essential_8point — 3D `two_view` op

• Data kinds: image2d × image2d → matrix

• Call: import fullseye as fs; fs.ledger.essential_8point(pts1, pts2, K1, K2=None) (to call the implementation directly, import twoview; twoview.essential_8point(pts1, pts2, K1, K2=None); from the registry, ops3d.get("essential_8point"))

Usage

The essential matrix E directly from correspondences and K. → E (3,3).

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

手順: `fundamental_8point(pts1, pts2) で F を推定し、E = K2ᵀ F K1` を作ってから SVD で特異値を (1, 1, 0) に置き換える(本質行列の性質。結果の Frobenius ノルムは √2 に固定される)。

• `K1 (3,3) は画像 1 の内部行列、K2 を省略すると K1` を両画像に使う(同一カメラの前提)。

• 対応点は画素座標 (N,2)。検証と例外は `fundamental_8point と同じ(8 点未満・点数不一致・非有限・(N,2) でない入力は ValueError`)。

• E の符号は不定で、(R, t) は 4 候補に分かれる。分解と cheirality による一意化までまとめて行うのが `recover_pose`。

• 外れ値に無防備。平面・純回転の退化も本 op では検出しない(`recover_pose` が検出する)。決定論的。

Background guides (the physics and conventions behind this op)

• depth_sensors — 深度センサの知識 — 測距原理・実機の値・欠測の出方

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)

• sfm_recon — py -3.11 examples_3d/sfm_recon.py

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

fuse_to_voxel

Same category (`two_view`)

fundamental_8point · recover_pose · triangulate · sampson_distance

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

essential_8point — 3D two_view op