typed op• 資料種類:signal → signal
• 呼叫:fullseye.apply(img, "tb_fly_tau_from_expansion", a=0.5, b=0.5)(2-D 的模型是一張圖 + 兩個純量旋鈕 a,b∈[0,1])
*圖為在 128×128 合成輸入上實際執行的輸出。左為輸入，右為輸出。點雲以俯視散點顯示(亮度 = z)，一維序列為折線，體資料為沿 z 的最大值投影，影片為中間影格，複數影像為振幅；無法成像的回傳值直接顯示數值。*
*旋鈕 a 不改變輸出(實測: 0.1 / 0.5 / 0.9 相同)。*
*旋鈕 b 不改變輸出(實測: 0.1 / 0.5 / 0.9 相同)。*
階段(前置運算子 → 本運算子，由左至右):
▸ tb_fly_tau_from_expansion: stages (docs site)
換別的影像(合成場景 / 照片 / 硬幣。上排為輸入，下排為對應輸出。旋鈕取預設):
▸ tb_fly_tau_from_expansion: other inputs (docs site)
> 該運算子的說明尚無譯文,以下照原文給出。
Time-to-contact from optical expansion — the tau margin.
From the subtended angle and its rate::
shape="disk": tau = sin(theta) / theta'
shape="sphere": tau = 2*tan(theta/2) / theta'
`theta_signal` is the full subtended angle over time, radians.
★ The two object models differ by 33% at a 60-degree subtense (`sin 60 = 0.866`
vs `2 tan 30 = 1.155`); using the wrong one silently mis-times a landing, so
the model is a required, named choice rather than a default guess.
theta_signal: the full subtended angle per sample, radians.
dt_s: the sample interval, seconds.
shape: `"disk" (a frontal circular disk) or "sphere"`.
Returns a 1-D float64 array of the time-to-contact per sample, seconds.
Non-expanding samples (`theta' <= 0) return NaN` — a documented
non-finite, because a contracting or static angle has no time-to-contact and
inventing one would be a plausible-wrong number. (The registry op
`tb_fly_tau_from_expansion` must return a finite signal, so it replaces those
NaN by the signal fallback without recording a fallback event —
`backend_safe.NONFINITE_BY_DESIGN`; call this function directly to keep the NaN.)
Ground truth: for the model's own object geometry (`theta = 2 asin(l/d)` for a
sphere, `theta = 2 atan(l/d) for a disk) approaching at speed |v|`, the
returned tau equals the true distance-over-speed `d/|v|` (pinned in the
tests).
Raises `ValueError`: a non-1-D / empty / too-short (< 3) / non-finite
*theta_signal*, a signal over :data:MAX_SIGNAL_POINTS, a non-positive *dt_s*,
and an unknown *shape*. A non-expanding angle is not an error — it is the
documented `NaN` return above.
Typed bridge of the flyvision op `fly_tau_from_expansion into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b` are unused.
• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。
• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。
下面的程式已確認可以執行(與圖相同的輸入)。在 Studio 說明中，此區塊會變成按鈕，可當場載入並執行。
img_to_signal 0.50 0.50 tb_fly_tau_from_expansion 0.50 0.50
▸ Load this pipeline · Load & run
下面的範例呼叫的是底層帳本運算子 fly_tau_from_expansion。此橋接運算子只是把同一實作適配為 fn(v, a, b) 慣例，行為完全相同(只是呼叫形式不同)。
• poc_fly_vision — py -3.11 examples/poc_fly_vision.py
signal 作為輸入)identity · tb_create_funct_1d_array · tb_smooth_funct_1d_gauss · tb_smooth_funct_1d_mean · tb_derivate_funct_1d · tb_integrate_funct_1d · tb_zero_crossings_funct_1d · tb_abs_funct_1d
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*Provenance: ops.py — 2D 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.