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TopoGaussian: Inferring Internal Topology Structures from Visual Clues
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Proposes TopoGaussian, a mesh-free pipeline that combines Gaussian Splatting, a particle-based differentiable simulator, and particle/neural-SDF/quadric topology representations to infer hidden interior structure of opaque objects from photos and videos.
Problem
Inferring a physically consistent internal topology (e.g., cavities, mass distribution) of an opaque object from multi-view photos and motion video, without CT/MRI or mesh-based volumetric filling.
Approach
Replaces mesh-based FEM simulation with a fully particle-based differentiable simulator (rigid and soft bodies, pneumatic actuation, penalty collision) operating directly on Gaussian Splatting point clouds, and optimizes interior topology through three representations (per-particle variables, neural SDF, quadric SDF) using simulator gradients.
Key results
- Volumetric shape generation is 5.26x faster than PGSR (voxel size=0.05), 4.81x faster than PGSR (voxel size=0.2), and 1.28x faster than Gaussian Surfels on average.
- Reconstruction quality (smoothness metric, lower is better) is 2.33x, 2.50x, and 2.55x better than the respective PGSR and Gaussian Surfels baselines on average.
- On the wobbly doll, the optimized interior reproduces the recorded 4.0 Hz oscillation, while a solid initial guess gives 2.4 Hz.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the particle-based TopoGaussian pipeline instead of mesh-based PGSR (voxel size=0.05) | TopoGaussian · Six rigid-body experiments | volumetric shape generation time: 5.26 times faster | Helped |
| Use the particle-based TopoGaussian pipeline instead of mesh-based PGSR (voxel size=0.2) | TopoGaussian · Six rigid-body experiments | volumetric shape generation time: 4.81 times faster | Helped |
| Use the particle-based TopoGaussian pipeline instead of Gaussian Surfels | TopoGaussian · Six rigid-body experiments | volumetric shape generation time: 1.28 times faster | Helped |
| Use TopoGaussian rather than mesh-based baselines | TopoGaussian · Six rigid-body experiments | reconstruction quality: 2.33 times better; 2.50 times better; 2.55 times better | Helped |
| Replace neural implicit surface with quadrics (ablation) | TopoGaussian topology representation · Six reconstruction examples | reconstruction quality | No clear effect |
| Vary the initial point density across 12226, 20480, 29160, 40000, and 69120 points (ablation) | TopoGaussian · Wobbly doll | topology distribution quality | No clear effect |
| Double the object size (ablation) | TopoGaussian · Hawk | optimized topology | No clear effect |
| Double the material density (ablation) | TopoGaussian · Hawk | optimized topology | No clear effect |
| Add rigid-body collision handling (ablation) | TopoGaussian · Rigid ball dropping on floor | trajectory match | Helped |
| Vary lighting condition and camera pose (ablation) | TopoGaussian · Synthetic wobbly doll | optimized topology | No clear effect |
Surprising findings
- Gaussian Surfels fails to output a visually correct result on the cow example, and fails on several other synthetic objects.
- Neural implicit and quadric surface topology representations show no obvious quality difference.
Limitations
- Focuses on a single object with only two material types.
- Neural implicit surface and soft-body optimization remain slow and offline.
- Does not compare against dynamic NeRF or 4D Gaussian methods, which only model surfaces.
Experimental setup
Datasets: synthetic dataset of rigid and soft objects with textures real-world videos of wobbly doll, pneumatic finger, hawk, qiqi
Benchmarks: TopoGaussian synthetic dataset (frog, cow, pear, etc.)
Metrics: optimization loss (L2) volumetric shape generation time smoothness (Laplacian of surface normal) density difference to ground truth
Baselines: PGSR Gaussian Surfels
Builds on: PhysGaussian DiffPD ChainQueen Gaussian Splatting
Closest papers by meaning
- Topology-Aware 3D Gaussian Splatting: Leveraging Persistent Homology for Optimized Structural Integrity (AAAI 2025 · similarity 0.86)
- FruitNinja: 3D Object Interior Texture Generation with Gaussian Splatting (CVPR 2025 · similarity 0.85)
- Structure from Collision (CVPR 2025 · similarity 0.85)
- SuGaR: Surface-Aligned Gaussian Splatting for Efficient 3D Mesh Reconstruction and High-Quality Mesh Rendering (CVPR 2024 · similarity 0.85)
- OmniPhysGS: 3D Constitutive Gaussians for General Physics-Based Dynamics Generation (ICLR 2025 · similarity 0.84)
- VA-GS: Enhancing the Geometric Representation of Gaussian Splatting via View Alignment (NeurIPS 2025 · similarity 0.84)
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