procrustes_align — SHAPESTAT `procrustes` op

• Data kinds: points × points → points

• Call: import fullseye as fs; fs.ledger.procrustes_align(source, target, scaling: 'bool' = True, reflection: 'bool' = False) (to call the implementation directly, import shapestats; shapestats.procrustes_align(source, target, scaling: 'bool' = True, reflection: 'bool' = False); from the registry, opsshapestat.get("procrustes_align"))

Usage

> This operator's description has not been translated yet. The original text follows as it is.

*source* を *target* に重ねた点。→ `(N, 3)(:func:procrustes_fit` の適用)。

`M = procrustes_fit(source, target, scaling, reflection)` を求め、

`source @ M[:3, :3].T + M[:3, 3]` を返す。変換は重心合わせ + SVD による回転

(+ 任意でスケール)の相似変換で、i 番目どうしが対応していることが前提。

対応の無い点群を渡しても例外は出ず、意味の無い配置が返る(その場合は

ICP 系の登録を使う)。

• `source, target: (N, 3)、同じ N、有限。N = 1` でも通る(並進のみ)。

• `scaling=True: 大きさの違いも吸収する。False` なら剛体変換。

`source` が全点同一(広がり 0)のときスケールは 1 のまま。

• `reflection=False(既定): det(R) = +1 を強制。True` にすると鏡像も

許す ―― 左右非対称性を測る用途では消えてしまうので通常は既定のまま。

• 返り値: `(N, 3) float64。残差を数値で欲しいなら procrustes_distance`、

変換行列そのものは `procrustes_fit`。

• 失敗: `ValueError(形が (N, 3) でない、N` 不一致、非有限)。

多数の形を同時に揃えるなら `generalized_procrustes`。

Detailed usage guide

• shape_statistics family guide

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.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• shapestat_landmark_tour — py -3.11 examples/shapestat_landmark_tour.py

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

shape_perturb · procrustes_fit · procrustes_distance · shape_project · shape_mahalanobis · mirror_plane_from_pairs · landmark_asymmetry · signed_surface_distance

Same category (`procrustes`)

procrustes_fit · procrustes_distance · generalized_procrustes · shape_mean

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

procrustes_align — SHAPESTAT procrustes op