typed op• Data kinds: signal → signal
• Call: fullseye.apply(img, "tb_fly_tau_from_expansion", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])
*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*
*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
Stages (the ops that come before → this op, left to right):
▸ tb_fly_tau_from_expansion: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_fly_tau_from_expansion: other inputs (docs site)
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.
• 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 program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.
img_to_signal 0.50 0.50 tb_fly_tau_from_expansion 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op fly_tau_from_expansion. This bridge op is the same implementation adapted to the fn(v, a, b) convention, so the behaviour carries over unchanged (only the call form differs).
• poc_fly_vision — py -3.11 examples/poc_fly_vision.py
signal as input)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 operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.