CVPR 2025 · Source-reviewed citation guide
HotSpot: Signed Distance Function Optimization with an Asymptotically Sufficient Condition
Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · Highlight
HotSpot uses a screened-Poisson heat loss as an asymptotically sufficient condition for neural signed-distance-function optimization, improving stability while naturally penalizing excess surface area.
When to cite this work
Cite HotSpot for neural implicit surface reconstruction from unoriented points when the argument concerns sufficient SDF constraints, optimization stability, topology, or surface-area regularization.
- Comparing losses for neural signed distance functions rather than treating the eikonal condition as sufficient.
- Discussing stable reconstruction, distance accuracy, or topology from unoriented point observations, with sparse-boundary failure modes made explicit.
Contribution
What this paper adds
- Derives a screened-Poisson heat loss whose limiting solution supplies an asymptotically sufficient SDF condition.
- Provides convergence, approximation-error, and optimization-stability analysis.
- Connects the objective to a natural surface-area penalty and evaluates it across 2D and 3D reconstruction tasks.
Evidence
What the paper reports
- On the reported 2D benchmark, HotSpot reached 0.9870 IoU and 0.0014 Chamfer distance, compared with 0.7882 and 0.0055 for DiGS and 0.6620 and 0.0073 for StEik.
- On the evaluated ShapeNet subset, HotSpot reached 0.9796 IoU and 0.0029 Chamfer distance; SAL retained slightly lower overall RMSE and MAE, so the results do not show universal metric dominance.
- The topology ablation reports correct topology on all 14 tested 2D shapes.
Boundary
What it does not establish
- The experiments target 2D and 3D reconstruction from unoriented point positions, including a 260-shape, 13-category ShapeNet subset; they do not establish superiority for every implicit-representation task.
- Sparse boundary sampling, high absorption, or an over-strong heat term can tear boundaries or collapse a signed solution toward an unsigned distance.
- Boundary weight and spatial scaling remain tuning considerations.
Paper abstract
The authors' summary
We propose HotSpot, a method for optimizing neural signed distance functions by using the solution of a screened Poisson equation, which provides an asymptotically sufficient condition to ensure the output converges to a true distance function. In contrast, existing losses, such as the eikonal loss, act as necessary but insufficient constraints and cannot guarantee that the recovered implicit function represents a true distance function, even if the output minimizes these losses almost everywhere. Furthermore, the eikonal loss suffers from stability issues in optimization. Finally, in conventional optimizations, area loss is indispensable but distorts the output. We address these challenges by designing a loss function that, when minimized, converges to the true distance function, ensures stability, and naturally penalizes large surface area. We present theoretical analysis and experiments on both challenging 2D and 3D datasets and show that our method provides better surface reconstruction and more accurate distance approximation.
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