	$\times$	66	–	–	0	.54
RPE t , 1 frame	$\checkmark$	$\times$	40	68	3	18	.69
RPE t , 10 frames	$\checkmark$	$\times$	38	66	11	9	.65
DTE [ 40 ]	$\checkmark$	$\times$	$1.3{\times}10^{5}$	–	11	9	.65

Table 5: Rows: six scores. Columns: tests on Sintel with the 11 models. ATE’s rotation error: the rotation error under ATE’s alignment. Detects rotation: true centres rotated by 20 ∘ against the orientations score worse than the truth. ATE’s form: an RMS position error under one global alignment. µs per clip: one CPU thread, alone and with the rotation error under the same alignment (+rot.: RPE r for RPE t , –: none; ATE’s rotation error includes ATE; method in the appendix).

>

ref: of the 11 models, those beating every image-free reference (six camera-axis lines and, except for DTE, a static camera; –: undefined, as these positions do not fix the rotation). Flips: of 55 model pairs, those whose order reverses when only the weaker model is half straightened.

\tau_{\text{ref}}

: Kendall

\tau

with the models’ mean ATE rank on TUM and full Wild-SLAM, from other data, not a true ranking. Arithmetic means over clips.

Appendix figures & tables22 assets

Supplementary material from the paper’s appendix.

Appendix

Development
			correct (%)
Set	pairs	SNR	$R^{2}_{\text{line}}$	error	$c=0$	criterion	+refit	gains	certified
Sintel	154	0.86	69	63	98	97	100	108	104
TUM	88	6.1	81	92	93	95	100	17	13
TUM-X	330	11	85	94	94	91	100	37	8
Bonn	154	2.6	75	73	86	95	99.4	38	30

Appendix

Table S1: All rows of Tab. 3 , with the development benchmarks by dataset (all windows). Correct (%): straightness alone (gain if

R^{2}_{\text{line}}\geq 0.9513

), error alone (gain if

N/r\geq 0.3165

r

the RMS radius of the true path), each threshold the one with the highest accuracy on the development pairs (smallest such value on ties); Eq. 5 with

c=0

and with the measured

c

, and the criterion with the refit’s first-order term (+refit, the refit term in Appendix S1 ). Gains: pairs whose ATE falls under half straightening; certified: those that Eq. 5 with the measured

c

identifies. The condition is sufficient, not necessary, after refitting, so a pair it does not certify is not predicted to lose. Missed gains are typically smaller: a median ATE decrease of 6.2%, against 36.4% for certified gains, on the development and held-out pairs (ScanNet: 13.3% against 23.2%).

Method	ATE	method date	source	value	14	Sim(3)	note
UniQuery4R	0.0310	2026-08	2608.17283	own	–	–	d
VGGT-Omega	0.0400	2026-05	median of 5	re-eval.	0	1	d
GenCeption (Specialist - L)	0.0500	2026-07	2607.09024	own	–	–
PURE (DA3)	0.0520	2026-10	2610.14698	own	–	yes
SpatialTrackerV2	0.0540	2025-07	2507.12462	own	–	yes	g
LASER (Pi3)	0.0610	2025-12	2512.13680	own	–	yes

Appendix

Table S2 : The 110 points of Fig. 2 , one per method paper (its best variant), sorted by ATE; values to four decimals (medians where several). The line scores 0.0915, so a published 0.092 lies above it, and 85 points lie above it. Method date: first arXiv version of the method. Value: the method’s own value (own) or the median of re-evaluations (re-eval.). Source: the paper that reported the value, or the number of re-evaluations whose median is used when the method’s own paper reports none. 14 and Sim(3): whether the source states the 14 clips and a similarity (scale) alignment (for a median: in how many of its sources, the number in the source column). Notes: a: the source’s CUT3R row (0.086) lies below all 26 other CUT3R values (0.134–0.235); b: the source does not state its Sintel clips for pose, and uses 18 clips for depth; c: the source compares with AnyCam’s mean error and may report a mean; d: the source’s VGGT row (0.100) lies far below the median of 30 other VGGT values (0.171), and our run of UniQuery4R’s released model scores 0.033; e: the source states a “slightly revised” setup without details; f: the source’s VGGT4D row equals VGGT4D’s subset-clip value; g: the source’s VGGT row (0.082) lies far below the median of 30 other VGGT values (0.171), and our run of SpatialTrackerV2’s released full pipeline scores 0.115, two re-evaluations 0.126 and 0.133. Excluded sources: Tab. S3 .

Source (arXiv)	lowest	exclusion basis	methods
2602.24290	0.012	two-frame inputs, ground-truth intrinsics	UFO-4D
2411.13291	0.015	9 of the 14 clips	DATAP-SfM (COLMAP subset)
2605.12774	0.017	18 clips, scale-normalised (MegaSaM setup)	DROID-SLAM, MegaSaM, VGGT, ViPE, WildGS-SLAM, WildPose, pi3
2412.04463	0.018	18 clips, scale-normalised (MegaSaM setup)	ACE-Zero, ACE-Zero (calibrated), CasualSAM, CasualSAM (calibrated), LEAP-VO (calibrated), MegaSaM, MegaSaM (calibrated), MonST3R, ParticleSfM, ParticleSfM (calibrated), RoDynRF, RoDynRF (calibrated)
2512.06868	0.019	CasualSAM/MegaSaM setup, cm units	BA-Track, DynSLAM-3DPrior, WildGS-SLAM
2605.10525	0.020	video-depth protocol; ATE undefined	DA3 (GemDepth), GemDepth, VGGT (GemDepth)

Appendix

Table S3 : The 35 excluded sources and their exclusion bases, sorted by their lowest excluded value (88 values in all; results/lit_excluded_v2.csv).

Clip	$\pi^{3}$	$\pi^{3}$ X	VGGT	DA3-S	DA3-B	DA3-L	DA3-G	MapAny.	CUT3R	TTT3R	StrVGGT	Line
alley_2	0.007	0.013	0.009	0.036	0.032	0.010	0.006	0.032	0.030	0.025	0.033	0.039
ambush_4	0.045	0.059	0.168	0.145	0.086	0.062	0.063	0.109	0.162	0.158	0.139	0.110
ambush_5	0.038	0.023	0.043	0.104	0.086	0.044	0.039	0.083	0.073	0.073	0.095	0.032
ambush_6	0.042	0.045	0.155	0.257	0.305	0.146	0.212	0.295	0.292	0.242	0.255	0.129
cave_2	0.257	0.922	1.195	0.554	0.335	0.892	0.704	1.195	0.940	1.071	0.968	0.270
cave_4	0.022	0.018	0.095	0.133	0.101	0.041	0.011	0.110	0.154	0.146	0.080	0.046

Appendix

Table S4 : Per-clip ATE on the 14 Sintel clips (official protocol). Line: the line along the optical axis (all six axis directions give the same ATE).

Clip	$\pi^{3}$	$\pi^{3}$ X	VGGT	DA3-S	DA3-B	DA3-L	DA3-G	MapAny.	CUT3R	TTT3R	StrVGGT	Line
alley_2	0.013	0.014	0.011	0.051	0.039	0.018	0.006	0.034	0.040	0.034	0.041	0.479
ambush_4	0.047	0.059	0.169	0.168	0.116	0.067	0.071	0.129	0.177	0.175	0.159	0.177
ambush_5	0.073	0.084	0.069	0.109	0.096	0.093	0.062	0.086	0.080	0.073	0.110	0.253
ambush_6	0.048	0.050	0.185	0.288	0.315	0.155	0.300	0.303	0.310	0.289	0.258	0.138
cave_2	0.570	1.223	1.223	0.948	0.867	1.222	1.031	1.223	1.208	1.223	1.223	1.223
cave_4	0.028	0.025	0.096	0.200	0.157	0.045	0.017	0.164	0.207	0.186	0.120	0.250

Appendix

Table S5 : Per-clip PA-ATE on the 14 Sintel clips (official protocol). Line: constant orientation, along the one camera-axis direction (of six) with the lowest mean, as in Tab. 1 .

Figure S1 : Direction of travel (the constant-velocity fit of the camera centres) expressed in each frame’s camera axes, as an azimuth in the camera’s horizontal plane (0 ∘ : along the optical axis). (a) alley_2:

\pi^{3}

’s prediction and the same prediction with its centres rotated by 30 ∘ against its orientations, which has the same ATE. (b) temple_3:

\pi^{3}

X, best of the eleven models by ATE, and DA3-Giant, best by PA-ATE.

	line beats	ATE		PA-ATE
Clip left out	(ATE)	gain	rev.	gain	rev.
none (all 14)	10	11	22	8	10
alley_2	10	11	22	8	10
ambush_4	10	11	22	8	11
ambush_5	10	10	21	8	10
ambush_6	10	11	23	8	10

Appendix

Table S6 : Leaving out one Sintel clip at a time (means over the remaining 13). Line beats: models with a higher mean ATE than the line. Gain: models improved by half straightening. Rev.: of 55 pairwise orders, those reversed when only the weaker model is straightened.

		arithmetic mean over clips					geometric mean over clips
Score	rot.	$>$ ref	gain	rev.	split	$\tau_{\text{ref}}$	$>$ ref	gain	rev.	split	$\tau_{\text{ref}}$
ATE (positions)	$\times$	1	11	22	.46	.54	3	7	14	.74	.80
rotation error	$\checkmark$	–	2	0	.19	.54	–	4	0	.44	.76
RPE t , 1 frame	$\checkmark$	3	11	18	.54	.69	3	11	23	.81	.69
RPE t , 10 frames	$\checkmark$	11	6	9	.38	.65	11	7	10	.71	.83
DTE [ 40 ]	$\checkmark$	11	8	9	.50	.65	11	7	8	.66	.83

Appendix

Table S7: All six scores of Tab. 5 on the Sintel tests (11 models), means over the 14 clips. Rotation error: under ATE’s alignment. Rot.: detects true centres rotated by 20 ∘ against the orientations.

>

ref: models beating every image-free reference (lines along the six camera axes and, except for DTE, a static camera); –: undefined. Gain: models improved by half straightening. Rev.: of 55 orders, those reversed when only the weaker model is straightened. Split: mean Kendall

\tau

between the rankings on two halves of the clips (all 1,716 splits).

\tau_{\text{ref}}

\tau

with the mean ATE rank on TUM and full Wild-SLAM, a reference from other data, not a true ranking. On TUM and Wild-SLAM no model gains under ATE, RPE t over 10 frames, DTE or PA-ATE.

Score	Over clips	gaining	reversals	$\tau_{\text{ref}}$
ATE	arithmetic mean	11	22	0.54
ATE	median	4	8	0.80
ATE	geometric mean	7	14	0.80
PA-ATE	arithmetic mean	8	10	0.69
PA-ATE	median	3	1	0.91
PA-ATE	geometric mean	7	8	0.83

Appendix

Table S8: Sintel, eleven models, straightening at

\alpha=0.5

. Gaining: of the 11 models, those whose aggregate score improves. Reversals: of the 55 pairwise orders, those that flip when only the weaker model is straightened.

\tau_{\text{ref}}

: Kendall

\tau

with the mean rank on TUM and full Wild-SLAM (clip-bootstrap 95% intervals, in row order, 0.24–0.87, 0.57–0.91, 0.65–0.94, 0.35–0.91, 0.50–0.94, 0.69–0.94; paired interval of the difference under geometric means

-0.07

to 0.19; tools/tauref_gain_ci.py, tools/tauref_gmean_ci.py).

Score	$>$ ref	gain	rev.	split	$\tau_{\text{ref}}$
ATE (positions)	4	4	8	.61	.80
rotation error	–	3	0	.06	.65
RPE t , 1 frame	3	11	18	.67	.69
RPE t , 10 frames	11	3	4	.68	.91
DTE	11	5	3	.55	.69
PA-ATE	11	3	1	.59	.91

Appendix

Table S9: Table S7 with medians over clips (tools/comparison_table_median.py). The conclusions are those of the arithmetic and geometric means: the three orientation-aware scores other than the rotation error and consecutive-frame RPE t rank every image-free reference below every model, and fewer orders reverse under them than under ATE.

Figure S2 : Known-answer test on ground-truth trajectories: camera centres rotated about their centroid against the camera orientations, about a fixed axis. Median over clips and the three axes, in units of the trajectory’s RMS radius.

	Sintel		TUM		Wild-SLAM
Added orientation error	chordal	$L_{1}$	chordal	$L_{1}$	chordal	$L_{1}$
none	1.00	1.00	1.00	1.00	1.00	1.00
per-frame noise 5 ∘	0.98	0.99	1.00	1.00	0.99	0.98
constant bias 5 ∘	0.96	0.96	0.89	0.89	0.89	0.85
drift 5 ∘	0.96	0.96	0.93	0.93	0.96	0.93
drift 15 ∘	0.93	0.93	0.85	0.85	0.85	0.89

Appendix

Table S10 : Stability of the PA-ATE ranking of the 11 models when the predicted orientations are perturbed: Kendall

\tau

with the unperturbed ranking, mean over 5 seeds. Each perturbation multiplies the predicted orientations on the right (in the camera frame). Random rotations are the exponential map of a zero-mean isotropic Gaussian rotation vector, scaled to the stated RMS norm: per-frame noise, an independent rotation per frame of RMS norm 5 ∘ ; constant bias, 5 ∘ about the camera

y

-axis for every frame; drift, a rotation about the camera

y

-axis growing linearly from 0 to 5 ∘ or 15 ∘ over the clip; outlier frames, 10% of the frames, chosen at random, each rotated by a random rotation whose RMS norm is drawn uniformly from 30 ∘ to 90 ∘ per frame; burst, one contiguous block of 20% of the frames at a random position, all rotated by one random rotation of RMS norm 20 ∘ . Chordal: the closed-form anchor of Eq. 6 , used throughout.

L_{1}

: a robust geodesic

L_{1}

rotation average (iteratively reweighted) as the anchor (results/package1/stress_summary.csv).

		arithmetic mean over clips					geometric mean over clips
Score	rot.	$>$ ref	gain	rev.	split	$\tau_{\text{ref}}$	$>$ ref	gain	rev.	split	$\tau_{\text{ref}}$
joint fit (positions + orientations)	$\checkmark$	11	8	14	.46	.65	11	7	9	.72	.87
APE, full pose (evo)	$\checkmark$	11	8	3	.23	.65	11	4	0	.46	.76
first-frame alignment	$\checkmark$	11	7	5	.38	.57	11	7	9	.63	.87
$1-$ AUC@30 (RRA/RTA)	$\checkmark$	11	11	11	.60	.76	11	11	15	.73	.76
PA-ATE ( Tab. 5 )	$\boldsymbol{\checkmark}$	11	8	10	.47	.69	11	7	8	.74	.83

Appendix

Table S11: Further scores under the tests and column definitions of Tab. S7 (Sintel, 11 models; medians in results/package1/alt_scores_table.csv). Joint fit: one similarity fitted to positions and orientations together, with the orientation term weighted by the squared RMS radius [ 62 ] ; APE, full pose: the error of the whole pose after the position alignment, which mixes position and rotation units; first-frame alignment: the alignment fixed by the first pose, with a least-squares scale; AUC@30: area under the accuracy curve of the larger of the relative rotation and translation-direction errors over all frame pairs, up to 30 ∘ [ 71 ] , reported as

1-

AUC so that lower is better (results/package1/alt_scores_table.csv).

Data	filter	gap	scale	ATE	reproj.	reproj. worse	ATE	reproj.
				line rank		rotated	straightened better
Sintel	depthonly_d2	1	median ratio	2	11	11	10	3
Sintel	depthonly_d2	5	median ratio	2	10	11	10	4
Sintel	depthonly_d2	10	median ratio	2	11	10	10	6
Sintel	f1_d2	1	median ratio	2	11	11	10	2
Sintel	f1_d2	1	umeyama	2	11	11	10	6

Appendix

Table S12 : Reprojection results over all 26 settings (means over clips, full predicted poses). Filters: f1/f2, flow threshold 1 or 2 px; d2/d5 (Sintel) and d3/d5 (TUM), depth tolerance in %; p, TUM person masks; depthonly, depth check only. Scale: median ratio of displacements or the Umeyama scale. Rotated: models whose reprojection error rises when the centres are rotated by 30 ∘ against the orientations. Straightened: models improved by full straightening (

\alpha=1

Figure S3 : As Fig. 4 , with arithmetic means over clips on both axes. The line ranks 2nd of 12 by ATE on Sintel. Only DA3-Small has a larger mean reprojection error (84 px), set by points it places behind the camera on cave_2. Rotating centres against orientations leaves ATE unchanged and raises the reprojection error of every model.

Figure S4 : Within-clip Spearman correlation between each score and the static-point reprojection error of the frame pairs at each gap, over the 11 models’ predictions with their rotated and straightened versions (as in Tab. S13 ), mean over clips. Gaps covered by fewer than half of a dataset’s clips are not drawn. On TUM and ScanNet one frame gap is 0.1 s.

			RPE t ,			PA-ATE $-$ ATE,
	predictions	ATE	10 fr.	DTE	PA-ATE	95%
Sintel	unmodified	0.59	0.71	0.63	0.64	$-0.01$ to $+0.11$
	+ rotated	0.34	0.65	0.64	0.63	$+0.15$ to $+0.44$
	+ rotated, straightened	0.32	0.62	0.61	0.61	$+0.16$ to $+0.45$
TUM	unmodified	0.84	0.87	0.86	0.86	$-0.01$ to $+0.07$
	+ rotated	0.62	0.78	0.76	0.75	$-0.06$ to $+0.35$

Appendix

Table S13: Within-clip Spearman correlation between each score and the static-point reprojection error (pairs 5 frames apart) over the 11 models’ predictions, mean over clips (Sintel 14, TUM 8, ScanNet 94). RPE t over 10 frames and DTE are the other scores of Tab. 5 that rank every image-free reference below every model. Last column: clip-bootstrap percentile interval of PA-ATE minus ATE. Clips, not predictions, are resampled, since the rotated and straightened versions of a model are not independent samples. Rotated: centres rotated by 30 ∘ against the orientations. Straightened: half and full straightening (tools/score_geometry.py; results/reprojection_full/score_geometry.json).

All pairs, full reprojection (%)
	Sintel	TUM	ScanNet
model pairs (clip $\times$ pair)	770	440	5170
same choice (%)	88.2	92.7	91.4
effect	$+$ 0.8	$+$ 0.2	$-$ 0.6
95% interval	$-$ 1.2 to $+$ 2.8	$-$ 0.6 to $+$ 1.0	$-$ 1.2 to $-$ 0.04
All pairs, translation-only (%)

Appendix

Table S14: Reprojection error of the model each score picks, PA-ATE against ATE. Positive values favour PA-ATE. Exploratory, post hoc.

	KITTI, 2 s		KITTI, 10 s
Image-free line	ATE	PA-ATE	ATE	PA-ATE
forward (optical axis)	0.204	0.278	2.96	3.26
backward, sideways and up	0.204	5.73	2.96	30.2

Appendix

Table S15: Constant-velocity lines with constant orientation, along four camera-frame directions; mean over the 22 KITTI windows of each length, in metres. For the three wrong directions the fitted scale is zero, so the score is the trajectory’s RMS radius.

	KITTI window
Score	2 s	10 s	30 s	60 s
ATE	7	8	4	2
RPE t , 10 frames	9	6	2	1
DTE	6	8	4	2
PA-ATE	7	7	3	2
rotation error under the anchor	11	11	11	11

Appendix

Table S16: Of the 11 models, those whose mean score over the KITTI windows (22 at 2 and 10 s, 20 at 30 and 60 s) is below that of the forward line, a constant-velocity line along the optical axis with constant orientation.

	Lightspeed (36 clips)			DyCheck (12)		ADT (8)
Model	ATE	half	PA-ATE ∗	ATE	PA-ATE	ATE	PA-ATE
VGGT- $\Omega$	0.028	0.056	0.011	0.005	0.005	0.010	0.011
$\pi^{3}$ X	0.040	0.060	0.015	0.009	0.010	0.010	0.011
$\pi^{3}$	0.044	0.058	0.018	0.010	0.012	0.014	0.015
DA3-Giant	0.050	0.067	0.012	0.005	0.006	0.008	0.008
DA3-Large	0.144	0.112	0.044	0.009	0.010	0.055	0.065

Appendix

Table S17: The three benchmarks registered before any model ran ( Appendix S9 ): mean ATE, for Lightspeed also after half straightening, and PA-ATE for the eight offline models and VGGT-

\Omega

. Last row: the image-free line under ATE and the best of the image-free references (six camera-axis lines, static camera) under PA-ATE. ∗ Lightspeed PA-ATE over the 11 clips whose ground-truth orientations agree with the models ( Appendix S9 ); there the line’s ATE is 0.038. Lightspeed and DyCheck in their units, ADT in metres (tools/build_newbench_supp.py).

Method	ATE $\downarrow$	PA-ATE $\downarrow$	ATE $\downarrow$	median $\downarrow$	PA-ATE $\downarrow$	rot. $\downarrow$	RPE ${}_{t}\downarrow$	RPE ${}_{r}\downarrow$	DTE $\downarrow$	cl.
	TUM (8 clips)		ScanNet (94 clips)
$\pi^{3}$	0.015	0.016	0.030	0.027	0.038	1.15	0.0124	0.345	0.038	0
Line (no images)	0.148	0.162	0.232	0.210	0.364	27.84	0.0306	1.869	0.274	–
DA3-Giant	0.012	0.014	0.032	0.029	0.041	1.19	0.0128	0.362	0.042	0
$\pi^{3}$ X	0.011	0.013	0.030	0.027	0.038	1.12	0.0124	0.345	0.037	0
DA3-Base	0.029	0.032	0.059	0.047	0.076	3.31	0.0233	1.152	0.076	5

Appendix

Table S18: TUM and ScanNet, official protocol; means over clips unless marked. PA-ATE: pose-anchored ATE; rot.: its rotation error (degrees); RPE between consecutive frames (RPE r in degrees); DTE [ 40 ] . For the line: constant orientation and, for PA-ATE, RPE and DTE, the camera-axis direction, of six, with the lowest mean PA-ATE (for DTE, its own lowest). Its rotation error, under the orientation anchor, is that of a constant orientation, and straightening leaves it unchanged. Cl.: ScanNet clips on which half straightening lowers the ATE. ScanNet: first 90 frames at stride 3 of the 100 test scenes, 6 with invalid ground-truth poses dropped.

Camera Pose Estimation

Camera pose estimation recovers a camera’s position and orientation from images, visual features, scene geometry, and sometimes sensor measurements.

See all 257 papers

Sep 14, 2026

Comparing Trajectories from Positions Alone: Curvature-Based Time Alignment and Drift Error Metric

In field robotics, acquiring independent large-scale reference trajectories more accurate than the evaluated estimates remains an open challenge. The domain is widely reliant on Absolute Trajectory Error (ATE) and Relative Pose Error (RPE), computed with automated tools, that rest on assumptions and evaluation parameters rarely made explicit. When unreported, the errors can be misleading and hinder fair comparisons. This paper introduces a trajectory-evaluation protocol for standardized and reliable accuracy assessment in state estimation, localization, and Simultaneous Localization And Mapping (SLAM). The approach combines a novel temporal alignment method based on curvature signals with an error metric normalized by travelled distance. We explicitly account for temporal synchronization, sampling alignment, and extrinsic calibration, quantifying their influence through a sensitivity analysis. The proposed protocol contributes to more rigorous, reproducible, and standardized trajectory evaluation.

Effie Daum, Daniele De Martini, Claire Dune +1

Northern Robotics Laboratory, Université Laval, Québec City, Québec, Canada · Mobile Robotics Group, Oxford Robotics Institute, University of Oxford, Oxford, United Kingdom

Trajectory Generation Robot Localization

Ask PDF

Oct 22, 2026

PnP*: A certifiable solver for Perspective-n-Point

Estimating a camera pose from 3D-2D correspondences - Perspective-n-Point - is one of the most fundamental problems in computer vision. Existing methods either solve a minimal problem or replace the objective with an easier one. Surprisingly, no scalable certifiable solver for the actual Maximum Likelihood Estimation (MLE) exists. We propose PnP*, the first practical solver that guarantees efficient computation and returns a certifiable globally optimal solution. We prove that the underlying convex relaxation is exact under moderate noise, which to our knowledge is the first stability guarantee for any relaxation for the MLE of PnP. Furthermore, we reduce the relaxation by exploiting chordal sparsity pattern and quotient ring reduction such that the relaxation is tractable and scalable. The stability and scalability results are verified numerically, as PnP* returns a provably correct camera pose at over 10 Hz.

Bang-Shien Chen, Caitrin E. Eaton, David M. Rosen

Northeastern University, Boston, MA 02115, USA. · Draper, Cambridge, MA 02139, USA.

Camera Pose Estimation Convex Relaxation

Ask PDF

May 7, 2026

TriDE: Triangle-Consistent Translation Directions for Global Camera Pose Estimation

Pairwise translation directions are a key input to camera location estimation in global structure-from-motion. Existing estimators usually process each image pair independently, producing directions that may be locally plausible but inconsistent with the other relative directions in the viewing graph. To jointly estimate the direction, we propose TriDE, which exploits camera-triangle consistency as an efficient higher-order verification signal. Instead of solving a costly global nonlinear optimization problem that is sensitive to initialization, TriDE refines unreliable pairwise directions through message passing between directions and their incident weighted triangles. This information propagation strategy enables us to establish a strong phase-transition bound for exact recovery under a realistic random corruption model. Experiments on real image graphs show that TriDE improves direction accuracy by a large margin and yields better downstream camera locations, providing a practical link between local pairwise estimation and global camera pose geometry.

Francisco Chen, Yiran Wang, Yunpeng Shi

Department of Mathematics University of California, Davis

Multi-View Geometry Relative Pose Estimation Camera Pose Estimation Structure from Motion

Ask PDF

Abstract

Camera Pose Estimation

Explore similar work

Comparing Trajectories from Positions Alone: Curvature-Based Time Alignment and Drift Error Metric

PnP*: A certifiable solver for Perspective-n-Point

TriDE: Triangle-Consistent Translation Directions for Global Camera Pose Estimation