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REVIEW 4 major objections 6 minor 59 references

Surf-NeRF: Surface Regularised Neural Radiance Fields

T0 review · 4 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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Pith's one-line read Surf-NeRF claims that steering a NeRF toward a surface light field with four regularisation losses and a permutohedral lattice encoding yields 27.9 percent more accurate surface normals than grid-based reflection-parameterised baselines…

desk verdict Surf-NeRF's normal-accuracy gains are real on the tested benchmark, but the abstract's promise of 'maintaining visual fidelity' is too strong—the Toaster scene shows a 3.5 dB PSNR drop. read the letter →

arxiv 2411.18652 v2 pith:KJAWBMFG submitted 2024-11-27 cs.CV

Jack Naylor , Viorela Ila , Donald G. Dansereau This is my paper · ORCID
classification cs.CV
keywords neuralradiancefieldssurfacelightregularisationpermutohedrallatticeshape-radianceambiguitynormalestimationview-dependentappearancecurriculumlearning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Neural radiance fields (NeRFs) reconstruct scenes from photos, but they are prone to shape-radiance ambiguity: the network can invent ghost geometry to explain reflections and highlights, producing surfaces that look right from the training views but are wrong in 3D. Surf-NeRF tries to fix this by steering the representation toward a surface light field, in which colour is emitted from a smooth surface and splits into a Lambertian (view-independent) part and a view-dependent specular part. The paper introduces four regularisation terms—density smoothness, normal consistency, Lambertian bias, and specular total variation—applied at the first surface point along each ray, together with a permutohedral lattice hash encoding that represents curved geometry better than cubic grids. On the Shiny Objects benchmark, this yields 27.9 percent more accurate surface normals than a grid-based Ref-NeRF baseline (10.60° vs 14.70° mean angular error) with comparable PSNR and SSIM. If the claim holds, it would make radiance-field reconstructions trustworthy for geometry-critical tasks such as robotic manipulation and 3D modelling.

What carries the argument

The load-bearing object is the surface light field—a model in which all radiance originates from a piecewise smooth surface and is written as a Lambertian diffuse colour plus a view-dependent specular term—and the mechanism that enforces it is a set of four local regularisation losses evaluated at a first-surface point $x^*$ per ray. A permutohedral lattice hash encoding (a memory-efficient lattice of regular tetrahedra used for feature interpolation) carries the geometric side of the argument: it represents curved, non-planar density regions more accurately than the cubic hash grids of previous work. The regularisation terms are: density smoothness $L_d$, which penalises density away from the surface plane; normal consistency $L_n$, which aligns nearby normals; Lambertian bias $L_b$, which removes view-independent energy from the specular colour channel; and specular total variation $L_s$, which smooths the view-dependent colour over the viewing sphere. A curriculum schedule (regularising every $2^k$ iterations, from every 512 early to every 4 late) applies these losses with increasing frequency, and the sampling geometry scales with the radial variance of the integrated positional encoding so that regularisation stays at the scale of a single pixel as the representation converges.

What would settle it

Render a synthetic scene with known ground-truth geometry that contains a genuinely volumetric element—for example a hair strand or a wisp of smoke rendered with volumetric scattering—train Surf-NeRF and the unregularised Zip+Ref-NeRF baseline on identical views, and compare predicted normals and depth to ground truth; if the regularised model's normal MAE or depth RMSE is worse than the baseline's, the first-surface assumption that locates the regularisation is falsified.

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Extended reading notes

Core claim

The paper's central claim is that a NeRF, which is normally free to place density anywhere along a ray, can be conditioned to find real surface geometry by regularising it toward a surface light field. The method first locates a candidate surface point on each ray using a first-surface assumption (the first point whose rendering weight exceeds the ray's median weight), then samples the density field in a small ball around that point and the view-dependent colour through a set of viewing directions. Four losses push these samples to behave like a surface: density is penalised away from a plane perpendicular to the local normal, neighbour normals are encouraged to align, the specular colour is penalised for containing a view-independent (Lambertian) bias, and the specular colour is smoothed by total variation across the viewing sphere. The regularisation is scheduled so that it is applied rarely early in training and increasingly often later, and the cubic hash grid of Zip-NeRF is replaced by a permutohedral lattice, whose regular tetrahedra interpolate features more faithfully over curved surfaces. The result, the paper reports, is a 27.9 percent reduction in normal error on the Shiny Objects dataset compared with the grid-based reflection-parameterised baseline, with colour fidelity nearly unchanged and a physically more consistent separation of diffuse and specular appearance.

Load-bearing premise

The method assumes that each ray's radiance comes from a solid first surface—the first point where the rendering weight passes the ray's median—and that the scene is piecewise smooth; if the real scene is volumetric (hair, smoke, subsurface scattering) or contains strong interreflections, the regularisation is applied at the wrong location and can degrade both geometry and appearance.

Editorial extensions

If this is right

  • On the Shiny Objects dataset, Surf-NeRF lowers surface-normal mean angular error from 14.70° (Zip+Ref-NeRF) to 10.60°, a 27.9 percent improvement, while PSNR and SSIM remain comparable (32.82 dB vs 33.14 dB).
  • The regularisation separates Lambertian and specular appearance: diffuse content such as racing stripes and toast moves into the diffuse channel, leaving reflections in the specular channel.
  • The method works as a fine-tuning step: applying the regularisation losses to an already-trained ZipNeRF or Zip+Ref-NeRF model improves normals (e.g., from 24.21° to 23.57° median MAE on the car scene) without re-training from scratch.
  • The permutohedral lattice alone improves normals over a cubic grid (13.76° vs 14.70° MAE), and the full combination produces the largest gain, so the two contributions are complementary.
  • The curriculum schedule keeps the added training cost near 25 percent rather than doubling compute, since regularisation is applied on every $2^k$ iterations.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Our inference: the first-surface assumption is the fragile point; scenes dominated by hair, smoke, or subsurface scattering would likely see the regularisation push density to a wrong 'surface,' so a natural test is to weight the losses by the spread of the ray's weight distribution, weakening the terms where density is genuinely volumetric.
  • Our inference: the Lambertian-bias loss encodes a general principle—view-independent energy in the view-dependent channel is a symptom of shape-radiance ambiguity—so the same loss could be transplanted to other reflectance decomposition or inverse-rendering systems even when their geometry is not a NeRF density field.
  • Our inference: because the spatial sampling terms depend only on density and normals, they should transfer to explicit radiance representations such as 3D Gaussian splatting, where the analogous regularisation would pull Gaussians onto a smoother surface and might reduce the need for 'background' Gaussians that explain reflections.
  • Our inference: the median-weight surface heuristic could be validated or replaced by comparing against a depth sensor; on scenes with known ground-truth depth, measuring how often the chosen $x^*$ lies within a pixel's worth of the true surface would quantify the ceiling of the approach.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. Surf-NeRF proposes a surface-light-field-inspired regularisation framework applied to the Zip-NeRF/Ref-NeRF pipeline in order to improve the geometric accuracy of grid-based neural radiance fields. The method locates candidate surfaces along rays using a first-surface weight criterion, constructs local spatial and directional sample batches around those points, and applies four losses: density smoothness (Ld), normal consistency (Ln), a Lambertian/specular bias penalty (Lb), and a spherical total-variation term on the specular colour (Ls), under a curriculum schedule that increases regularisation frequency as training progresses. The cubic hash encoding of Zip-NeRF is replaced by a permutohedral lattice encoding. Reported results claim a 27.9% improvement in surface-normal MAE over the Zip+Ref-NeRF baseline on the Shiny Objects dataset (10.60 versus 14.70 degrees) with broadly maintained rendering quality, alongside a new four-scene Koala dataset and a finetuning experiment demonstrating applicability to existing NeRF variants.

Significance. If the central claim holds, the contribution is a useful one: it gives a practical recipe for improving normals in already-good grid-based NeRF pipelines with modest training-time overhead (about 25% under the chosen schedule), and it evaluates the method more thoroughly than is typical, with ablations, a parameter study, and a finetuning stage (Table 6). The Koala dataset with robotic-arm poses is a concrete resource for the reflective-object setting, and the supplementary material is unusually complete on sampling details and hyperparameter values. The headline normal-accuracy result is credible, and because evaluation uses held-out ground-truth normals, the comparison against baselines that do not optimise these losses is fair. The main weakness is that the second half of the central claim — that visual fidelity is maintained 'without greatly sacrificing' it — is an average statement contradicted by per-scene results on exactly the reflective objects the method targets, and the paper's independent geometric metric (disparity RMSE) is not improved over the directly comparable baseline.

major comments (4)
  1. [Section 4.1, Table F.1] The claim of 'comparable performance to Ref-NeRF in visual fidelity' (Section 4.1) and of improving geometry 'without greatly sacrificing visual fidelity' (Section 5) is not supported on a per-scene basis. On the Toaster scene of Shiny Objects, Surf-NeRF drops to 20.76 dB PSNR and 0.869 SSIM from the Zip+Ref-NeRF baseline's 24.29 dB and 0.921 SSIM (Table F.1), a 3.53 dB (14.5% relative) PSNR loss, and the Teapot scene drops by 1.63 dB (46.09 to 44.46 dB). These are precisely the reflective-object cases the method targets. The aggregates in Table 1 (32.82 versus 33.14 dB) are dominated by the roughly 44-46 dB Teapot scene and mask both losses. Section 4.6 admits 'slightly reduced PSNR scores', but the Toaster magnitude is not slight. The manuscript should qualify the fidelity claim per scene, state the worst-case scene when summarising the trade-off, and analyse why regularisation degrades Toaster (for example the interreflection behaviour noted in Figure F.2).
  2. [Table 1, Table F.1, Section 5] The disparity-RMSE claims are contradicted by the paper's own tables. The caption of Table F.1 states 'We achieve improvements in all cases for disparity', but against Zip+Ref-NeRF the RMSE worsens on Coffee (0.203 to 0.205), Helmet (0.193 to 0.200), and Teapot (0.157 to 0.168), and the headline grid RMSE in Table 1 worsens from 0.195 to 0.198. The Conclusion's 'up to 27.8% in normals and 6.7% in disparity' has no identifiable source for the 6.7% figure: against the directly comparable Zip+Ref-NeRF baseline the disparity error is flat or worse, and a 6-7% improvement can only be obtained relative to weaker non-reflection baselines such as MipNeRF. This matters because normal MAE is the one metric directly optimised by Ln, while disparity RMSE is the paper's most independent geometry signal and it does not improve. The disparity claims should be corrected to the comparisons actually supported by the tables.
  3. [Tables 1 and 5, Supp. D and E] There are no error bars or repeated runs, and all free parameters — lambda_d, lambda_n, lambda_b, lambda_s (Supp. E), the curriculum start/end frequencies (Table 5), and k for the specular total variation (Supp. D) — were selected on the same Shiny Objects benchmark on which the headline numbers are reported. Table 5 shows the result is highly sensitive to the regularisation frequency: MAE ranges from 10.60 to 28.37 degrees and PSNR from 29.77 to 32.82 as the schedule changes, so the chosen 512/4 schedule is doing real work rather than being a benign default. The manuscript should report variance over at least a few seeds and should validate the chosen schedule and weights on a held-out split or on the Koala dataset rather than only on the benchmark used for Table 1.
  4. [Section 3.3, Sections 1 and 5] The first-surface assumption is load-bearing: the median-weight criterion of Section 3.3 decides where all four regularisation terms are applied, and when it fails — for multi-modal weight distributions, volumetric effects, subsurface scattering, or hair — the regularisation is applied at the wrong location and can degrade both geometry and appearance. The limitation is acknowledged in Section 4.6, but the Introduction and Conclusion claim the method is 'a key step in enabling radiance-based representations for geometry critical applications' such as robotic manipulation and navigation, which involve exactly these unmodelled phenomena. The claims of generality should be scoped to opaque, surface-like geometry, and the failure mode of the median selection (for example in semi-transparent or interreflecting regions as shown in Figure F.2) should be discussed in the main text rather than only in the limitations paragraph.
minor comments (6)
  1. [Abstract and Section 5] The improvement is stated as '28%' in the abstract and '27.8%' in the conclusion; the correct figure from Table 1 is 27.9%, and the two statements should be made consistent.
  2. [Table 4] The meaning of checkmarks in the '⋆' column conflicts with the legend, which says '⋆ ablates deterministic sphere sampling'; since the final row (Ours) checks both ⋆ and #, the table reads as though the proposed method ablates both components. Clarify whether ✓ means 'included' or 'ablated'.
  3. [Table 3 and Table F.3] The Table 3 caption, 'Surface regularisation helps scene convergence around complex specular geometry improving PSNR', is true only against Zip+Ref-NeRF (23.69 dB); against plain ZipNeRF (27.79 dB), Surf-NeRF's 26.86 dB is a drop, and per-scene (Table F.3) Surf-NeRF loses to ZipNeRF on three of the four scenes. The caption should name the baseline to which the claim refers.
  4. [Table F.3, Shiny Ball scene] The Zip+Ref-NeRF baseline collapses to 15.47 dB PSNR and 0.435 SSIM on Shiny Ball, far outside the range of all other baselines; the manuscript should state whether that baseline run is valid, since a broken baseline inflates the apparent improvement of Surf-NeRF on that scene.
  5. [Section 3.6] The statement that the curriculum schedule adds 'approximately a 25% increase to training time' should be derived explicitly from the stated start/end frequencies (every 512 iterations down to every 4) and the fraction of regularised steps, since the reader cannot reproduce this number from the text as written.
  6. [Figure D.1] The polar plots in Figure D.1 lack readable axis labels and a caption-level explanation of what is plotted (the spliced forward/backward hemispheres of specular sample directions); clarifying this would make the graph total-variation construction in Eq. (8) much easier to follow.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the reported normal-accuracy and appearance-separation results are evaluated against held-out ground truth and external baselines, not against the regularisation losses themselves.

full rationale

Surf-NeRF's derivation chain is self-contained. The four regularisation losses (Ld, Ln, Lb, Ls) in Sections 3.4 and 3.5 are defined directly in terms of the network's own density, normals, and specular colour, and none of them is fit to ground-truth normals or to the reported MAE values. The headline normal-accuracy gain (10.60 vs 14.70 degrees MAE in Table 1) is measured against held-out ground-truth normals from the Shiny Objects dataset, while Ln only penalises local misalignment between predicted normals at neighbouring samples around a candidate surface; it does not encode the ground-truth normal direction and therefore does not force the reported MAE by construction. Similarly, the specular-bias loss Lb and total-variation loss Ls directly shape the specular channel, but the paper does not present a numerical 'separation metric' as a prediction; the qualitative separation figures are demonstrations of the method's intended behaviour, not a fitted quantity being renamed as an outcome. The paper contains no load-bearing self-citations; its prior-art anchors (Ref-NeRF, ZipNeRF, PermutoSDF, and surface light fields) are external and cited as building blocks, not as authority for the regularisation outcome. The first-surface assumption (Section 3.3) and the Toaster scene PSNR drop (Table F.1) are genuine correctness and robustness concerns, but they concern whether the method works where its assumptions fail or where per-scene quality degrades, not whether the derivations reduce to their inputs. The regularisation schedule (512/4) is selected via a parameter study on the same benchmark, which is a model-selection risk, but the reported normal metric remains an externally evaluated held-out quantity. No circular step can be exhibited from the paper's equations or citations.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

The central claim rests on the surface light field assumption, the first-surface median-weight heuristic, the density-gradient-as-normal convention, and several hand-chosen hyperparameters and schedules. No new physical particles, forces, or conserved quantities are introduced; the Koala dataset is a new benchmark asset rather than an invented entity.

free parameters (6)
  • lambda_d (density smoothness weight) = 1e-1
    Given in Supplement E; chosen by hand to balance geometry and photometric loss, appears in Equation 4.
  • lambda_n (normal consistency weight) = 1e-1
    Given in Supplement E; weight for the normal consistency loss in Equation 5.
  • lambda_b (specular bias weight) = 3e-2
    Given in Supplement E; weight for the Lambertian bias loss in Equation 6.
  • lambda_s (specular total variation weight) = 1e-3
    Given in Supplement E; weight for the specular total variation loss in Equation 7.
  • Curriculum regularisation frequency schedule = 512 steps initially, 4 steps at the end
    Selected via the parameter study in Table 5 as the Pareto-optimal trade-off between geometry improvement and visual fidelity.
  • k-nearest neighbours for specular total variation = 3
    Supplement D states that higher values produced minimal geometric improvement and marginally reduced visual fidelity.
assumptions (6)
  • domain assumption Scene radiance is well approximated by a surface light field, meaning light originates from a piecewise smooth surface geometry.
    Introduced in Section 3.1 and used to justify all four regularisation terms; the paper's own limitations section notes this degrades volumetric elements like hair and subsurface scattering.
  • domain assumption The first point along a ray with rendering weight above the median weight is a reliable candidate surface location.
    Section 3.3 defines the candidate surface this way; this first-surface assumption drives the spatial and directional sampling batches.
  • domain assumption Density gradient approximates surface normals as n approximately equal to negative gradient of density.
    Section 3.3 states this standard NeRF convention and uses it in the normal consistency loss.
  • domain assumption A permutohedral lattice provides better volumetric coverage and interpolation for non-planar geometry than cubic grids.
    Section 3.2 argues this from the sphere covering problem and prior work, but the improvement is partly contested by the ablations where lattice alone does not always improve all metrics.
  • ad hoc to paper A total variation prior on specular colour over viewing angles encourages a physically correct Lambertian and specular separation.
    This is a new hand-designed prior introduced by the paper itself, not an externally verified physical law; it is evaluated only through qualitative appearance separation.
  • ad hoc to paper Curriculum learning with rare early regularisation and frequent late regularisation preserves photometric fidelity while improving geometry.
    The schedule is introduced in Section 3.6 and tuned in Table 5; the paper's own results show that too-frequent regularisation (128/1) severely degrades geometry.

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Cite this review

Pith. "Pith review of Surf-NeRF: Surface Regularised Neural Radiance Fields." pith.science (2026). https://pith.science/paper/KJAWBMFG

@misc{pith2026241118652,
  author       = {Pith},
  title        = {Pith review of: Surf-NeRF: Surface Regularised Neural Radiance Fields},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/KJAWBMFG}},
  note         = {Machine review of arXiv:2411.18652}
}
read the original abstract

Neural Radiance Fields (NeRFs) provide a high fidelity, continuous scene representation that can realistically represent complex behaviour of light. Despite works like Ref-NeRF improving geometry through physics-inspired models, the ability for a NeRF to overcome shape-radiance ambiguity and converge to a representation consistent with real geometry remains limited. We demonstrate how both curriculum learning of a surface light field model and using a lattice-based hash encoding helps a NeRF converge towards a more geometrically accurate scene representation. We introduce four regularisation terms to impose geometric smoothness, consistency of normals, and a separation of Lambertian and specular appearance at geometry in the scene, conforming to physical models. Our approach yields 28% more accurate normals than traditional grid-based NeRF variants with reflection parameterisation. Our approach more accurately separates view-dependent appearance, conditioning a NeRF to have a geometric representation consistent with the captured scene. We demonstrate compatibility of our method with existing NeRF variants, as a key step in enabling radiance-based representations for geometry critical applications.

Figures

Figures reproduced from arXiv: 2411.18652 by the authors.

Figure 1
Figure 1. Surf-NeRF uses a permutohedral lattice encoding and [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. An overview of the Surf-NeRF methodology. We use a first surface assumption of light to locate samples [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. A visual depiction of the two sampling batches localised [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 5
Figure 5. Figure 5: Appearance separation between Surf-NeRF and base [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 4
Figure 4. Figure 4: Geometry comparison between normals achieved by [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 6
Figure 6. Figure 6: The “Gold Head” and “Shiny Ball” scenes from the [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Reference graph

Works this paper leans on

59 extracted references · 53 canonical work pages

  1. [1]

    Fast high-dimensional filtering using the permutohedral lat- tice

    Andrew Adams, Jongmin Baek, and Myers Abraham Davis. Fast high-dimensional filtering using the permutohedral lat- tice. In Computer graphics forum , pages 753–762. Wiley Online Library, 2010. 3

    work page 2010

  2. [2]

    Fast random rotation matrices

    James Arvo. Fast random rotation matrices. In Graphics Gems III (IBM V ersion) , pages 117–120. Academic Press,

    work page

  3. [3]

    Neural RGB-D Sur- face Reconstruction

    Dejan Azinovi ´c, Ricardo Martin-Brualla, Dan B Goldman, Matthias Nießner, and Justus Thies. Neural RGB-D Sur- face Reconstruction. In Proceedings of the IEEE/CVF Con- ference on Computer Vision and Pattern Recognition , pages 6290–6301, 2022. 2

    work page 2022

  4. [4]

    Mip-NeRF: A multiscale representation for anti-aliasing neural radiance fields

    Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-NeRF: A multiscale representation for anti-aliasing neural radiance fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 5855– 5864, 2021. 2, 3, 4, 5

    work page 2021

  5. [5]

    Mip-NeRF 360: Unbounded anti-aliased neural radiance fields

    Jonathan T Barron, Ben Mildenhall, Dor V erbin, Pratul P Srinivasan, and Peter Hedman. Mip-NeRF 360: Unbounded anti-aliased neural radiance fields. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5470–5479, 2022. 5, 6

    work page 2022

  6. [6]

    Barron, Ben Mildenhall, Dor V erbin, Pratul P

    Jonathan T. Barron, Ben Mildenhall, Dor V erbin, Pratul P . Srinivasan, and Peter Hedman. Zip-NeRF: Anti-Aliased Grid-Based Neural Radiance Fields. In Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV), pages 19697–19705, 2023. 2, 4, 6

    work page 2023

  7. [7]

    Barron, Keunhong Park, Ben Mildenhall, John Flynn, Dor V erbin, Pratul Srinivasan, Peter Hedman, Philipp Henzler, and Ricardo Martin-Brualla

    Jonathan T. Barron, Keunhong Park, Ben Mildenhall, John Flynn, Dor V erbin, Pratul Srinivasan, Peter Hedman, Philipp Henzler, and Ricardo Martin-Brualla. CamP Zip-NeRF: A Code Release for CamP and Zip-NeRF, 2024. 3, 5, 6

    work page 2024

  8. [8]

    Eikonal Fields for Refractive Novel-view Synthesis

    Mojtaba Bemana, Karol Myszkowski, Jeppe Revall Frisvad, Hans-Peter Seidel, and Tobias Ritschel. Eikonal Fields for Refractive Novel-view Synthesis. In ACM SIGGRAPH 2022 Conference Proceedings, pages 1–9, 2022. 2

    work page 2022

Show all 59 references
  1. [9]

    The Plenoptic Function and The Elements of Early Vision

    James R Bergen and Edward H Adelson. The Plenoptic Function and The Elements of Early Vision. Computational Models of Visual Processing, 1:8, 1991. 3

    1991

  2. [10]

    NeRD: Neural Reflectance Decomposition from Image Collections

    Mark Boss, Raphael Braun, V arun Jampani, Jonathan T Bar- ron, Ce Liu, and Hendrik Lensch. NeRD: Neural Reflectance Decomposition from Image Collections. In Proceedings of the IEEE/CVF International Conference on Computer Vi- sion, pages 12684–12694, 2021. 3

    2021

  3. [11]

    Neural-PIL: Neu- ral Pre-Integrated Lighting for Reflectance Decomposition

    Mark Boss, V arun Jampani, Raphael Braun, Ce Liu, Jonathan Barron, and Hendrik Lensch. Neural-PIL: Neu- ral Pre-Integrated Lighting for Reflectance Decomposition. Advances in Neural Information Processing Systems , 34: 10691–10704, 2021. 3

    2021

  4. [12]

    Barron, Hendrik Lensch, and V arun Jampani

    Mark Boss, Andreas Engelhardt, Abhishek Kar, Y uanzhen Li, Deqing Sun, Jonathan T. Barron, Hendrik Lensch, and V arun Jampani. SAMURAI: Shape And Material from Un- constrained Real-world Arbitrary Image collections. In Ad- vances in Neural Information Processing Systems , 2022. 3

    2022

  5. [13]

    JAX: composable transformations of Python+NumPy programs, 2018

    James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclau- rin, George Necula, Adam Paszke, Jake V anderPlas, Skye Wanderman-Milne, and Qiao Zhang. JAX: composable transformations of Python+NumPy programs, 2018. 6

    2018

  6. [14]

    Diffeomorphic Neural Surface Parameterization for 3D and Reflectance Acquisition

    Ziang Cheng, Hongdong Li, Richard Hartley, Yinqiang Zheng, and Imari Sato. Diffeomorphic Neural Surface Parameterization for 3D and Reflectance Acquisition. In ACM SIGGRAPH 2022 Conference Proceedings , pages 1– 10, 2022. 3

    2022

  7. [15]

    Sphere packings, lattices and groups

    John Horton Conway and Neil James Alexander Sloane. Sphere packings, lattices and groups . Springer Science & Business Media, 2013. 3

    2013

  8. [16]

    Sphere-guided training of neural implicit surfaces

    Andreea Dogaru, Andrei-Timotei Ardelean, Savva Ignatyev, Egor Zakharov, and Evgeny Burnaev. Sphere-guided training of neural implicit surfaces. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 20844–20853, 2023. 2

    2023

  9. [17]

    Hanebeck

    Daniel Frisch and Uwe D. Hanebeck. Deterministic V on Mises–Fisher sampling on the sphere using fibonacci lat- tices. In 2023 IEEE Symposium Sensor Data Fusion and International Conference on Multisensor Fusion and Inte- gration (SDF-MFI), pages 1–8, 2023. 4

    2023

  10. [18]

    Geo-Neus: Geometry-Consistent Neural Implicit Sur- faces Learning for Multi-view Reconstruction

    Qiancheng Fu, Qingshan Xu, Y ew-Soon Ong, and Wenbing Tao. Geo-Neus: Geometry-Consistent Neural Implicit Sur- faces Learning for Multi-view Reconstruction. In Advances in Neural Information Processing Systems , 2022. 2, 3

    2022

  11. [19]

    Intrinsic Light Field Im- ages

    Elena Garces, Jose I Echevarria, Wen Zhang, Hongzhi Wu, Kun Zhou, and Diego Gutierrez. Intrinsic Light Field Im- ages. In Computer Graphics F orum, pages 589–599. Wiley Online Library, 2017. 3

    2017

  12. [20]

    A Survey on Intrinsic Images: Delv- ing Deep into Lambert and Beyond

    Elena Garces, Carlos Rodriguez-Pardo, Dan Casas, and Jorge Lopez-Moreno. A Survey on Intrinsic Images: Delv- ing Deep into Lambert and Beyond. Int. J. Comput. Vision , 130(3):836–868, 2022. 3

    2022

  13. [21]

    Ref-NeUS: Ambiguity-reduced neural implicit sur- face learning for multi-view reconstruction with reflection

    Wenhang Ge, Tao Hu, Haoyu Zhao, Shu Liu, and Ying-Cong Chen. Ref-NeUS: Ambiguity-reduced neural implicit sur- face learning for multi-view reconstruction with reflection. In Proceedings of the IEEE/CVF International Conference on Computer Vision, pages 4251–4260, 2023. 3

    2023

  14. [22]

    Radiant foam: Real-time differen- tiable ray tracing

    Shrisudhan Govindarajan, Daniel Rebain, Kwang Moo Yi, and Andrea Tagliasacchi. Radiant foam: Real-time differen- tiable ray tracing. arXiv preprint arXiv:2502.01157 , 2025. 2

    2025 arXiv

  15. [23]

    NeRFReN: Neural Radiance Fields with Reflec- tions

    Y uan-Chen Guo, Di Kang, Linchao Bao, Y u He, and Song- Hai Zhang. NeRFReN: Neural Radiance Fields with Reflec- tions. In Proceedings of the IEEE/CVF Conference on Com- puter Vision and Pattern Recognition , pages 18409–18418, 2022. 2

    2022

  16. [24]

    2d gaussian splatting for geometrically ac- curate radiance fields

    Binbin Huang, Zehao Y u, Anpei Chen, Andreas Geiger, and Shenghua Gao. 2d gaussian splatting for geometrically ac- curate radiance fields. In ACM SIGGRAPH 2024 conference papers, pages 1–11, 2024. 2

    2024

  17. [25]

    Neural fields in robotics: A survey

    Muhammad Zubair Irshad, Mauro Comi, Y en-Chen Lin, Nick Heppert, Abhinav V alada, Rares Ambrus, Zsolt Kira, and Jonathan Tremblay. Neural fields in robotics: A survey. arXiv preprint arXiv:2410.20220, 2024. 2

    2024 arXiv

  18. [26]

    Geometry field splatting with gaussian sur- 9 fels

    Kaiwen Jiang, V enkataram Sivaram, Cheng Peng, and Ravi Ramamoorthi. Geometry field splatting with gaussian sur- 9 fels. In Proceedings of the Computer Vision and Pattern Recognition Conference, pages 5752–5762, 2025. 2

    2025

  19. [27]

    3d gaussian splatting for real-time radiance field rendering

    Bernhard Kerbl, Georgios Kopanas, Thomas Leimk ¨uhler, and George Drettakis. 3d gaussian splatting for real-time radiance field rendering. ACM Trans. Graph., 42(4):139–1, 2023. 2

    2023

  20. [28]

    InfoNeRF: Ray entropy minimization for few-shot neural volume ren- dering

    Mijeong Kim, Seonguk Seo, and Bohyung Han. InfoNeRF: Ray entropy minimization for few-shot neural volume ren- dering. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 12912– 12921, 2022. 2

    2022

  21. [29]

    Geogaussian: Geometry-aware gaussian splatting for scene rendering

    Y anyan Li, Chenyu Lyu, Y an Di, Guangyao Zhai, Gim Hee Lee, and Federico Tombari. Geogaussian: Geometry-aware gaussian splatting for scene rendering. In European Confer- ence on Computer Vision , pages 441–457. Springer, 2024. 2

    2024

  22. [30]

    CGIntrinsics: Better Intrinsic Image Decomposition through Physically-Based Rendering

    Zhengqi Li and Noah Snavely. CGIntrinsics: Better Intrinsic Image Decomposition through Physically-Based Rendering. In Proceedings of the European Conference on Computer Vi- sion (ECCV), 2018. 3

    2018

  23. [31]

    Deformable beta splatting

    Rong Liu, Dylan Sun, Meida Chen, Y ue Wang, and An- drew Feng. Deformable beta splatting. arXiv preprint arXiv:2501.18630, 2025. 2

    2025 arXiv

  24. [32]

    SpecNeRF: Gaussian directional encoding for specular reflections

    Li Ma, V asu Agrawal, Haithem Turki, Changil Kim, Chen Gao, Pedro Sander, Michael Zollh ¨ofer, and Christian Richardt. SpecNeRF: Gaussian directional encoding for specular reflections. arXiv preprint arXiv:2312.13102, 2023. 2

    2023 arXiv

  25. [33]

    NeRF in the Wild: Neural Radiance Fields for Uncon- strained Photo Collections

    Ricardo Martin-Brualla, Noha Radwan, Mehdi SM Sajjadi, Jonathan T Barron, Alexey Dosovitskiy, and Daniel Duck- worth. NeRF in the Wild: Neural Radiance Fields for Uncon- strained Photo Collections. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recogn...

    2021

  26. [34]

    Srinivasan, Matthew Tancik, Jonathan T

    Ben Mildenhall, Pratul P . Srinivasan, Matthew Tancik, Jonathan T. Barron, Ravi Ramamoorthi, and Ren Ng. NeRF: Representing Scenes as Neural Radiance Fields for View Synthesis. In ECCV, 2020. 1, 2, 3

    2020

  27. [35]

    Instant neural graphics primitives with a multires- olution hash encoding

    Thomas M ¨uller, Alex Evans, Christoph Schied, and Alexan- der Keller. Instant neural graphics primitives with a multires- olution hash encoding. ACM Trans. Graph. , 41(4):102:1– 102:15, 2022. 3, 4

    2022

  28. [36]

    Reg- NeRF: Regularizing Neural Radiance Fields for View Syn- thesis From Sparse Inputs

    Michael Niemeyer, Jonathan T Barron, Ben Mildenhall, Mehdi SM Sajjadi, Andreas Geiger, and Noha Radwan. Reg- NeRF: Regularizing Neural Radiance Fields for View Syn- thesis From Sparse Inputs. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition ...

    2022

  29. [37]

    UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction

    Michael Oechsle, Songyou Peng, and Andreas Geiger. UNISURF: Unifying Neural Implicit Surfaces and Radiance Fields for Multi-View Reconstruction. In Proceedings of the IEEE/CVF International Conference on Computer Vision , pages 5589–5599, 2021. 2, 4

    2021

  30. [38]

    LolNeRF: Learn From One Look

    Daniel Rebain, Mark Matthews, Kwang Moo Yi, Dmitry Lagun, and Andrea Tagliasacchi. LolNeRF: Learn From One Look. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition , pages 1558– 1567, 2022. 2

    2022

  31. [39]

    Permutosdf: Fast multi-view reconstruction with implicit surfaces using per- mutohedral lattices

    Radu Alexandru Rosu and Sven Behnke. Permutosdf: Fast multi-view reconstruction with implicit surfaces using per- mutohedral lattices. In Proceedings of the IEEE/CVF Con- ference on Computer Vision and Pattern Recognition , pages 8466–8475, 2023. 3, 4

    2023

  32. [40]

    Fleet, and Andrea Tagliasacchi

    Sara Sabour, Suhani V ora, Daniel Duckworth, Ivan Krasin, David J. Fleet, and Andrea Tagliasacchi. Robustnerf: Ig- noring distractors with robust losses. In 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pages 20626–20636, 2023. 2

    2023

  33. [41]

    SimpleNeRF: Regularizing sparse input neu- ral radiance fields with simpler solutions

    Nagabhushan Somraj, Adithyan Karanayil, and Rajiv Soundararajan. SimpleNeRF: Regularizing sparse input neu- ral radiance fields with simpler solutions. In SIGGRAPH Asia 2023 Conference Papers , New Y ork, NY , USA, 2023. Association for Computing Machinery. 3

    2023

  34. [42]

    Block-NeRF: Scalable Large Scene Neural View Synthesis

    Matthew Tancik, Vincent Casser, Xinchen Y an, Sabeek Pradhan, Ben Mildenhall, Pratul P Srinivasan, Jonathan T Barron, and Henrik Kretzschmar. Block-NeRF: Scalable Large Scene Neural View Synthesis. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recogn...

    2022

  35. [43]

    Ref-NeRF: Structured View-Dependent Appearance For Neural Radi- ance Fields

    Dor V erbin, Peter Hedman, Ben Mildenhall, Todd Zickler, Jonathan T Barron, and Pratul P Srinivasan. Ref-NeRF: Structured View-Dependent Appearance For Neural Radi- ance Fields. In 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) , pages 5481–5490. IE...

    2022

  36. [44]

    NeRF-Casting: Improved view-dependent ap- pearance with consistent reflections

    Dor V erbin, Pratul P Srinivasan, Peter Hedman, Ben Milden- hall, Benjamin Attal, Richard Szeliski, and Jonathan T Barron. NeRF-Casting: Improved view-dependent ap- pearance with consistent reflections. arXiv preprint arXiv:2405.14871, 2024. 2

    2024 arXiv

  37. [45]

    NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Recon- struction

    Yiming Wang, Qin Han, Marc Habermann, Kostas Dani- ilidis, Christian Theobalt, and Lingjie Liu. NeuS2: Fast Learning of Neural Implicit Surfaces for Multi-view Recon- struction. arXiv preprint arXiv:2212.05231, 2022. 3

    2022 arXiv

  38. [46]

    Learning 3d geometry and feature consistent gaussian splat- ting for object removal

    Y uxin Wang, Qianyi Wu, Guofeng Zhang, and Dan Xu. Learning 3d geometry and feature consistent gaussian splat- ting for object removal. In European Conference on Com- puter Vision, pages 1–17. Springer, 2024. 2

    2024

  39. [47]

    Normal-gs: 3d gaussian splatting with normal-involved rendering

    Meng Wei, Qianyi Wu, Jianmin Zheng, Hamid Rezatofighi, and Jianfei Cai. Normal-gs: 3d gaussian splatting with normal-involved rendering. In The Thirty-eighth Annual Conference on Neural Information Processing Systems , 2024. 2

    2024

  40. [48]

    Wood, Daniel I

    Daniel N. Wood, Daniel I. Azuma, Ken Aldinger, Brian Cur- less, Tom Duchamp, David H. Salesin, and Werner Stuetzle. Surface Light Fields for 3D Photography. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques , page 287–296, USA, 2000. ...

    2000

  41. [49]

    Neumesh: Learning Disentangled Neural Mesh-Based Implicit Field for Geometry and Texture Editing

    Bangbang Y ang, Chong Bao, Junyi Zeng, Hujun Bao, Yinda Zhang, Zhaopeng Cui, and Guofeng Zhang. Neumesh: Learning Disentangled Neural Mesh-Based Implicit Field for Geometry and Texture Editing. In Computer Vision– ECCV 2022: 17th European Conference, Tel Aviv, Israel, October ...

    2022

  42. [50]

    NeILF: Neural Incident Light Field for Physically-Based Material Estimation

    Y ao Y ao, Jingyang Zhang, Jingbo Liu, Yihang Qu, Tian Fang, David McKinnon, Y anghai Tsin, and Long Quan. NeILF: Neural Incident Light Field for Physically-Based Material Estimation. In Computer Vision–ECCV 2022: 17th European Conference, Tel Aviv, Israel, October 23–27, 2022...

    2022

  43. [51]

    V olume Rendering of Neural Implicit Surfaces

    Lior Y ariv, Jiatao Gu, Y oni Kasten, and Y aron Lipman. V olume Rendering of Neural Implicit Surfaces. Advances in Neural Information Processing Systems , 34:4805–4815,

  44. [52]

    MonoSDF: Exploring Monocu- lar Geometric Cues for Neural Implicit Surface Reconstruc- tion

    Zehao Y u, Songyou Peng, Michael Niemeyer, Torsten Sat- tler, and Andreas Geiger. MonoSDF: Exploring Monocu- lar Geometric Cues for Neural Implicit Surface Reconstruc- tion. In Advances in Neural Information Processing Systems, 2022. 2

    2022

  45. [53]

    NeRS: Neural Reflectance Surfaces for Sparse- view 3D Reconstruction in the Wild

    Jason Zhang, Gengshan Y ang, Shubham Tulsiani, and Deva Ramanan. NeRS: Neural Reflectance Surfaces for Sparse- view 3D Reconstruction in the Wild. Advances in Neural Information Processing Systems, 34:29835–29847, 2021. 3

    2021

  46. [54]

    IRON: Inverse Rendering by Optimizing Neural SDFs and Materials from Photometric Images

    Kai Zhang, Fujun Luan, Zhengqi Li, and Noah Snavely. IRON: Inverse Rendering by Optimizing Neural SDFs and Materials from Photometric Images. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 5565–5574, 2022. 3

    2022

  47. [55]

    Nerfac- tor: Neural Factorization of Shape and Reflectance Under an Unknown Illumination

    Xiuming Zhang, Pratul P Srinivasan, Boyang Deng, Paul De- bevec, William T Freeman, and Jonathan T Barron. Nerfac- tor: Neural Factorization of Shape and Reflectance Under an Unknown Illumination. ACM Transactions on Graphics (TOG), 40(6):1–18, 2021. 4

    2021

  48. [56]

    VDN-NeRF: Resolving shape- radiance ambiguity via view-dependence normalization

    Bingfan Zhu, Y anchao Y ang, Xulong Wang, Y ouyi Zheng, and Leonidas Guibas. VDN-NeRF: Resolving shape- radiance ambiguity via view-dependence normalization. In Proceedings of the IEEE/CVF Conference on Computer Vi- sion and Pattern Recognition (CVPR) , pages 35–45, 2023. 3 11...

    2023

  49. [58]

    We see that the lattice uniformly distributes sample directions, taking into account the warping close to the poles

    0 θ (rad) (c) Directions through which we sample. We see that the lattice uniformly distributes sample directions, taking into account the warping close to the poles. 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 r 5 10 15 20 25 30 35 40Sampling Density (Num. Points/ u3) (d) The density...

  50. [59]

    Example directional polar coordinate map

    0 θ (rad) Figure D.1. Example directional polar coordinate map. The spliced forward and backward facing directions creates two inter- leaved sampling patterns, which is no longer regular. To address this, we use a graph total variation adapted for locations on the sphere accou...

  51. [614]

    Springer, 2022. 3 10

    2022

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.