looming op• データ種: matrix × table → table
• 呼び出し: import fullseye as fs; fs.ledger.fly_expansion_readout(flow, lattice, axis=None, weights=None) (実装を直接呼ぶなら import flyvision; flyvision.fly_expansion_readout(flow, lattice, axis=None, weights=None)、台帳から引くなら opsflyvision.get("fly_expansion_readout"))
眼全体の流れから衝突時間 τ を読む —— 縦縞のアパーチャ効果は厳密に 2τ。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
A fronto-parallel surface approached at speed v from distance d moves the line of sight at polar angle theta outward at sin theta cos theta / tau with tau = d/v. This op projects the measured flow onto the outward radial direction and fits that one number, 1/tau, by weighted least
squares::
1/tau = sum w f_r sin cos / sum w (sin cos)^2
and, independently, fits a linear field f = A x + b on the gnomonic plane and reads the divergence tr A, which sceneflow converts the same way (ttc = 2/div).
The reason to have both: a correlation-type detector only sees the motion component across a contrast edge. Over vertical stripes every edge is vertical, so the elevation component of the flow is lost (the aperture problem), the radial projection keeps on average half the expansion, and both readouts return 2 tau — the surface looks twice as far as it is. A checkerboard has edges in both directions and returns tau. That is the identity How et al. (2020) argued from, written as a number.
flow: (n, 2) azimuth/elevation flow per ommatidium (radians per
second), the return of fly_flow_from_directions.
lattice: the eye it was measured on (hexagonal or Vogel).
axis: the direction of travel = focus of expansion, body coordinates;
None = the lattice's optical axis.
weights: None or (n,) non-negative weights (e.g. 0 on the rim, where
fly_flow_from_directions reports nothing).
Returns a dict {"tau_s", "rate_1_s", "tau_div_s", "divergence_1_s", "aperture_ratio", "residual_rms", "n_ommatidia"} — the radial-fit time-to-contact and its rate, the divergence-fit time-to-contact and the divergence, the ratio of the smaller to the larger diagonal of A (1 for isotropic expansion, 0 under a pure aperture effect), the rms of the radial residual and how many ommatidia voted. A non-expanding field (rate <= 0) returns NaN for the time-to-contact — a documented non-finite, as in fly_tau_from_expansion: a receding surface has no time-to-contact.
Ground truth (pinned in the tests): the exact plane flow returns tau_s == tau and tau_div_s == tau to 1e-9 (the divergence is fitted on gnomonic velocities, where a plane approach is exactly linear); the same flow with its elevation component removed returns 2 tau from both readouts within 1% on a 10-degree field (aperture_ratio 0) — a hexagonal lattice is 6-fold symmetric, so sum cos^2 phi = sum sin^2 phi over it, and the residual is the sphere's departure from that plane.
Raises ValueError: a *flow* that is not (n, 2) for this lattice (an empty *flow* is refused), non-finite entries, a malformed *lattice* / *axis* / *weights*, all-zero weights, and fewer than 6 voting ommatidia.
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• poc_zebra_stripes_fly_eye — py -3.11 examples/poc_zebra_stripes_fly_eye.py
table を入力に取れる)fly_t4t5_field · fly_flow_from_directions · fly_matched_filter · fly_egomotion_from_flow · fly_eye_merge · fly_view_plane_texture · fly_hex_resample · lattice_moire_peak
looming)fly_lgmd_eta · fly_tau_from_expansion
*Provenance: flyvision.py — FLYVISION operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.