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← report

Point-cloud slicing: what each approach is good for, and what to combine

z%Y-%m-%d %H:%Mu · fcp v5.2 (CUDA) · bench prototypes in scripts/ (package untouched) · numbers: report/ablation.csv (u rows), built by scripts/ablation.py and scripts/synth.py · gallery (parts and slices of every object): z not built yetz.

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1. Test set

10 watertight meshes, upright on +z (parts_report.OBJ): battery (synthetic stepped box), dress (solid envelope), elephant, two bowls (ObjectFolder, GSO), mug, dino, shoe, loaf pan (thin steel walls), horse. Noisy meshes (noisy.html): a smooth one-to-one 3D displacement field, σ = 0.2 / 0.6 / 1 % of the diagonal along the normal, topology kept (no face turned over, no self-crossing section); the loaf pan's source is full of slivers, so its 0.6 / 1 % versions reach only 0.21 / 0.27 %. Clouds: 10 000 and 2 048 points (seeded): area-uniform from the clean and from each noisy mesh; per-point Gaussian noise of 0.12 / 0.6 / 1.2 % of the diagonal on clean samples (PCPNet's protocol, tags pn*); variable density on the clean mesh (dgrad: kept with probability falling 10:1 along x; dstripe: stripes along y kept with probability 1 and 0.2): 180 clouds. The mesh route's parts on the mesh the cloud came from are the parts reference; errors are against the clean mesh (mean of the symmetric nearest-point distance, 50k samples per side, over the diagonal). 128 layers, 1024 atoms, up = +z.

2. Configurations

  • package: fcp.encode (surf slicer, tracked-fit, fit_tol "auto").
  • pointtest: the package's slices; a track is cut only where one height fit fails to explain the layer's points (two-sided, 2 spacings, p95) (pointfit.py).
  • A: the slicer's rings refitted to their own points (slab within a spacing, moved onto the plane along the surface; points by face from the normals; N from the point count; self-loops cut) (ringfit.py).
  • hybrid: A by default; on every layer the contours of the layer below (U) and above (D), carried and refitted, replace the whole layer when they are backed by points, fit them, explain as many points, fill nothing new and keep every trusted slicer ring (hybrid.py). hybrid-gated: U/D only where the slicer's layer is suspicious (an untrusted ring, or a solid sliver under 3 spacings wide).
  • "+pointtest": the same slices, cut by the point test.
  • thinwall: thin walls (a parallel face 0.4–1.5 spacings along the normal) added to the slicer's field as a band (thinwall.py).
  • eps: one scale ε = max(spacing, 4σ), σ the cloud's per-point noise given to the encoder (0 for clean, mesh-noise and density clouds): the slicer's support, band and inlier distance × ε/spacing, the minimum loop × (ε/spacing)², cuts by the point test (eps.py).

3. Summary per cloud type

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4. Per object

parts · mean error ×10⁻³ of the diagonal. Bold: parts closest to the mesh's, lowest error.

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5. Inventory of approaches

From docs/pointcloud-slicer.md, docs/surf_issues.md, docs/noisy_clouds.md, docs/HANDOVER_surf_noise_v52.md, docs/consolidation/RESULTS.md, api/DECISIONS.md 22 / 25, api/OPEN.md 9, the research repository (fousd-3d: overnight logs, ShapeNet diagnosis, pc-slicer prototypes) and this session's prototypes.

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stageapproachsourcewhat it doesevidenceverdictrings / parts

6. This session's pages

parts at 200k · parts at 10k (all prototypes) · the dino's cuts · A vs B · middle slices · loaf pan · GSO bowl · dino · noisy meshes

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Findings, from the 1 980 runs below (10 objects × 18 cloud types × 11 configurations) and the gallery.

The idea that unifies what works: the encoder works at one scale ε, the finest detail the input supports, ε = max(point spacing, 4σ) with the noise σ given as an encoder parameter (0 for a clean cloud). Surfaces closer than ε merge, loops smaller than ε² vanish, and a part is cut only where one smooth height fit fails to explain the points (configuration eps: eps.py). On a clean cloud ε is the spacing and this is the package's slicer with the point test.

  1. Per-point noise: eps turns the explosion into a description at the noise level. 10k points, all objects, against the mesh's 139 parts: 0.6 % noise 1 385 → 314 parts, error 0.85× the package's; 1.2 % noise 3 277 → 153 parts, error 0.57×. At 2 048 points and 1.2 %: 742 → 185 parts, error 1.17× (thin limbs are below ε there). Measured on the way: the slicer's support, band and inlier distance must scale with ε and the minimum loop with ε² (ε or a fixed loop leave the specks); the cut margin and the thin-wall rule must not (scaled by ε they delete geometry). C = 4 (report/eps_*.txt).
  2. The point test is the cut rule (also inside eps). Everywhere about 10 % fewer parts at the same error at 10k and within 5 % at 2 048; on some organic shapes it keeps pieces the mesh cuts (dress, dino at 10k).
  3. Thin walls are an orientation failure. A wall thinner than about a spacing is oriented as one sheet, so the inner face reads the cavity as inside: the slicer's inside band sits beside the wall and its zero line breaks (field pages). The thin-wall band (thinwall.py) fixes part of it at 10k (loaf pan 74 → 57 parts, error 16.6 → 9.9; shoe 30 → 26) and leaves thick objects unchanged, but it overthickens walls at 2 048 and the wall is not always closed (thinwall.html). The gated hybrid repairs the same rings from neighbouring layers at 5× the cost.
  4. Ring refitting (A, the hybrid) gives cleaner rings, not fewer parts, and costs accuracy at 2 048 (8–14 %).
  5. Variable density: the same idea per point. No global scale fits a cloud whose density varies (a global ε from the 90th-percentile spacing roughly halves the parts, report/eps_density.txt). With ε measured per point, εi = max(local spacingi, 4σ), setting that point's RIMLS support, band, plane-fit inlier distance and the minimum loop around it (configuration local, surf_local.py, CPU): gradient density at 10k 927 → 274 parts at 0.53× the package's error, striped 1 362 → 637 at 0.85×, gradient at 2 048 564 → 264 at 0.88×; per-point noise as global ε (0.6 %: 315 parts at 0.73×; 1.2 %: 168 at 0.67×); clean and mesh-noise clouds about the package's. One measured detail: the flood's balls follow the local spacing, not ε (it seals sampling gaps, and noise opens none; scaling it by 4σ cost up to 50 % error at 1.2 % noise, report/local_flood.txt). Weak spot: per-point noise at 2 048 points (0.6 %: 1.13× the package's error).
  6. Noise estimation is not solved. A local quadric fit reads thick shapes' noise (horse 0.55 % for 0.6 %) but takes a thin wall's two faces for noise (clean mug 0.84 %), and at 2 048 everything reads high: σ is a parameter, not estimated (report/sigma_estimators.txt).
  7. 2 048 points is past the sampling limit for this set: about twice the mesh's parts in every configuration, some features gone.

Recommended, in the paper's words: "Every point carries the resolution the input supports there, ε = max(its local spacing, 4σ) for a given noise σ. The slicer resolves nothing finer: its implicit surface is fitted at each point's ε, loops smaller than ε² are dropped, and a part is cut only where one smooth fit along the height fails to explain the points." In the package: a noise= parameter (σ in world units, default 0), the per-point ε in the surf slicer's kernels (CUDA and numba: support, band, inlier distance, minimum loop; the flood on the local spacing), and the point test as the cut rule for clouds (configuration local). Later: the thin-wall band with its width from the measured wall, and an estimate of σ that does not read thin walls as noise.

The package is untouched; every prototype is in scripts/. A change to the package is a decision for api/DECISIONS.md, with these tables.

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