Journal of Graphics ›› 2026, Vol. 47 ›› Issue (3): 564-575.DOI: 10.11996/JG.j.2095-302X.2026030564
• Image Processing and Computer Vision • Previous Articles Next Articles
LIAO Jiankang1, ZHANG Yanci1,2(
)
Received:2025-10-11
Accepted:2026-03-26
Online:2026-06-30
Published:2026-06-30
Contact:
ZHANG Yanci
CLC Number:
LIAO Jiankang, ZHANG Yanci. Frequency intensity Gaussian splatting for over-reconstruction issue[J]. Journal of Graphics, 2026, 47(3): 564-575.
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URL: http://www.txxb.com.cn/EN/10.11996/JG.j.2095-302X.2026030564
| Method | Mip-NeRF360 | Tanks & Temples | Deep Blending | Ref-Real | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SSIM↑ | PSNR↑ | LPIPS↓ | SSIM↑ | PSNR↑ | LPIPS↓ | SSIM↑ | PSNR↑ | LPIPS↓ | SSIM↑ | PSNR↑ | LPIPS↓ | |
| 3DGS | 0.815 | 27.21 | 0.214 | 0.841 | 23.14 | 0.183 | 0.903 | 29.41 | 0.243 | 0.636 | 23.52 | 0.277 |
| SteepGS* | 0.809 | 27.31 | 0.221 | 0.845 | 23.55 | 0.178 | 0.904 | 29.62 | 0.246 | 0.642 | 23.60 | 0.269 |
| Perceptual-GS* | 0.829 | 27.74 | 0.185 | 0.856 | 23.87 | 0.150 | 0.906 | 29.88 | 0.231 | 0.643 | 23.62 | 0.249 |
| FreGS | 0.826 | 27.85 | 0.209 | 0.849 | 23.96 | 0.178 | 0.904 | 29.93 | 0.240 | 一 | 一 | 一 |
| Pixel-GS* | 0.818 | 27.48 | 0.207 | 0.846 | 23.74 | 0.175 | 0.899 | 29.47 | 0.249 | 0.642 | 23.63 | 0.264 |
| AbsGS* | 0.820 | 27.49 | 0.191 | 0.854 | 23.66 | 0.156 | 0.898 | 29.55 | 0.235 | 0.634 | 23.39 | 0.269 |
| Ours | 0.827 | 27.57 | 0.174 | 0.857 | 23.64 | 0.137 | 0.898 | 29.26 | 0.231 | 0.648 | 23.59 | 0.236 |
Table 1 Quantitative results of rendering quality
| Method | Mip-NeRF360 | Tanks & Temples | Deep Blending | Ref-Real | ||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| SSIM↑ | PSNR↑ | LPIPS↓ | SSIM↑ | PSNR↑ | LPIPS↓ | SSIM↑ | PSNR↑ | LPIPS↓ | SSIM↑ | PSNR↑ | LPIPS↓ | |
| 3DGS | 0.815 | 27.21 | 0.214 | 0.841 | 23.14 | 0.183 | 0.903 | 29.41 | 0.243 | 0.636 | 23.52 | 0.277 |
| SteepGS* | 0.809 | 27.31 | 0.221 | 0.845 | 23.55 | 0.178 | 0.904 | 29.62 | 0.246 | 0.642 | 23.60 | 0.269 |
| Perceptual-GS* | 0.829 | 27.74 | 0.185 | 0.856 | 23.87 | 0.150 | 0.906 | 29.88 | 0.231 | 0.643 | 23.62 | 0.249 |
| FreGS | 0.826 | 27.85 | 0.209 | 0.849 | 23.96 | 0.178 | 0.904 | 29.93 | 0.240 | 一 | 一 | 一 |
| Pixel-GS* | 0.818 | 27.48 | 0.207 | 0.846 | 23.74 | 0.175 | 0.899 | 29.47 | 0.249 | 0.642 | 23.63 | 0.264 |
| AbsGS* | 0.820 | 27.49 | 0.191 | 0.854 | 23.66 | 0.156 | 0.898 | 29.55 | 0.235 | 0.634 | 23.39 | 0.269 |
| Ours | 0.827 | 27.57 | 0.174 | 0.857 | 23.64 | 0.137 | 0.898 | 29.26 | 0.231 | 0.648 | 23.59 | 0.236 |
| Method | Mip-NeRF360 (outdoor) | Tanks & Tem-ples | Ref-Real |
|---|---|---|---|
| 3DGS | 9.65 | 2.89 | 5.34 |
| Pixel-GS | 6.74 | 2.45 | 4.43 |
| Perceptual-GS | 4.39 | 1.93 | 3.07 |
| AbsGS | 4.07 | 1.52 | 3.15 |
| Ours | 1.80 | 0.86 | 2.00 |
Table 2 Percentage of regions with large frequency intensity differences in images
| Method | Mip-NeRF360 (outdoor) | Tanks & Tem-ples | Ref-Real |
|---|---|---|---|
| 3DGS | 9.65 | 2.89 | 5.34 |
| Pixel-GS | 6.74 | 2.45 | 4.43 |
| Perceptual-GS | 4.39 | 1.93 | 3.07 |
| AbsGS | 4.07 | 1.52 | 3.15 |
| Ours | 1.80 | 0.86 | 2.00 |
| Method | Mip-NeRF360 (outdoor) | Tanks & Tem-ples | Ref-Real |
|---|---|---|---|
| 3DGS | 1.83 | 1.72 | 2.66 |
| Pixel-GS | 2.75 | 1.43 | 3.30 |
| Perceptual-GS | 3.11 | 1.83 | 4.06 |
| AbsGS | 2.53 | 2.02 | 3.40 |
| Ours | 4.00 | 2.20 | 5.50 |
Table 3 The percentage of Gaussians allocated by each method
| Method | Mip-NeRF360 (outdoor) | Tanks & Tem-ples | Ref-Real |
|---|---|---|---|
| 3DGS | 1.83 | 1.72 | 2.66 |
| Pixel-GS | 2.75 | 1.43 | 3.30 |
| Perceptual-GS | 3.11 | 1.83 | 4.06 |
| AbsGS | 2.53 | 2.02 | 3.40 |
| Ours | 4.00 | 2.20 | 5.50 |
Fig. 8 Visualization of frequency intensity maps and the frequency-intensity regularization process((a) visualization of frequency intensity maps; (b) visualization of the frequency-intensity regularization process)
| Method | Mip-NeRF360 | Tanks & Temples | ||||
|---|---|---|---|---|---|---|
| SSIM↑ | PSNR↑ | LPIPS↓ | SSIM↑ | PSNR↑ | LPIPS↓ | |
| Base | 0.815 | 27.21 | 0.214 | 0.841 | 23.14 | 0.183 |
| Base+FI | 0.817 | 27.26 | 0.190 | 0.853 | 23.66 | 0.157 |
| Base+GE | 0.818 | 27.48 | 0.192 | 0.857 | 23.72 | 0.148 |
| Base+FI+GE | 0.827 | 27.57 | 0.174 | 0.857 | 23.64 | 0.137 |
Table 4 Ablation study quantitative results
| Method | Mip-NeRF360 | Tanks & Temples | ||||
|---|---|---|---|---|---|---|
| SSIM↑ | PSNR↑ | LPIPS↓ | SSIM↑ | PSNR↑ | LPIPS↓ | |
| Base | 0.815 | 27.21 | 0.214 | 0.841 | 23.14 | 0.183 |
| Base+FI | 0.817 | 27.26 | 0.190 | 0.853 | 23.66 | 0.157 |
| Base+GE | 0.818 | 27.48 | 0.192 | 0.857 | 23.72 | 0.148 |
| Base+FI+GE | 0.827 | 27.57 | 0.174 | 0.857 | 23.64 | 0.137 |
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