moment_axes — 3D `match_pose` op

• Data kinds: points → axes

• Call: import fullseye as fs; fs.ledger.moment_axes(points, weights=None) (to call the implementation directly, import match3d; match3d.moment_axes(points, weights=None); from the registry, ops3d.get("moment_axes"))

Usage

The centroid and principal axes (the eigenvectors of the inertia tensor) of a point set or weighted points. The basis of pose estimation.

> The detailed description below is the original text — the summary and the headings are translated.

返り値 (centroid(3,), axes(3,3) 列=主軸, eigvals(3,))。固有値降順。回転の正準化に使う。

定義: `w を総和 1 に正規化し、重心 c = Σ w p、散布行列 C = Σ w (p−c)(p−c)ᵀ`

(共分散。慣性テンソル `tr(C)I − C と固有ベクトルは共通で固有値の順序が逆)を eigh` で

分解する。`axes[:, i]` が i 番目に大きい固有値の主軸(降順)。固有値は分散(長さ²)。

• 固有ベクトルの符号は任意で、`axes は左手系(det=−1)になり得る(match_pca` は第 3 軸を

反転して右手系にしている)。

• `weights` は長さ N。総和 0 は 0 除算で NaN(例外は出ない)。点数 0 は失敗する(検証は無い)。

• 主軸が縮退(球など)なら軸の向きは不定。

後段: `match_pca、obb`(有向 bbox)、正準姿勢への回転。

References (sample data, literature)

• 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.

Runnable examples (verified samples that actually call this op)

• itokawa_pose_canonical — py -3.11 examples_3d/itokawa_pose_canonical.py

Ops the type connects to (they accept `axes` as input)

fuse_to_voxel

Same category (`match_pose`)

match_phase_3d · match_pca · match_logpolar_z

*Provenance: match3d.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

moment_axes — 3D match_pose op