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Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance
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Fits neural SDFs to raw point clouds without normals by moving guiding points in small homotopy steps through exterior level sets, plus a SION metric for shape difficulty.
Problem
Fitting neural signed distance functions to raw, normal-free point clouds fails when the target geometry differs greatly from the spherical network initialization, causing the standard losses to give poor descent directions and local minima.
Approach
Introduces guiding points that represent an intermediate surface and moves them in small incremental steps toward the input points through a sequence of exterior level sets (a homotopy), re-optimizing the network at each step; also proposes the self-intersecting outward normal (SION) percentage metric to quantify shape difficulty.
Key results
- On the ShapeNet subset without normals, the method reaches mean IoU 0.9729 and mean squared chamfer 3.72e-5, outperforming prior normal-free methods such as DiGS and SAP.
- On the 20 highest-SION shapes, mean IoU is 0.9153 versus 0.7651 for OG-S and 0.7108 for DiGS (both normal-free).
- Ablation on the 20 highest-SION shapes shows that gradual homotopy through intermediate level sets (delta0=4, deltaf=1) gives the best mean IoU (0.9153) versus 0.2795 with no guidance.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PG-SDF instead of OG-S | Shape reconstruction from ShapeNet point clouds · ShapeNet | squared Chamfer (mean): 3.75e-5 -> 3.72e-5 | Helped |
| Use PG-SDF instead of DiGS | Shape reconstruction from ShapeNet point clouds · ShapeNet | IoU (mean): 0.9390 -> 0.9729 | Helped |
| Use PG-SDF instead of OG-S | Shape reconstruction from point clouds · ShapeNet, 20 highest-SION shapes | squared Chamfer (mean): 1.31e-4 -> 5.51e-5 | Helped |
| Use PG-SDF instead of OG-S | Shape reconstruction from point clouds · ShapeNet, 20 highest-SION shapes | IoU (mean): 0.7651 -> 0.9153 | Helped |
| Add high exterior level set initialization instead of spherical initialization (ablation) | PG-SDF · ShapeNet, 20 highest-SION shapes | IoU (mean): 0.2795 -> 0.5694 | Helped |
| Add point guidance (ablation) | PG-SDF with high exterior level set initialization · ShapeNet, 20 highest-SION shapes | IoU (mean): 0.5694 -> 0.8657 | Helped |
| Continue point guidance from δf=2δX to δf=δX (ablation) | PG-SDF · ShapeNet, 20 highest-SION shapes | IoU (mean): 0.8657 -> 0.9153 | Helped |
| Use intermediate level-set targets instead of guiding directly to the final target (ablation) | PG-SDF · ShapeNet, 20 highest-SION shapes | IoU (mean): 0.8538 -> 0.9153 | Helped |
| Use the full gradual point-guidance schedule rather than stopping at δf=2δX (ablation) | PG-SDF · ShapeNet, 20 highest-SION shapes | squared Chamfer (mean): 9.89e-5 -> 5.51e-5 | Helped |
| Use the full gradual point-guidance schedule rather than guiding directly to the final target (ablation) | PG-SDF · ShapeNet, 20 highest-SION shapes | squared Chamfer (mean): 8.08e-5 -> 5.51e-5 | Helped |
Surprising findings
- Using the proposed point guidance also improves reconstruction when ground-truth normals are available (Ours+N with GT normals beats SPSR-free baselines on mean chamfer in Table 1).
Limitations
- Not robust to high outlier fractions or large noise scales.
- Does not handle large occlusions well since they are treated as concavities to explore.
- Runtime averages 10 minutes per shape and grows with shape difficulty.
Experimental setup
Datasets: ShapeNet
Benchmarks: ShapeNet
Metrics: squared chamfer distance interior IoU
Baselines: SPSR IGR SIREN FFN NSP DiGS SAL SAP OG-INR
Builds on: IGR Neural Pull DiGS Point2Mesh SIREN
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