extent_signature — 3D `shape_descriptor` op

• Data kinds: points → descriptor

• Call: import fullseye as fs; fs.ledger.extent_signature(points) -> 'np.ndarray' (to call the implementation directly, import descriptors3d; descriptors3d.extent_signature(points) -> 'np.ndarray'; from the registry, ops3d.get("extent_signature"))

Usage

The ratios of the extent along the PCA principal axes (the eigenvectors of the covariance).

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

共分散行列の固有値は回転に不変。ここでは固有値の平方根(= 各主軸方向の標準偏差、

長さの次元)を降順に並べ、総和 1 に正規化して (3,) ベクトルにする。これにより

絶対スケールが消え、回転・平行移動・スケールに不変な「形の細長さ」指標になる。

• 等方的な形状(球・立方体)→ 3 成分がほぼ等値 [~0.33, ~0.33, ~0.33]

• 細長い棒 → 1 成分が突出 [~0.9, ~0.05, ~0.05]

Parameters

----------

points : array_like, shape (N, 3)

点群。N >= 3 が必要(共分散を意味のある形で作るため)。

Returns

-------

np.ndarray, shape (3,)

降順・総和 1 に正規化した広がりベクトル。

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)

• shape_desc_pose — py -3.11 examples_3d/shape_desc_pose.py

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

fuse_to_voxel · shape_distance

Same category (`shape_descriptor`)

d2_distribution · a3_distribution · describe · shape_distance

*Provenance: descriptors3d.py — 3D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

extent_signature — 3D shape_descriptor op