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Enhancing Implicit Shape Generators Using Topological Regularizations
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Adds topological regularization to implicit (DeepSDF) 3D shape generators by learning a persistent-diagram generator that aligns PD distributions and enforces PD smoothness, improving topological generalization on ShapeNet chairs and tables.
Problem
Implicit 3D shape generators fitted to limited training data produce topological artifacts (broken legs, thin structures, small holes) that standard distribution-alignment training does not fix.
Approach
Learn a PointNet-based persistent diagram (PD) generator with a rectification layer that keeps points above the diagonal, align each synthetic shape's PD with the PD generator output, and add a PD smoothness loss on the generator so PDs interpolate smoothly rather than inheriting SDF interpolation artifacts.
Key results
- On chair, Ours-DeepSDF reduces PD-LAP from 1.86 (DeepSDF-VAD) to 0.86 (about 71% relative improvement) and Ours-DeepSDF-SE reaches 0.77 vs 1.75 for DeepSDF-SE-VAD.
- On table, Ours-DeepSDF-SE achieves PD-LAP 0.88 in CD-mean-relevant comparison and PD-LAP 0.94 on sofa vs 2.23 for DeepSDF-SE-VAD, outperforming 3DShape2VecSet (1.12 table PD-LAP, 1.64 sofa PD-LAP).
- Ablations show removing PD smoothness or PD training degrades PD-LAP, with removing PD training increasing chair PD-LAP by 85.71% relative to the full model.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add topological regularization to DeepSDF | DeepSDF-VAD · ShapeNet chair and table | PD-LAP: 71.3%/69.2% | Helped |
| add topological regularization to DeepSDF-SE | DeepSDF-SE-VAD · ShapeNet chair and table | PD-LAP: 72.9%/70.9% | Helped |
| add PD smoothness loss (ablation) | Ours-DeepSDF-SE · ShapeNet chair | PD-LAP: 0.98 -> 0.77 | Helped |
| add PD smoothness loss (ablation) | Ours-DeepSDF-SE · ShapeNet table | CD-mean: 1.64 -> 1.33 | Helped |
| add PD smoothness loss (ablation) | Ours-DeepSDF-SE · ShapeNet table | PD-LAP: 0.88 -> 0.92 | Hurt |
| add training-shape PD alignment term (ablation) | Ours-DeepSDF-SE · ShapeNet chair | PD-LAP: 1.43 -> 0.77 | Helped |
| add training-shape PD alignment term (ablation) | Ours-DeepSDF-SE · ShapeNet table | CD-mean: 1.55 -> 1.33 | Helped |
| add training-shape PD alignment term (ablation) | Ours-DeepSDF-SE · ShapeNet table | PD-LAP: 1.64 -> 0.88 | Helped |
Surprising findings
- Simply aligning PD distributions is insufficient; shuffling PD targets of synthetic shapes leaves the PD distribution unchanged, so a PD smoothness term is needed.
- Lipschitz-regularized SDF interpolations introduce unwanted topological artifacts, so the tight SDF-level bound does not translate into smooth PD behavior.
Limitations
- Standard persistent diagrams lack location information, limiting the effect of topological regularization.
- PD computation is computationally costly and not GPU-parallelized.
- Only static implicit shapes on two (three in table) ShapeNet categories evaluated.
Experimental setup
Datasets: ShapeNet chair ShapeNet table ShapeNet sofa
Benchmarks: ShapeNet chair ShapeNet table ShapeNet sofa
Metrics: CD-mean (Chamfer distance) PD-LAP (Wasserstein PD distribution distance)
Baselines: DeepSDF-VAD DeepSDF-SE-VAD 3DShape2VecSet Lipschitz regularization (Liu et al. 2022a)
Builds on: DeepSDF StEik PD optimization (Gabrielsson et al. 2020) PointNet Wasserstein PD distance
Closest papers by meaning
- GPLD3D: Latent Diffusion of 3D Shape Generative Models by Enforcing Geometric and Physical Priors (CVPR 2024 · similarity 0.89)
- GenCorres: Consistent Shape Matching via Coupled Implicit-Explicit Shape Generative Models (ICLR 2024 · similarity 0.88)
- Flow-Corrected Shape Optimization: Taming Manifold Drift in High-Dimensional 3D Models (NeurIPS 2026 · similarity 0.88)
- Physically-Aware Generative Network for 3D Shape Modeling (CVPR 2021 · similarity 0.87)
- Towards Scalable Topological Regularizers (ICLR 2025 · similarity 0.87)
- DTGBrepGen: A Novel B-rep Generative Model through Decoupling Topology and Geometry (CVPR 2025 · similarity 0.85)
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