G2S-ICP SLAM: Geometry-aware Gaussian Splatting ICP SLAM

Euntai Kim; Gyuhyeon Pak; Hae Min Cho

REVIEW 4 major objections 5 minor 1 cited by

G2S-ICP SLAM: Geometry-aware Gaussian Splatting ICP SLAM

T0 review · 4 major / 5 minor · reviewed 2026-08-15 · deepseek-v4-flash

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Pith's one-line read Modeling every map point as a flat 2D disk aligned with the local surface lets a Gaussian-Splatting RGB-D SLAM system reconstruct geometry far more accurately and completely in real time, while keeping pose tracking competitive.

desk verdict Plausible surface-aligned Gaussian SLAM idea undercut by an unexplained baseline discrepancy and a shaky GICP derivation; worth refereeing after the numbers are fixed. read the letter →

arxiv 2507.18344 v1 pith:HPY5ZOHJ submitted 2025-07-24 cs.RO

Gyuhyeon Pak , Hae Min Cho , Euntai Kim This is my paper · ORCID

classification cs.RO

keywords 2DGaussianSplattingRGB-DSLAMGeneralizedICPcameratrackingsurfacereconstructiondepthconsistencygeometry-awarelossreal-time

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

This paper claims that the geometric shape of the Gaussian primitive is the bottleneck in Gaussian-Splatting SLAM: volumetric 3D ellipsoids let each surface point be seen at different depths from different views, while a 2D Gaussian disk constrained to the local tangent plane removes that ambiguity. It embeds this anisotropy into a Generalized ICP tracker by giving every source point a covariance with zero variance along the surface normal, and it supervises mapping with photometric, depth, and surface-normal losses. On Replica the reported average Depth L1 falls to 0.74 cm, versus 20.54 cm for the reproduced GS-ICP SLAM baseline, with higher precision and recall while running at 30 FPS. The upshot is that real-time dense mapping can have surface-consistent geometry without sacrificing photorealistic rendering.

What carries the argument

The load-bearing object is the 2D Gaussian disk, a surface element with covariance $C_k = R_k S_k S_k^T R_k^T$, where $R_k=[t_1,t_2,n_k]$ and $S_k=\operatorname{diag}(s_1,s_2,0)$. Its role is to force each primitive's spatial uncertainty onto the local tangent plane, eliminating depth ambiguity along the normal; the same covariance is used both in rendering and, as an anisotropic prior on source points, inside the Generalized ICP Mahalanobis-distance registration. A distance-aware initialization $s_1,s_2 \propto 1/z^p$ and a geometry-aware normal loss complete the mechanism.

What would settle it

On a Replica or TUM sequence, compute the eigenvalues of the combined covariance $C_{\mathrm{tgt}} + T C_{\mathrm{src}} T^T$ for every correspondence during GICP tracking and record the condition number. If any matrix is singular or near-singular and replacing $S=\operatorname{diag}(s_1,s_2,0)$ with $S=\operatorname{diag}(s_1,s_2,10^{-6})$ leaves ATE and Depth L1 essentially unchanged, the core claim that zero normal variance drives the improvement is falsified. A second check: run the full method with the geometry-aware normal loss removed ($\lambda_{\mathrm{GAN}}=0$) and compare Depth L1; if it jumps back toward 2 cm, most of the reconstruction gain comes from the loss, not the disk representation.

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Extended reading notes

Core claim

The central claim is that surface-aligned 2D Gaussian disks, not volumetric 3D ellipsoids, should be the primitive of a real-time Gaussian Splatting SLAM system. Each Gaussian is parameterized by a center $p_k$, a rotation $R_k=[t_1,t_2,n_k]$ built from two tangent vectors and the surface normal, and a scale matrix $S_k=\operatorname{diag}(s_1,s_2,0)$, so its support collapses onto the local tangent plane. The same covariance, with zero variance along the normal, is injected into each source point's distribution in the Generalized ICP registration, so tracking and mapping share one geometric prior. A geometry-aware loss then supervises rendered color, depth, and surface normals, and the scale is initialized from sensor depth so pixels far away grow larger Gaussians. The result, the paper argues, is a map that is geometrically accurate and complete while pose estimation remains at least as accurate as the 3D-ellipsoid baselines.

Load-bearing premise

The load-bearing premise is that setting every Gaussian's variance along the surface normal to exactly zero in the GICP covariance stays numerically stable and that this zero normal variance is what improves tracking; the paper specifies no regularization term to keep the Mahalanobis distance invertible.

Editorial extensions

If this is right

If the central claim holds, Gaussian-Splatting SLAM can produce depth-accurate surface meshes directly, with reported Replica Depth L1 under 1 cm, rather than relying on post-hoc TSDF fusion to clean up volumetric artifacts.
Tracking does not pay a price for the geometric prior: average ATE on Replica is reported at 0.15 cm, slightly better than the 3D-ellipsoid baseline, so surface constraints can serve as a regularization signal rather than a handicap.
Reconstruction completeness improves substantially (F1 81.57% on Replica vs 6.04% for the reproduced GS-ICP baseline), so the approach addresses holes and missing structures in real-time maps.
Rendering quality drops slightly (PSNR 36.88 dB vs 37.92 dB for the baseline) but stays competitive with other real-time GS SLAM systems, meaning the geometric gains come at a modest photometric cost.
Because the GICP formulation is unchanged and only the covariance prior is injected, the method slots into existing RGB-D GS-ICP pipelines without architectural redesign.

Reading between the lines

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

Editorial inference: if the zero-normal covariance is regularized in the GICP distance, the reported tracking gains may persist with better numerical conditioning; a direct ablation with $S=\operatorname{diag}(s_1,s_2,\epsilon)$ would separate the geometric prior from the singularity concern.
Editorial inference: the same tangent-plane covariance could be applied to monocular or stereo Gaussian-Splatting SLAM where depth is estimated, but the zero-variance normal becomes harder to justify when depth is uncertain; testing on real noisy sensors would show how much of the Replica gain transfers.
Editorial inference: the geometry-aware normal loss may be the main driver of the depth-L1 improvement, since the ablation shows the 2D-disk switch alone reduces depth error from 4.18 cm to 2.08 cm while the full optimization brings it to 0.44 cm; isolating these two contributions on TUM-RGBD would clarify the mechanism.
Editorial inference: applying the same normal and depth supervision to volumetric 3DGS SLAM without the disk constraint could test whether the flat primitive or the supervision is responsible, offering a clean control experiment.

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Key take: the core idea—putting 2D Gaussian disks into a GICP tracker with an anisotropic covariance prior—is legitimately new, and the internal ablation shows it works. But the headline comparison against GS-ICP SLAM is built on a baseline number (20.54 cm Depth L1) that conflicts with the paper's own ablation baseline (4.18 cm) at identical PSNR, so the 96% improvement claim doesn't hold up yet. The GICP derivation also has a sign error and the zero-variance covariance is left singular without regularization.

What's actually good: the integration is not trivial; using the same 2D Gaussian representation for both tracking and mapping is a sensible design choice, and the normal-consistency loss is a natural fit. The ablation on Replica is clean: depth L1 goes from 4.18 to 2.08 with the disk representation, then to 0.44 with the geometry-aware loss. That is credible internal evidence that the components do something. The system runs at 30 FPS, matching GS-ICP SLAM, and the qualitative figures show visibly cleaner meshes. The paper is clearly written and the related work is fair.

The soft spots: first, the external comparison. Table I says GS-ICP SLAM* (official code) gets 20.54 cm, but Table V's baseline—which has the same PSNR as GS-ICP SLAM in Table III—gets 4.18 cm. The asterisk doesn't explain that. One of these numbers is wrong, or the two tables aren't measuring the same thing. The paper never tells you which. That's a load-bearing flaw for the main claim. Second, Eqs. (11)-(12) write the GICP objective as an argmax of the squared Mahalanobis distance; MLE minimizes it. The surrounding text says 'minimizing', so it's probably a typo, but it needs fixing. Third, the paper says S=diag(s1,s2,0) for all Gaussians, making the covariance singular, and never mentions adding a small epsilon to keep the Mahalanobis distance invertible. That may just be an implementation detail omitted for brevity, but it's the kind of thing a reviewer needs to see.

This paper deserves a serious referee, but not in its current form. The baseline must be re-run or the discrepancy explained, and the GICP math needs to be made correct and concrete. If that happens, the result would be a solid within-subfield contribution for dense RGB-D SLAM. I'd send it to review, but I'd ask the authors to be very specific about the baseline.

Referee Report

4 major / 5 minor

Summary. The paper proposes G2S-ICP SLAM, an RGB-D Gaussian Splatting SLAM system that represents the scene with surface-aligned 2D Gaussian disks instead of volumetric 3D ellipsoids. The 2D disks are integrated into a Generalized ICP (GICP) tracker through an anisotropic planar covariance prior, and the mapping is supervised by photometric, depth, and normal consistency losses, together with a distance-aware scale initialization. The system is evaluated on the Replica and TUM-RGBD datasets, reporting real-time operation at about 30 FPS, a 0.74 cm average Depth L1 on Replica, competitive ATE, and slightly lower rendering quality compared to its main baseline, GS-ICP SLAM.

Significance. If the claims hold, the paper addresses a real limitation of volumetric 3DGS-based SLAM, namely multi-view depth inconsistency, by enforcing a surface-aligned representation within both tracking and mapping. The use of external benchmarks, ablations, and quantitative comparisons against several recent baselines is a strength, as is the explicit reporting of runtime. However, the central quantitative claims currently rest on an internally inconsistent baseline reproduction and on an underspecified tracking formulation, so the contribution cannot be fully validated from the manuscript as written.

major comments (4)

[Table I vs. Table V] The reported comparison against the main baseline is internally inconsistent. Table I lists GS-ICP SLAM* with an average Depth L1 of 20.54 cm, while Table V, whose 'Baseline' row has the same PSNR (37.92 dB) as the GS-ICP SLAM* row in Table III, reports a rendered Depth L1 of 4.180 cm. If the baseline in Table V is GS-ICP SLAM, the two tables cannot both be correct; if it is a different 3D-Gaussian system, the caption and text do not identify it. This discrepancy directly affects the claimed 96% depth improvement over the main baseline and must be resolved with a consistent evaluation protocol.
[Eq. (11)-(12), Section III-B] The maximum-likelihood derivation of the GICP objective has a sign error. The Gaussian log-likelihood is proportional to -d^T Sigma^{-1} d, so Eq. (12) should minimize (or maximize the negative of) the squared Mahalanobis distance, not maximize the positive term as written. As stated, the objective would prefer arbitrarily large residuals. Please correct the equation and verify that the implemented tracking objective matches the corrected form.
[Section III-C, Eq. (1), Eqs. (9)-(12)] The 2D disk covariance S = diag(s1, s2, 0) is singular, yet the GICP formulation in Eqs. (9)-(12) requires the inverse of C_src and C_tgt. The paper does not specify any epsilon regularization, pseudo-inverse, or rank-deficient handling. Furthermore, the text says the 2D anisotropic covariance is embedded into each C_src_m, but the construction of C_src from the depth-map neighborhood (Section III-B) and the exact substitution with the 2D disk covariance are not given. This missing detail is load-bearing for the claimed tracking improvement and must be clarified.
[Table I vs. Table V, Section V-E] The full model's depth accuracy is reported differently in two tables. Table I gives G2S-ICP SLAM an average Depth L1 of 0.74 cm on Replica, while Table V reports the full model's 'Rendered Depth L1' as 0.437 cm. If these are the same metric, the discrepancy needs explanation; if they are different metrics (e.g., rendered depth versus TSDF-integrated mesh depth), the definitions should be stated explicitly in the evaluation section.

minor comments (5)

[Throughout] There are many typographical errors, e.g., 'Exisiting', 'aprroaches', 'incorportate', 'Generailzed', 'transfromation', 'awrae', 'coparisons', and 'incredible' in Table IV's caption. A careful proofread is needed.
[Eq. (4)] The 2D Gaussian kernel is written as G(q) = exp(u^2+v^2 / 2), which lacks the negative sign; it should be exp(-(u^2+v^2)/2).
[Eq. (6)] The alpha term in the depth rendering equation is written as 'alpha G_j(x)' instead of 'alpha_j G_j(x)', consistent with Eq. (5).
[Eq. (17)] There is a stray period in 'lambda_d L_d .' before the plus sign; the equation should read L = lambda_p L_p + lambda_d L_d + lambda_GAN L_GAN.
[Section V-C] The phrase 'achieves the lowest tracking performance' should be 'achieves the lowest tracking error'; otherwise it contradicts the following sentence.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity found; the central claims are evaluated against external benchmarks and do not reduce to fitted inputs or self-citations.

full rationale

The paper's central derivation chain is self-contained and not circular. The surface-aligned 2D Gaussian representation in Eqs. (1)-(4) is adopted from the external 2DGS work [14] and defined as a modeling choice, not derived from the evaluation target. The GICP tracking objective in Eqs. (8)-(12) is the standard generalized ICP maximum-likelihood formulation from Segal et al. [15]; injecting the anisotropic covariance S=diag(s1,s2,0) is a structural prior, not a parameter fitted to the reported depth or tracking results. The scale regularization in Eq. (13) uses hyperparameter p set empirically, but this is a conventional hyperparameter and does not encode the benchmark outcomes. The loss function in Eq. (17) combines photometric, depth, and normal terms with fixed weights, and the normal supervision in Eq. (15) uses ground-truth depth gradients; none of these terms is defined in terms of the final accuracy numbers. The reported improvements are measured against external datasets (Replica, TUM-RGBD) and against baselines reproduced from official code, so the quantitative claims are empirical rather than tautological. The paper does cite the authors' own prior work [6] in the related-work section, but that citation is not load-bearing for any derivation or prediction and does not support the central claims. The significant internal inconsistency between the reproduced GS-ICP SLAM baseline in Table I (20.54 cm Depth L1) and the ablation baseline in Table V (4.18 cm) is a serious correctness and reproducibility concern, but it is not a circularity: no equation or prediction reduces to its own input, and the inconsistency does not make the proposed method's results true by definition. Therefore, no circular step can be identified, and the appropriate score is 0.

Assumptions & free parameters 4 free parameters · 4 assumptions · 0 invented entities

The system relies on standard math (Gaussian distributions, GICP), domain assumptions about depth and normals, and one ad hoc numerical assumption: that zero normal variance in the covariance is usable in GICP without regularization. Four hyperparameters (p and three loss weights) are hand-chosen. No new physical or algorithmic entities are invented.

free parameters (4)

p (distance-aware scaling exponent) = 0.333
Section III-D, Eq. (13); controls how Gaussian scale shrinks with depth, chosen empirically to balance visual uniformity and pose stability.
lambda_P (photometric loss weight) = 1.0
Section V-A; hand-set hyperparameter.
lambda_D (depth loss weight) = 0.1
Section V-A; hand-set hyperparameter.
lambda_GAN (normal loss weight) = 0.05
Section V-A; hand-set hyperparameter.

assumptions (4)

domain assumption 2D Gaussian disks with zero scale along the normal are a valid surface representation for both rendering and GICP tracking.
Borrowed from 2DGS [14]; the paper assumes planar primitives resolve multi-view depth inconsistency (Section III-A).
standard math The GICP residual dm is Gaussian with covariance C_tgt + T C_src T^T.
Standard GICP derivation, Eq. (9)-(10).
ad hoc to paper Per-point covariances can be set to the 2D disk covariance with exactly zero normal variance without numerical degeneration in the Mahalanobis distance.
Section III-C sets S=diag(s1,s2,0) for all Gaussians but does not specify the epsilon regularization used to keep the covariance invertible.
domain assumption Normals computed from depth gradients are reliable supervision for rendered normals.
Used in Eq. (14)-(15); noisy depth on TUM-RGBD would degrade this signal.

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Cite this review

Pith. "Pith review of G2S-ICP SLAM: Geometry-aware Gaussian Splatting ICP SLAM." pith.science (2026). https://pith.science/paper/HPY5ZOHJ

@misc{pith2026250718344,
  author       = {Pith},
  title        = {Pith review of: G2S-ICP SLAM: Geometry-aware Gaussian Splatting ICP SLAM},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/HPY5ZOHJ}},
  note         = {Machine review of arXiv:2507.18344}
}

read the original abstract

In this paper, we present a novel geometry-aware RGB-D Gaussian Splatting SLAM system, named G2S-ICP SLAM. The proposed method performs high-fidelity 3D reconstruction and robust camera pose tracking in real-time by representing each scene element using a Gaussian distribution constrained to the local tangent plane. This effectively models the local surface as a 2D Gaussian disk aligned with the underlying geometry, leading to more consistent depth interpretation across multiple viewpoints compared to conventional 3D ellipsoid-based representations with isotropic uncertainty. To integrate this representation into the SLAM pipeline, we embed the surface-aligned Gaussian disks into a Generalized ICP framework by introducing anisotropic covariance prior without altering the underlying registration formulation. Furthermore we propose a geometry-aware loss that supervises photometric, depth, and normal consistency. Our system achieves real-time operation while preserving both visual and geometric fidelity. Extensive experiments on the Replica and TUM-RGBD datasets demonstrate that G2S-ICP SLAM outperforms prior SLAM systems in terms of localization accuracy, reconstruction completeness, while maintaining the rendering quality.

Figures

Figures reproduced from arXiv: 2507.18344 by the authors.

**Figure 2.** Overview pipeline. G2S-ICP SLAM takes RGB and depth images as input to construct geometrically consistent 3D maps in real time. To enhance multi-view depth consistency, we represent each point as a surface-aligned 2D Gaussian disk instead of a volumetric ellipsoid. In the tracking stage, this representation is integrated into a 2D Gaussian-based Generalized ICP (GICP) to estimate camera motion. During mapping, we op… view at source ↗

**Figure 3.** Depth Inconsistency of 3D Gaussian Ellipsoids in [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗

Figures from the paper (3 more)

**Figure 4.** Figure 4: Qualitative Results on Replica dataset. (a), (b) show reconstructed mesh maps of [PITH_FULL_IMAGE:figures/full_fig_p005_4.png]

**Figure 5.** Figure 5: Qualitative Results on Replica dataset. (a), (b) visualize RGB renderings, depth renderings, and depth error maps [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]

**Figure 6.** Figure 6: Ablation study on modules. Each row shows the [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

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Forward citations

Cited by 1 Pith paper

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Reference graph

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Pith tools

Reviewed August 15, 2026 · model on record in the stance chip above.

[1] [1]

Orb-slam: a versatile and accurate monocular slam system,

R. Mur-Artal, J. M. M. Montiel, and J. D. Tardos, “Orb-slam: a versatile and accurate monocular slam system,” IEEE transactions on robotics, vol. 31, no. 5, pp. 1147–1163, 2015

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