Voxurf: Voxel-based Efficient and Accurate Neural Surface Reconstruction

1 INTRODUCTION

• Fully implicit MLP methods require hours per scene, while explicit voxel methods train faster but can produce noisy, hole-filled surfaces that do not faithfully represent geometry.The cited voxel methods achieve rendering performance at a training cost below 20 minutes.Source: §1 · p. 1
• The naïve combination of SDF-based rendering and voxel grids loses geometry detail and adds noise, as voxel features can break color-geometry dependency and unconstrained grids lack spatial coherence.Independent voxel optimization also limits information sharing and can introduce local minima.Source: §1 · p. 2
• Voxurf uses two-stage training, a dual color network, hierarchical geometry features, and regularization to recover details while encouraging coherent geometry and smoother surfaces.The two color subnetworks work in synergy to represent a complex color field while preserving color-geometry dependency.Source: §1 · p. 2
• Around 20x speedup over NeuS accompanies lower Chamfer Distance on DTU; Voxurf also reports higher surface and novel-view synthesis quality with finer details.Training time is reduced from over 5 hours to 15 minutes on a single Nvidia A100 GPU.Source: §1 · p. 2
• The paper also contributes empirical analysis of architecture design for explicit volumetric surface reconstruction.The experiments evaluate DTU and BlendedMVS, with novel view synthesis as an auxiliary task.Source: §1 · pp. 2–3

Multi-view 3D reconstruction

• Implicit surface-rendering methods use ray-surface intersection colors but require accurate object masks and careful weight initialization; volume-rendering methods unify radiance fields and implicit surfaces, while pure MLPs train slowly.The cited surface-rendering works are Niemeyer et al. (2020), Yariv et al. (2020), Liu et al. (2020b), and Kellnhofer et al. (2021); volume-rendering works include Wang et al. (2021), Yariv et al. (2021), and Oechsle et al. (2021).Source: §2 · p. 3

Explicit volumetric representation

• Explicit methods such as Plenoxels, TensoRF, and DVGO improve rendering efficiency, but the cited approaches are not designed to faithfully reconstruct scene geometry.Voxurf instead targets photo-realistic novel views and high-quality surfaces with fine details.Source: §2 · p. 3

Volume rendering with SDF representation

• NeuS samples points along each camera ray and integrates their colors; its opacity formula distinguishes it from NeRF and uses the SDF and a sigmoid function.The ray is parameterized by the camera center and viewing direction, with ordered discrete samples.Source: §3 · p. 3

Explicit volumetric representation

• DVGO represents geometry with density voxels and predicts color using a shallow MLP supplied with interpolated voxel features, position, and viewing direction.The feature interpolation is trilinear.Source: §3 · pp. 3–4

Naïve Combination

• In the architecture comparison, learnable features help maintain a coherent shape but can suppress geometry details by disturbing the color-geometry dependency built by surface normals.The figure compares cases with optional normal and feature inputs to the color network.Source: Figure 2 · p. 4
• Replacing DVGO volume rendering with the SDF-based scheme serves as the naïve baseline, but it can hardly produce satisfactory results.The reported surface is continuous but noisy and loses geometry details.Source: §3 · p. 4, Figure 2 · p. 4

The key to maintaining a coherent coarse shape

• Local features alleviate geometry corruption from an under-capacity color MLP when images contain rapid color shifts, supporting coherent coarse shape.The comparison reports improvement when the local feature is incorporated in both illustrated settings.Source: §4 · p. 4

The key to reconstructing accurate geometry details

• With moderate texture and diffuse reflection, surface normals support geometry details, whereas adding learnable features disturbs color-geometry dependency and leaves details missing.Adding the feature does not further reduce Chamfer Distance in the described case.Source: §4 · p. 4

The reason for noisy surfaces

• Under-constrained voxel grids lack spatial coherence and are vulnerable to local minima, harming surface continuity and smoothness.The study suggests using regional geometry cues rather than information from only a local point.Source: §4 · p. 5

5 METHODOLOGY

• Voxurf trains in two stages, first attaining a coherent coarse shape and then recovering fine details.Its designs also include a dual color network, a hierarchical geometry feature, and smoothness priors.Source: §5 · p. 5

5.1 COARSE SHAPE INITIALIZATION

• Coarse initialization starts from an ellipsoid-like SDF zero level set and uses Gaussian-smoothed SDF queries for ray marching.A shallow MLP takes the normal, local feature, embedded position, and viewing direction as inputs.Source: §5.1 · p. 5

5.2 FINE GEOMETRY OPTIMIZATION

• The dual color network combines geometry-conditioned and feature-conditioned subnetworks to preserve color-geometry dependency while supporting rapid color learning.Detaching operations stabilize optimization of the geometry-conditioned network under its own reconstruction loss.Source: §5.2 · p. 6
• The hierarchical geometry feature uses neighboring SDF values and gradients from a larger region to encourage information propagation across voxels.This addresses the limited information sharing of pointwise trilinear interpolation, which can lead to local minima and degenerate solutions.Source: §5.2 · p. 6

5.3 SMOOTHNESS PRIORS

• Smoothness priors apply total variation to the SDF grid and a Gaussian-based smoothness loss to its gradients.The gradient term encourages smooth surfaces and alleviates noisy points in free space.Source: §5.3 · pp. 6–7

6 EXPERIMENTS

• The experiments use DTU for quantitative and qualitative comparisons and show qualitative results on challenging BlendedMVS scenes, with a clean background for fair comparisons.Additional comparisons with non-empty backgrounds and more methods are included in supplementary materials.Source: §6 · p. 7

6.1 COMPARISONS

• NeuS and Voxurf produce accurate, continuous surfaces, while DVGO shows noise and holes; Voxurf better recovers fine geometry than NeuS.The qualitative comparisons cover DTU and BlendedMVS, and NeuS sometimes misses thin details through over-smoothing.Source: §6.1 · pp. 7–8, Figure 4 · p. 8, Figure 5 · p. 8
• Voxurf outperforms DVGO and NeuS on surface reconstruction and novel view synthesis across the reported metrics, with around 20x speedup over NeuS.The study evaluates surface reconstruction, novel view synthesis, and training time.Source: §6.1 · p. 8

6.2 ANALYSIS

• The dual color network and hierarchical geometry feature each improve the baseline, and their combination produces the best result.The dual color network improves rendering and supports geometry learning; the hierarchical feature promotes accurate surface reconstruction.Source: §6.2 · pp. 8–9, Table 3 · p. 9, Table 4 · p. 9
• Gaussian convolution alleviates holes and noise during coarse initialization, while TV and gradient-smoothness regularization further encourage smooth surfaces.Regularization also helps maintain smoothness during fine optimization; post-processing improves visualization smoothness while maintaining accurate structure.Source: §6.2 · p. 9, Figure 7 · p. 9

7 CONCLUSION

• Voxurf’s two-stage framework, dual color network, hierarchical geometry feature, and gradient smoothness loss support efficient, high-quality surface reconstruction.The framework first attains a coherent coarse shape, then recovers fine details.Source: §7 · p. 9

A.1 DATASETS.

• DTU evaluation uses 15 scenes with 49 or 64 posed multiview images per scene, while BlendedMVS evaluation presents qualitative comparisons on seven selected challenging scenes.DTU comparisons use ground-truth point clouds for Chamfer Distance; the selected BlendedMVS scenes come from a 113-scene dataset.Source: §A.1 · p. 10

A.2 IMPLEMENTATION DETAILS

• The implementation trains a coarse initialization stage for 10k iterations and a fine geometry stage for 20k iterations, then upsamples the fine SDF grid from resolution 160^3 to 256^3.The appendix also specifies shared hyperparameters across scenes, a batch of 8,192 rays, and the learning-rate schedule for s.Source: §A.2 · p. 10

A.3 DETAILS FOR BASELINE METHODS

• The baseline set includes mask-based IDR and NeuS, plus no-mask methods including Colmap, UNISURF, VolSDF, NeRF, and NeuS.Results for the no-mask comparison are adopted from the original papers.Source: §A.3 · pp. 10–11

B.1 NOVEL VIEW SYNTHESIS.

• On DTU novel view synthesis, Voxurf outperforms the baselines on PSNR, SSIM, and LPIPS.Rendered test-view examples are shown in supplementary figures.Source: §B.1 · pp. 11–12, Table R1 · p. 11
• For hierarchical geometry, performance improves with feature level before converging after level 2.0; combining Gradient and SDF features gives the best result.The gradient smoothness loss is also reported effective in the quantitative smoothness-prior ablation.Source: Table R3 · p. 12, Table R4 · p. 12, Table R5 · p. 12

B.2 COMPARISONS FOR THE W/O MASK SETTING.

• For non-clean backgrounds, Voxurf inverts points outside the unit sphere into the sphere and represents the background with density and feature voxel grids plus a shallow MLP.The paper reports comparisons under this without-mask setting in Table R2.Source: §B.2 · p. 12

B.3 ADDITIONAL ABLATION STUDIES AND ANALYSIS

• The hierarchical-geometry ablations examine level selection and the effects of gradient and SDF value.Source: §B.3 · p. 12
• Removing the coarse-training Gaussian kernel raises CD from 0.72 to 0.74; removing post-processing lowers CD from 0.720 to 0.715 but slightly sacrifices visualization quality.The gradient smoothness loss is effective in quantitative comparisons.Source: §B.3 · p. 12
• Increasing resolution from 128^3 through 192^3 to 256^3 lowers CD but increases training time; 320^3 gives similar CD to 256^3 at higher cost, so 256^3 is the default.Source: §B.3 · p. 12
• Stage 1 produces a coherent coarse shape, while Stage 2 recovers fine details and preserves the overall structure established in Stage 1.Source: §B.3 · p. 12
• For DVGO surface extraction, thresholds that are too small produce floating noise, while thresholds that are too large create holes; the paper selects 0.1.Source: §B.3 · p. 13, Figure S2 · p. 13

C DVGO+NEUS W/ SMOOTHNESS

• For DVGO+NeuS, Gaussian post-processing alone smooths surfaces but worsens CD; combining smoothness designs yields smooth surfaces and lower CD, though Voxurf remains better.Source: C DVGO+NEUS W/ SMOOTHNESS · pp. 13–14
• Voxurf outperforms DVGO+NeuS with all tested smoothness designs; training takes 14min for Voxurf versus 15min for the smoothed baseline.The smoothed baseline takes 15min, up from 12min without those designs.Source: C DVGO+NEUS W/ SMOOTHNESS · p. 14

D DISCUSSIONS ON THE ASSUMPTION OF COLOR-GEOMETRY DEPENDENCY

• Textures uncorrelated with geometry can cause relief-like artifacts; multi-view consistency can largely alleviate them, and Voxurf is least affected, but fully addressing them is out of scope.Source: D DISCUSSIONS ON THE ASSUMPTION OF… · p. 14, Figure S4 · p. 15

E EVALUATIONS ON NEW DATASETS

• On Synthetic-NeRF and Synthetic-NSVF, Voxurf avoids DVGO's heavy noise and produces more accurate thin structures than NeuS in qualitative comparisons.Source: E EVALUATIONS ON NEW DATASETS · p. 15
• On Synthetic-NeRF and Synthetic-NSVF, Voxurf achieves average PSNRs of 32.38 and 35.18, while DVGO achieves 31.95 and 35.08, respectively.These datasets lack publicly available 3D ground truth for evaluation.Source: E EVALUATIONS ON NEW DATASETS · p. 15

F QUALITATIVE RESULTS ON LARGE SCENES

• On ScanNet scenes 0050, 0580, and 0616, Voxurf models the layout and some details but reconstructs planes such as floors and walls unsatisfactorily.The evaluation uses MiDaS-estimated depth and normals as extra supervision.Source: F QUALITATIVE RESULTS ON LARGE SCENES · p. 16, Figure S6 · p. 16

• On the shared scene, Point-NeRF's neural points have CD 0.56 versus Voxurf's 0.37; Poisson reconstruction raises Point-NeRF's CD to 1.77.Source: G COMPARISONS WITH MORE METHODS · p. 16
• The DTU novel-view-synthesis results are not directly comparable because Point-NeRF and Voxurf use different training and testing scenes and splits.Source: G COMPARISONS WITH MORE METHODS · p. 16

H LIMITATIONS

• Printed textures can still create relief-like artifacts under color-geometry dependence, even though Voxurf is relatively less affected; addressing the artifacts remains future work.Source: H LIMITATIONS · p. 17
• View-conditioned emitted radiance is insufficient for accurate surfaces with little texture, strong reflection, or transparency because of ambiguity.Source: H LIMITATIONS · p. 17

I ADDITIONAL QUALITATIVE COMPARISONS

• The additional qualitative comparisons cover novel-view synthesis on DTU and surface reconstruction on DTU and BlendedMVS.Source: I ADDITIONAL QUALITATIVE COMPARISONS · p. 17, Figure S8 · p. 18, Figure S9 · p. 19