SGI: Structured 2D Gaussians for Efficient and Compact Large Image Representation

Zixuan Pan; Kaiyuan Tang; Jun Xia; Yifan Qin; Lin Gu; Chaoli Wang; Jianxu Chen; Yiyu Shi

cs.CVMar 8, 2026

SGI: Structured 2D Gaussians for Efficient and Compact Large Image Representation

Authors: Zixuan Pan, Kaiyuan Tang, Jun Xia, Yifan Qin, Lin Gu, Chaoli Wang, Jianxu Chen, Yiyu Shi

Organizations: University of Notre Dame · Tohoku University · Leibniz-Institut für Analytische Wissenschaften – ISAS – e.V.

Abstract

2D Gaussian Splatting has emerged as a novel image representation technique that can support efficient rendering on low-end devices. However, scaling to high-resolution images requires optimizing and storing millions of unstructured Gaussian primitives independently, leading to slow convergence and redundant parameters. To address this, we propose Structured Gaussian Image (SGI), a compact and efficient framework for representing high-resolution images. SGI decomposes a complex image into multi-scale local spaces defined by a set of seeds. Each seed corresponds to a spatially coherent region and, together with lightweight multi-layer perceptrons (MLPs), generates structured implicit 2D neural Gaussians. This seed-based formulation imposes structural regularity on otherwise unstructured Gaussian primitives, which facilitates entropy-based compression at the seed level to reduce the total storage. However, optimizing seed parameters directly on high-resolution images is a challenging and non-trivial task. Therefore, we designed a multi-scale fitting strategy that refines the seed representation in a coarse-to-fine manner, substantially accelerating convergence. Quantitative and qualitative evaluations demonstrate that SGI achieves up to 7.5x compression over prior non-quantized 2D Gaussian methods and 1.6x over quantized ones, while also delivering 1.6x and 6.5x faster optimization, respectively, without degrading, and often improving, image fidelity. Code is available at https://github.com/zx-pan/SGI.

Figures & tables

Panel of Figure 1 — Figure 1: Image representation results on the FGF2 [ 28 ] and ICB [ 35 ] datasets. The x-axis (log scale) denotes optimization time in minutes, and the y-axis shows PSNR (dB). Each point represents a specific model configuration, with the area of the circle indicating its storage size. For GaussianImage and our SGI, we plot performance curves obtained by varying the number of Gaussian primitives. Our SGI consistently achieves a favorable trade-off between fidelity, compactness, and optimization time.

Figure 2: The overall pipeline of SGI. We first introduce (a) seed-based 2D neural Gaussians , where each seed predicts a group of 2D Gaussian primitives via two shared MLPs for decoding color and covariance. To accelerate optimization, we adopt a (b) multi-scale fitting strategy that progressively refines the representation from coarse to fine using a Gaussian pyramid. Finally, we leverage (c) neural entropy coding to further compress the explicit seed attributes for compact representation.

Method	FGF2					ICB
Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Opt. Time $\downarrow$	Size $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Opt. Time $\downarrow$	Size $\downarrow$
SIREN [ 41 ] (NeurIPS’20)	22.05	0.8020	0.4831	$649.71$	15.79	27.62	0.8600	0.3817	$363.34$	$15.79$
I-NGP [ 33 ] (TOG’22)	28.55	0.9592	0.1043	$72.32$	$21.07$	33.09	0.9532	0.1176	$48.11$	$21.07$
HAC [ 14 ] (ECCV’24)	25.15	0.9226	0.1767	$261.69$	$16.78$	34.47	0.9801	0.0688	$270.57$	$13.52$
GaussianImage [ 54 ] (ECCV’24)	27.30	0.9457	0.1342	$322.17$	$23.37$	31.09	0.9330	0.1462	$282.61$	$23.37$
Our SGI (low-rate)	31.24	0.9863	0.0731	48.43	$16.33$	35.27	0.9853	0.0575	44.75	12.30

Table 1: Quantitative results on FGF2 and ICB. Optimization time is in minutes, and model size is in megabytes (MB). To fit INR-based methods (SIREN and I-NGP) on these large-scale datasets under limited GPU memory, we adopt a patch-based training strategy that loads randomly sampled coordinate and pixel batches from CPU to GPU on the fly. Our SGI is evaluated in two settings: low-rate (3.5M Gaussians) and high-rate (10M Gaussians), both demonstrating strong trade-offs between fidelity, compactness, and optimization efficiency. Darker blue and darker red highlights indicate the best-performing method within the low-rate and high-rate groups, respectively, in each metric. Reported numbers are averaged per image across the dataset.

Panel of Figure 3 — Figure 3: Visual comparisons on the FGF2 and ICB (w/ zoom-in cases and error maps). Qualitative results on representative examples from FGF2 (top) and ICB (bottom), comparing SGI with I-NGP [ 33 ] , Scaffold-GS [ 30 ] , LIG [ 57 ] , and GaussianImage [ 54 ] . Zoom-in regions highlight perceptual differences. In the third row of each block, we visualize the per-pixel reconstruction error using heatmaps, where warmer colors (e.g., yellow) indicate higher deviation from the ground truth. PSNR (dB) and storage size (MB) for each method are shown below the visualizations.

Method	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Opt. Time $\downarrow$	Size $\downarrow$
SIREN [ 41 ] (NeurIPS’20)	28.09	0.8843	0.3654	$983.48$	$15.79$
I-NGP [ 33 ] (TOG’22)	35.57	0.9763	0.0518	$129.96$	$21.07$
GaussianImage [ 54 ] (ECCV’24)	25.75	0.6404	0.4006	$407.70$	$23.37$
Our SGI (low-rate)	33.96	0.9743	0.1196	103.43	10.05
3DGS [ 27 ] (TOG’23)	38.51	0.9957	0.0192	$723.43$	$787.73$
LIG [ 57 ] (AAAI’25)	34.33	0.9714	0.1386	106.82	$106.81$

Table 2: Quantitative results on STimage. Optimization time is in minutes, and model size is in megabytes (MB). To fit INR-based methods (SIREN and I-NGP) on these large-scale datasets under limited GPU memory, we adopt a patch-based training strategy that loads randomly sampled coordinate and pixel batches from CPU to GPU on the fly. Our SGI is evaluated in two settings: low-rate (3.5M Gaussians) and high-rate (10M Gaussians), both demonstrating strong trade-offs between fidelity, compactness, and optimization efficiency. Darker blue and darker red highlights indicate the best-performing method within the low-rate and high-rate groups, respectively, in each metric. Reported numbers are averaged per image across the dataset.

$K$	FGF2					ICB
$K$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Opt. Time (Min) $\downarrow$	Size (MB) $\downarrow$	PSNR $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Opt. Time (Min) $\downarrow$	Size (MB) $\downarrow$
5	31.29	0.9861	0.0698	44.27	18.48	35.03	0.9841	0.0626	44.70	13.64
10	31.24	0.9863	0.0731	48.43	16.33	35.27	0.9853	0.0575	44.75	12.30
15	30.61	0.9836	0.0828	55.33	15.32	34.88	0.9842	0.0599	50.60	11.48
20	30.62	0.9834	0.0809	56.02	14.83	34.57	0.9824	0.0668	53.37	10.87

Table 3: Ablation studies on # of Gaussians

K

in each seed.

$\lambda$	FGF2		ICB
$\lambda$	PSNR $\uparrow$	Size (MB) $\downarrow$	PSNR $\uparrow$	Size (MB) $\downarrow$
0	32.36	104.08	36.13	102.35
0.0005	31.30	18.93	35.48	14.90
0.001	31.24	16.33	35.27	12.30
0.003	30.21	11.93	33.51	8.34

Table 4: Ablation studies on

\lambda

L

$M$	FGF2		ICB
$M$	PSNR $\uparrow$	Opt. Time (Min) $\downarrow$	PSNR $\uparrow$	Opt. Time (Min) $\downarrow$
1	30.58	71.59	35.02	70.63
2	30.60	55.96	35.06	49.90
3	31.24	48.43	35.27	44.75
4	30.56	42.27	33.78	37.67

Table 5: Ablation studies on multi-scale fitting.

Number of Gaussians	$\boldsymbol{x_{a}}$	$\boldsymbol{f_{a}}$	$\{\boldsymbol{s_{o}},\boldsymbol{s_{a}}\}$	$\boldsymbol{\delta}$	$\mathcal{H}$	MLPs	Total Size
3.5e6	0.9995	7.8689	1.5427	5.7646	0.0293	0.1273	16.3324
7.0e6	1.8360	15.5719	2.4960	11.0664	0.0292	0.1273	31.1268
1.0e7	2.4442	20.5720	3.3549	15.2157	0.0298	0.1273	41.7439

Table 6: The storage size (MB) of each component of our method evaluated on the FGF2 dataset.

Panel of Figure 4 — Figure 4: Visual comparison with traditional image codec method JPEG on the ICB dataset at low Bpp. We report the bit per pixel (bpp) and PSNR (dB) for each method below the visualizations.

Figure 5: Rate-distortion curves of our approach and different compression baselines on ICB dataset in PSNR.

Appendix figures & tables4 assets

Supplementary material from the paper’s appendix.

Appendix

Component	Learning rate
Seed position $\boldsymbol{x_{a}}$	0
Offsets $\boldsymbol{\delta}$	0.01
Seed feature $\boldsymbol{f_{a}}$	0.0075
Scaling $\{\boldsymbol{s_{o}},\boldsymbol{s_{a}}\}$	0.007
$\text{MLP}_{c}$	0.008
$\text{MLP}_{\Sigma}$	0.004

Appendix

Table A1 : Details of the learning rates in SGI.

Method	$\times 2$	$\times 4$	$\times 8$
Bilinear interpolation	28.40	27.24	26.86
SGI	28.88	27.58	27.17

Appendix

Table A2 : Unsupervised super-resolution performance on a DIV2K sample. Quantitative results are measured in PSNR (dB).

Method	PSNR (dB) $\uparrow$	SSIM $\uparrow$	LPIPS $\downarrow$	Opt. Time $\downarrow$	Size $\downarrow$
SIREN (NeurIPS’20)	24.71	0.6432	0.5019	$28.37$	$0.45$
GaussianImage (ECCV’24)	35.22	0.9327	0.1469	$21.91$	$3.07$
LIG (AAAI’25)	44.87	0.9904	0.0113	$9.97$	$15.26$
Our SGI (low-rate)	28.69	0.8206	0.3163	$3.31$	$0.33$
Our SGI (med-rate)	37.72	0.9643	0.0778	$6.80$	$1.82$
Our SGI (high-rate)	44.03	0.9872	0.0298	$15.64$	$5.40$

Appendix

Table A3 : Comparisons on DIV2K. Optimization time is in minutes, and model size is in MB. Numbers are averaged per image.

Panel of Figure 15 — Figure A1 : Visual comparisons on STimage (w/ zoom-in cases and error maps). Zoom-in regions highlight perceptual differences. The third row shows per-pixel reconstruction error heatmaps, where warmer colors (e.g., yellow) indicate larger deviations from the ground truth. PSNR (dB) and storage size (MB) for each method are shown below the visualizations.

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