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Large Images are Gaussians: High-Quality Large Image Representation with Levels of 2D Gaussian Splatting

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

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Pith's one-line read Two-stage Gaussian splats fit 9K images at 42 dB

desk verdict The central scaling claim against GaussianImage is compromised by an iteration-count mismatch; the paper's design ideas are solid but the headline numbers need re-derivation under matched training budgets. read the letter →

arxiv 2502.09039 v1 pith:PJGUGS2W submitted 2025-02-13 cs.CV cs.AI

Lingting Zhu , Guying Lin , Jinnan Chen , Xinjie Zhang , Zhenchao Jin , Zhao Wang , Lequan Yu This is my paper
classification cs.CVcs.AI
keywords 2DGaussiansplattinglargeimagerepresentationLevel-of-Gaussiancovariancematrixoptimizationimplicitneuralhistopathologysatelliteimageryfitting
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 presents Large Images are Gaussians (LIG), a 2D Gaussian splatting representation that fits very large images—histopathology slides at 9K resolution, satellite images at 4K, and natural images at 2K—by optimizing tens of millions of Gaussian points directly in image space. The paper argues that prior Gaussian-based image fitters, notably GaussianImage, degrade as the number of Gaussian points grows, while LIG's quality improves monotonically with the point budget, reaching 42.19 dB PSNR on 9K histopathology images. Two modifications are said to unlock this scaling: optimizing the full symmetric 2×2 covariance matrix directly instead of through a rotation-and-scale decomposition, and a two-level 'Level-of-Gaussian' scheme that fits a coarse low-frequency initialization first and then the high-frequency residual. A careful reader would care because explicit, GPU-friendly Gaussian representations are proposed as a scalable alternative to grid-based implicit neural representations, which run into memory limits and slow decoding at high resolution.

What carries the argument

The mechanism is the Level-of-Gaussian pipeline on a modified 2D Gaussian splat. Each splat keeps the 8-parameter form (position, covariance, weighted color) of GaussianImage, but the covariance is optimized directly as a symmetric 2×2 matrix; in the rasterizer, any pixel–Gaussian pair with $\sigma_n = \frac{1}{2} d_n^T \Sigma_n^{-1} d_n$ negative is dropped from the $\alpha$-blending sum, which removes every provably non-positive-semi-definite matrix. Then LOG trains two levels: level 0 fits the downsampled image with 12.5% of the Gaussians, and level 1 fits the min-max normalized difference image with the remaining 87.5%, with level 0 frozen during level 1 training so that fewer parameters carry gradients and memory stays bounded. The two-stage design is what lets quality climb as the point count reaches tens of millions.

What would settle it

Retrain LIG on the 9K STimage set at 5.5e7 Gaussians with every covariance matrix projected to positive semi-definite after each optimizer step, keeping the two-level pipeline otherwise identical. If PSNR falls materially below the reported 42.19 dB, the quality gain depends on keeping indefinite matrices, not just on the Level-of-Gaussian or direct optimization.

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Extended reading notes

Core claim

The central claim is that 2D Gaussian splatting can be made to fit very large images at high quality if two conditions hold: the covariance is optimized directly as a symmetric matrix, with any contribution whose negative exponent falls below zero filtered out during rasterization, and the fitting target is decomposed into two levels—a small group of Gaussians reconstructs the downsampled low-frequency image, then the main group fits the min-max normalized difference between the upsampled first-level render and the target. Under that design, fitting quality rises as the number of Gaussians grows, from 37.47 to 42.19 dB on 9K STimage as the budget goes from 3.5e7 to 5.5e7 points, while GaussianImage stays flat or falls. The paper claims this is the first GS-based representation that extends successfully to large images, and backs it with ablations showing both the direct covariance optimization and the Level-of-Gaussian mechanism contribute.

Load-bearing premise

The load-bearing premise is that dropping every pixel–Gaussian pair with $\sigma_n < 0$ keeps optimization stable and well-graded when tens of millions of non-positive-semi-definite covariance matrices are optimized directly; if the filter lets the fit drift, or if the retained indefinite matrices are the true source of the quality gain, the scaling behavior will not transfer to other large images.

Editorial extensions

If this is right

  • If LIG is right, explicit 2D Gaussian representations can be scaled to very large images without the memory blowup of grid-based implicit neural representations.
  • Quality becomes a tunable point budget: the same pipeline yields higher PSNR as the Gaussian count increases, so users can trade storage and training time against fidelity.
  • The two-level residual scheme (low-frequency first, normalized high-frequency difference second) should transfer to other large-signal fitting problems, not just still images.
  • Because the first level is frozen during second-level training, memory stays bounded enough to fit 9K images on a single GPU.

Reading between the lines

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

  • Testable extension: projecting each covariance matrix to positive semi-definite after every update, while keeping the two levels, would reveal how much of the reported gain depends on retaining indefinite matrices.
  • The two-level residual trick could be applied tile-wise to gigapixel whole-slide images, though the paper does not address tile-boundary artifacts.
  • The compact 8-parameter per-Gaussian format and the stored min-max scaler suggest a direct path to learned compression of large images, a direction the paper flags as future work.
  • Because L1 fits a normalized residual, the choice of min-max normalization could be ablated; a raw-difference variant would isolate the contribution of conditioning the second-stage target.
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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 introduces LIG, a 2D Gaussian splatting representation for large images. It makes two main changes relative to GaussianImage: (1) it optimizes the 2D covariance matrix directly instead of using a rotation/scale decomposition, filtering out Gaussian points with negative sigma during rasterization, and (2) it uses a two-level Level-of-Gaussian scheme, where a small set of Gaussians first fits a downsampled low-frequency target and a larger set then fits the normalized difference image. The authors report large PSNR gains over GaussianImage on 2K, 4K, and 9K images, with quality increasing as the number of Gaussians grows, and they provide ablations for the two components, training-memory comparisons, and code.

Significance. If the reported scaling behavior holds, LIG is a useful step toward making explicit Gaussian-based image representations practical at high resolution: it combines a coarse-to-fine fitting target with a direct covariance parameterization that appears to remain stable at tens of millions of Gaussians. The paper includes experiments on diverse data types (histopathology, satellite, natural images), reports training memory and FPS, and releases code, all of which strengthen the empirical contribution. However, the central quantitative claim rests on a comparison whose optimization budget is internally inconsistent, and one of the two claimed design components is not isolated in the ablations. The core idea is plausible, but the evidence as presented does not yet establish that the gains come from the representation rather than from an unfair or uncontrolled training setup.

major comments (4)
  1. [Implementation Details; Table 4; Table 1] The training budget for the main results is contradictory. The Implementation Details section states that 'The training steps for L0 and L1 are set to the same, 30,000 steps in our implementation,' while Table 4 reports iterations from 1e5 to 5e5 and says that '3e5 iterations representing a compromise point adopted in our experiments.' The 3e5 row of Table 4 matches the main PSNR values in Table 1 (e.g., 39.82 dB on STimage at 4.5e7 points and 56.05 dB on FGF2 at 1.4e7 points), so the reader cannot tell whether GaussianImage was allowed the same optimization budget as LIG. Since the paper's central claim is the scaling contrast in Figure 1 and Table 2, the authors must state the exact iteration count used for every method and either rerun GaussianImage with matched iterations and re-tuned hyperparameters or demonstrate that the published GaussianImage numbers already use this budget.
  2. [Table 3] The evidence for the benefit of low-frequency initialization is confounded by point count. Each row compares a single-level model with only |N1| Gaussians against the two-level model with |N0|+|N1| Gaussians, so the PSNR improvement could come from the additional |N0| Gaussians rather than from the coarse target. To support the claim that the L0 target helps, the comparison should hold the total number of Gaussians fixed, for example by training a single-level model with |N0|+|N1| points or by giving L0 a zero/random target with the same total point budget. In addition, the point ratios in Table 3 are inconsistent with Eq. (5) and r=0.125: for instance, 4,375,000 / 30,625,000 = 1/7, not 0.125, and the stated totals do not match the 3.5e7/5.5e7 settings used elsewhere.
  3. [2D Gaussians Formulation; Table 2] The claimed benefit of direct covariance optimization is not isolated from other implementation differences. Table 2 compares GaussianImage with 'Ours w/o LOG', but 'Ours w/o LOG' differs from GaussianImage not only in the covariance parameterization but also in the re-implemented CUDA kernels, initialization, and possibly other details. The text states only that 'we find that optimizing the decomposed parameters can be challenging when the Gaussian points are numerous' without reporting a controlled comparison. A head-to-head experiment within the same pipeline (decomposed covariance vs. direct covariance with the same optimizer, iterations, and initialization) is needed to attribute the large-point-count improvement to the representation variant rather than to unrelated engineering changes.
  4. [2D Gaussians Formulation, Eq. (4)] The paper's own text acknowledges that filtering sigma_n < 0 does not guarantee that all retained covariance matrices are positive semi-definite, because the condition in Eq. (4) is verified only on the finite set of queried pixel centers. Since the method optimizes tens of millions of potentially indefinite covariance matrices and the headline results depend on stability at 5.5e7 Gaussians, the manuscript should report at least one piece of supporting evidence, such as the fraction of active Gaussians with indefinite covariance during training, the fraction of filtered points, or convergence curves showing that gradient behavior does not degrade at the largest scale. Without this, the scaling claim rests on an empirical observation whose transfer to other large images is not yet validated.
minor comments (5)
  1. [Table 4] The caption 'The number for Gaussian points are (4.5e7, 1.4e7) for two datasets' is ambiguous; please clarify which tuple element belongs to which dataset and whether these are total or per-level point counts.
  2. [Levels of 2D Gaussians, Eq. (7)] The final image is not explicitly defined: after L1 is trained on the normalized difference target, the reconstruction must combine Render(L0) and Render(L1), but this combination formula is not given in the main text.
  3. [Figure 4] The caption states that difference images are shifted to 0.5 for visualization; please state explicitly whether the same shift and scaling are applied to both the LIG and the GaussianImage difference images.
  4. [Table 1] The note '3.5e7 denotes 3 × 10^7' uses a nonstandard exponent notation; using '×10^7' consistently would improve readability.
  5. [2D Gaussians Formulation] The phrase 'semi-implicit fitters' is used without definition; please define or rephrase it.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: LIG is an empirical fitting benchmark whose reported gains are validated by ablations and external baselines, not by construction.

full rationale

LIG's contribution is a representation change (direct covariance optimization plus a two-level Gaussian scheme) evaluated by PSNR/FPS on external datasets. The pipeline fits Gaussian parameters to target images and measures reconstruction quality; no reported number is defined as the value of a fitted parameter, so the 'predictions' are not forced by construction. The PSD-filter argument (Eqs. 3-4) is a mathematical implication about positive semi-definite matrices and is acknowledged to be only a sufficient filter ('we cannot ensure that all covariance matrices producing positive sigma have physical meanings'), so it is a stated limitation rather than a circular derivation. Related-work citations to prior work by the same group (e.g., Zhu et al. 2024) are contextual and not load-bearing. The only notable issue is an internal inconsistency between Implementation Details ('The training steps for L0 and L1 are set to the same, 30,000 steps') and Table 4 ('3e5 iterations representing a compromise point adopted in our experiments'); this affects comparability of baselines and is a correctness risk, not circularity, because the comparison still relies on independent optimization of external baselines. Ablations (Table 2, Table 3) support the two design choices by held-in fitting performance, which is standard for representation fitting tasks. Therefore no circular step meeting the required evidence threshold is present.

Assumptions & free parameters 2 free parameters · 3 assumptions · 0 invented entities

The central claim rests on the chosen hyperparameters r and level count, plus three modeling assumptions: the PSD-filter heuristic, the two-level residual decomposition, and adoption of GaussianImage's 8-parameter representation. No new physical entities are introduced.

free parameters (2)
  • r (level-0 allocation ratio) = 0.125
    Eq. (5): |N0| = r|N1| with r set to 0.125 in experiments; chosen by hand, not predicted. Affects PSNR/memory trade-off.
  • number of levels = 2
    Level-of-Gaussian section: 'we set the level number as 2' for all resolutions based on training/inference cost; justification deferred to Supplementary.
assumptions (3)
  • ad hoc to paper Filtering sigma_n < 0 during rendering removes non-PSD covariance matrices and leaves a well-behaved optimization target
    Section '2D Gaussians Formulation' Eq. (3)-(4). Paper proves contrapositive but admits retained matrices may still be non-PSD; gradient behavior through this filter is not analyzed.
  • domain assumption Two-level coarse-to-fine residual decomposition with downsampled target and normalized difference image improves fidelity for any large image
    Levels of 2D Gaussians section; validated only empirically on three dataset families, not derived.
  • domain assumption The 8-parameter 2DGS representation with accumulated summation from GaussianImage is a valid image fitting model
    Preliminaries section; adopted from Zhang et al. 2024a without re-derivation.

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Cite this review

Pith. "Pith review of Large Images are Gaussians: High-Quality Large Image Representation with Levels of 2D Gaussian Splatting." pith.science (2026). https://pith.science/paper/PJGUGS2W

@misc{pith2026250209039,
  author       = {Pith},
  title        = {Pith review of: Large Images are Gaussians: High-Quality Large Image Representation with Levels of 2D Gaussian Splatting},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/PJGUGS2W}},
  note         = {Machine review of arXiv:2502.09039}
}
read the original abstract

While Implicit Neural Representations (INRs) have demonstrated significant success in image representation, they are often hindered by large training memory and slow decoding speed. Recently, Gaussian Splatting (GS) has emerged as a promising solution in 3D reconstruction due to its high-quality novel view synthesis and rapid rendering capabilities, positioning it as a valuable tool for a broad spectrum of applications. In particular, a GS-based representation, 2DGS, has shown potential for image fitting. In our work, we present \textbf{L}arge \textbf{I}mages are \textbf{G}aussians (\textbf{LIG}), which delves deeper into the application of 2DGS for image representations, addressing the challenge of fitting large images with 2DGS in the situation of numerous Gaussian points, through two distinct modifications: 1) we adopt a variant of representation and optimization strategy, facilitating the fitting of a large number of Gaussian points; 2) we propose a Level-of-Gaussian approach for reconstructing both coarse low-frequency initialization and fine high-frequency details. Consequently, we successfully represent large images as Gaussian points and achieve high-quality large image representation, demonstrating its efficacy across various types of large images. Code is available at {\href{https://github.com/HKU-MedAI/LIG}{https://github.com/HKU-MedAI/LIG}}.

Figures

Figures reproduced from arXiv: 2502.09039 by the authors.

Figure 1
Figure 1. Comparison of LIG and GaussianImage on large image fitting quality. GaussianImage performs badly when optimizing a large number of Gaussian points on im￾ages of high resolutions, whereas ours consistently delivers quality improvements as the number of Gaussian points in￾creases. The phenomenon is observed in multiple datasets. representation, a notable example is the Local Implicit Im￾age Function (Chen, Liu, and Wa… view at source ↗
Figure 2
Figure 2. LIG is capable of representing large images with high quality. We show cases including a histopathology image and a satellite image, showing multi-resolution patches with PSNR values displayed at the bottom-right corner of each image. slow for large batches. These limitations become particu￾larly critical when dealing with larger target signals, e.g., large images, which is the primary focus of our work. 3D Gaussian… view at source ↗
Figure 3
Figure 3. Illustration of our proposed Level-of-Gaussian approach, aiming at fitting large images with two levels of Gaussian points. In the first stage, we allocate parts of Gaussian points to form L0 Gaussians for learning the low￾frequency initialization from the down-sampled image. In the second stage, L1 Gaussians learn the high-frequency de￾tails on the difference between the up-sampled estimation and the target. We pre… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Qualitative comparison between LIG and GaussianImage on STimage and FGF2 samples. We show small patches from the rendered images and the GT images. The difference images are shift to 0.5 for visualization. datasets. The FPS results are tested on the same environ￾ment. …

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.