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HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Condition
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Proposes HotSpot, a neural signed distance function loss based on a screened Poisson heat equation whose minimizer converges to the true distance as the absorption parameter grows.
Problem
Neural signed distance function optimization from point clouds: eikonal loss is only a necessary, not sufficient, condition for a true distance function, optimization is unstable, and surface-area regularization distorts the distance field.
Approach
Replace the eikonal-only constraint with a heat loss derived from a screened Poisson equation via the substitution h = exp(-omega|u|), whose minimizer gives an asymptotically sufficient condition for the true distance (error bounded and decreasing linearly in 1/omega), while penalizing surface area without distorting the distance field.
Key results
- On ShapeNet subset, HotSpot reaches IoU 0.9796 vs 0.9641 for StEik and 0.9636 for DiGS, with Chamfer 0.0029.
- On the 2D dataset, HotSpot achieves IoU 0.9870 vs 0.7882 for DiGS and 0.6620 for StEik.
- Runtime for 100 iterations is lower than StEik (e.g., 4.49s vs 5.65s for 5x128 network).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use HotSpot instead of DiGS | 2D SDF reconstruction · 2D dataset | IoU: 0.7882 -> 0.9870 | Helped |
| Use HotSpot instead of StEik | 2D SDF reconstruction · 2D dataset | IoU: 0.6620 -> 0.9870 | Helped |
| Use HotSpot instead of StEik | ShapeNet reconstruction · ShapeNet | IoU: 0.9641 -> 0.9796 | Helped |
| Use HotSpot instead of SAL | ShapeNet distance approximation · ShapeNet | RMSE: 0.0251 -> 0.0281 | Hurt |
| Add the heat loss to boundary and eikonal losses (ablation) | 2D SDF reconstruction · 2D dataset | IoU: 0.8192 -> 0.9851 | Helped |
| Add the heat loss to boundary and SAL losses (ablation) | 2D SDF reconstruction · 2D dataset | IoU: 0.8936 -> 0.9851 | Helped |
| Remove the area loss from DiGS losses (ablation) | DiGS · 2D dataset | IoU: 0.6338 -> 0.3907 | Hurt |
| Use full DiGS losses instead of removing its area loss (ablation) | DiGS · 2D dataset | IoU: 0.3907 -> 0.6338 | Helped |
| Remove the area loss from StEik losses (ablation) | StEik · 2D dataset | IoU: 0.6037 -> 0.2938 | Hurt |
| Use full StEik losses instead of removing its area loss (ablation) | StEik · 2D dataset | IoU: 0.2938 -> 0.6037 | Helped |
Surprising findings
- Coarea/area-only losses lead to a Euler-Lagrange solution whose gradient does not have unit norm, so they cannot shape a signed distance function.
- Under sparse points and high absorption, too-weak boundary weight makes the signed distance collapse to an unsigned distance.
Limitations
- Very sparse boundaries with high absorption can cause collapse to an unsigned distance; requires careful boundary weight and omega tuning.
- Large omega can cause floating-point round-off and reduce optimizer effectiveness; the eikonal loss is combined to compensate.
- Applications to inverse rendering and very sparse point clouds are left to future work.
Experimental setup
Datasets: ShapeNet Surface Reconstruction Benchmark (SRB) high-genus shapes from Mehta et al. custom 2D shape dataset (14 shapes)
Benchmarks: custom 2D dataset (14 shapes) ShapeNet subset (260 shapes) SRB high-genus shapes (Mehta et al.)
Metrics: IoU Chamfer distance Hausdorff distance RMSE MAE SMAPE RMSE0.1 MAE0.1 SMAPE0.1 sphere tracing iteration count
Baselines: IGR SAL DiGS StEik SIREN PHASE
Builds on: eikonal loss (IGR) DiGS StEik PHASE SAL
Closest papers by meaning
- Neural Signed Distance Function Inference through Splatting 3D Gaussians Pulled on Zero-Level Set (NeurIPS 2024 · similarity 0.87)
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- DUDF: Differentiable Unsigned Distance Fields with Hyperbolic Scaling (CVPR 2024 · similarity 0.86)
- MultiPull: Detailing Signed Distance Functions by Pulling Multi-Level Queries at Multi-Step (NeurIPS 2024 · similarity 0.86)
- Inferring Neural Signed Distance Functions by Overfitting on Single Noisy Point Clouds through Finetuning Data-Driven based Priors (NeurIPS 2024 · similarity 0.85)
- Toward Robust Neural Reconstruction from Sparse Point Sets (CVPR 2025 · similarity 0.85)
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