Research map / Point clouds / Shape and surface completion
NeuralIndicator: Implicit Surface Reconstruction from Neural Indicator Priors
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Proposes NeuralIndicator, an unsupervised neural implicit surface reconstruction method that jointly learns a smooth indicator function (via FFT-solved PDE over oriented points) and an SDF network, using the indicator as a global shape prior, without normals.
Problem
Surface reconstruction from unoriented, incomplete and/or noisy point clouds with complex topology, where local shape priors in neural implicit learning are insufficiently reliable.
Approach
Generate a differentiable smooth indicator function from learnable oriented points by solving a gradient-smoothness PDE with FFT on a voxel grid, and use its global shape prior (indicator loss, absolute distance loss, SDF and Eikonal losses) to regularize the neural implicit function, avoiding explicit normal estimation.
Key results
- Achieves lowest CD1 and CD2 and highest F-score on ABC, FAMOUS, Thingi10K and Reconbench among unsupervised methods, e.g., ABC CD1 1.5 and F 79 vs. N-ILMS 1.6 and 78.
- Supervised methods LIG, NDC and NKSR achieve better CD2 than the proposed method on the synthetic benchmarks (mean CD2 scaled 1e5: NDC 12.4 vs. ours 77.0).
- On noisy variants, mean CD2 (x100) of 0.33 vs. PCP 0.39, SAP 0.38, and PSR 3.15.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add the indicator loss Lind (ablation) | NeuralIndicator · Test dataset | CD1: 1.38 -> 1.31 | Helped |
| add the absolute distance loss Ludf (ablation) | NeuralIndicator · Test dataset | CD1: 1.67 -> 1.31 | Helped |
| add the SDF loss Lsdf (ablation) | NeuralIndicator · Test dataset | CD1: 1.41 -> 1.31 | Helped |
| add the CD loss LCD (ablation) | NeuralIndicator · Test dataset | CD1: 1.52 -> 1.31 | Helped |
| add the Eikonal loss Lek (ablation) | NeuralIndicator · Test dataset | CD1: 1.32 -> 1.31 | Helped |
| increase SIFG voxel resolution from 32× to 256× (ablation) | NeuralIndicator · Test dataset | CD1: 1.47 -> 1.28 | Helped |
| use NeuralIndicator instead of prior unsupervised approaches | surface reconstruction · ABC, FAMOUS, Thingi10K, Reconbench | CD1: ABC: 1.7 -> 1.5; FAMOUS: 1.1 -> 1.0; Thingi10K: 1.0 -> 0.9; Reconbench: 0.71 -> 0.65 | Helped |
| use NeuralIndicator instead of iPSR | surface reconstruction · FAMOUS | CD2 (×100): 0.03 -> 0.03 | No clear effect |
| use NeuralIndicator instead of iPSR | surface reconstruction · Reconbench | CD2 (×100): 0.48 -> 0.49 | Hurt |
| use NeuralIndicator instead of supervised approaches | surface reconstruction · ABC, FAMOUS, Thingi10K, Reconbench | CD2 (×105): FAMOUS: 51.2 -> 30.2; Reconbench: 5.1 -> 4.9; ABC: 45.7 -> 121.7; Thingi10K: 62.6 -> 151.6 | Mixed |
Surprising findings
- The method slightly outperforms PSR and iPSR, which use ground-truth normals, on the synthetic benchmarks.
- On 3D Scene large-scale reconstruction, the method achieves similar accuracy to PCP rather than clearly outperforming it.
Limitations
- Fails on highly incomplete point clouds from occlusions because only geometry priors are used.
- Large holes near boundary areas are not filled since no prior distinguishes empty space from surface.
- Per-shape optimization with no GPU-parallel acceleration in the current implementation, and slower than some baselines.
Experimental setup
Datasets: ABC FAMOUS Reconbench Thingi10K DPoint 3D Scene
Benchmarks: ABC FAMOUS Thingi10K Reconbench DPoint 3D Scene
Metrics: CD1 CD2 F-score precision recall
Baselines: PSR iPSR Point2Mesh Iso-Points SAP OnSurf PCP NeuralTPS Neural-IMLS Point2Surf LIG NDC
Builds on: Shape As Points (SAP) SAL Point2Mesh Poisson surface reconstruction Remelli et al. differentiable projection
Closest papers by meaning
- Iso-Points: Optimizing Neural Implicit Surfaces With Hybrid Representations (CVPR 2021 · similarity 0.90)
- Implicit Geometric Regularization for Learning Shapes (ICML 2020 · similarity 0.88)
- NeuSurf: On-Surface Priors for Neural Surface Reconstruction from Sparse Input Views (AAAI 2024 · similarity 0.88)
- Neural Unsigned Distance Fields for Implicit Function Learning (NeurIPS 2020 · similarity 0.88)
- Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance (CVPR 2024 · similarity 0.87)
- LISR: Learning Linear 3D Implicit Surface Representation Using Compactly Supported Radial Basis Functions (AAAI 2024 · similarity 0.86)
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