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CrossSDF: 3D Reconstruction of Thin Structures From Cross-Sections
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Proposes CrossSDF, a hash-plus-Fourier-feature neural SDF method that reconstructs thin 3D structures from arbitrary planar cross-sections using a symmetric-difference loss and adaptive per-contour sampling.
Problem
Reconstructing 3D geometry, especially thin branching structures, from sparse arbitrary planar cross-sections without gaps, ridging, over-smoothing, or topological breaks.
Approach
Learn a 3D neural SDF supervised by 2D SDF labels on the cross-sections, but only on the symmetric difference between predicted and target interior/exterior (plus on-contour samples), avoiding forced 2D SDF agreement ("laddering"); combine with per-contour adaptive sampling and a hybrid hash-grid plus random Fourier feature encoding.
Key results
- On thin structures CrossSDF achieves the lowest Chamfer and Hausdorff distances on most objects, e.g., Alveolis CD 0.35 vs 0.44 for Screened Poisson (aligned) while OReX gets 3.6.
- On thick structures CrossSDF gives the best CD on most objects, e.g., Armadillo aligned CD 0.80 vs 0.86 for OReX and 1.4 for Screened Poisson.
- On real CT scans CrossSDF achieves average 2D IoU 0.79 on hepatic vessels vs 0.71 for OReX and 0.24 for Poisson.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| add Fourier features to the hash encoding (ablation) | CrossSDF · Balloon Dog, aligned | CD (×100): 0.30 -> 0.24 | Helped |
| use the symmetric difference loss instead of L1 loss between predicted and target 2D SDF labels (ablation) | CrossSDF · Balloon Dog, aligned | CD (×100): 0.57 -> 0.24 | Helped |
| use adaptive contour sampling instead of OReX sampling (ablation) | CrossSDF · Alveolis, aligned | CD (×100): 0.82 -> 0.35 | Helped |
| add minimum surface loss (ablation) | CrossSDF · Alveolis, aligned | CD (×100): 0.54 -> 0.35 | Helped |
| use hybrid hash and Fourier encoding instead of only Fourier encoding (ablation) | CrossSDF · Alveolis, aligned | CD (×100): 0.94 -> 0.35 | Helped |
| use the symmetric difference loss instead of L1 loss on Ωoff (ablation) | CrossSDF · Balloon Dog, aligned | HD (×100): 4.3 -> 3.0 | Helped |
| reduce the number of input cross-sections from 75 to 50 (ablation) | CrossSDF · Cerebral, non-aligned | CD (×100): 0.26 -> 0.51 | Hurt |
| reduce the number of input cross-sections from 75 to 25 (ablation) | CrossSDF · Cerebral, non-aligned | CD (×100): 0.26 -> 2.1 | Hurt |
Surprising findings
- Screened Poisson achieves better Hausdorff distance than CrossSDF on several thin structures (e.g., Pulmonary, Coro) despite visible ridging artifacts.
- Fitting a 3D SDF directly to 2D SDF labels produces 'laddering' artifacts on parallel slices, motivating the symmetric difference loss.
Limitations
- Fails to accurately reconstruct objects from very sparse slices (e.g., 25 slices on thin structures).
- Optimization-based per-shape fitting is slower than feed-forward predictions and does not use data-driven priors.
- Connected component counts for CrossSDF remain above ground truth on some thin structures (e.g., 176 vs 1 on Heart non-aligned).
Experimental setup
Datasets: Thin structures dataset from Rebain/Mesh collection (six patient-specific meshes, 75-100 cross-sections) Thick structures meshes from OReX (25 cross-sections) IRCADb-01 CT scans Medical Decathlon CT scans
Benchmarks: thin structures benchmark (Alveolis, Cerebral, Coronaries, Coro, Heart, Pulmonary) thick structures (Armadillo, Balloon Dog, Elephant, Eight, Hand, Brain) IRCADb-01 and Medical Decathlon CT slices
Metrics: Chamfer Distance Hausdorff Distance connected components 2D IoU
Baselines: OReX Screened Poisson Reconstruction POCO Neural-IMLS
Builds on: OReX Instant-NGP hash encoding Random Fourier features Eikonal regularization Screened Poisson reconstruction
Closest papers by meaning
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