Other Alternatives
- Chamfer distance
- Earth Mover’s Distance (EMD)
- Normal consistency loss
- Curvature loss
- Learned feature-space loss (via PointNet / DGCNN embeddings)
What is FPFH
FPFH (Fast Point Feature Histograms) describe local geometric structure using histograms of normal relationships.
Potential advantages
- Captures local geometry structure
- More invariant to small spatial shifts
- Encodes curvature and surface shape
- Could penalize structural distortion rather than just point displacement
Potential problems
- Non-differentiability
- FPFH involves:
- Normal estimation
- Neighborhood selection
- Histogram binning
- Histogram binning is not naturally differentiable.
- Nearest-neighbor search for features adds more non-smooth operations.
- Instability
- Normals are sensitive to noise.
- Small geometry changes may cause large feature changes.
- Heavy computation
- Much more expensive than Chamfer distance.
