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arxiv: 2606.05124 · v1 · pith:W3FWZK5Qnew · submitted 2026-06-03 · 💻 cs.GR · cs.CV· cs.LG

Geometry Gaussians: Decoupling Appearance and Geometry in Gaussian Splatting

Hongyu Zhou , Zorah L\"ahner This is my paper

Pith reviewed 2026-06-28 03:01 UTC · model grok-4.3

classification 💻 cs.GR cs.CVcs.LG
keywords 3D Gaussian Splattingnovel view synthesisgeometry reconstructionopacity decouplingtransparent objectssurface representationappearance-geometry conflict
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The pith

Default 3D Gaussian Splatting cannot represent texture and geometry simultaneously without dedicated per-splat parameters.

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

The paper establishes that standard 3D Gaussian Splatting optimization inherently conflicts when modeling both appearance and geometry at once. This is demonstrated through controlled training experiments that supply complete ground-truth information for texture and surface shape. The authors introduce one extra geometry-specific opacity value assigned to each Gaussian splat, optionally combined with a transparency-focused optimization schedule. The resulting representation yields higher appearance rendering quality together with more accurate extracted geometry, with the largest gains appearing in scenes that contain transparent objects.

Core claim

3DGS in its default form is inherently unsuited to represent texture and geometry at the same time. Applying a single additional geometry opacity parameter to each splat, together with an optional transparency-curated optimization pipeline, produces improved rendering and geometry performance on a wide variety of datasets.

What carries the argument

an additional per-splat geometry opacity parameter that separates geometric density from the appearance opacity used during color rendering

If this is right

  • Higher novel-view rendering fidelity while extracting more accurate surfaces
  • Particularly large gains on scenes containing transparent surfaces
  • Effective improvement whether geometric supervision comes from ground truth or from off-the-shelf vision models
  • No modification required to the core differentiable splatting formulation

Where Pith is reading between the lines

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

  • The same per-attribute opacity separation could be tested on other attribute bundles inside Gaussian representations, such as view-dependent effects or material parameters.
  • The observed conflict may appear in any single-representation method that jointly optimizes photometric and geometric losses, suggesting attribute-specific parameters as a general design pattern.
  • Future surface-extraction pipelines that ingest Gaussian models could adopt the geometry opacity directly as a surface indicator rather than post-processing the combined opacity field.

Load-bearing premise

That one extra geometry opacity value per splat is sufficient to eliminate the observed optimization conflict without any other changes to the splatting equations or training procedure.

What would settle it

Persistent appearance-geometry quality trade-offs on ground-truth-supervised training runs after the geometry opacity parameter has been added would show that the proposed change does not resolve the underlying incompatibility.

Figures

Figures reproduced from arXiv: 2606.05124 by Hongyu Zhou, Zorah L\"ahner.

Figure 1
Figure 1. Figure 1: Comparison of 3DGS trained with full knowledge of the texture and geometry (in form of depth maps) without and with our method. A single additional parameter opacitygeo for each splat allows to capture the full scene information by separating color from geometry information which is especially important for transparent objects. Abstract. After the success of 3D Gaussian Splatting (3DGS) for novel view synt… view at source ↗
Figure 2
Figure 2. Figure 2: (A) In most objects color and geometry of a view locate at the same point. (B) For transpar￾ent objects, color is determined by objects behind the geometry. (C) If the object behind is seen from a different view point, the color ren￾dering through transparency can be accurately represented. Existing geometry extraction methods rely on opacity thresholds [43], or simultaneous recon￾struction with another ge… view at source ↗
Figure 3
Figure 3. Figure 3: Overview. We add a new parameter opacitygeo to each splat which is used to render depth and normal maps while the default opacity is now opacitycolor and only responsible for rendering the RGB images. The geometric part is optimized by supervi￾sion from vision foundation models, together geometric regularization from PGSR [4]. In addition, we segment transparent parts that serve for masking in the geometri… view at source ↗
Figure 4
Figure 4. Figure 4: Rendering result for experiments with ground-truth depth and geometry opac￾ity. Without the separation of geometry and rendering through opacitygeo the rendering removes details on transparent objects. 5 Experiments This section contains all experimental results. Details about the implementation can be found in the supplementary material. 5.1 Datasets We use the following datasets for evaluation: TransLab … view at source ↗
Figure 5
Figure 5. Figure 5: Qualitative results on the TransLab dataset. Our results are the most faithful to the ground-truth, even in comparison to transparent-oriented method TSGS, and in presence of highly complex transparent overlaps. 5.4 Geometry from Vision Foundation Models When using predicted depth from foundation models, small inaccuracies and mis￾alignment is common, especially for transparent surfaces. In this section, w… view at source ↗
Figure 6
Figure 6. Figure 6: Qualitative comparison on the NeRF Synthetic dataset. Our method recon￾structs accurate geometry even in presence of highly reflective material which is not explicitly modeled in the pipeline. 5.5 Ablation Study TransLab PSNR↑ CD↓ F1↑ Full model 39.95 ± 3.25 1.665 ± 0.266 0.960 ± 0.019 - Opacitygeo 37.81 ± 3.08 1.679 ± 0.293 0.957 ± 0.019 - VGGT 39.88 ± 3.06 2.245 ± 0.311 0.920 ± 0.036 - DKT 40.08 ± 3.47 1… view at source ↗
Figure 7
Figure 7. Figure 7: Qualitative examples for the ablation study. Even though removing DKT leads to the lowest Chamfer distance in Tab. 5, it is clearly visible that the reconstruction of the test tubes is insufficient. of Gaussian Splatting, so the rendering quality decreases when the geometry opacity is removed. In [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
read the original abstract

After the success of 3D Gaussian Splatting (3DGS) for novel view synthesis, many works have explored how to also use it for geometric surface representation. However, extracting accurate geometric information directly from 3DGS remains challenging and can often reduce the appearance rendering quality. In this work, we show that 3DGS in its default form is inheritedly unsuited to represent texture and geometry at the same time, by training with complete ground-truth texture and geometry information. We also propose a simple solution by applying a single additional geometry opacity parameter to each splat, together with an optional transparency-curated optimization pipeline. Our experiments, both with ground-truth and vision foundation model geometric input, show that this change leads to improved rendering and geometry performance on a wide variety of dataset, and especially complex scenes with transparent objects benefit significantly from our method.

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 / 0 minor

Summary. The manuscript claims that 3D Gaussian Splatting in its default form is inherently unsuited to jointly represent texture/appearance and geometry, demonstrated via training experiments that supply complete ground-truth information for both tasks. It proposes a minimal fix consisting of one additional per-splat geometry opacity parameter together with an optional transparency-curated optimization pipeline, and states that this yields improved rendering and geometry performance on multiple datasets, with the largest gains on complex scenes containing transparent objects.

Significance. If the empirical results hold under quantitative scrutiny, the work would supply a lightweight, representationally minimal change that isolates and mitigates a known tension in 3DGS between appearance and geometry objectives. The use of ground-truth supervision to surface the conflict is a methodological strength that avoids circularity with standard self-supervised fitting. The significance remains provisional, however, because the central claim that a single extra opacity parameter is representationally sufficient (rather than merely an optimization aid) rests on an untested assumption about shared parameters.

major comments (2)
  1. [Abstract] Abstract: the central claim that default 3DGS is 'inherently unsuited' and that the added geometry opacity 'leads to improved rendering and geometry performance' is presented without any quantitative metrics, baselines, error analysis, or dataset-specific numbers, which is load-bearing for evaluating whether the single-parameter change actually resolves the conflict.
  2. [Method] Method description: the assertion that one additional per-splat geometry opacity parameter (plus optional pipeline) suffices to decouple appearance and geometry is load-bearing, yet position, covariance, and spherical-harmonic coefficients remain shared; the GT-training experiment only demonstrates joint-optimization difficulty and does not establish that opacity alone removes representational conflicts, especially for transparent objects where the largest gains are claimed.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments and for acknowledging the methodological value of our ground-truth supervision experiments. We respond to each major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the central claim that default 3DGS is 'inherently unsuited' and that the added geometry opacity 'leads to improved rendering and geometry performance' is presented without any quantitative metrics, baselines, error analysis, or dataset-specific numbers, which is load-bearing for evaluating whether the single-parameter change actually resolves the conflict.

    Authors: We agree that the abstract would be strengthened by including key quantitative results. The full manuscript contains detailed metrics (PSNR/SSIM/LPIPS for rendering and geometry error measures such as Chamfer distance) with baselines and dataset breakdowns in the experiments section. We will revise the abstract to report representative quantitative gains, particularly on complex scenes. revision: yes

  2. Referee: [Method] Method description: the assertion that one additional per-splat geometry opacity parameter (plus optional pipeline) suffices to decouple appearance and geometry is load-bearing, yet position, covariance, and spherical-harmonic coefficients remain shared; the GT-training experiment only demonstrates joint-optimization difficulty and does not establish that opacity alone removes representational conflicts, especially for transparent objects where the largest gains are claimed.

    Authors: The ground-truth training experiment isolates the conflict by supplying perfect supervision for both tasks; the observed degradation under joint optimization directly indicates that the shared parameters create an inherent tension that cannot be resolved by optimization alone. Adding a dedicated geometry opacity allows the appearance parameters to optimize for rendering while the geometry opacity handles surface representation. Our results, including ablations and evaluations on transparent-object scenes, show consistent gains in both rendering and geometry metrics. We therefore maintain that the change addresses a representational issue, though we acknowledge that further parameters could be explored in future work. revision: no

Circularity Check

0 steps flagged

No circularity; claims rest on external-GT empirical experiments with no derivations or self-referential reductions

full rationale

The paper advances an empirical claim that default 3DGS cannot jointly represent texture and geometry, demonstrated by training on complete external ground-truth data, followed by a proposed heuristic (one extra per-splat geometry opacity plus optional transparency pipeline). No equations, derivations, fitted parameters renamed as predictions, or self-citation chains appear in the provided text. The central argument is therefore not forced by construction or internal re-use; it is tested against independent benchmarks. This matches the default expectation of no significant circularity.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 0 invented entities

Based solely on abstract; the method adds one new per-splat parameter but introduces no other free parameters, axioms, or invented entities beyond the standard 3DGS framework.

free parameters (1)
  • geometry opacity
    New per-splat scalar introduced to control geometry representation separately from appearance.

pith-pipeline@v0.9.1-grok · 6026 in / 1023 out tokens · 101215 ms · 2026-06-28T03:01:47.786763+00:00 · methodology

discussion (0)

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