HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details

Yiqun WangIvan SkorokhodovPeter Wonka

article2022NeurIPS166 citations

Presents a neural surface reconstruction framework that recovers fine geometric details without 3D supervision by decomposing signed distance functions into base and displacement fields and applying spatially adaptive optimization.

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Reconstructing high-fidelity three-dimensional surfaces from two-dimensional images without direct 3D supervision is a key capability for modern visual computing and simulation. While recent neural implicit rendering methods have improved geometry extraction, they struggle to capture fine-grained high-frequency details, frequently producing overly smoothed surfaces or suffering from optimization instability when attempting to learn complex geometries.

The article evaluates a novel neural surface reconstruction framework, termed HF-NeuS, designed to accurately recover sharp, high-frequency geometric details from multi-view images. The main objective is to establish an improved mathematical formulation and multi-scale learning architecture that outperforms existing neural implicit surface techniques.

To achieve this, the approach introduces three core components. First, it re-evaluates the volume rendering formulation by directly modeling optical transparency as a transformed signed distance function, which simplifies density derivations and avoids numerical instabilities. Second, it separates the surface representation into two distinct neural networks—a base surface network and an implicit displacement network—trained via a coarse-to-fine frequency progression to stabilize optimization without requiring 3D supervision. Third, it implements a spatially adaptive scale mechanism that dynamically increases sampling and model precision near regions where surface errors and steep gradient changes occur. The authors benchmarked this framework against established methods (including NeuS, VolSDF, and NeRF) across 15 DTU multi-view stereo scenes, 6 NeRF-Synthetic scenes, and 3 BlendedMVS scenes.

The quantitative and qualitative findings demonstrate substantial performance gains. On the standard 15-scene DTU benchmark, the proposed framework improved the mean Chamfer distance to 0.77, compared to 0.86 for VolSDF and 0.87 for NeuS, representing an approximate 10% to 11% reduction in geometric error. On datasets characterized by sharp features and intricate structures, the performance advantage widened significantly; for instance, the synthetic dataset average error dropped to 1.12, outperforming NeuS (1.97) by over 40%. The method also achieved superior rendering fidelity, yielding higher image reconstruction quality (PSNR) across all evaluated benchmarks. Visually, the framework successfully reconstructed thin structures, small apertures, and sharp corners—such as cables and repeating geometric patterns—that competing methods blurred or missed entirely.

These results indicate that decomposing neural implicit geometries and applying spatially targeted optimization can overcome traditional smoothing trade-offs in neural rendering. For technical leaders and practitioners, this means automated 3D visual reconstruction pipelines can achieve higher geometrical precision without requiring specialized 3D scanning hardware or manual touch-ups, potentially reducing production costs in asset modeling and spatial mapping. While earlier methods struggled when high frequencies were introduced directly into a single network, the displacement architecture provides a stable path forward.

Organizations developing automated 3D modeling pipelines should consider adopting dual-implicit function architectures with coarse-to-fine scheduling to resolve fine structural details. Future development should focus on testing the framework under diverse and varying lighting conditions and exploring performance optimizations to mitigate the additional computational overhead introduced by the secondary displacement network.

Users should note specific limitations: very thin or lattice-like features (such as rope netting) can still cause radiance overfitting where visual appearances render correctly but surface extraction fails, and regions with weak textures or shifting illumination remain difficult to reconstruct reliably. Nonetheless, given the consistent cross-dataset benchmarks and rigorous ablation results, confidence in the framework's core improvements is high.

King Abdullah University of Science and Technology 3d reconstruction reconstruction surface reconstruction high-frequency details neural implicit surfaces

arXiv: 2206.07850

Paper: NeuS: Learning Neural Implicit Surfaces by Volume Rendering for Multi-view Reconstruction, Peng Wang et al. (2021). NeuS provides the foundational neural volume rendering formulation based on signed distance functions that HF-NeuS directly builds upon and improves.
Paper: Volume Rendering of Neural Implicit Surfaces, Lior Yariv et al. (2021). VolSDF introduces key mathematical derivations linking SDFs to volumetric density and transparency in neural implicit rendering, establishing core theory analyzed by HF-NeuS.
Paper: Geometry-Consistent Neural Shape Representation with Implicit Displacement Fields, Yifan Wang et al. (2022). This work establishes the strategy of decomposing implicit geometry into base shapes and displacement fields to capture fine surface details stably.
Paper: Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains, Matthew Tancik et al. (2020). Fourier Features explains the spectral bias of coordinate networks toward low frequencies, motivating HF-NeuS's high-frequency detail decomposition.
Paper: NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis, Ben Mildenhall et al. (2020). NeRF introduces the fundamental differentiable volume rendering framework utilized and adapted for implicit surface modeling.
Paper: DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation, Jeong Joon Park et al. (2019). DeepSDF introduced continuous neural signed distance functions as implicit 3D shape representations, foundational to neural surface reconstruction.

Paper: PermutoSDF: Fast Multi-View Reconstruction with Implicit Surfaces Using Permutohedral Lattices, Radu Alexandru Rosu et al. (2023). PermutoSDF advances neural implicit surface reconstruction with permutohedral lattices to rapidly optimize detailed SDF geometry without sacrificing high-frequency fidelity.
Paper: NeuralUDF: Learning Unsigned Distance Fields for Multi-View Reconstruction of Surfaces with Arbitrary Topologies, Xiaoxiao Long et al. (2023). NeuralUDF builds on neural implicit volume rendering by transitioning from signed distance functions to unsigned distance fields to support open, non-watertight topologies.
Paper: NeUDF: Leaning Neural Unsigned Distance Fields with Volume Rendering, Yu-Tao Liu et al. (2023). NeUDF extends neural volume rendering beyond standard SDF limitations using unbiased weight formulations tailored for complex, non-watertight surfaces.
Paper: VolRecon: Volume Rendering of Signed Ray Distance Functions for Generalizable Multi-View Reconstruction, Yufan Ren et al. (2023). VolRecon generalizes volume rendering of implicit distance functions to novel scenes across multi-view inputs without requiring per-scene retraining.

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Abstract

Neural rendering can be used to reconstruct implicit representations of shapes without 3D supervision. However, current neural surface reconstruction methods have difficulty learning high-frequency geometry details, so the reconstructed shapes are often over-smoothed. We develop HF-NeuS, a novel method to improve the quality of surface reconstruction in neural rendering. We follow recent work to model surfaces as signed distance functions (SDFs). First, we offer a derivation to analyze the relationship between the SDF, the volume density, the transparency function, and the weighting function used in the volume rendering equation and propose to model transparency as a transformed SDF. Second, we observe that attempting to jointly encode high-frequency and low-frequency components in a single SDF leads to unstable optimization. We propose to decompose the SDF into base and displacement functions with a coarse-to-fine strategy to increase the high-frequency details gradually. Finally, we design an adaptive optimization strategy that makes the training process focus on improving those regions near the surface where the SDFs have artifacts. Our qualitative and quantitative results show that our method can reconstruct fine-grained surface details and obtain better surface reconstruction quality than the current state of the art. Code available at https://github.com/yiqun-wang/HFS.

Topics

3d reconstruction reconstruction

Keywords

surface reconstruction high-frequency details neural implicit surfaces multi-view reconstruction neural radiance fields implicit displacement fields high-frequency positional encoding neural rendering NeRF-synthetic dataset space carving

1 Introduction
2 Related Work
3 Method
3.1 Modeling transparency as transformed SDF
3.2 Implicit displacement field without 3D supervision
3.3 Modeling an adaptive transparency function
4 Experiments
5 Conclusion
Acknowledgements
References

Knowls

Knowl 1 — Transparency modeled as a transformed signed distance function
theoretical result
HF-NeuS represents the surface as the zero level set of a signed distance function $f:\mathbb{R}^3\to\mathbb{R}$ and embeds this function into volume rendering by defining the ray transparency directly as $T(t)=\Psi(f(\mathbf r(t)))$ , where $\mathbf r(t)=\mathbf o+t\mathbf d$ is a camera ray, $t$ is distance along the ray, and $\Psi$ maps signed distances to values in $[0,1]$ .

For volume density $\sigma$ and rendering weight $w(t)=T(t)\sigma(\mathbf r(t))$ , the transparency relation is $w(t)=-T'(t)$ . Under the paper's planar-surface and single-ray-intersection assumption, the weighting function is maximized at the surface when $T'(t)$ is minimized there. If the ray starts outside the object, the signed distance decreases from positive values to negative values along the ray; therefore, a suitable distance-to-transparency function must be monotone increasing from $0$ to $1$ and have its steepest slope at signed distance zero.

HF-NeuS uses the normalized logistic family
$T(t)=\Psi_s(f(\mathbf r(t)))=\frac{1}{1+\exp\!\left(-s f(\mathbf r(t))\right)},$
where $s>0$ controls the slope of the transformation and hence the localization precision of the reconstructed surface. The formulation is not restricted to the logistic function, but the logistic choice is used in the method.
Knowl 2 — Explicit density and rendering discretization from the transformed SDF
equation
Given the differentiable transparency $T(t)=\Psi_s(f(\mathbf r(t)))$ , HF-NeuS obtains the volume density from the transparency derivative as
$\sigma(\mathbf r(t))=-\frac{T'(t)}{T(t)}.$
For a unit ray direction $\mathbf d$ , the logistic derivative gives the pointwise density used in discretized rendering:
$\sigma(\mathbf r(t_i))=s\left[\Psi_s\!\left(f(\mathbf r(t_i))\right)-1\right]\,\nabla f(\mathbf r(t_i))\cdot\mathbf d,$
where $t_i$ is the $i$ -th sample depth, $\nabla f$ is the spatial gradient of the SDF, and $\nabla f\cdot\mathbf d$ is the directional derivative along the ray. For samples separated by $\Delta t_i=t_{i+1}-t_i$ , the alpha-composition opacity is $\alpha_i=1-\exp(-\sigma_i\Delta t_i)$ ; when a ray encounters multiple surfaces, HF-NeuS clamps $\alpha_i$ to $[0,1]$ .

Because transparency is explicit, the method can use inverse-CDF sampling and does not require the two distinct section-point and midpoint sets used by NeuS or the more involved error-controlled sampling procedure of VolSDF. The resulting geometry and color are evaluated at the same samples.
Knowl 3 — Implicit displacement field for high-frequency surface geometry
model/method
HF-NeuS decomposes the detailed signed distance field into a base SDF $f_b$ and a scalar implicit displacement field. The base SDF defines a coarse surface, while the displacement field moves points along the base-surface normal to represent fine geometric details.

Let $\mathbf x_b$ be a point on the base surface, let $\mathbf n_b=\nabla f_b(\mathbf x_b)/\|\nabla f_b(\mathbf x_b)\|_2$ be its normal, and let $f_d'(\mathbf x_b)$ be the displacement from the base surface to the detailed surface. The intended correspondence satisfies
$f_b\!\left(\mathbf x_b+f_d'(\mathbf x_b)\mathbf n_b\right)=0.$
In the inverse direction, for a query point $\mathbf x$ , HF-NeuS evaluates the combined SDF approximately as
$f(\mathbf x)=f_b\!\left(\mathbf x-f_d(\mathbf x)\mathbf n(\mathbf x)\right),$
where $f_d(\mathbf x)$ is the displacement value and $\mathbf n(\mathbf x)$ is the normal estimated from the base SDF at $\mathbf x$ . The approximation assumes that the displacement transformation applies to neighboring iso-surfaces, not only to the zero level set, and that the base and detailed points are sufficiently close for the normal at the detailed point to replace the normal at the corresponding base point. The displacement magnitude is constrained using a factor proportional to the derivative $\Psi_s'(f_b)$ , concentrating the displacement near the base surface.
Knowl 4 — Coarse-to-fine positional encoding of base and displacement fields
model/method
HF-NeuS uses separate positional encodings and multilayer perceptrons for the base and displacement fields. For a position $\mathbf x\in\mathbb{R}^3$ , frequency band $j$ , and maximum band count $L$ , the unweighted encoding is
$\gamma(\mathbf x)=[\gamma_0(\mathbf x),\ldots,\gamma_{L-1}(\mathbf x)],\qquad \gamma_j(\mathbf x)=\left[\sin(2^j\pi\mathbf x),\cos(2^j\pi\mathbf x)\right],$
with sine and cosine applied componentwise. To prevent noisy high-frequency image information from destabilizing SDF learning, band $j$ is multiplied by a progressive weight controlled by $\alpha\in[0,1]$ :
$\gamma_j(\mathbf x,\alpha)= \frac{1-\cos\!\left(\operatorname{clamp}(\alpha L-j,0,1)\pi\right)}{2}\,\gamma_j(\mathbf x).$
The parameter $\alpha$ is increased by $1/n_{\max}$ per training iteration until it reaches $1$ , where $n_{\max}$ is the maximum number of iterations. HF-NeuS uses two eight-layer MLPs, $\mathrm{MLP}_b$ and $\mathrm{MLP}_d$ , to model the base and displacement functions separately. Their encoding schedules use $\alpha_b=0.5\alpha_d$ , so the displacement field receives higher frequencies sooner. The displacement output is applied along the base-SDF normal and is scaled by the surface-localizing factor based on $\Psi_s'(f_b)$ .
Knowl 5 — Spatially adaptive transparency scale
model/method
A single global logistic scale $s$ gives every spatial location the same transparency sharpness, even though combining a base SDF with a displacement field can cause the Eikonal condition to be violated locally. HF-NeuS therefore increases the scale near locations whose SDF gradient norm is unusually large.

For $K$ samples along a ray, let $f_i=f(\mathbf r(t_i))$ , let $\nabla f_i$ be the spatial gradient at sample $i$ , and define normalized weights
$\omega_i=\frac{\Psi_s'(f_i)}{\sum_{j=1}^{K}\Psi_s'(f_j)}, \qquad \sum_{i=1}^{K}\omega_i=1.$
The effective scale is
$s_{\mathrm{eff}}=s\exp\!\left(\sum_{i=1}^{K}\omega_i\|\nabla f_i\|_2-1\right),$
and the adaptive transparency is
$T(t)=\frac{1}{1+\exp\!\left(-s_{\mathrm{eff}}f(\mathbf r(t))\right)}.$
When the weighted gradient norm exceeds one, the effective scale increases, sharpening the transparency transition and magnifying local SDF errors near the surface. The same adaptive scale is used during hierarchical sampling, causing more samples to be allocated where the SDF changes abruptly and directing optimization toward problematic regions.
Knowl 6 — Joint radiance and two-field Eikonal training
model/method
HF-NeuS trains the base SDF $f_b$ and detailed SDF $f$ using a radiance reconstruction loss together with Eikonal regularization on both fields. For $M$ rendered rays with predicted colors $\hat{\mathbf C}_q$ and observed colors $\mathbf C_q$ , and $N$ regularization points $\mathbf x_k$ , the loss is
$\mathcal L= \frac{1}{M}\sum_{q=1}^{M}\left\|\hat{\mathbf C}_q-\mathbf C_q\right\|_1 +\frac{1}{N}\sum_{k=1}^{N} \left[ \left(\|\nabla f_b(\mathbf x_k)\|_2-1\right)^2 +\left(\|\nabla f(\mathbf x_k)\|_2-1\right)^2 \right].$
The first term fits the input image colors through volume rendering; the second encourages both neural fields to behave as signed distance functions. Training uses Adam with learning rate $5\times10^{-4}$ and two eight-layer MLPs. For each ray, HF-NeuS first samples 64 points uniformly, evaluates the SDF values and gradients, computes the adaptive-scale gain, and then adds 64 samples using the updated sampling weights. The reported implementation uses an NVIDIA A100 40 GB GPU.
Knowl 7 — Multi-dataset evaluation protocol for surface reconstruction
experimental setup
HF-NeuS is evaluated against NeRF, VolSDF, and NeuS using the methods' default parameters and recommended iteration counts. Surfaces are extracted from the learned implicit fields using an SDF threshold of $25$ .

The evaluation includes 15 DTU scenes, six NeRF-synthetic scenes, and three BlendedMVS scenes. DTU provides 49 or 64 views per scene at $1600\times1200$ resolution; NeRF-synthetic provides 100 views at $800\times800$ resolution; and BlendedMVS images have resolution $768\times576$ . All three datasets provide ground-truth surfaces and camera poses. The NeRF-synthetic and BlendedMVS selections emphasize thin structures, sharp edges, or repeated high-frequency geometry.

Surface quality is measured by Chamfer distance, with lower values preferred. For DTU, the reported fidelity is the mean of accuracy from the reconstruction to the ground truth and completeness from the ground truth to the reconstruction. Background regions are removed for DTU and BlendedMVS evaluation, while disconnected components are removed for NeRF-synthetic evaluation. Image agreement is measured by PSNR, with higher values preferred.
Knowl 8 — Improved fidelity and image quality on challenging scenes
empirical result
HF-NeuS achieves the best reported mean surface fidelity and PSNR among the compared methods. On the 15-scene DTU benchmark, the mean Chamfer distances are 1.49 for NeRF, 0.86 for VolSDF, 0.87 for NeuS, and 0.77 for HF-NeuS; the corresponding mean PSNR values are 30.65, 30.38, 31.97, and 32.33 dB.

On the six NeRF-synthetic scenes, the reported mean fidelity values, in the paper's $10^{-2}$ metric scale, are 3.36 for NeRF, 2.37 for VolSDF, 1.97 for NeuS, and 1.12 for HF-NeuS. Their mean PSNR values are 31.09, 26.86, 28.05, and 28.66 dB, respectively. On the three BlendedMVS scenes, the corresponding mean fidelity values are 1.07, 0.63, 0.43, and 0.38, and the mean PSNR values are 28.02, 28.25, 28.63, and 29.15 dB.

The qualitative reconstructions show that the advantage is concentrated on fine geometry: HF-NeuS recovers more distinct Lego-block details and small holes, sharper robot contours and horns, clearer bird feathers, and the thin microphone power cord. NeRF can obtain competitive PSNR while producing substantially poorer surfaces, demonstrating that image fidelity alone does not guarantee accurate geometric reconstruction.
Knowl 9 — Ablation isolates the benefits of coarse-to-fine learning, displacement fields, and adaptive scale
empirical result
The ablation compares a NeuS baseline (Base), direct high-frequency positional encoding (Base+H), coarse-to-fine high-frequency encoding (Base+C2F), an implicit displacement field with direct high frequencies (IDF+H), an implicit displacement field with coarse-to-fine encoding (IDF+C2F), and the full method, which additionally uses spatially adaptive $s$ . The reported values are means over three scenes per dataset; lower Chamfer distance and higher PSNR are better.

For DTU, the Chamfer distances for Base, Base+H, Base+C2F, IDF+H, IDF+C2F, and Full are respectively $1.08$ , $1.20$ , $1.07$ , $1.25$ , $0.89$ , and $0.78$ . Their PSNR values are $31.77$ , $32.73$ , $32.56$ , $32.69$ , $32.13$ , and $32.49$ dB.

For NeRF-synthetic, the corresponding Chamfer distances are $2.51$ , $3.61$ , $2.95$ , $2.83$ , $1.35$ , and $0.91$ , with PSNR values $28.39$ , $30.52$ , $30.63$ , $30.12$ , $29.88$ , and $30.31$ dB.

For BlendedMVS, the Chamfer results are $0.43$ , fail, $0.63$ , $0.47$ , $0.41$ , and $0.38$ , with PSNR values $28.63$ , fail, $27.35$ , $28.20$ , $28.95$ , and $29.15$ dB. Directly activating high frequencies can overfit or destabilize training, whereas the displacement field substantially improves fidelity. The adaptive-scale component provides an additional improvement on the more complex scenes.
Knowl 10 — Remaining failure cases and computational limitation
limitation
HF-NeuS can still overfit image radiance without reconstructing the corresponding geometry. In the ship example, the grid of ropes is visible in rendered images but is not accurately represented on the surface, and some individual thin ropes disappear entirely. The method also has failure cases where it performs worse than competing methods; one reported DTU example contains variable lighting and weak texture, making details on the object's belly difficult to infer. Finally, adding the implicit displacement field increases computation time.

Coverage note — No substantial contributed material was omitted; supplementary-only implementation details and background or related-work discussions were excluded.

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Citation

MLA

Wang, Y., et al. “HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details”. Advances in Neural Information Processing Systems, vol. 35, 2022, pp. 1966–78, https://proceedings.neurips.cc/paper_files/paper/2022/file/0ce8e3434c7b486bbddff9745b2a1722-Paper-Conference.pdf.

APA

Wang, Y., Skorokhodov, I., & Wonka, P. (2022). HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details. Advances in Neural Information Processing Systems, 35, 1966–1978. https://proceedings.neurips.cc/paper_files/paper/2022/file/0ce8e3434c7b486bbddff9745b2a1722-Paper-Conference.pdf

Chicago

Wang, Y., I. Skorokhodov, and P. Wonka. 2022. “HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details”. Advances in Neural Information Processing Systems 35: 1966–78. https://proceedings.neurips.cc/paper_files/paper/2022/file/0ce8e3434c7b486bbddff9745b2a1722-Paper-Conference.pdf.

Harvard

Wang, Y., Skorokhodov, I. and Wonka, P. (2022) “HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details”, Advances in Neural Information Processing Systems. Curran Associates, Inc., pp. 1966–1978. Available at: https://proceedings.neurips.cc/paper_files/paper/2022/file/0ce8e3434c7b486bbddff9745b2a1722-Paper-Conference.pdf.

Vancouver

1. Wang Y, Skorokhodov I, Wonka P (2022) HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details. In: Advances in Neural Information Processing Systems. Curran Associates, Inc., pp 1966–1978

BibTeX

@inproceedings{wang2022neus,
  title = {HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details},
  author = {Wang, Yiqun and Skorokhodov, Ivan and Wonka, Peter},
  year = {2022},
  booktitle = {Advances in Neural Information Processing Systems},
  publisher = {Curran Associates, Inc.},
  volume = {35},
  pages = {1966-1978},
  url = {https://proceedings.neurips.cc/paper_files/paper/2022/file/0ce8e3434c7b486bbddff9745b2a1722-Paper-Conference.pdf}
}

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HF-NeuS: Improved Surface Reconstruction Using High-Frequency Details

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Transparency modeled as a transformed signed distance function

Knowl 2 — Explicit density and rendering discretization from the transformed SDF

Knowl 3 — Implicit displacement field for high-frequency surface geometry

Knowl 4 — Coarse-to-fine positional encoding of base and displacement fields

Knowl 5 — Spatially adaptive transparency scale

Knowl 6 — Joint radiance and two-field Eikonal training

Knowl 7 — Multi-dataset evaluation protocol for surface reconstruction

Knowl 8 — Improved fidelity and image quality on challenging scenes

Knowl 9 — Ablation isolates the benefits of coarse-to-fine learning, displacement fields, and adaptive scale

Knowl 10 — Remaining failure cases and computational limitation

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