moment_invariant op• Data kinds: points → table
• Call: import fullseye as fs; fs.ledger.central_moments(points, max_order: 'int' = 3) -> 'dict' (to call the implementation directly, import moments3d; moments3d.central_moments(points, max_order: 'int' = 3) -> 'dict'; from the registry, ops3d.get("central_moments"))
The centroid-centred central moments μ_{pqr} (translation invariant; keys are (p,q,r)).
μ_{pqr} = mean( (x-x̄)^p (y-ȳ)^q (z-z̄)^r ). Includes all orders with p+q+r <= max_order. Computed after subtracting the centroid, so it is exactly translation invariant. Under the equal-mass convention μ_{000}=1, and the 1st-order moments μ_{100}=μ_{010}=μ_{001}=0 (a consequence of centring).
points : array_like, shape (N, 3)
Point cloud.
max_order : int
Maximum order p+q+r to include (default 3). 0 or greater.
dict[tuple[int, int, int], float]
(p, q, r) → μ_{pqr}.
Notes:
• The number of keys in the returned dict is all combinations with p+q+r <= max_order (20 for max_order=3). Values are float (a mean, so divided by the number of points).
• Units are length^(p+q+r). Translation invariant but not invariant to rotation or scale (for rotation invariants see moment_invariants / principal_moments).
• 2nd-order moments such as (2,0,0), (1,1,0) are exactly the population covariance (divided by N), the same material as inertia_tensor.
• Higher orders are dominated by points far from the centroid, so they are sensitive to outliers. Consider statistical_outlier_removal or similar beforehand.
• Input is (N,3), N >= 1. max_order < 0, invalid shape or non-finite values raise ValueError. Deterministic.
• 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.
• moment_invariants — py -3.11 examples_3d/moment_invariants.py
table as input)fuse_to_voxel · mesh_select_lod
moment_invariant)moment_invariants · principal_moments · inertia_tensor
*Provenance: moments3d.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.