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REVIEW 4 major objections 5 minor 32 references

ErpGS: Equirectangular Image Rendering enhanced with 3D Gaussian Regularization

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read ErpGS claims that equirectangular 360-degree novel-view synthesis is made more accurate by regularizing the scale of 3D Gaussians and aligning rendered normals with depth-derived normals, and reports consistent gains over prior neural and…

desk verdict Solid incremental improvement to omnidirectional 3DGS with a reproducible core, but the unspecified OmniScenes mask confounds part of the headline claim. read the letter →

arxiv 2505.19883 v2 pith:OH2M6UAR submitted 2025-05-26 cs.CV

Shintaro Ito , Natsuki Takama , Koichi Ito , Hwann-Tzong Chen , Takafumi Aoki This is my paper · ORCID
classification cs.CV
keywords equirectangularprojectionnovelviewsynthesis3DGaussiansplattinggeometricregularizationscaledistortion-awareweightingviewpoint-dependentmaskomnidirectionalimaging
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

The paper argues that when 3D Gaussian splatting is applied to 360-degree equirectangular images, the projection's strong distortion produces extremely large 3D Gaussians that smear renderings, and that this can be corrected with regularizations rather than scene-specific threshold pruning. ErpGS adds a geometric term aligning rendered normals with depth-derived normals, a scale term that shrinks and flattens Gaussians, a latitude-dependent weight that compensates for the unequal pixel areas of equirectangular projection, and a viewpoint-dependent mask that hides camera rigs and other obstacles. In experiments on three public datasets, the method reports higher PSNR and SSIM and lower LPIPS than prior neural and Gaussian baselines, EgoNeRF, ODGS, and OmniGS. The appeal is practical: better novel-view synthesis from cheap 360-degree cameras would improve VR/AR, robotic mapping, and 3D scene capture without expensive multi-camera rigs.

What carries the argument

Omnidirectional Gaussian splatting with an ERP camera model is the base: each 3D Gaussian is projected to image coordinates via longitude and latitude (Eqs. 2-3), and its image covariance is obtained through the Jacobian of the ERP transform (Eq. 4), so rasterization proceeds like 3DGS but in equirectangular space. The load-bearing additions are four. Geometric regularization renders a depth map and a normal map from the Gaussians and enforces agreement through a depth-normal error $DNE(p)=|\nabla I(p)|^2\|N_d(p)-N(p)\|$, using tangent-plane neighbor selection that accounts for ERP distortion. Scale regularization penalizes large Gaussian axis lengths via $\frac{1}{N_g}\sum_i\|s_i\|_2^2$ and flattening via $\|\min(s_x,s_y,s_z)\|_1$, suppressing the pathological large Gaussians. The distortion-aware weight $W=\int_{\theta_0}^{\theta_1}\int_{\phi_0}^{\phi_1}\cos\theta\,d\theta\,d\phi$ reweights losses toward low-latitude pixels. A viewpoint-dependent mask $M_p$ is applied to the color and depth-normal losses to discount obstacles. The paper's argument is that these work together: the weight fixes the input distortion, the normal alignment fixes geometry, and scale and flattening fix the bloated Gaussians.

What would settle it

Run ErpGS on OmniScenes with the mask removed and with a mask generated automatically from the training views (for example, by detecting pixels with high reprojection error between nearby cameras), then compare PSNR and SSIM in the same unmasked region; if the gap to OmniGS and ODGS disappears or reverses, the mask rather than the scale or geometric regularization is carrying the reported improvement.

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Extended reading notes

Core claim

The central claim is that existing omnidirectional 3D Gaussian splatting methods fail on equirectangular images because the ERP projection maps the same solid angle to very different pixel areas at different latitudes, and the standard covariance projection produces oversized Gaussians that render as flat, inconsistent haze. ErpGS counteracts this in four linked moves: a scale-regularization loss $L_s$ that penalizes large axis lengths and a flattening loss $L_f$ that presses Gaussians into thin planar slabs; a geometric regularization that computes depth-normals using neighboring pixels selected on the tangent plane of the unit sphere (Eqs. 9-10) and aligns them with the normals rasterized from Gaussians (Eqs. 11-12); a distortion-aware weight $W$ (Eq. 14) that integrates the cosine-latitude area factor over each pixel; and a viewpoint-dependent mask $M_p$ that removes obstacles appearing inconsistently between views. The total loss (Eq. 18) combines these, and the paper reports that the full model is more accurate than all three baselines on every scene of OmniBlender, Ricoh 360, and OmniScenes, with the distortion-aware weight being the most impactful component in the ablation.

Load-bearing premise

The paper's reported advantage on the real-world OmniScenes dataset relies on a viewpoint-dependent mask that removes obstacles, but it never explains how that mask is obtained; if the mask is hand-labeled or uses extra test-time information, the gains could be due to the mask rather than to the new regularizations.

Editorial extensions

If this is right

  • Omnidirectional 3D Gaussian methods should not prune large Gaussians by a per-scene threshold; explicit scale and flattening regularization achieves the same effect inside the optimization, removing a hand-tuned parameter.
  • The tangent-plane neighbor selection gives a concrete recipe for computing depth-normals on any equirectangular image, and the same recipe could be reused in other sphere-based depth estimation tasks.
  • The distortion-aware weight shows that per-pixel footprint, not just inverse-latitude heuristics, should enter the loss when training on 360-degree images; the ablation indicates this alone improves quantitative scores.
  • The viewpoint-dependent mask is presented as essential for egocentric 360-degree capture, where the camera rig appears in every frame; the paper restricts its OmniScenes evaluation to the unmasked region, so the reported advantage there is for obstacle-free pixels.

Reading between the lines

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

  • The paper leaves the generation of the viewpoint-dependent mask unspecified; if it were automated from multi-view geometric consistency, ErpGS could be applied to new captures without manual annotation, and the OmniScenes results would be more convincing.
  • The flattening and scale losses together push Gaussians toward thin planar slabs, which may make ErpGS naturally suited to surface reconstruction and mesh extraction, a direction the paper does not explore.
  • The distortion-aware weight $W$ could double as a sampling probability density for next-best-view selection or image downsampling, possibly improving training efficiency on 360-degree data.
  • Because the paper's improvements are most visible on real-world egocentric captures, a natural next test is video sequences with moving obstacles, where the viewpoint-dependent mask would need to be estimated per frame rather than per scene.
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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 / 5 minor

Summary. The paper proposes ErpGS, a 3D Gaussian Splatting variant for novel-view synthesis from equirectangular (ERP) images. The method adds four components to a standard omnidirectional 3DGS pipeline: a geometric regularization that encourages consistency between rendered normals and normals computed from rendered depth using ERP-aware neighbor selection, a scale regularization with a flattening term to suppress oversized 3D Gaussians, per-pixel distortion-aware weights in the losses, and a viewpoint-dependent mask intended to suppress obstacles such as camera rigs and stands. Experiments compare ErpGS with EgoNeRF, ODGS, and an author reimplementation of OmniGS on OmniBlender, Ricoh 360, and OmniScenes, reporting improved PSNR/SSIM/LPIPS in most scenes, together with an ablation study on OmniBlender.

Significance. If the reported results hold, ErpGS is a practically useful set of modifications for omnidirectional 3DGS: the distortion-aware weighting is well motivated by ERP geometry, the depth-normal regularization addresses floaters in a principled way, and the ablation study indicates that each component contributes. The paper does not provide machine-checked proofs or released code, and the main evaluation depends on an author-reproduced baseline and an underspecified mask, so the strength of the claims is currently limited. The core idea is defensible and the experiments are on standard public datasets, which makes the contribution potentially valuable to the omnidirectional NVS community.

major comments (4)
  1. [Sec. 3.4, Sec. 4.1] The viewpoint-dependent mask M_p is introduced in Eqs. (15) and (16) and is used for all OmniScenes experiments, but the paper never states how M_p is generated. Section 4.1 says only that 'we introduce a mask for ErpGS' on OmniScenes and that metrics are then computed only in unmasked regions. This is load-bearing: Eqs. (15) and (16) train ErpGS exclusively on masked pixels, while the baselines are trained on the full images, so the OmniScenes rows of Table 1 conflate the effect of the proposed regularizations with the effect of discarding obstacle pixels from the loss. The authors must specify the mask-generation procedure (manual annotation, semantic segmentation, or known camera-rig geometry) and should report results for baselines trained with the same masked loss to establish a fair comparison.
  2. [Sec. 4.1] The OmniGS baseline in Table 1 is an author reimplementation, as stated: 'Because the code for OmniGS was not publicly available at the time of writing, the OmniGS used in this experiment was reproduced and implemented by the authors.' No validation of this reimplementation against the numbers reported in the original OmniGS paper is provided. Since OmniGS is one of the three principal baselines, the authors should either release their reimplementation, report its agreement with original OmniGS results on the same scenes, or use a public implementation; otherwise the comparative claims against OmniGS are unverified.
  3. [Sec. 4.2, Table 1] No error bars, confidence intervals, or numbers of random seeds are reported, and several claimed improvements are small in absolute terms (e.g., OmniScenes 'pyebaek' PSNR 27.08 vs 26.67 for OmniGS; 'wedding-hall' 27.35 vs 26.99). Because 3DGS optimization is stochastic, these margins may not be significant. This concern is heightened by the fact that EgoNeRF has higher PSNR than ErpGS on Ricoh360 'center' (29.42 vs 28.63) and 'farm' (22.58 vs 21.66). Please report means and standard deviations over multiple runs, or otherwise provide statistical support for the claimed improvements.
  4. [Sec. 4.2] The text states that 'ErpGS exhibits better rendering performance than the other methods on all datasets,' but Table 1 directly contradicts this on PSNR for two Ricoh360 scenes, and the very next sentence concedes only 'equal or better' accuracy for those scenes. The claims in the abstract and in Section 4.2 should be qualified to match the actual results, e.g., 'better on most scenes and metrics.'
minor comments (5)
  1. [Eq. (14)] The integration limits theta0, theta1, phi0, and phi1 in the distortion-aware weight W are never defined. Please state explicitly that W is the area of the pixel footprint on the unit sphere and give the formula used to compute the per-pixel bounds.
  2. [Sec. 4.1] The sentence 'When the mask is introduced, the accuracy is evaluated only in the unmasked region for all methods' needs a precise definition of the unmasked region and the aggregation rule for spherical-image metrics; without this, the OmniScenes rows of Table 1 are not reproducible.
  3. [Sec. 4.3, Fig. 3] The sentence 'removing the regularization term from the proposed method removes large 3D Gaussians and improves the rendering accuracy' contradicts the preceding statement that the 'w/o Ls' ablation degrades quality due to large 3D Gaussians. Please correct the wording to say that removing the scale regularization leaves large Gaussians and degrades accuracy.
  4. [Tables 1 and 2] Table 2 reports both LPIPS(A) and LPIPS(V), while Table 1 reports only LPIPS(A). Please state clearly which feature extractor is used for the main comparisons and why the VGG-based LPIPS is omitted from Table 1.
  5. [Sec. 4.3] The ablation study is performed only on OmniBlender. Given that the mask is the main confound in the OmniScenes experiments, an ablation of the mask term on OmniScenes would substantially clarify its contribution to the reported gains.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: ErpGS's regularizations are externally grounded and its evaluations use held-out views.

full rationale

The paper's derivation chain is self-contained. ErpGS is an empirical 3DGS variant; its contributions are loss terms: geometric depth-normal consistency (Eq. 12), scale and flattening regularizers (Eq. 13), ERP solid-angle weighting (Eq. 14), and a viewpoint-dependent mask in Eqs. 15-16. None of these quantities is fitted to the reported benchmark numbers; the weights lambda_dn, lambda_f, lambda_s are fixed hyperparameters (lambda_dn=0.01, lambda_f=100, lambda_s=0.01) chosen before evaluation, not solved from the test targets, so Table 1's PSNR/SSIM/LPIPS comparisons are not predictions forced by construction. The geometric regularization reuses published depth-normal and tangent-plane neighbor formulas [16,18], the flattening loss explicitly cites prior work [19,16], and the distortion weight is the standard cos(theta) area element; these are external or mathematical ingredients, not self-citation load-bearing. The only self-citation is reference [11] in a related-work sentence about single-image panorama NVS; it does not support any central derivation. The under-specified viewpoint-dependent mask in Section 3.4 is a reproducibility and fairness concern for the OmniScenes rows, not a circular reduction: no equation defines the mask in terms of the outputs it is used to measure, and the mask does not encode the reported metrics by construction. Therefore no circular step is exhibited.

Assumptions & free parameters 3 free parameters · 5 assumptions · 0 invented entities

The method relies on three manually chosen loss weights and an unspecified viewpoint-dependent mask. The ERP projection and depth-normal regularizers are standard from cited work. No new physical entities are introduced.

free parameters (3)
  • lambda_dn = 0.01
    Manually chosen loss weight for depth-normal regularization, set by the authors.
  • lambda_f = 100
    Manually chosen loss weight for the flattening term Lf, set by the authors.
  • lambda_s = 0.01
    Manually chosen loss weight for the scale regularization Ls, set by the authors.
assumptions (5)
  • standard math Equirectangular projection model mapping camera rays to latitude and longitude (Eqs. 2-3) is the correct camera model.
    Standard model for 360-degree cameras; the paper explicitly adopts it.
  • standard math The affine approximation for projecting Gaussian covariance to image space (Eq. 4) is valid.
    Borrowed from EWA volume splatting [15]; standard in 3DGS literature.
  • standard math Tangent-plane neighbor selection via Eqs. (9)-(10) correctly identifies ERP image neighbors on the sphere.
    Derived from spherical geometry in SphereNet [18].
  • domain assumption Rendered Gaussian normals should match normals computed from the rendered depth map (Eqs. 11-12).
    This is the geometric regularization premise from PGSR [16], adapted to ERP images.
  • ad hoc to paper A viewpoint-dependent mask M_p that labels obstacle pixels is available for training and evaluation.
    Losses in Eqs. (15)-(16) require this mask, but the paper never specifies how M_p is obtained or computed.

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Cite this review

Pith. "Pith review of ErpGS: Equirectangular Image Rendering enhanced with 3D Gaussian Regularization." pith.science (2026). https://pith.science/paper/OH2M6UAR

@misc{pith2026250519883,
  author       = {Pith},
  title        = {Pith review of: ErpGS: Equirectangular Image Rendering enhanced with 3D Gaussian Regularization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OH2M6UAR}},
  note         = {Machine review of arXiv:2505.19883}
}
read the original abstract

The use of multi-view images acquired by a 360-degree camera can reconstruct a 3D space with a wide area. There are 3D reconstruction methods from equirectangular images based on NeRF and 3DGS, as well as Novel View Synthesis (NVS) methods. On the other hand, it is necessary to overcome the large distortion caused by the projection model of a 360-degree camera when equirectangular images are used. In 3DGS-based methods, the large distortion of the 360-degree camera model generates extremely large 3D Gaussians, resulting in poor rendering accuracy. We propose ErpGS, which is Omnidirectional GS based on 3DGS to realize NVS addressing the problems. ErpGS introduce some rendering accuracy improvement techniques: geometric regularization, scale regularization, and distortion-aware weights and a mask to suppress the effects of obstacles in equirectangular images. Through experiments on public datasets, we demonstrate that ErpGS can render novel view images more accurately than conventional methods.

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Reference graph

Works this paper leans on

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    With the rapid development of Novel View Synthesis (NVS ) technologies, many methods have been proposed for reconstr ucting a large space from a large number of images [1, 2]

    INTRODUCTION 3D reconstruction from images taken from multiple viewpoin ts is an essential technique that can be applied to VR/AR, robotics, and 3D map creation, since such images can be captured by a standard cam- era. With the rapid development of Novel View Synthesis (NVS ) technologies, many methods have been proposed for reconstr ucting a large space...

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    ErpGS: Equirectangular Image Rendering enhanced with 3D Gaussian Regularization

    RELATED WORK NVS methods such as NeRF [8] and 3DGS [9] are rapidly develop- ing, which can learn a 3D space representation from multiple images and render photorealistic images. NVS methods for ERP image s based on NeRF have been proposed to render an unknown viewpoint image from a single image [10, 11, 12]. Although these method s re- quire only a single...

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    EXPERIMENTS We demonstrate the effectiveness of ErpGS for NVS using publ ic datasets. 4.1. Experimental Setup Dataset — In the experiments, we use the three public datasets: OmniBlender [4], Ricoh 360 [4], and OmniScenes [21]. Om- niBlender [4] consists of indoor/outdoor scenes synthesiz ed from Blender projects [22]. Ricoh 360 [4] consists of outdoor sce...

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    CONCLUSION We proposed ErpGS, which is Omnidirectional GS based on 3DGS to realize NVS addressing problems inherent in ERP images. E rpGS introduced some rendering accuracy improvement technique s: ge- ometric regularization, scale regularization, and distor tion-aware weights and a mask to suppress the effects of obstacles in the ERP images. Through expe...

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