Research map / 3D vision / Gaussian splatting
Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity
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Proposes Topology-GS, which adds a persistent-homology-based interpolation (LPVI) for sparse point clouds and a persistent-barcode loss (PersLoss) on rendered images to improve 3D Gaussian Splatting novel-view synthesis.
Problem
3D Gaussian Splatting renderings lose structural integrity: SfM point clouds are sparse in low-curvature regions (hurting pixel-level detail), and pixel-level losses do not constrain feature-level/perceptual similarity (LPIPS).
Approach
LPVI switches between 3D and PCA-projected 2D Voronoi interpolation based on a Wasserstein-distance TopoDiff check of persistence diagrams, and PersLoss compares truncated persistence barcodes of rendered and ground-truth images treated as point clouds in RGB space.
Key results
- Topology-GS reaches 29.50 PSNR / 0.874 SSIM / 0.179 LPIPS on Mip-NeRF360, versus 28.84 / 0.848 / 0.220 for the Scaffold-GS baseline.
- On Tanks & Temples, Topology-GS reports 24.26 PSNR and 0.160 LPIPS, and on Deep Blending 30.45 PSNR and 0.245 LPIPS, both best-or-near-best among compared methods.
- Ablation: LPVI alone improves Mip-NeRF360 PSNR from 28.84 to 29.47, while PersLoss alone reduces LPIPS from 0.220 to 0.185.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add LPVI interpolation (ablation) | Scaffold-GS · Mip-NeRF360 | PSNR: 28.84 -> 29.47 | Helped |
| add LPVI interpolation (ablation) | Scaffold-GS · Tanks & Temples | PSNR: 23.96 -> 24.22 | Helped |
| add LPVI interpolation (ablation) | Scaffold-GS · Deep Blending | PSNR: 30.21 -> 30.42 | Helped |
| add PersLoss (ablation) | Scaffold-GS · Mip-NeRF360 | LPIPS: 0.220 -> 0.185 | Helped |
| add PersLoss (ablation) | Scaffold-GS · Tanks & Temples | LPIPS: 0.177 -> 0.168 | Helped |
| add PersLoss (ablation) | Scaffold-GS · Deep Blending | LPIPS: 0.254 -> 0.249 | Helped |
| replace LPVI with random interpolation (ablation) | Scaffold-GS · Mip-NeRF360, Tanks & Temples, and Deep Blending | PSNR | Mixed |
| replace LPVI with DEBLUR (ablation) | Scaffold-GS · Mip-NeRF360, Tanks & Temples, and Deep Blending | PSNR | Mixed |
| replace LPVI with SAGS (ablation) | Scaffold-GS · Mip-NeRF360, Tanks & Temples, and Deep Blending | PSNR | Mixed |
| increase the retained number of 0-dimensional features k0 (ablation) | PersLoss · Deep Blending | LPIPS | Hurt |
| increase the retained numbers of 1D and 2D features k1 and k2 (ablation) | PersLoss · Deep Blending | LPIPS | No clear effect |
| increase k0, k1, and k2 by an order of magnitude (ablation) | PersLoss · Deep Blending | LPIPS | Hurt |
Surprising findings
- Random point interpolation and DEBLUR-style uniform densification disrupt topology and underperform LPVI, while SAGS helps only within low-curvature regions.
- Adding LPVI increases average memory by up to ~20MB on some benchmarks, yet the authors argue final point counts stay similar to baseline after training.
Limitations
- Convergence guarantee relies on assumptions (e.g., small truncation B, relaxed PersLoss bound A2) that are not fully verified empirically.
- PersLoss activated only in specific ADC-stage rounds because persistent homology computation is costly.
- Hyperparameters (K_max, K_min, threshold, lambda, k0-k2) require tuning per dataset.
Experimental setup
Datasets: Mip-NeRF360 Tanks & Temples Deep Blending NeRF_Synthetic BungeeNeRF IMW2020
Benchmarks: Mip-NeRF360 Tanks & Temples Deep Blending NeRF_Synthetic BungeeNeRF
Metrics: PSNR SSIM LPIPS average memory training time FPS
Baselines: 3D-GS Scaffold-GS Mip-Splatting 2D-GS Revised-GS Pixel-GS DEBLUR SAGS GOF
Builds on: 3D Gaussian Splatting Scaffold-GS persistent homology alpha complex Mip-Splatting
Closest papers by meaning
- VA-GS: Enhancing the Geometric Representation of Gaussian Splatting via View Alignment (NeurIPS 2025 · similarity 0.90)
- Structure Consistent Gaussian Splatting with Matching Prior for Few-shot Novel View Synthesis (NeurIPS 2024 · similarity 0.90)
- GaussianSpa: An "Optimizing-Sparsifying" Simplification Framework for Compact and High-Quality 3D Gaussian Splatting (CVPR 2025 · similarity 0.90)
- IBGS: Image-Based Gaussian Splatting (NeurIPS 2025 · similarity 0.89)
- ReorgGS: Equivalent Distribution Reorganization for 3D Gaussian Splatting (NeurIPS 2026 · similarity 0.89)
- DisC-GS: Discontinuity-aware Gaussian Splatting (NeurIPS 2024 · similarity 0.89)
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