Research map / 3D vision / Face and shape
Improving Neural Network Surface Processing with Principal Curvatures
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Proposes using discrete principal curvatures (κ1, κ2) and Gaussian curvature as per-vertex input features for neural surface processing, showing gains over HKS, SHOT and xyz inputs across PointNet++, Delta Net and Diffusion Net on segmentation and classification.
Problem
Neural networks for surface processing typically use extrinsic vertex coordinates or overly complex descriptors as input, with little consideration of how well the input representation captures surface geometry.
Approach
Use the principal curvatures (eigenvalues of the discrete shape operator, computed via multi-scale osculating-jet quadratic fitting) as a compact, local, isometry-invariant input representation for surface neural networks, compared against HKS, SHOT and coordinates.
Key results
- On human pose segmentation with PointNet++, principal curvatures reach 80.6% accuracy versus 69.6% for xyz; Diffusion Net improves from 94.7% to 97.4%.
- On RNA molecule segmentation with PointNet++, principal curvatures give 72.4% vs 35.4% for xyz, outperforming SHOT64 (71.9%) and HKS (70.2%).
- On Shrec11 classification, Gaussian curvature gives the best results (96.2% PointNet++, 98.8% Delta Net, 99.1% Diffusion Net), while principal curvatures lead on segmentation; curvature computation is faster than HKS at scales up to 500k points.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace xyz input with principal curvatures (κ1, κ2) | PointNet++ · Human part segmentation | accuracy (%): 69.6 -> 80.6 | Helped |
| Replace xyz input with principal curvatures (κ1, κ2) | Delta Net · Human part segmentation | accuracy (%): 72.4 -> 86.8 | Helped |
| Replace xyz input with principal curvatures (κ1, κ2) | Diffusion Net · Human part segmentation | accuracy (%): 94.7 -> 97.4 | Helped |
| Replace xyz input with principal curvatures (κ1, κ2) | PointNet++ · Molecular segmentation | accuracy (%): 35.4 -> 72.4 | Helped |
| Replace xyz input with principal curvatures (κ1, κ2) | Delta Net · Molecular segmentation | accuracy (%): 29.2 -> 55.5 | Helped |
| Replace xyz input with principal curvatures (κ1, κ2) | Diffusion Net · Molecular segmentation | accuracy (%): 82.6 -> 89.4 | Helped |
| Replace xyz input with Gaussian curvature (κ) | PointNet++ · Shrec11 classification | accuracy (%): 71.5 -> 96.2 | Helped |
| Replace xyz input with Gaussian curvature (κ) | Delta Net · Shrec11 classification | accuracy (%): 75.7 -> 98.8 | Helped |
| Replace xyz input with Gaussian curvature (κ) | Diffusion Net · Shrec11 classification | accuracy (%): 80.3 -> 99.1 | Helped |
| Use Gaussian curvature instead of principal curvatures (κ1, κ2) | PointNet++ · Shrec11 classification | accuracy (%): 85.7 -> 96.2 | Helped |
| Use principal curvatures (κ1, κ2) instead of SHOT64 | Delta Net · Molecular segmentation | accuracy (%): 56.5 -> 55.5 | Hurt |
| Use principal curvatures (κ1, κ2) instead of HKS | Diffusion Net · Shrec11 classification | accuracy (%): 98.9 -> 94.2 | Hurt |
Surprising findings
- Gaussian curvature outperforms principal curvatures on classification, contrary to the paper's hypothesis that principal curvatures are the optimal representation.
- Coordinates outperform the more complex representations (HKS, SHOT) for Delta Net on human pose segmentation.
Limitations
- Gaussian curvature beats principal curvatures on classification, so the claim that principal curvature is universally best is not fully supported.
- Only three architectures and three datasets tested; the paper notes future work to cover wider tasks and architectures.
- No compute resource details for the training experiments; the code link is promised only after review.
Experimental setup
Datasets: Human pose composite dataset (FAUST, SCAPE, Adobe, MIT, SHREC07) RNA molecules segmentation dataset Shrec11
Benchmarks: Human pose segmentation RNA molecules segmentation Shrec11 classification
Metrics: accuracy balanced accuracy F1 score specificity computation time
Baselines: xyz coordinates HKS SHOT16 SHOT64 Gaussian curvature
Builds on: PointNet++ Diffusion Net Delta Net HKS SHOT
Closest papers by meaning
- Neural Surface Maps (CVPR 2021 · similarity 0.90)
- Neural Convolutional Surfaces (CVPR 2022 · similarity 0.89)
- Flatten Anything: Unsupervised Neural Surface Parameterization (NeurIPS 2024 · similarity 0.86)
- Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance (CVPR 2024 · similarity 0.86)
- CoFie: Learning Compact Neural Surface Representations with Coordinate Fields (NeurIPS 2024 · similarity 0.85)
- Geometry-Informed Neural Networks (ICML 2025 · similarity 0.85)
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