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arxiv: 2604.15941 · v1 · submitted 2026-04-17 · 💻 cs.CV · cs.GR

Neural Gabor Splatting: Enhanced Gaussian Splatting with Neural Gabor for High-frequency Surface Reconstruction

Haato Watanabe , Nobuyuki Umetani This is my paper

Pith reviewed 2026-05-10 08:20 UTC · model grok-4.3

classification 💻 cs.CV cs.GR
keywords 3D Gaussian SplattingHigh-frequency ReconstructionNovel View SynthesisSurface ReconstructionMulti-layer PerceptronNeural Radiance FieldsDensification Strategy
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The pith

Each Gaussian primitive gains a lightweight neural network to represent multiple colors internally, cutting the primitive count needed for sharp high-frequency details.

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

Standard 3D Gaussian splatting reconstructs scenes quickly from images but forces the total number of primitives to grow rapidly whenever the scene contains sharp color changes or fine patterns, because each primitive can hold only one constant color. The paper introduces Neural Gabor Splatting, which equips every Gaussian with a small multi-layer perceptron so that a single primitive can produce a continuous range of colors across its area. A separate frequency-aware rule then measures how much high-frequency energy remains unexplained and uses that signal to decide whether to clone or prune primitives. Experiments on Mip-NeRF360 and dedicated high-frequency test sets show that the combined changes produce accurate surfaces while keeping the primitive budget far lower than baseline Gaussian splatting.

Core claim

Neural Gabor Splatting augments each explicit Gaussian primitive with a lightweight multi-layer perceptron that models a wide range of color variations inside one primitive; a frequency-aware densification strategy then selects primitives for pruning or cloning according to their frequency energy, allowing accurate reconstruction of challenging high-frequency surfaces on standard benchmarks such as Mip-NeRF360 and specialized checkered-pattern datasets.

What carries the argument

lightweight multi-layer perceptron attached to each Gaussian primitive that models color variations within a single primitive

If this is right

  • High-frequency scenes such as checkered patterns can be represented with substantially fewer primitives than standard 3D Gaussian splatting.
  • Real-time rendering speed and post-processing convenience are preserved because the total number of primitives stays lower.
  • Surface reconstruction quality improves on both everyday benchmarks like Mip-NeRF360 and on deliberately difficult high-frequency test sets.
  • Ablation studies confirm that removing either the per-primitive network or the frequency-based densification step degrades performance.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same per-primitive network idea could be extended to model other spatially varying attributes such as normals or specular coefficients inside one primitive.
  • Memory usage for large-scale outdoor scenes would drop if the frequency-aware rule generalizes beyond the tested indoor and synthetic sets.
  • The approach suggests a broader pattern: replacing constant attributes on explicit primitives with tiny local networks may become a standard way to raise representational power without sacrificing explicitness.

Load-bearing premise

A lightweight multi-layer perceptron attached to each Gaussian can model a wide range of color variations within a single primitive without introducing visible artifacts or excessive compute, and frequency energy alone is sufficient to decide which primitives to prune or clone.

What would settle it

Running the method on the checkered-pattern high-frequency dataset and observing that the final primitive count remains comparable to ordinary 3D Gaussian splatting or that color transitions still exhibit visible banding or aliasing would falsify the central claim.

Figures

Figures reproduced from arXiv: 2604.15941 by Haato Watanabe, Nobuyuki Umetani.

Figure 1
Figure 1. Figure 1: While 3D Gaussian splatting struggles to represent fine texture using single-colored primitives—leading to numerous needle [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Coordinate transformation in 2D Gaussian splatting [ [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Overview of the neural Gabor primitive. The output color is parameterized by local 2D coordinates obtained from the 2D Gaussian splatting primitive’s affine transformation from 3D space. Given the 2D local coordinates and view direction, a lightweight MLP outputs RGB color through a SIREN activation function. This design enables each primitive to model spatially varying and view-dependent appearance within… view at source ↗
Figure 4
Figure 4. Figure 4: Overview of the frequency-aware densification strategy. (a) Band-limited frequency components are extracted from both the rendered image and the ground truth using FFT, band-pass filtering, and inverse FFT, followed by local averaging to obtain a robust frequency-domain error map. (b) The per-pixel frequency error is projected onto each Gaussian primitive based on its contribution, and primitives with high… view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative NVS results of benchmark and High-Frequency datasets. Novel view rendering results of outside and inside scenes. Our method provides a clear, sharp visual of the fine details, despite the same amount of data. count is adjusted to match the target footprint. For NEST and NTS, we reduce the capacity of their appearance rep￾resentations to match the target memory footprint by lower￾ing the resolut… view at source ↗
Figure 6
Figure 6. Figure 6: Comparison under varying data budgets on the B [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Visual comparison between Textured Gaussians and our method on High-Frequency dataset. Our method expresses high-frequency texture successfully, while Textured Gaussians produces elongated monotonous color primitives due to the sep￾aration of initial primitive shape training and subsequent texture training. ble 7 reports the quantitative results on the High-Frequency dataset [33]. Across all metrics, our m… view at source ↗
Figure 8
Figure 8. Figure 8: Additional qualitative comparisons on Mip-NeRF 360 with identical data size. Our method produces higher visual fidelity compared to 2DGS and 3D Gabor Splatting. 3D Gabor Splatting tends to generate color artifacts (circled) due to the absence of view￾dependent modeling. 13 [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Additional qualitative comparisons on the High-Frequency and DTU datasets under identical data size. Our method better preserves fine-grained patterns—such as intricate clothing textures and thin structures—especially when the primitive count is limited. 14 [PITH_FULL_IMAGE:figures/full_fig_p014_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Visual comparisons with NEST and NTS under matched memory budgets. Results on the BOOTS scene from the High￾Frequency dataset and the BONSAI scene from Mip-NeRF360 are shown. Each group includes the full image and a corresponding zoomed￾in image highlighting fine-scale structures. 15 [PITH_FULL_IMAGE:figures/full_fig_p015_10.png] view at source ↗
read the original abstract

Recent years have witnessed the rapid emergence of 3D Gaussian splatting (3DGS) as a powerful approach for 3D reconstruction and novel view synthesis. Its explicit representation with Gaussian primitives enables fast training, real-time rendering, and convenient post-processing such as editing and surface reconstruction. However, 3DGS suffers from a critical drawback: the number of primitives grows drastically for scenes with high-frequency appearance details, since each primitive can represent only a single color, requiring multiple primitives for every sharp color transition. To overcome this limitation, we propose neural Gabor splatting, which augments each Gaussian primitive with a lightweight multi-layer perceptron that models a wide range of color variations within a single primitive. To further control primitive numbers, we introduce a frequency-aware densification strategy that selects mismatch primitives for pruning and cloning based on frequency energy. Our method achieves accurate reconstruction of challenging high-frequency surfaces. We demonstrate its effectiveness through extensive experiments on both standard benchmarks, such as Mip-NeRF360 and High-Frequency datasets (e.g., checkered patterns), supported by comprehensive ablation studies.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The paper introduces Neural Gabor Splatting, an extension of 3D Gaussian Splatting (3DGS) designed to handle high-frequency surface details more efficiently. Standard 3DGS requires a large number of primitives for sharp color transitions because each Gaussian represents only a single color. The proposed method augments each primitive with a lightweight multi-layer perceptron (Neural Gabor) to model a range of color variations within one primitive and adds a frequency-aware densification strategy that prunes or clones primitives based on frequency energy. Claims of accurate high-frequency reconstruction are supported by experiments on Mip-NeRF360, custom high-frequency datasets (e.g., checkered patterns), and ablation studies.

Significance. If the improvements in reconstruction quality and primitive efficiency hold after controlling for training details and parameter counts, the approach could meaningfully reduce memory and compute demands for complex scenes in novel view synthesis and surface reconstruction tasks. The explicit primitive representation is retained while addressing a known scalability issue of 3DGS; the ablation studies provide a starting point for validating the design choices.

major comments (2)
  1. [Experiments] The central claim that a lightweight MLP per Gaussian can model wide color variations without visible artifacts or excessive compute is load-bearing, yet the experiments section provides no controlled comparison of total parameter count (MLP weights plus Gaussians) against a baseline 3DGS run with equivalent total capacity. Without this, it is unclear whether the reported gains stem from the Neural Gabor component or simply from additional degrees of freedom.
  2. [Method and Ablations] The frequency-aware densification strategy depends on a frequency energy threshold (a free parameter listed in the method). The ablation studies do not report sensitivity of final primitive count or PSNR to this threshold across scenes; a single fixed value may not generalize, undermining the claim that frequency energy alone suffices to decide pruning/cloning.
minor comments (2)
  1. [Method] Notation for the Neural Gabor MLP output (how it modulates the Gaussian color during splatting) should be defined explicitly with an equation in the method section to improve reproducibility.
  2. [Figures] Figure captions for qualitative results on high-frequency scenes should include the number of primitives used by each method for direct visual comparison.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and revise the manuscript to strengthen the presentation of results.

read point-by-point responses

  1. Referee: [Experiments] The central claim that a lightweight MLP per Gaussian can model wide color variations without visible artifacts or excessive compute is load-bearing, yet the experiments section provides no controlled comparison of total parameter count (MLP weights plus Gaussians) against a baseline 3DGS run with equivalent total capacity. Without this, it is unclear whether the reported gains stem from the Neural Gabor component or simply from additional degrees of freedom.

    Authors: We acknowledge this is a valid concern. In the revised manuscript we add a controlled experiment that matches total parameter count between Neural Gabor Splatting and a standard 3DGS baseline by increasing the number of Gaussians in the baseline until the aggregate parameter budget (MLP weights included) is equivalent. The new results show that Neural Gabor Splatting still yields higher PSNR and visibly sharper high-frequency detail while using fewer primitives, indicating the improvement is not merely due to extra capacity. These findings are placed in Section 4.3 with an accompanying table. revision: yes

  2. Referee: [Method and Ablations] The frequency-aware densification strategy depends on a frequency energy threshold (a free parameter listed in the method). The ablation studies do not report sensitivity of final primitive count or PSNR to this threshold across scenes; a single fixed value may not generalize, undermining the claim that frequency energy alone suffices to decide pruning/cloning.

    Authors: We agree that sensitivity analysis for the frequency-energy threshold is useful. We have extended the ablation studies to vary the threshold across a range of values on multiple scenes (Mip-NeRF360 and the custom high-frequency sets) and report the resulting primitive counts and PSNR. The data indicate stable performance within a broad operating range, confirming that frequency energy remains an effective decision criterion. The method section is also updated to document the default threshold choice and its rationale. revision: yes

Circularity Check

0 steps flagged

No circularity: method introduces independent architectural components validated empirically

full rationale

The paper proposes Neural Gabor Splatting by attaching a lightweight MLP to each Gaussian primitive to model intra-primitive color variations and adds a frequency-energy-based densification rule. These are presented as new design choices, not derived from or defined in terms of the final reconstruction metric. Experiments on Mip-NeRF360 and high-frequency datasets serve as external validation rather than tautological fits. No self-citation chains, fitted parameters renamed as predictions, or ansatzes smuggled via prior work appear in the provided text. The central claim therefore remains independent of its inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The approach rests on the universal approximation property of MLPs and the assumption that frequency content can be measured locally from rendered images to guide primitive management; no new physical constants or entities are introduced.

free parameters (2)
  • MLP weights per primitive
    Learned during training; the paper treats them as part of the model rather than reporting them as fixed constants.
  • Frequency energy threshold for densification
    Controls pruning and cloning decisions; value chosen to balance primitive count and quality.
axioms (2)
  • domain assumption A small MLP can represent arbitrary color functions inside the support of one Gaussian primitive
    Invoked when the authors state that the MLP models a wide range of color variations within a single primitive.
  • domain assumption Frequency energy extracted from rendered images is a reliable proxy for reconstruction mismatch
    Used to justify the frequency-aware densification strategy.

pith-pipeline@v0.9.0 · 5494 in / 1509 out tokens · 39694 ms · 2026-05-10T08:20:48.018640+00:00 · methodology

discussion (0)

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