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EigenGS Representation: From Eigenspace to Gaussian Image Space
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Proposes EigenGS, which learns 2D Gaussian splats for PCA eigenimages so that a new image's Gaussian initialization can be derived instantly, then refined with a frequency-aware two-phase scheme.
Problem
Per-image optimization of 2D Gaussian image representations (GaussianImage) starts from random initialization and converges slowly; PCA is fast but ignores local spatial structure.
Approach
Learn 2D Gaussians that represent the PCA eigenbasis of a training set; projecting a new image onto the basis gives coefficients that fold into Gaussian weights, yielding an instant Gaussian initialization for image-space fitting. A frequency-aware two-phase training allocates Gaussians to low- and high-frequency eigencomponents to avoid tiny-Gaussian artifacts.
Key results
- On FFHQ with 20,000 Gaussians, EigenGS (300 components) reaches 41.8 dB PSNR at 10,000 iterations vs 40.1 dB for GaussianImage.
- EigenGS initialization starts at 28.0-28.9 dB PSNR on FFHQ at iteration 0, versus GaussianImage at about 10.4 dB by iteration 100.
- Within 1000 iterations, over 80% of FFHQ test samples reach 35 dB with EigenGS, compared to 0% for GaussianImage.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| initialize image-space Gaussians from the learned eigenspace representation | EigenGS versus GaussianImage · FFHQ test, 100 iterations | PSNR: 10.4 ± 1.7 -> 34.4 ± 2.4 | Helped |
| initialize image-space Gaussians from the learned eigenspace representation | EigenGS versus GaussianImage · FFHQ test, 10,000 iterations | PSNR: 40.1 ± 1.9 -> 41.8 ± 2.4 | Helped |
| train EigenGS on Cats and transfer it to CelebA | EigenGS · CelebA test | PSNR: 45.2 ± 2.8 -> 48.2 ± 3.1 | Helped |
| train EigenGS on ImageNet and transfer it to CelebA | EigenGS · CelebA test | PSNR: 45.2 ± 2.8 -> 47.3 ± 3.1 | Helped |
| train EigenGS on ImageNet and transfer it to Cats | EigenGS · Cats test | PSNR | Helped |
| use YCbCr instead of RGB (ablation) | EigenGS · CelebA, FFHQ, Cats, and Cars | PSNR: 39.5 -> 47.2; 34.9 -> 41.8; 38.5 -> 45.7; 36.4 -> 44.7 | Helped |
| add frequency-aware learning (ablation) | EigenGS-YCbCr · CelebA | PSNR: 48.0 -> 47.2 | Hurt |
| add frequency-aware learning (ablation) | EigenGS-YCbCr · FFHQ | PSNR: 40.7 -> 41.8 | Helped |
| add frequency-aware learning (ablation) | EigenGS-YCbCr · Cats | PSNR: 46.1 -> 45.7 | Hurt |
| add frequency-aware learning (ablation) | EigenGS-YCbCr · Cars | PSNR: 43.5 -> 44.7 | Helped |
| add frequency-aware learning (ablation) | EigenGS-YCbCr · CelebA, FFHQ, Cats, and Cars | PSNR: -0.8 dB and -0.4 dB | Mixed |
Surprising findings
- The number of PCA components mainly affects early-stage convergence rather than final reconstruction quality.
- Frequency-aware learning slightly decreases PSNR on smaller-resolution datasets (CelebA -0.8 dB, Cats -0.4 dB).
Limitations
- Frequency-aware learning reduces quality on low-resolution datasets such as CelebA and Cats.
- Cross-dataset initialization shows domain-specific shadow artifacts.
- Gains on Stanford Cars are smaller due to varied viewpoints and larger dimensions.
Experimental setup
Datasets: CelebA FFHQ Cats Stanford Cars ImageNet
Benchmarks: FFHQ CelebA Cats Stanford Cars
Metrics: PSNR SSIM convergence time percentage of images above PSNR threshold
Baselines: GaussianImage standard PCA reconstruction
Builds on: GaussianImage 3D Gaussian Splatting PCA
Closest papers by meaning
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