Surface Reconstruction from Range Scans Under Visibility Constraints

Gabriel Lenain; Edmond Boyer; Jean Ponce

cs.CVOct 13, 2026

Surface Reconstruction from Range Scans Under Visibility Constraints

Authors: Gabriel Lenain, Edmond Boyer, Jean Ponce

Organizations: Inria Paris · École normale supérieure - PSL · Univ. Grenoble Alpes, Inria · CNRS, Grenoble INP, LJK ·

Abstract

Surface reconstruction from range scans is challenging in the presence of noise and outliers, as fidelity to observations must be balanced against sensitivity to measurement errors. Yet, most neural approaches discard the sensor positions and corresponding visibility information, compensating for this loss with geometric priors or regularization terms. We instead formulate surface reconstruction as robust regression of the predicted first surface intersection along each acquisition ray against its measured depth, which penalizes predicted surface intersections within the segment between the sensor and the observed point. We represent the surface as the zero set of a 1-Lipschitz multi-layer perceptron, allowing the use of linearly convergent sphere tracing to compute the first hit, and use a robust Huber loss for regression. Our formulation requires neither oriented normals, sampled off-surface points, nor an eikonal loss. Comparisons with the state of the art on synthetic and real data with varying levels of noise and outlier contamination demonstrate competitive performance on clean data and much improved fidelity and robustness under even moderate corruption. Our analysis further confirms a trade-off between fidelity and robustness: greater fitting capacity improves data fidelity in the clean case but increases sensitivity to the measurement errors inherent in real acquisitions, with a sweet spot typically emerging at intermediate capacity.

Figures & tables

Figure 1: Surface reconstruction for synthetic data corrupted by (top) noise and (center) outliers, and for (bottom) real LiDAR data. A single integer, the positional encoding level $L$ , controls the fidelity-robustness trade-off. We use $L=2$ , a good compromise in our experiments. Circled numbers rank methods by Chamfer distance for synthetic data and mean absolute depth error for real data.

Panel of Figure 2 — Figure 2: Method overview. Sensor-point pairs define acquisition rays; sphere tracing locates the predicted first surface intersection, and incidence weighting locally converts the depth residual into a surface-distance residual.

Figure 3: Observation-supported SRB evaluation. Orange denotes surface regions excluded by the $2h_{0}$ support mask.

	Clean ( $\lambda=0$ )				Noise ( $\lambda=1$ )
Method	$\mathrm{CD}_{1}\downarrow$	$\mathrm{NC}\uparrow$	$\mathrm{CD}_{1}^{\mathrm{obs}}\downarrow$	$\mathrm{NC}^{\mathrm{obs}}\uparrow$	$\mathrm{CD}_{1}\downarrow$	$\mathrm{NC}\uparrow$	$\mathrm{CD}_{1}^{\mathrm{obs}}\downarrow$	$\mathrm{NC}^{\mathrm{obs}}\uparrow$
Neural implicit
Ours ( $L=0$ )	0.163 $\pm$ 0.005	0.958 $\pm$ 0.001	0.101 $\pm$ 0.003	0.970 $\pm$ 0.001	0.310 $\pm$ 0.016	0.906 $\pm$ 0.006	0.226 $\pm$ 0.005	0.921 $\pm$ 0.004
Ours ( $L=2$ )	0.127 $\pm$ 0.002	0.970 $\pm$ 0.001	0.073 $\pm$ 0.001	0.982 $\pm$ 0.0002	0.381 $\pm$ 0.002	0.781 $\pm$ 0.002	0.296 $\pm$ 0.004	0.794 $\pm$ 0.002
Ours ( $L=6$ )	0.133 $\pm$ 0.003	0.974 $\pm$ 0.002	0.064 $\pm$ 0.002	0.987 $\pm$ 0.003	0.542 $\pm$ 0.009	0.543 $\pm$ 0.008	0.409 $\pm$ 0.007	0.544 $\pm$ 0.006
NDF-vis	0.613 $\pm$ 0.063	0.893 $\pm$ 0.003	0.423 $\pm$ 0.037	0.920 $\pm$ 0.003	1.098 $\pm$ 0.194	0.871 $\pm$ 0.003	0.834 $\pm$ 0.149	0.901 $\pm$ 0.0004

Table 1: SRB results under scanner noise. Mean

\pm

std. over three seeds for stochastic methods; best/second-best neural implicit results are bold/underlined. Per-shape results are in Appendix D .

Figure 4: Qualitative Gargoyle reconstructions under scanner noise: $\lambda=0$ (top) and $\lambda=1$ (bottom).

Figure 5: SRB performance across scanner-noise levels. Larger

L

improves clean fidelity but reduces robustness. Ours (

L=2

) provides a good compromise.

	Metric	Ours ( $L=0$ )	Ours ( $L=2$ )	Ours ( $L=6$ )	NDF-vis	DiffCD	N.-Pull	SAL	DiGS	SPSR	Labat.
Iso	$\mathrm{CD}_{2}\,(10^{-4})\downarrow$	2.58	2.26	2.47	5.51	2.53	10.1	112	5.89	46.1	3.04
	$\mathrm{NC}\uparrow$	0.91	0.91	0.90	0.89	0.84	0.76	0.85	0.68	0.84	0.79
	$\mathrm{IoU}\uparrow$	0.84	0.85	0.82	0.72	0.75	0.64	0.63	0.46	0.63	0.79
Ray	$\mathrm{CD}_{2}\,(10^{-4})\downarrow$	2.23	2.12	2.18	6.66	2.45	14.8	150	5.83	45.0	3.02
	$\mathrm{NC}\uparrow$	0.92	0.92	0.91	0.89	0.88	0.79	0.85	0.71	0.84	0.81
	$\mathrm{IoU}\uparrow$	0.86	0.86	0.85	0.70	0.78	0.63	0.62	0.58	0.64	0.79

Table 2: ShapeNet reconstruction under Gaussian noise with 3K input points. Mean over 65 test shapes, except SAL, which is averaged over successfully scored shapes. Best/second-best neural implicit results are shown in bold/underlined.

Figure 6: Qualitative ShapeNet airplane results under isotropic and ray-aligned Gaussian noise.

	Clean ( $\alpha=0$ )				Outliers ( $\alpha=0.2$ )
Method	$\mathrm{CD}_{1}\downarrow$	$\mathrm{NC}\uparrow$	$\mathrm{CD}_{1}^{\mathrm{obs}}\downarrow$	$\mathrm{NC}^{\mathrm{obs}}\uparrow$	$\mathrm{CD}_{1}\downarrow$	$\mathrm{NC}\uparrow$	$\mathrm{CD}_{1}^{\mathrm{obs}}\downarrow$	$\mathrm{NC}^{\mathrm{obs}}\uparrow$
Neural implicit
Ours ( $L=0$ )	0.155 $\pm$ 0.003	0.961 $\pm$ 0.002	0.098 $\pm$ 0.002	0.973 $\pm$ 0.001	0.173 $\pm$ 0.013	0.954 $\pm$ 0.003	0.107 $\pm$ 0.005	0.968 $\pm$ 0.002
Ours ( $L=2$ )	0.119 $\pm$ 0.003	0.974 $\pm$ 0.001	0.070 $\pm$ 0.002	0.985 $\pm$ 0.001	0.122 $\pm$ 0.004	0.968 $\pm$ 0.001	0.080 $\pm$ 0.002	0.981 $\pm$ 0.001
Ours ( $L=6$ )	0.127 $\pm$ 0.004	0.977 $\pm$ 0.0009	0.061 $\pm$ 0.002	0.989 $\pm$ 0.0006	0.414 $\pm$ 0.018	0.818 $\pm$ 0.0018	0.151 $\pm$ 0.007	0.870 $\pm$ 0.0003
NDF-vis	0.697 $\pm$ 0.085	0.885 $\pm$ 0.003	0.463 $\pm$ 0.054	0.916 $\pm$ 0.003	5.492 $\pm$ 0.280	0.723 $\pm$ 0.010	2.144 $\pm$ 0.268	0.832 $\pm$ 0.009

Table 3: SRB results under outliers. Mean

\pm

std. over three seeds for stochastic methods; best/second-best neural implicit results are bold/underlined. Per-shape results are in Appendix D .

	Neural implicit							Classical
	Ours ( $L=0$ )	Ours ( $L=2$ )	NDF-vis	DiffCD	Neural-Pull	SAL	DiGS	SPSR	Labatut
MAE (cm) $\downarrow$	2.24 $\pm$ 0.17	2.07 $\pm$ 0.17	11.30 $\pm$ 0.52	4.84 $\pm$ 0.32	5.56 $\pm$ 0.30	8.34 $\pm$ 0.39	5.66 $\pm$ 0.29	2.84 $\pm$ 0.25	4.07 $\pm$ 0.28
Hit (%) $\uparrow$	99.7 $\pm$ 0.13	99.4 $\pm$ 0.24	83.4 $\pm$ 3.62	99.7 $\pm$ 0.15	90.3 $\pm$ 2.72	96.3 $\pm$ 0.58	99.5 $\pm$ 0.09	99.7 $\pm$ 0.08	98.8 $\pm$ 0.40
$I@2\,\mathrm{cm}$ (%) $\uparrow$	61.9 $\pm$ 3.7	66.0 $\pm$ 4.0	1.3 $\pm$ 0.5	33.1 $\pm$ 3.3	20.5 $\pm$ 1.2	6.5 $\pm$ 0.8	25.0 $\pm$ 2.5	58.5 $\pm$ 3.8	45.5 $\pm$ 3.3

Table 4: ARKitScenes sofa reconstruction from 2.34M iPad LiDAR points. Evaluation over 36 FARO frames; mean

\pm

standard deviation across frames. Best/second-best results are bold/underlined.

Figure 7: Qualitative KITTI reconstruction.

Variant	Clean ( $\lambda=0$ )		Noise ( $\lambda=1$ )		Outliers ( $\alpha=0.2$ )
	$\mathrm{CD}_{1}\downarrow$	$\mathrm{NC}\uparrow$	$\mathrm{CD}_{1}\downarrow$	$\mathrm{NC}\uparrow$	$\mathrm{CD}_{1}\downarrow$	$\mathrm{NC}\uparrow$
Ours ( $L=0$ )	$0.163_{\scriptscriptstyle\pm 0.005}$	$0.958_{\scriptscriptstyle\pm 0.001}$	$0.310_{\scriptscriptstyle\pm 0.016}$	$0.906_{\scriptscriptstyle\pm 0.006}$	$\mathbf{0.173}_{\scriptscriptstyle\pm 0.013}$	$\mathbf{0.954}_{\scriptscriptstyle\pm 0.003}$
$\ell_{1}$ loss	$0.188_{\scriptscriptstyle\pm 0.0004}$	$0.950_{\scriptscriptstyle\pm 0.0007}$	$0.296_{\scriptscriptstyle\pm 0.001}$	$0.911_{\scriptscriptstyle\pm 0.004}$	$0.185_{\scriptscriptstyle\pm 0.004}$	$0.950_{\scriptscriptstyle\pm 0.002}$
$\ell_{2}$ loss	$0.195_{\scriptscriptstyle\pm 0.002}$	$0.951_{\scriptscriptstyle\pm 0.001}$	$0.308_{\scriptscriptstyle\pm 0.002}$	$\mathbf{0.921}_{\scriptscriptstyle\pm 0.0002}$	$1.111_{\scriptscriptstyle\pm 0.010}$	$0.708_{\scriptscriptstyle\pm 0.0015}$
$-\,w_{\theta,i}$	$0.177_{\scriptscriptstyle\pm 0.046}$	$0.955_{\scriptscriptstyle\pm 0.016}$	$0.302_{\scriptscriptstyle\pm 0.036}$	$0.917_{\scriptscriptstyle\pm 0.013}$	$0.237_{\scriptscriptstyle\pm 0.006}$	$0.950_{\scriptscriptstyle\pm 0.0015}$
$-$ rescaling	$0.199_{\scriptscriptstyle\pm 0.004}$	$0.947_{\scriptscriptstyle\pm 0.0007}$	$0.339_{\scriptscriptstyle\pm 0.002}$	$0.902_{\scriptscriptstyle\pm 0.0005}$	$0.231_{\scriptscriptstyle\pm 0.009}$	$0.929_{\scriptscriptstyle\pm 0.003}$

Table 5: SRB ablations, averaged over the five shapes; mean

\pm

standard deviation over three seeds.

Appendix figures & tables36 assets

Supplementary material from the paper’s appendix.

Appendix

Panel of Figure 8 — Figure 8: SRB acquisition protocol. Scanner poses lie on $\mathbb{S}(r)$ ; rays are cast through a uniform grid, and their first surface intersections are retained.

Panel of Figure 9 — Figure 9: ShapeNet acquisition protocol. Virtual sensors lie on two concentric spheres; uniformly sampled targets on the enclosing sphere define ray directions, and the first surface intersections are retained.

Figure 10: Qualitative reconstruction on DTU MVS scenes 37, 69, 105 and 122. Ours (SW $L=6$ ) uses Sandwich layers (SW; Appendix C.3 ).

Figure 11: Sensitivity of

\mathrm{CD}_{1}^{\mathrm{obs}}

to the support threshold

\beta h_{0}

on clean SRB (

\lambda=0

), averaged over the five shapes;

\beta=\infty

recovers

\mathrm{CD}_{1}

Figure 12: Observation-supported SRB regions under the $2h_{0}$ support mask; orange denotes removed surface regions.

Figure 13: ARKitScenes held-out depth inlier rate

I@\tau

as a function of the threshold

\tau

Relative radius $\tau$	$\lambda=0$	$\lambda=1$	$\alpha=0$	$\alpha=0.2$
1.0	76.7	72.2	81.5	88.1
0.9	80.9	75.9	85.3	86.3
0.8	83.1	77.6	86.8	82.5
0.7	83.9	77.6	87.0	78.2
0.6	82.4	75.3	85.1	72.9

Appendix

Table 6: Certified free-space volume

\operatorname{CFV}_{\tau}

(%) for Ours (

L=0

, no rescale) within concentric sub-balls of the initialization domain;

\tau=1

denotes the full initialization ball.

Figure 14: Certified volumetric free-space regions on a single SRB shape.

Variant	SRB $\lambda=0$		SRB $\lambda=1$		SRB $\alpha=0.2$
	$\boldsymbol{\mathrm{CD}}_{1}\downarrow$	$\mathbf{NC}\uparrow$	$\boldsymbol{\mathrm{CD}}_{1}\downarrow$	$\mathbf{NC}\uparrow$	$\boldsymbol{\mathrm{CD}}_{1}\downarrow$	$\mathbf{NC}\uparrow$
ReLU + eikonal	0.366	0.906	0.421	0.891	1.249	0.786
CPL + eikonal	3.013	0.685	2.946	0.689	4.963	0.628
CPL + hKR	0.576	0.940	0.719	0.940	1.226	0.915
Ours ( $L=0$ )	0.158	0.959	0.296	0.911	0.165	0.956

Appendix

Table 7: Additional SRB objective ablations. Results use a single seed and are averaged over the five SRB shapes. ReLU + eikonal uses the same first-hit loss and differs from Ours only by its architecture.

Figure 15: Sensitivity of Ours (

L=0

) to the Huber scale

\delta

on a single SRB shape, with

\delta

normalized by its default value

\delta_{0}

. We use

\delta_{0}=0.05

on clean data and

\delta_{0}=0.005

with outliers (

\alpha=0.2

);

\ell_{1}

and

\ell_{2}

losses are shown for reference.

Setting	Backbone	$\mathrm{CD}_{1}$ $\downarrow$	$\mathrm{NC}\uparrow$	$\mathrm{CD}_{1}^{\mathrm{obs}}\downarrow$	$\mathrm{NC}^{\mathrm{obs}}\uparrow$
$\lambda=0$	CPL	0.1584	0.9597	0.0984	0.9698
	Sandwich	0.1307	0.9728	0.0801	0.9820
$\lambda=1$	CPL	0.2950	0.9139	0.2205	0.9271
	Sandwich	0.2818	0.9084	0.2229	0.9204
$\alpha=0.2$	CPL	0.1650	0.9571	0.1062	0.9697
	Sandwich	0.1311	0.9687	0.0882	0.9791

Appendix

Table 8: Preliminary single seed comparison of CPL and Sandwich backbones on SRB.

Figure 16: Ratio of the depth residual to the true projection distance

d(p_{i},\mathcal{S}_{\theta})

during a 25

k

-step fit on a single SRB shape with

\lambda=0

(median and

p_{10}

–

p_{90}

over 4

k

rays). Solid curves use incidence weighting; dashed curves remove it.

Figure 17: Density of $\|\nabla_{x}f_{\theta}(x)\|_{2}$ at points sampled along the traced rays on the five SRB shapes under $\lambda=0$ , $\lambda=1$ , and $\alpha=0.2$ ( $82k$ samples per curve and $16,384$ per shape). The axis is clipped at $2$ .

$L$	Setting	No rescale	Rescaled	$\Delta$
2	$\lambda=0$	0.124	0.128	+0.004 $(+3.2\%)$
2	$\lambda=1$	0.425	0.381	-0.044 $(-10.4\%)$
2	$\alpha=0.2$	0.125	0.122	-0.003 $(-2.4\%)$
6	$\lambda=0$	0.134	0.133	-0.001 $(-0.7\%)$
6	$\lambda=1$	0.543	0.542	-0.001 $(-0.2\%)$
6	$\alpha=0.2$	0.489	0.414	-0.075 $(-15.3\%)$

Appendix

Table 9: Effect of empirical rescaling for the

L=2

and

L=6

variants under noise and outliers. Values are

\Delta

(rescale

-

no rescale), averaged over the five SRB shapes for a single seed.

Variant	Rays	Dropped	Huber linear	Huber quadratic
Ours ( $L=6$ )	Inlier	2.4%	5.9%	91.7%
	Outlier	41.0%	57.0%	2.1%
Ours ( $L=0$ )	Inlier	0.8%	8.0%	91.2%
	Outlier	39.3%	60.1%	0.6%

Appendix

Table 10: Ray statistics at convergence on SRB with outliers (

\alpha=0.2

), averaged over the five shapes. Dropped rays are those for which sphere tracing finds no valid hit. Non-grazing rays are partitioned by the Huber regime of their weighted residual.

$\sigma/h_{\mathrm{NN}}$	Position error / standoff	CD $\downarrow$	NC $\uparrow$
0	0.0%	0.071	0.976
2	0.9%	0.071	0.976
4	1.8%	0.077	0.973
8	3.7%	0.079	0.975
16	7.4%	0.098	0.971

Appendix

Table 11: Sensitivity to sensor-position perturbations on a single SRB shape at

\lambda=0

	Neural implicit									Classical
Shape	$L=0$	$L=2$	$L=4$	$L=6$	DiffCD	N.-Pull	DiGS	NDF-vis	SAL	SPSR
Anchor	0.0309	0.0186	0.0124	0.0118	0.0095	0.0248	0.0389	0.3024	0.4796	0.0413
Daratech	0.1156	0.0366	0.0160	0.0134	0.0337	0.3983	0.0256	0.4017	0.4271	0.1027
DC	0.0407	0.0238	0.0119	0.0085	0.0114	0.3917	0.0278	0.5725	0.4795	0.0580
Gargoyle	0.0825	0.0441	0.0249	0.0136	0.0198	0.0324	0.0390	0.6962	0.6387	0.0639
Lord Quas	0.0291	0.0148	0.0102	0.0064	0.0132	0.0143	0.0306	0.2317	0.4496	0.0339

Appendix

Table 12: Clean-SRB data fidelity. Mean input-to-surface distance; best/second-best neural implicit results are bold/underlined. Labatut is omitted since its Delaunay surface is constructed from the inputs.

Figure 18: Clean-SRB surface error maps across the five shapes. Colors show distance to the ground-truth surface normalized by object radius.

Figure 19: Mean

\mathrm{CD}_{1}

(left) and

\mathrm{CD}_{1}^{\mathrm{obs}}

(right) as a function of

L

under outlier fractions

\alpha

on SRB.

Figure 20: Mean

\mathrm{CD}_{1}

(left) and

\mathrm{CD}_{1}^{\mathrm{obs}}

(right) as a function of

L

under scanner noise

\lambda

on SRB, on a single seed.

Figure 21: Effect of $L$ in a weakly observed concave region.

Figure 22: Mean SRB

\mathrm{CD}_{1}

with one seed during training under scanner noise (top) and outlier fractions (bottom).

Method	Raw $\mathrm{CD}_{1}\downarrow$	LCC $\mathrm{CD}_{1}\downarrow$	Raw NC $\uparrow$	LCC NC $\uparrow$
Ours ( $L=0$ )	0.173	0.172	0.954	0.955
Ours ( $L=2$ )	0.122	0.122	0.968	0.969
Ours ( $L=6$ )	0.414	0.397	0.818	0.820
NDF-vis	5.492	5.472	0.723	0.723
Neural-Pull	3.420	6.680	0.756	0.714
DiffCD	3.354	3.319	0.806	0.809

Appendix

Table 13: Effect of largest-connected-component filtering on SRB with outliers (

\alpha=0.2

(a) Method comparison			(b) Step budget
Method	Time $\downarrow$	Peak GPU (GB) $\downarrow$	Steps	Budget	CD ${}_{1}\downarrow$	$\Delta$
SAL	$\sim$ 1 min	0.73	5k	20%	0.171	+21.3%
Neural-Pull	$\sim$ 5 min	0.42	10k	40%	0.145	+2.8%
NDF-vis	$\sim$ 10 min	0.63	15k	60%	0.144	+2.1%
DiGS	$\sim$ 20 min	2.94	20k	80%	0.141	+0.0%
DiffCD	$\sim$ 40 min	2.52	25k	100%	0.141	—

Appendix

Table 14: Left: wall-clock training time and peak GPU memory on one SRB shape using an NVIDIA RTX 6000. Right:

\mathrm{CD}_{1}

averaged over the five SRB shapes at intermediate mesh resolution

256^{3}

for Ours (

L=6

) every

5k

training steps.

Model	$\mathbb{E}[k]/K$	Mean $k$	Reaching $K$	Converged (%)
Ours ( $L=0$ , no rescale)	40.8%	78.4	2.13%	$99.92/\mathbf{99.96}/100.00$
Ours ( $L=0$ )	9.4%	18.1	0.002%	$99.91/\mathbf{99.96}/99.99$
Ours ( $L=6$ )	22.2%	42.6	0.08%	$98.73/\mathbf{99.37}/99.92$

Appendix

Table 15: sphere tracing workload over SRB training rays with

K=192

. Convergence rates are min/mean/max over the five SRB shapes.

Figure 23: Mean SRB

\mathrm{CD}_{1}

and NC across increasing scanner-noise levels

\lambda

		Clean ( $\lambda=0$ )						Noise ( $\lambda=1$ )
Method	Metric	Anchor	Daratech	DC	Gargoyle	L. Quas	Mean	Anchor	Daratech	DC	Gargoyle	L. Quas	Mean
Neural implicit
Ours ( $L=0$ )	$\mathrm{CD}_{1}$ $\downarrow$	0.195	0.286	0.107	0.149	0.077	0.163 $\pm$ 0.005	0.337	0.412	0.261	0.291	0.252	0.310 $\pm$ 0.016
Ours ( $L=0$ )	$\mathrm{NC}\uparrow$	0.978	0.903	0.973	0.952	0.983	0.958 $\pm$ 0.0011	0.939	0.851	0.915	0.902	0.920	0.906 $\pm$ 0.0060
Ours ( $L=2$ )	$\mathrm{CD}_{1}$ $\downarrow$	0.186	0.200	0.088	0.108	0.055	0.127 $\pm$ 0.002	0.403	0.445	0.368	0.376	0.312	0.381 $\pm$ 0.002
Ours ( $L=2$ )	$\mathrm{NC}\uparrow$	0.979	0.934	0.979	0.969	0.991	0.970 $\pm$ 0.001	0.865	0.676	0.757	0.818	0.788	0.781 $\pm$ 0.002

Appendix

Table 16: Per-shape SRB reconstruction under clean input (

\lambda=0

) and scanner noise (

\lambda=1

). Stochastic results use three seeds; best neural implicit results are shown in bold.

		Clean ( $\lambda=0$ )						Noise ( $\lambda=1$ )
Method	Metric	Anchor	Daratech	DC	Gargoyle	L. Quas	Mean	Anchor	Daratech	DC	Gargoyle	L. Quas	Mean
Neural implicit
Ours ( $L=0$ )	$\mathrm{CD}_{1}^{\mathrm{obs}}\downarrow$	0.078	0.146	0.090	0.126	0.066	0.101 $\pm$ 0.003	0.194	0.262	0.234	0.245	0.196	0.226 $\pm$ 0.005
Ours ( $L=0$ )	$\mathrm{NC}^{\mathrm{obs}}\uparrow$	0.991	0.932	0.980	0.961	0.987	0.970 $\pm$ 0.0007	0.956	0.875	0.926	0.916	0.931	0.921 $\pm$ 0.004
Ours ( $L=2$ )	$\mathrm{CD}_{1}^{\mathrm{obs}}\downarrow$	0.070	0.077	0.073	0.094	0.050	0.073 $\pm$ 0.001	0.248	0.325	0.327	0.303	0.277	0.296 $\pm$ 0.004
Ours ( $L=2$ )	$\mathrm{NC}^{\mathrm{obs}}\uparrow$	0.993	0.962	0.987	0.976	0.994	0.982 $\pm$ 0.0002	0.889	0.686	0.768	0.833	0.794	0.794 $\pm$ 0.002

Appendix

Table 17: Per-shape observation-supported SRB results under clean input (

\lambda=0

) and scanner noise (

\lambda=1

), using the

2h_{0}

support threshold. Stochastic results use three seeds; best neural implicit results are shown in bold.

Figure 24: Mean SRB

\mathrm{CD}_{1}

and NC across increasing outlier levels

\alpha

Figure 25: Qualitative Gargoyle reconstructions across increasing outlier levels $\alpha$ .

		Clean ( $\alpha=0$ )						Outliers ( $\alpha=0.2$ )
Method	Metric	Anchor	Daratech	DC	Gargoyle	L. Quas	Mean	Anchor	Daratech	DC	Gargoyle	L. Quas	Mean
Neural implicit
Ours ( $L=0$ )	$\mathrm{CD}_{1}$ $\downarrow$	0.196	0.274	0.098	0.141	0.067	0.155 $\pm$ 0.003	0.202	0.275	0.118	0.194	0.073	0.173 $\pm$ 0.013
Ours ( $L=0$ )	$\mathrm{NC}\uparrow$	0.977	0.907	0.976	0.956	0.987	0.961 $\pm$ 0.0015	0.971	0.910	0.966	0.937	0.986	0.954 $\pm$ 0.0032
Ours ( $L=2$ )	$\mathrm{CD}_{1}$ $\downarrow$	0.195	0.153	0.084	0.109	0.055	0.119 $\pm$ 0.003	0.149	0.154	0.100	0.142	0.065	0.122 $\pm$ 0.004
Ours ( $L=2$ )	$\mathrm{NC}\uparrow$	0.977	0.951	0.982	0.969	0.992	0.974 $\pm$ 0.001	0.982	0.939	0.974	0.958	0.990	0.968 $\pm$ 0.001

Appendix

Table 18: Per-shape SRB reconstruction without outliers (

\alpha=0

) and with outliers (

\alpha=0.2

). Stochastic results use three seeds; best neural implicit results are shown in bold.

		Clean ( $\alpha=0$ )						Outliers ( $\alpha=0.2$ )
Method	Metric	Anchor	Daratech	DC	Gargoyle	L. Quas	Mean	Anchor	Daratech	DC	Gargoyle	L. Quas	Mean
Neural implicit
Ours ( $L=0$ )	$\mathrm{CD}_{1}^{\mathrm{obs}}\downarrow$	0.078	0.141	0.086	0.123	0.060	0.098 $\pm$ 0.002	0.096	0.135	0.099	0.137	0.068	0.107 $\pm$ 0.005
Ours ( $L=0$ )	$\mathrm{NC}^{\mathrm{obs}}\uparrow$	0.991	0.936	0.982	0.963	0.990	0.973 $\pm$ 0.0009	0.984	0.939	0.974	0.952	0.988	0.968 $\pm$ 0.002
Ours ( $L=2$ )	$\mathrm{CD}_{1}^{\mathrm{obs}}\downarrow$	0.069	0.067	0.070	0.094	0.050	0.070 $\pm$ 0.002	0.078	0.078	0.081	0.105	0.060	0.080 $\pm$ 0.002
Ours ( $L=2$ )	$\mathrm{NC}^{\mathrm{obs}}\uparrow$	0.993	0.974	0.988	0.977	0.994	0.985 $\pm$ 0.001	0.993	0.968	0.983	0.971	0.992	0.981 $\pm$ 0.001

Appendix

Table 19: Per-shape observation-supported SRB results without outliers (

\alpha=0

) and with outliers (

\alpha=0.2

), using the

2h_{0}

support threshold. Stochastic results use three seeds; best neural implicit results are shown in bold.

Method	Anchor	Daratech	DC	Gargoyle	Lord Quas	Mean
$\mathrm{CD}_{1}\downarrow$
Labatut	1.166	0.213	0.107	0.353	0.082	0.384
Ours ( $L=0$ )	0.264	0.271	0.109	0.161	0.078	0.177
Ours ( $L=2$ )	0.206	0.177	0.099	0.134	0.068	0.137
$\mathrm{NC}\uparrow$
Labatut	0.948	0.894	0.955	0.948	0.966	0.942

Appendix

Table 20: SRB with ray-aligned outliers. Left: reconstruction metrics with

10\%

of rays having corrupted range. Right: qualitative results on Gargoyle.

Category	Noise	Ours ( $L=0$ )	Ours ( $L=6$ )	NDF-vis	DiffCD	N.-P	SAL	DiGS	SPSR	Labat.
Airplane	Iso.	$\boldsymbol{3.72\mathrm{e}^{-5}}$	$5.16\mathrm{e}^{-5}$	$4.32\mathrm{e}^{-4}$	$5.57\mathrm{e}^{-5}$	$1.75\mathrm{e}^{-4}$	$7.70\mathrm{e}^{-3}$	$1.07\mathrm{e}^{-4}$	$9.66\mathrm{e}^{-5}$	$8.93\mathrm{e}^{-5}$
	Ray	$\boldsymbol{2.91\mathrm{e}^{-5}}$	$3.78\mathrm{e}^{-5}$	$1.18\mathrm{e}^{-3}$	$4.30\mathrm{e}^{-5}$	$1.12\mathrm{e}^{-3}$	$6.81\mathrm{e}^{-3}$	$1.24\mathrm{e}^{-4}$	$9.36\mathrm{e}^{-5}$	$1.25\mathrm{e}^{-4}$
Bench	Iso.	$1.39\mathrm{e}^{-4}$	$\boldsymbol{1.33\mathrm{e}^{-4}}$	$3.09\mathrm{e}^{-4}$	$1.74\mathrm{e}^{-4}$	$1.75\mathrm{e}^{-3}$	$1.93\mathrm{e}^{-3}$	$2.52\mathrm{e}^{-4}$	$1.08\mathrm{e}^{-2}$	$1.73\mathrm{e}^{-4}$
	Ray	$1.59\mathrm{e}^{-4}$	$\boldsymbol{1.08\mathrm{e}^{-4}}$	$3.43\mathrm{e}^{-4}$	$1.65\mathrm{e}^{-4}$	$5.29\mathrm{e}^{-4}$	$1.15\mathrm{e}^{-2}$	$2.13\mathrm{e}^{-4}$	$1.11\mathrm{e}^{-2}$	$2.11\mathrm{e}^{-4}$
Cabinet	Iso.	$9.73\mathrm{e}^{-4}$	$\boldsymbol{8.52\mathrm{e}^{-4}}$	$1.27\mathrm{e}^{-3}$	$1.12\mathrm{e}^{-3}$	$1.79\mathrm{e}^{-3}$	$3.69\mathrm{e}^{-3}$	$1.41\mathrm{e}^{-3}$	$3.22\mathrm{e}^{-3}$	$9.58\mathrm{e}^{-4}$
	Ray	$9.40\mathrm{e}^{-4}$	$\boldsymbol{7.55\mathrm{e}^{-4}}$	$1.51\mathrm{e}^{-3}$	$1.12\mathrm{e}^{-3}$	$1.82\mathrm{e}^{-3}$	$4.06\mathrm{e}^{-3}$	$1.39\mathrm{e}^{-3}$	$3.10\mathrm{e}^{-3}$	$9.85\mathrm{e}^{-4}$

Appendix

Table 21: ShapeNet category-wise

\mathrm{CD}_{2}

under isotropic and ray-aligned Gaussian noise with 3K input points. Best neural implicit results are shown in bold.

Category	Noise	Ours ( $L=0$ )	Ours ( $L=6$ )	NDF-vis	DiffCD	N.-P	SAL	DiGS	SPSR	Labat.
Airplane	Iso.	0.90	0.87	0.86	0.82	0.73	0.79	0.62	0.85	0.73
	Ray	0.92	0.90	0.84	0.87	0.72	0.79	0.66	0.84	0.75
Bench	Iso.	0.88	0.88	0.88	0.83	0.75	0.89	0.65	0.76	0.77
	Ray	0.88	0.88	0.88	0.86	0.78	0.78	0.68	0.76	0.79
Cabinet	Iso.	0.86	0.87	0.83	0.84	0.76	0.83	0.66	0.81	0.79
	Ray	0.87	0.87	0.83	0.85	0.78	0.83	0.68	0.81	0.80

Appendix

Table 22: ShapeNet category-wise normal consistency under isotropic and ray-aligned Gaussian noise with 3K input points. Best neural implicit results are shown in bold.

Category	Noise	Ours ( $L=0$ )	Ours ( $L=6$ )	NDF-vis	DiffCD	N.-P	SAL	DiGS	SPSR	Labat.
Airplane	Iso.	0.82	0.79	0.57	0.75	0.63	0.57	0.23	0.74	0.73
	Ray	0.86	0.83	0.43	0.79	0.44	0.60	0.52	0.75	0.69
Bench	Iso.	0.82	0.80	0.70	0.62	0.58	0.75	0.38	0.40	0.76
	Ray	0.83	0.82	0.70	0.69	0.63	0.47	0.50	0.41	0.77
Cabinet	Iso.	0.82	0.85	0.76	0.74	0.71	0.71	0.58	0.66	0.81
	Ray	0.84	0.85	0.74	0.74	0.71	0.69	0.62	0.66	0.81

Appendix

Table 23: ShapeNet category-wise IoU under isotropic and ray-aligned Gaussian noise with 3K input points. Best neural implicit results are shown in bold.

3D Reconstruction

3D reconstruction recovers a scene’s shape, appearance, and camera motion from images, video, depth, or other sensor measurements.

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Aug 27, 2026

NeuDonatello: Uncertainty-Aware Framework for Accurate Neural SDF Learning

Neural surface reconstruction has emerged as a powerful paradigm for recovering high-quality 3D surfaces from multi-view images. However, recovering accurate geometry solely from RGB images remains challenging due to uncertainties arising from textureless regions, occlusions, and inherent scene ambiguities. Existing methods often overlook such uncertainties, leading to inaccurate estimates of the signed distance function (SDF). We introduce NeuDonatello, a novel framework that models and leverages SDF uncertainty to improve surface reconstruction. Central to our approach is to model spatially varying uncertainty using a Monte Carlo sampling strategy. Using this uncertainty, we develop an adaptive regularization that selectively strengthens geometric constraints where RGB supervision is unreliable, avoiding incorrect surface reconstruction. We further introduce an uncertainty-aware scale parameter for the SDF-to-density conversion. Conditioned on uncertainty, this design enables more accurate modeling of spatially varying densities. Extensive experiments demonstrate that NeuDonatello achieves state-of-the-art reconstruction accuracy, with robust performance across diverse scenes using only posed RGB images.

Alvin Jinsung Choi, Wanhee Kim, Taeyun Kim +3

Department of Computer Science The University of Texas at Austin Texas, USA · School of Electrical Engineering Korea Advanced Institute of Science and Technology (KAIST) Daejeon, Republic of Korea · Robotics Program Korea Advanced Institute of Science and Technology (KAIST) Daejeon, Republic of Korea +2

3D Reconstruction Multi-View 3D Reconstruction Signed Distance Functions Uncertainty Quantification

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Feb 27, 2026

Leveraging Geometric Prior Uncertainty and Complementary Constraints for High-Fidelity Neural Indoor Surface Reconstruction

Neural implicit surface reconstruction with signed distance function has made significant progress, but recovering fine details such as thin structures and complex geometries remains challenging due to unreliable or noisy geometric priors. Existing approaches rely on implicit uncertainty that arises during optimization to filter these priors, which is indirect and inefficient, and masking supervision in high-uncertainty regions further leads to under-constrained optimization. To address these issues, we propose GPU-SDF, a neural implicit framework for indoor surface reconstruction that leverages geometric prior uncertainty and complementary constraints. We introduce a self-supervised module that explicitly estimates prior uncertainty without auxiliary networks. Based on this estimation, we design an uncertainty-guided loss that modulates prior influence rather than discarding it, thereby retaining weak but informative cues. To address regions with high prior uncertainty, GPU-SDF further incorporates two complementary constraints: an edge distance field that strengthens boundary supervision and a multi-view consistency regularization that enforces geometric coherence. Extensive experiments confirm that GPU-SDF improves the reconstruction of fine details and serves as a plug-and-play enhancement for existing frameworks. Source code will be available at https://github.com/IRMVLab/GPU-SDF

Qiyu Feng, Jiwei Shan, Shing Shin Cheng +1

Department of Automation, Shanghai Jiao Tong University, Shanghai 200240, China. · Department of Mechanical and Automation Engineering and T Stone Robotics Institute, The Chinese University of Hong Kong, Hong Kong.

UQ for 3D Reconstruction 3D Reconstruction Indoor Scene Reconstruction Neural Representation Geometry Signed Distance Functions

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Mar 26, 2026

Neural Surface and Reflectance Modelling from 3D Radar Data

Robust scene representation is essential for autonomous systems to safely operate in challenging low-visibility environments. In these conditions, radar has a clear advantage over cameras and lidars due to its resilience to environmental factors such as fog, smoke, or dust. However, radar data is inherently sparse and noisy, making reliable 3D surface reconstruction challenging. To address this, we propose a neural implicit approach for 3D mapping from radar point clouds that jointly models scene geometry and view-dependent radar intensities. Our method leverages a memory-efficient hybrid feature encoding to learn a continuous Signed Distance Field (SDF) for surface reconstruction, while also capturing radar-specific reflective properties. We show that our approach produces smoother, more accurate 3D surface reconstructions compared to existing lidar-based reconstruction methods applied to radar data and can reconstruct view-dependent radar intensities. We also show that, in general, as input point clouds get sparser, neural implicit representations render more faithful surfaces than traditional explicit SDFs and meshing techniques.

Judith Treffler, Vladimír Kubelka, Henrik Andreasson +1

The authors are with ARC and the AASS RNP lab, Örebro University, Sweden

Implicit Neural Representations 3D Reconstruction Point Cloud Surface Reconstruction Remote Sensing

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Abstract

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