Boosting Metric Depth Completion via Training-Free Adaptive Response Geometry

Mia Zhang; Jizong Peng

cs.CVSep 28, 2026

Boosting Metric Depth Completion via Training-Free Adaptive Response Geometry

Authors: Mia Zhang, Jizong Peng

Organizations: dConstruct Robotics · University of Waterloo

Abstract

Depth completion aims to recover dense metric depth from sparse sensor measurements, increasingly leveraging visual foundation models as geometric priors. However, aligning these priors to true metric scale typically relies on rigid affine assumptions in predefined coordinate systems, leaving systematic calibration errors. Linearity in depth calibration depends on the response coordinate. We introduce adaptive response geometry, which makes the fixed choice of depth, log depth, or disparity an image-level unknown. A continuous response family unifies these coordinates and defines an explicit depth-dependent gain. We derive the response-gradient relation and estimate the response parameters in metric space. Hard-Dirichlet residual reconstruction completes the calibrated prior. Under deliberately incomplete metric observations, the training-free pipeline achieves macro AbsRel 0.0301 and macro NMed 14.04°, improving both aggregate measures over PriorDA, LDCM, and Any2Full. Linearity diagnostics examine how the selected response changes the depth relation and its metric error.

Figures & tables

Figure 1: Depth-dependent alignment differences can be alleviated by adapting a single global response coordinate, without assigning separate affine parameters to individual regions. (a) Colors indicate diagnostic point groups initialized from depth-percentile seeds and refined along the point bands, not semantic segments. (b) RANSAC reference lines show their different local slopes and intercepts. (c) The same points in the response coordinate with $\lambda=-11.41$ exhibit a more nearly shared linear trend; no lines are fitted in this panel.

Figure 2: Depth-dependent distortion remains after an affine fit in a fixed space. GDisp, GMetric, and GLog denote global affine alignment in disparity, metric depth, and log-depth, respectively. Top: scene reference and full-scene error maps. Bottom: predicted versus ground-truth depth in meters; blue paths trace local medians, and red denotes metric identity. The first column contains the scene reference above and the raw-prior relation below. Pearson $r$ characterizes the displayed relation; MAE measures held-out depth error. Trend error is the mean absolute vertical distance from the local-median path to metric identity; see Appendix A.4 .

Figure 3: A near-linear relation can still leave metric error. The first column pairs the scene reference with the raw-prior relation; each remaining column pairs one response with its relation.

	PriorDA		LDCM		Any2Full		PromptDA ∗		Ours
Subset	AbsRel	NMed	AbsRel	NMed	AbsRel	NMed	AbsRel	NMed	AbsRel	NMed
DIODE-in	0.0300	19.63	0.0281	13.04	0.0307	12.30	0.9943	77.59	0.0275	10.05
ETH3D	0.0228	24.34	0.0187	14.03	0.0254	13.12	0.9939	60.90	0.0180	11.52
iBims	0.0250	18.87	0.0203	11.67	0.0229	11.26	0.9939	65.96	0.0208	10.83
ARKit	0.0163	12.74	0.0145	9.40	0.0169	10.05	0.9876	71.84	0.0154	8.90
Barn	0.0276	16.37	0.0207	11.19	0.0362	11.85	0.9944	64.29	0.0251	10.43

Table 1: Per-subset comparison of complete methods. Lower is better for AbsRel and NMed.

Figure 4: Metric depth and surface geometry. (a) Macro comparison; the inset includes PromptDA and boxes the main-axis range. The arrow links Ours w/o Dirichlet to Ours. (b) Per-subset p50 results: depth error on the left and normal error on the right. The two views show aggregate performance and its variation across subsets. Baseline settings and stage normal quality are detailed in Appendices A.5 and C .

Figure 5: ARKit full-scene comparison. Columns show the reference, PriorDA, LDCM, Any2Full, and our method. (a) RGB reference and absolute depth-error maps; each title reports held-out MAE in meters. (b) Ground-truth normals and predicted normals for the same image. All error maps share the displayed scale, with purple above $0.3$ m.

Appendix figures & tables19 assets

Supplementary material from the paper’s appendix.

Appendix

AbsRel $\downarrow$
Method	DIODE	ETH3D	iBims	ARKit	Barn	Cat.	Ign.	Meet.	Truck
Raw MoGe-3	0.2707	0.0805	0.0773	0.0678	0.0857	0.1393	0.2643	0.1055	0.0925
PriorDA	0.0300	0.0228	0.0250	0.0163	0.0276	0.0499	0.0273	0.0631	0.0417
LDCM	0.0281	0.0187	0.0203	0.0145	0.0207	0.0792	0.0547	0.0507	0.0446
Any2Full	0.0307	0.0254	0.0229	0.0169	0.0362	0.0571	0.0326	0.0726	0.0513
PromptDA	0.9943	0.9939	0.9939	0.9876	0.9944	0.9960	0.9983	0.9917	0.9933

Appendix

Table A.1: P50 comparison across nine subsets. NMean is the per-image mean normal error in degrees. Detailed percentile behavior is shown in Fig. 6 .

Figure 6: Complete-system error distributions across nine subsets. Rows show p7–p93; columns show AbsRel and median normal error. Eight methods are shown: PriorDA, LDCM, Any2Full, KNN, LWLR, Poisson, Ours w/o Dirichlet, and Ours.

Figure 7: Depth effect of residual completion; each point is a subset p50.

Subset	Response AbsRel	Ours AbsRel	Response MAE	Ours MAE
DIODE-in	0.0356	0.0275	0.0792	0.0656
ETH3D	0.0269	0.0180	0.1476	0.1082
iBims	0.0223	0.0208	0.0604	0.0610
ARKit	0.0203	0.0154	0.0256	0.0209
Barn	0.0286	0.0251	0.2558	0.2258
Caterpillar	0.0701	0.0469	0.3049	0.2369

Appendix

Table B.1: Stage comparison at p50; MAE is in meters.

Subset	PriorDA	LDCM	Any2Full	PromptDA	Ours	Ours w/o Dirichlet
DIODE-in	29.74	24.46	20.57	77.26	20.55	16.71
ETH3D	37.69	27.07	24.93	67.47	23.84	22.28
iBims	29.53	22.26	19.60	67.68	20.99	16.33
ARKit	20.32	16.36	15.76	73.51	15.07	13.53
Barn	25.86	19.04	20.45	65.62	19.48	15.84
Caterpillar	41.48	41.17	32.02	74.94	34.37	27.77

Appendix

Table C.1: P50 mean normal error (degrees).

Subset	PriorDA	LDCM	Any2Full	PromptDA	Ours	Ours w/o Dirichlet
DIODE-in	19.63	13.04	12.30	77.59	10.05	9.10
ETH3D	24.34	14.03	13.12	60.90	11.52	10.68
iBims	18.87	11.67	11.26	65.96	10.83	8.63
ARKit	12.74	9.40	10.05	71.84	8.90	8.45
Barn	16.37	11.19	11.85	64.29	10.43	8.79
Caterpillar	31.69	31.38	21.10	74.32	22.65	17.01

Appendix

Table C.2: P50 median normal error (degrees).

Figure 8: Normal effect of residual completion; each point is a subset p50.

$\lambda_{\rm data}$	$\lambda_{\rm lap}$	MAE (m)	NMed (deg)
1e-4	1e-4	0.1326	14.31
1e-4	1e-3	0.1326	14.31
1e-4	1e-2	0.1326	14.31
1e-3	1e-4	0.1336	14.04
1e-3	1e-3	0.1336	14.04
1e-3	1e-2	0.1335	14.04

Appendix

Table D.1: Recorded residual-reconstruction weight sweep. MAE is in meters and NMed in degrees.

Figure 9: Reconstruction weight sensitivity.

DIODE-in
	MoGe-3		MoGe-2		MoGe-2 S		DAV2-L		DAV2-B
Method	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean
Raw	0.2707	18.37	0.2789	19.04	0.2578	22.55	–	–	–	–
Ours w/o Dirichlet	0.0356	16.71	0.0344	17.33	0.0493	21.18	0.0447	16.59	0.0454	17.22
Ours	0.0275	20.55	0.0272	20.77	0.0345	24.27	0.0331	20.25	0.0339	20.57
ETH3D

Appendix

Table E.1: Standard benchmarks: p50 comparison across monocular priors. NMean is mean normal error in degrees.

Barn
	MoGe-3		MoGe-2		MoGe-2 S		DAV2-L		DAV2-B
Method	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean
Raw	0.0857	15.35	0.1025	16.85	0.1190	19.74	–	–	–	–
Ours w/o Dirichlet	0.0286	15.84	0.0288	17.20	0.0402	20.23	0.0440	19.40	0.0430	19.57
Ours	0.0251	19.48	0.0251	20.17	0.0313	22.45	0.0347	22.71	0.0335	22.55
Caterpillar

Appendix

Table E.2: Tanks and Temples: p50 comparison across monocular priors. NMean is mean normal error in degrees.

DIODE
	MoGe-3		MoGe-2		MoGe-2 S		DAV2-L		DAV2-B
Method	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean
GDisp	0.0455	16.86	0.0454	17.50	0.0596	21.26	0.0526	16.54	0.0529	17.28
GMetric	0.0440	16.98	0.0443	17.48	0.0596	21.49	0.1519	30.82	0.1140	26.86
GLog	0.0416	16.63	0.0415	17.30	0.0551	21.15	0.0821	20.88	0.0744	19.72
Ours w/o Dirichlet	0.0356	16.71	0.0344	17.33	0.0493	21.18	0.0447	16.59	0.0454	17.22

Appendix

Table F.1: Standard benchmarks: p50 comparison of adaptive and fixed responses. Each backbone has paired AbsRel and mean normal error (degrees).

Barn
	MoGe-3		MoGe-2		MoGe-2 S		DAV2-L		DAV2-B
Method	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean	AbsRel	NMean
GDisp	0.0443	15.99	0.0441	17.28	0.0514	19.96	0.0642	19.23	0.0633	19.21
GMetric	0.1233	24.54	0.1256	25.85	0.1169	24.99	0.2057	39.09	0.2015	39.06
GLog	0.0670	17.68	0.0703	18.83	0.0693	20.74	0.1056	21.99	0.1066	22.07
Ours w/o Dirichlet	0.0286	15.84	0.0288	17.20	0.0402	20.23	0.0440	19.40	0.0430	19.57

Appendix

Table F.2: Tanks and Temples: p50 comparison of adaptive and fixed responses. Each backbone has paired AbsRel and mean normal error (degrees).

Subset	Images	Valid pixels	Valid fraction	Hole fraction	Largest comp.	Depth (m)
DIODE-in	325	227970748	.8270	.0002	.9940	1.523
ETH3D	454	459188168	.4926	.0313	.3470	2.075
iBims	100	28530051	.8479	.0006	.9997	1.633
ARKit	1141	197039280	.7589	.0013	.9141	.675
Barn	410	104872017	.2874	.0000	.9999	3.777
Caterpillar	383	71222396	.2145	.0191	.9994	2.378

Appendix

Table G.1: P16 reference-geometry statistics.

Subset	Images	Valid pixels	Valid fraction	Hole fraction	Largest comp.	Depth (m)
DIODE-in	325	227970748	.9938	.0025	1.0000	2.386
ETH3D	454	459188168	.6801	.0900	.5816	3.943
iBims	100	28530051	.9656	.0100	1.0000	2.650
ARKit	1141	197039280	.9056	.0164	.9953	1.198
Barn	410	104872017	.4565	.0001	1.0000	5.964
Caterpillar	383	71222396	.3469	.0362	.9998	3.426

Appendix

Table G.2: P50 reference-geometry statistics.

Subset	Images	Valid pixels	Valid fraction	Hole fraction	Largest comp.	Depth (m)
DIODE-in	325	227970748	.9998	.0197	1.0000	4.485
ETH3D	454	459188168	.8379	.1701	.8826	11.359
iBims	100	28530051	.9981	.0805	1.0000	4.468
ARKit	1141	197039280	.9799	.0536	.9999	1.932
Barn	410	104872017	.7183	.0018	1.0000	10.208
Caterpillar	383	71222396	.5187	.0504	1.0000	5.363

Appendix

Table G.3: P84 reference-geometry statistics.

Subset	Method	Valid p50	LCC p50	AbsRel	MAE (m)	Normal mean ( ∘ )	Normal median ( ∘ )	Failures
diode_in	PromptDA	0.9938	1.0000	0.0226	0.0567	20.5383	11.9354	0/0/0/0
arkit	PromptDA	0.9056	0.9953	0.0245	0.0314	17.2584	10.1660	0/0/3/3
Meetingroom	PromptDA	0.9686	0.9996	0.0565	0.2533	30.7781	19.3951	0/0/0/0
Ignatius	PromptDA	0.1554	0.9999	0.6307	1.5352	64.1742	48.4493	0/0/0/0

Appendix

Table G.4: P16 comparison. All four metrics use the same methods and subsets. Failure counts are listed in the order AbsRel / MAE / normal mean / normal median.

Subset	Method	Valid p50	LCC p50	AbsRel	MAE (m)	Normal mean ( ∘ )	Normal median ( ∘ )	Failures
diode_in	PromptDA	0.9938	1.0000	0.9943	2.0260	77.2586	77.5938	0/0/0/0
arkit	PromptDA	0.9056	0.9953	0.9876	0.9078	73.5105	71.8400	0/0/3/3
Meetingroom	PromptDA	0.9686	0.9996	0.9917	4.8201	69.0824	66.6804	0/0/0/0
Ignatius	PromptDA	0.1554	0.9999	0.9983	2.4738	75.2779	73.0478	0/0/0/0

Appendix

Table G.5: P50 comparison. All four metrics use the same methods and subsets. Failure counts are listed in the order AbsRel / MAE / normal mean / normal median.

Subset	Method	Valid p50	LCC p50	AbsRel	MAE (m)	Normal mean ( ∘ )	Normal median ( ∘ )	Failures
diode_in	PromptDA	0.9938	1.0000	0.9975	4.0551	89.2484	90.3284	0/0/0/0
arkit	PromptDA	0.9056	0.9953	0.9963	1.6984	87.6166	88.3735	0/0/3/3
Meetingroom	PromptDA	0.9686	0.9996	0.9956	6.7648	73.4394	72.4674	0/0/0/0
Ignatius	PromptDA	0.1554	0.9999	0.9988	3.6442	86.6829	88.2056	0/0/0/0

Appendix

Table G.6: P84 comparison. All four metrics use the same methods and subsets. Failure counts are listed in the order AbsRel / MAE / normal mean / normal median.

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FounRef: Robust, Structure-Preserving, and Fast Metric Refinement of Frozen Monocular Foundation Priors with Sparse Anchors

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University of the Bundeswehr Munich, Germany

Metric Depth Estimation Depth Completion Monocular Depth Estimation

Open paper AskPDF arXiv

Dense metric depth from cameras is essential to real-world 3D applications, yet achieving accuracy, faithful surface geometry, and fast inference simultaneously remains challenging. Monocular foundation models provide rich, transferable geometric priors but lack reliable metric scale, while depth-completion networks recover metric depth at the cost of geometric fidelity, cross-domain robustness, or speed. We present FounRef, a training-free method that aligns a frozen monocular foundation prior with sparse metric anchors to produce dense metric depth. FounRef is modular by design: its depth prior, anchor source, and refinement solver can each be replaced independently. We instantiate FounRef with MoGe-2 and LiDAR anchors. FounRef validates each anchor against the prior's dense depth prediction, rejecting inconsistencies caused by cross-sensor misalignment that geometry-only filters cannot detect. It then applies global and local metric corrections through a structure-preserving solver, retaining the prior's fine-grained geometry. FounRef requires no task-specific training and operates out of the box across unfamiliar cameras and scenes. On out-of-domain data, it delivers up to 24% lower depth error, 92% lower surface-normal noise, and almost 15x faster inference than DMD3C, a state-of-the-art depth-completion network. By decoupling metric alignment from geometry prediction, FounRef provides an accurate, geometrically faithful, and efficient approach to dense metric depth that can directly benefit from future advances in foundation models and metric sensors.

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