Marginalized Bundle Adjustment: Multi-View Camera Pose from Monocular Depth Estimates

Shengjie Zhu; Ahmed Abdelkader; Mark J. Matthews; Xiaoming Liu; Wen-Sheng Chu

cs.CVFeb 21, 2026

Marginalized Bundle Adjustment: Multi-View Camera Pose from Monocular Depth Estimates

Authors: Shengjie Zhu, Ahmed Abdelkader, Mark J. Matthews, Xiaoming Liu, Wen-Sheng Chu

Organizations: Google · Michigan State University

Abstract

Structure-from-Motion (SfM) is a fundamental 3D vision task for recovering camera parameters and scene geometry from multi-view images. While recent deep learning advances enable accurate Monocular Depth Estimation (MDE) from single images without depending on camera motion, integrating MDE into SfM remains a challenge. Unlike conventional triangulated sparse point clouds, MDE produces dense depth maps with significantly higher error variance. Inspired by modern RANSAC estimators, we propose Marginalized Bundle Adjustment (MBA) to mitigate MDE error variance leveraging its density. With MBA, we show that MDE depth maps are sufficiently accurate to yield SoTA or competitive results in SfM and camera relocalization tasks. Through extensive evaluations, we demonstrate consistently robust performance across varying scales, ranging from few-frame setups to large multi-view systems with thousands of images. Our method highlights the significant potential of MDE in multi-view 3D vision.

Figures & tables

Figure 1: Marginalized Bundle Adjustment (MBA). Our method registers monocular depth maps into a consistent 3D coordinate system. Red camera icons indicate the viewpoints of registered depth maps. Monocular depth provides a strong structural prior, yet its predictions are inherently high-variance, as reflected by the noisy appearance of the reconstructed point cloud. This makes classical Bundle Adjustment designed for accurate sparse point cloud ill-suited. We therefore introduce a RANSAC-inspired Bundle Adjustment objective that leverages the depth maps’ density to robustly accommodate their variance. Although depth-derived point clouds have lower visual fidelity, our experiments show that monocular depth already supports SoTA or competitive performance on diverse SfM benchmarks, as exemplified ScanNet [ 14 ] , IMC2021 [ 6 ] , and ETH3D [ 6 ] . It highlights significant potential of monocular depth models for multi-view vision tasks.

Dataset	ScanNet [ 15 ]	Tanks&Temples [ 30 ]	ETH3D [ 58 ]	IMC2021 [ 6 ]	7-Scenes [ 60 ]	Wayspots [ 8 ]
Images	$391$	$1{,}106$	$76$	$25$	$8{,}000$	$1{,}157$
Pairs	$21{,}982$	$210{,}894$	$1{,}571$	$300$	$282{,}209$	$666{,}598$

Table 1: Maximum Size of Pose Graph in each benchmarked dataset. The nodes and edges are its images and co-visible image pairs.

Figure 2: System Overview. With $N$ RGBs, the system consumes dense depth maps and pairwise correspondence inferred by pretrained models. The system outputs intrinsics, extrinsics, and frame-wise depth affine corrections scalars. A sparse $N\times N$ pose graph is built from co-visible frames using correspondences. Dense inputs are subsampled into a data matrix of $|\mathcal{E}|\times\kappa\times 5$ (graph edges count) for scalable multi-GPU optimization. After initialization, the Bundle Adjustment proceeds from coarse to fine. In coarse stage, the BA objective is evaluated and summed over “star-shaped” subgraph $\mathcal{G}_{i}$ of each frame $i$ . One subgraph includes itself plus its co‑visible neighbors, marked as one colored row in coarse pose graph. Fine stage computes with full graph. The BA applies gradient descent for fixed iterations.

Panel of Figure 3 — Figure 3: CDF and PDF of empirical residual distribution $\mathcal{R}$ . In Eq. 8 , our BA maximizes the area-under-the-curve of $\mathcal{R}$ ’s CDF curve up a maximum threshold. The BA automatically formulates a smoothed categorization of inliers versus outliers. The forward and backward computation ( Eqn. 10 & 11 ) at the residual $r$ is succinctly defined as indexing the curve at $F(r)$ and $p(r)$ .

Panel of Figure 4 — Figure 4: Dense Depth and Correspondence are inputs to our multi-view pose estimation system. We benchmark pose performance with depth map under diverse imaging conditions. Figures (a) to (e) include ScanNet [ 15 ] indoor images, T&T [ 30 ] and ETH3D [ 59 ] high resolution images, IMC2021 [ 6 ] internet-collected images, and Wayspots [ 8 ] flipped image. Fig. (f) visualizes dense correspondence.

Panel of Figure 5 — Figure 5: Camera Re-localization on 7-Scenes and Wayspots. Green and blue mark predicted and groundtruth odometry. We present challenging sequences of repetitive, textureless images. The images exhibit (1) scale changes, (2) flipping, and (3) a lack of distinguishable depth references. Consequently, the model predicts sub-optimal depth maps. Surprisingly, despite these significant challenges, depth maps still support accurate camera poses.

Scene	COLMAP [ 56 ]		ACE-Zero [ 10 ]		FlowMap [ 62 ]		VGG-SfM [ 73 ]		DF-SfM [ 28 ]		MASt3R-SfM [ 18 ]		MBA (Ours)
Scene	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA
courtyard	$56.3$	$60.0$	$4.0$	$1.9$	$7.5$	$3.6$	$50.5$	$51.2$	$80.7$	$74.8$	$89.8$	$64.4$	$94.7$	$94.7$
delivery area	$34.0$	$28.1$	$27.4$	$1.9$	$29.4$	$23.8$	$22.0$	$19.6$	$82.5$	$82.0$	$83.1$	$81.8$	$83.1$	$83.0$
electro	$53.3$	$48.5$	$16.9$	$7.9$	$2.5$	$1.2$	$79.9$	$58.6$	$82.8$	$81.2$	$100.0$	$95.5$	$95.6$	$78.2$
facade	$92.2$	$90.0$	$74.5$	$64.1$	$15.7$	$16.8$	$57.5$	$48.7$	$80.9$	$82.6$	$74.3$	$75.3$	$100.0$	$99.2$
kicker	$87.3$	$86.2$	$26.2$	$16.8$	$1.5$	$1.5$	$100.0$	$97.8$	$93.5$	$91.0$	$100.0$	$100.0$	$100.0$	$98.9$

Table 2: Structure-from-Motion benchmark on ETH3D dataset [ 58 ] in metrics RRA (

@5^{\circ}

) and RTA (

@5^{\circ}

) following MASt3R-SfM evaluation protocol. See performance with other MDE models at Supp.Tab. 13 . See detailed evaluation protocol at Supp.Sec. 7.5

Type	Method	AUC $@3^{\circ}$	AUC $@5^{\circ}$	AUC $@10^{\circ}$
Detector-Based	SIFT+NN + COLMAP [ 56 ] CVPR’16	$24.87$	$34.47$	$45.94$
	SIFT + NN + PixSfM [ 41 ] ICCV’21	$26.45$	$35.73$	$47.24$
	D2Net + NN + PixSfM [ 41 ] ICCV’21	$10.27$	$13.12$	$17.25$
	R2D2 + NN + PixSfM [ 41 ] ICCV’21	$32.44$	$42.55$	$55.01$
	SP + SG + PixSfM [ 41 ] ICCV’21	$46.30$	$58.43$	$71.62$
Detector-Free	LoFTR + PixSfM [ 41 ] ICCV’21	$44.06$	$56.16$	$69.61$

Table 3: Structure-from-Motion on IMC2021 [ 6 ] dataset in AUC metric. We are comparable or better than Dense-SfM, DF-SfM, Mast3r-SfM, PixSfM, VGG-SfM and VGGT without BA.

Method	Inference	RRA@5 $\uparrow$	RTA@5 $\uparrow$	ATE $\downarrow$	Registration $\uparrow$
Cut3R [ 75 ] CVPR’25	FeedForward	$18.8$	$25.8$	$0.017$	$100.0$
Spann3R [ 71 ] 3DV’25		$22.1$	$30.7$	$0.016$	$100.0$
SLAM3R [ 42 ] CVPR’25		$20.3$	$24.7$	$0.015$	$100.0$
VGGT-SLAM [ 43 ] arXiv’25		$57.3$	$67.9$	$\mathbf{0.008}$	$100.0$
Light3R-SfM [ 21 ] CVPR’25		$52.0$	$52.8$	$0.011$	$100.0$
SAIL [ 16 ] arXiv’25		$70.4$	$74.7$	$\mathbf{0.008}$	$100.0$

Table 4: Structure-from-Motion on Tanks&Temple [ 30 ] dataset.

Method	Depth	Corres.	$\text{ACC}@3^{\circ}$	$\text{ACC}@5^{\circ}$	$\text{ACC}@10^{\circ}$
COLMAP [ 56 ]	-	SuperPoint [ 17 ]	${0.342}$	${0.505}$	$0.670$
MBA (Ours)	ZoeDepth [ 5 ]	RoMa [ 20 ]	${0.372}$	${0.586}$	${0.811}$
	DUSt3R [ 79 ]	RoMa [ 20 ]	$0.403$	$\mathbf{0.615}$	$0.820$
	UniDepth [ 49 ]	RoMa [ 20 ]	$\mathbf{0.407}$	$0.612$	$\mathbf{0.823}$
	DUSt3R [ 79 ]	MASt3R [ 34 ]	$0.384$	$0.596$	$0.811$
	UniDepth [ 49 ]	MASt3R [ 34 ]	$0.393$	$0.598$	$0.817$

Table 5: Structure-from-Motion on the ScanNet dataset [ 15 ] .

Category	Method	Average (deg/cm)
FM	AS [ 55 ] PAMI’16	$5.1/2.46$
FM	HLoc [ 53 ] CVPR’19	$\mathbf{3.4}/\mathbf{1.07}$
E2E	SC-wLS [ 81 ] ECCV’22	$6.6/1.45$
	NeuMaps [ 65 ] CVPR’23	$3.1/1.09$
	PixLoc [ 54 ] CVPR’21	$\mathbf{2.9}/\mathbf{0.98}$
SCR	ACE [ 8 ] CVPR’23	$2.8/0.93$

Table 6: Camera relocalization performance benchmark on the 7-Scenes dataset [ 60 ] . Per-scene results are in Supp.Tab. 15 .

Scene	MAREPO [ 11 ]	$\text{DSAC}^{*}$ [ 9 ]	ACE [ 8 ]	MBA (Ours)
Cubes	$71.8\%$	$83.8\%$	$\mathbf{97.0\%}$	$75.1\%$
Bears	$80.7\%$	$82.6\%$	$80.7\%$	$\mathbf{100\%}$
Winter Sign	$0.0\%$	$0.2\%$	$1.0\%$	$\mathbf{9.3\%}$
Inscription	$37.1\%$	$54.1\%$	$\mathbf{49.0\%}$	$28.3\%$
The Rock	$99.8\%$	$\mathbf{100\%}$	$\mathbf{100\%}$	$\mathbf{100\%}$
Tendrils	$29.3\%$	$25.1\%$	$34.9\%$	$\mathbf{51.5\%}$

Table 7: Camera relocalization benchmark on the Wayspots [ 8 ] .

	MegaDepth			ScanNet
Method $\downarrow$ AUC $@$ $\rightarrow$	$5^{\circ}$ $\uparrow$	$10^{\circ}$ $\uparrow$	$20^{\circ}$ $\uparrow$	$5^{\circ}$ $\uparrow$	$10^{\circ}$ $\uparrow$	$20^{\circ}$ $\uparrow$
LoFTR [ 63 ] CVPR’21	52.8	69.2	81.2	22.1	40.8	57.6
PDC-Net+ [ 68 ] TPAMI’23	51.5	67.2	78.5	20.3	39.4	57.1
DKM [ 19 ] CVPR’23	60.4	74.9	85.1	29.4	50.7	68.3
PMatch [ 86 ] CVPR’23	61.4	75.7	85.7	29.4	50.1	67.4
RoMa [ 20 ] CVPR’24	62.6	76.7	86.3	31.8	53.4	70.9

Table 8: RoMa benchmark of two-view pose estimation with RANSAC on MegaDepth-1500 [ 38 ] and ScanNet-1500 [ 14 ] .

Dataset	Max Graph Size		Max Runtime
Dataset	Images	Pairs	Ours	COLMAP
ScanNet [ 15 ]	$391$	$43{,}964$	$2.98$ h	$0.91$ h
ETH3D [ 58 ]	$76$	$3{,}142$	$41$ min	$9$ min
IMC2021 [ 6 ]	$25$	$600$	$14$ min	$3$ min
7-Scenes [ 60 ]	$8{,}000$	$564{,}418$	$3.12$ h	$13.52$ h
Wayspots [ 8 ]	$1{,}157$	$1{,}333{,}196$	$4.72$ h	Crash

Table 9: Max Pose Graph and its Runtime in each benchmarked dataset. We run experiments on ScanNet, ETH3D, and IMC2021 with single

\text{V}100

GPU, and on 7-Scenes and Wayspots with eight.

Ablation	Method	RRA $@5^{\circ}$	RTA $@5^{\circ}$
Stages	Initialization	$62.6$	$41.0$
	Coarse	$97.1$	$87.9$
	Fine	$97.3$	$90.2$
Density	$\kappa=30$	$91.7$	$78.6$
	$\kappa=200$	$97.3$	$90.2$
	$\kappa=500$	$99.3$	$92.0$

Table 10: Ablations on ETH3D dataset.

Type	Method	ETH3D Dataset
Type	Method	AUC $@1^{\circ}$	AUC $@3^{\circ}$	AUC $@5^{\circ}$
Detector-Based	SIFT+NN + COLMAP [ 56 ] CVPR’16	$26.71$	$38.86$	$42.14$
	SIFT + NN + PixSfM [ 41 ] ICCV’21	$26.94$	$39.01$	$42.19$
	D2Net + NN + PixSfM [ 41 ] ICCV’21	$34.50$	$49.77$	$53.58$
	R2D2 + NN + PixSfM [ 41 ] ICCV’21	$43.58$	$62.09$	$66.89$
	SP + SG + PixSfM [ 41 ] ICCV’21	$50.82$	$68.52$	$72.86$

Table 11: Structure-from-Motion on ETH3D [ 59 , 58 ] dataset in metric AUC at multiple thresholds following DF-SfM.

		ATE $\downarrow$				RTA@3 $\uparrow$				AUC-R&T @ 3 $\uparrow$				RTA@1 $\uparrow$				AUC-R&T @ 1 $\uparrow$
	n_imgs	MBA (Ours)	FastMap [ 36 ]	GLOMAP [ 47 ]	COLMAP [ 56 ]	MBA (Ours)	FastMap [ 36 ]	GLOMAP [ 47 ]	COLMAP [ 56 ]	MBA (Ours)	FastMap [ 36 ]	GLOMAP [ 47 ]	COLMAP [ 56 ]	MBA (Ours)	FastMap [ 36 ]	GLOMAP [ 47 ]	COLMAP [ 56 ]	MBA (Ours)	FastMap [ 36 ]	GLOMAP [ 47 ]	COLMAP [ 56 ]
mipnerf360 (9)	215.6	5.0e-4	4.2e-4	3.3e-5	5.8e-5	99.6	99.9	100.0	100.0	85.5	97.4	98.2	97.2	87.3	99.8	100.0	99.7	66.1	92.4	94.6	91.9
tnt_advanced (6)	337.8	1.7e-2	6.4e-3	1.2e-2	1.2e-3	59.9	71.4	79.1	98.5	34.7	42.6	75.3	94.8	25.2	42.3	77.5	97.0	12.5	16.7	69.8	90.0
tnt_intermediate (8)	268.6	5.7e-3	7.8e-5	1.9e-5	2.6e-4	89.8	99.9	100.0	99.8	61.7	94.1	99.0	98.9	62.8	99.3	99.9	99.5	35.4	83.1	96.9	97.3
tnt_training (7)	470.1	3.8e-3	3.0e-3	1.1e-2	3.0e-4	88.8	87.8	88.7	99.9	63.2	77.2	87.9	99.5	63.6	82.1	88.6	99.9	31.9	60.5	86.3	98.7
nerf_osr (8)	402.8	1.4e-3	1.6e-3	1.1e-3	1.3e-3	89.8	91.7	92.0	92.1	69.3	70.9	71.9	71.7	54.4	71.1	71.9	71.7	35.0	43.2	45.2	44.7

Table 12: Pose accuracy comparison on MipNeRF360 [ 4 ] , Tanks and Temples [ 30 ] , NeRF-OSR [ 52 ] , DroneDeploy [ 50 ] , Urbanscene3D [ 39 ] , Mill-19 [ 70 ] , and Eyeful Tower [ 82 ] . We follow the evaluation protocol established by FastMap [ 36 ] for reporting pose accuracy metrics on these datasets. Note, [ 36 ] uses a different COLMAP groundtruth to Tab. 4 . For datasets with multiple scenes, we denote the average number of images as dataset-name(#scenes) . Results are listed separately for each scene in Mill-19 and Eyeful Tower. Metrics are color-coded with dark green for best performance and light green for competitive performance. Red denotes complete failures and gray indicates timeout (did not finish in one week).

Scene	COLMAP [ 56 ]		ACE-Zero [ 10 ]		FlowMap [ 62 ]		VGGSfM [ 73 ]		DF-SfM [ 28 ]		MASt3R-SfM [ 18 ]		Ours / DUSt3R [ 79 ]		Ours / ZoeDepth [ 5 ]		Ours / UniDepth [ 49 ]
Scene	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA	RRA	RTA
courtyard	$56.3$	$60.0$	$4.0$	$1.9$	$7.5$	$3.6$	$50.5$	$51.2$	$80.7$	$74.8$	$89.8$	$64.4$	$94.7$	$94.7$	$94.7$	$94.5$	$94.7$	$94.4$
delivery area	$34.0$	$28.1$	$27.4$	$1.9$	$29.4$	$23.8$	$22.0$	$19.6$	$82.5$	$82.0$	$83.1$	$81.8$	$83.1$	$83.0$	$87.8$	$82.0$	$83.1$	$83.1$
electro	$53.3$	$48.5$	$16.9$	$7.9$	$2.5$	$1.2$	$79.9$	$58.6$	$82.8$	$81.2$	$100.0$	$95.5$	$95.6$	$78.2$	$91.9$	$78.5$	$93.0$	$77.2$
facade	$92.2$	$90.0$	$74.5$	$64.1$	$15.7$	$16.8$	$57.5$	$48.7$	$80.9$	$82.6$	$74.3$	$75.3$	$100.0$	$99.2$	$100.0$	$97.4$	$80.9$	$86.0$
kicker	$87.3$	$86.2$	$26.2$	$16.8$	$1.5$	$1.5$	$100.0$	$97.8$	$93.5$	$91.0$	$100.0$	$100.0$	$100.0$	$98.9$	$100.0$	$98.5$	$100.0$	$98.0$

Table 13: Structure-from-Motion ablation with other Monocular Depth Models ZoeDepth and UniDepth on ETH3D dataset [ 59 , 58 ] .

Method	Depth	Corres.	Calibrated			Uncalibrated
Method	Depth	Corres.	$\text{Acc}@3^{\circ}$	$\text{Acc}@5^{\circ}$	$\text{Acc}@10^{\circ}$	$\text{Acc}@3^{\circ}$	$\text{Acc}@5^{\circ}$	$\text{Acc}@10^{\circ}$
COLMAP [ 56 ]	-	SuperPoint [ 17 ]	${0.398}$	$0.589$	$0.783$	${0.342}$	${0.505}$	$0.670$
MBA (Ours)	ZoeDepth [ 5 ]	RoMa [ 20 ]	$0.396$	${0.614}$	${0.823}$	${0.372}$	${0.586}$	${0.811}$
	DUSt3R [ 79 ]	RoMa [ 20 ]	$0.426$	$0.631$	$0.830$	$0.403$	$\mathbf{0.615}$	$0.820$
	UniDepth [ 49 ]	RoMa [ 20 ]	$0.432$	$0.636$	$0.833$	$\mathbf{0.407}$	$0.612$	$\mathbf{0.823}$
	DUSt3R [ 79 ]	MASt3R [ 34 ]	$0.432$	$0.639$	$0.837$	$0.384$	$0.596$	$0.811$

Table 14: Extended Structure-from-Motion Results on the ScanNet dataset [ 15 ] , with calibrated and uncalibrated cases.

Category	Method	Chess	Fire	Heads	Office	Pumpkin	Kitchen	Stairs	Average
FM	AS [ 55 ] PAMI’16	$4/1.96$	$3/1.53$	$2/1.45$	$9/3.61$	$8/3.10$	$7/3.37$	$3/2.22$	$5.1/2.46$
FM	HLoc [ 53 ] CVPR’19	$2/0.79$	$2/0.87$	$2/0.92$	$3/0.91$	$5/1.12$	$4/1.25$	$6/1.62$	$3.4/1.07$
E2E	SC-wLS [ 81 ] ECCV’22	$3/0.76$	$5/1.09$	$3/1.92$	$6/0.86$	$8/1.27$	$9/1.43$	$12/2.80$	$6.6/1.45$
	NeuMaps [ 65 ] CVPR’23	$2/0.81$	$3/1.11$	$2/1.17$	$3/0.98$	$4/1.11$	$4/1.33$	$4/1.12$	$3.1/1.09$
	PixLoc [ 54 ] CVPR’21	$2/0.80$	$2/0.73$	$1/0.82$	$3/0.82$	$4/1.21$	$3/1.20$	$5/1.30$	$2.9/0.98$
SCR	ACE [ 8 ] CVPR’23	$1.9/0.7$	$1.9/0.9$	$0.9/0.6$	$2.7/0.8$	$4.2/1.1$	$4.2/1.3$	$3.9/1.1$	$2.8/0.93$

Table 15: Extended Camera Relocalization Results on the 7-Scenes dataset [ 60 ] , with per-scene performance.

Camera Pose Estimation

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

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Jul 10, 2026J/K move · Enter open · S save

DGSfM: Depth-Guided Scale-Aware Global Structure-from-Motion

Sithu Aung, Viktor Kocur, Yaqing Ding, Torsten Sattler+1

VRG, FEE, Czech Technical University in Prague · FMPH, Comenius University in Bratislava · Southeast University+1

Multi-View Geometry 3D Reconstruction Camera Pose Estimation Structure from Motion

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Global Structure-from-Motion (SfM) is an efficient paradigm for recovering camera poses and sparse 3D structure from unordered images. However, its reliance on scale-ambiguous epipolar geometry makes global positioning sensitive to noisy baseline estimates and weak view-graph constraints, while false edges from visually ambiguous pairs can further degrade reconstruction. We propose DGSfM, a depth-aware global SfM pipeline that uses monocular depth maps as a scalable prior while preserving explicit multi-view optimization. For each image pair, we use a depth-aware relative pose solver to convert scale-ambiguous epipolar constraints into scale-aware relative pose constraints. We further improve robustness through view-graph filtering and depth-consistency-based correspondence pruning, which suppress false edges and matches that remain plausible under epipolar geometry alone. Finally, global scale averaging and depth-guided pose-point initialization align monocular depth maps into a common reconstruction scale and provide stable initialization for global positioning and bundle adjustment. Experiments on ETH3D and IMC2021 show that DGSfM consistently improves over strong global SfM baselines across sparse and dense matching front-ends, achieving substantial gains in pose accuracy. Code and project page: https://dgsfm.github.io/.

Abstract

Camera Pose Estimation

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