edges op• Data kinds: voxel → voxel
• Call: import fullseye as fs; fs.ledger.log_zero_crossings(vol, sigma: 'float' = 1.5, rel_thresh: 'float' = 0.001) -> 'np.ndarray' (to call the implementation directly, import edges3d; edges3d.log_zero_crossings(vol, sigma: 'float' = 1.5, rel_thresh: 'float' = 0.001) -> 'np.ndarray'; from the registry, ops3d.get("log_zero_crossings"))
Zero-crossing edges of the Laplacian of Gaussian.
vol : (D,H,W) array
Grey voxels.
sigma : float
Standard deviation of the LoG (> 0).
rel_thresh : float
Relative threshold that suppresses false crossings caused by numerical noise in flat regions. Adopted only when the LoG difference |a-b| of the crossing pair
exceeds rel_thresh * max|L|.
edge_mask : (D,H,W) bool
A mask that sets, of each adjacent pair whose sign changes, the side with the smaller |LoG| (the side closer to zero).
Two kinds of zero crossing are detected along each axis direction:
(1) Between-grid crossing — sign product a*b < 0 of an adjacent pair (a,b) (both sides non-zero with a sign flip). To keep the thickness down it is assigned to the 1 voxel of the pair with the smaller |LoG|.
(2) Grid-aligned crossing — the centre voxel is exactly zero (L==0) and its two neighbours have opposite signs (the sign passes through zero at that voxel). For a true edge on a grid-aligned surface such as an SDF-like grid, where the LoG is 0 exactly on a grid point, a*b is always 0 and (1) misses it, so that voxel is set as a crossing. Constant-zero regions have both neighbours 0 too, so Lm*Lp==0 and they are excluded (no false detection).
In both cases numerical noise in flat regions is suppressed by the relative threshold (rel_thresh * max|L|).
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• edges_3d — py -3.11 examples_3d/edges_3d.py
voxel as input)voxel_to_mips · voxel_to_mesh · signed_distance_field · to_points · sobel3d · hessian3d · curvature_maps · edt_jfa
edges)gradient3d · canny3d · link_edges · edge_points
*Provenance: edges3d.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.