looming op• Data kinds: matrix × table → table
• Call: import fullseye as fs; fs.ledger.fly_expansion_readout(flow, lattice, axis=None, weights=None) (to call the implementation directly, import flyvision; flyvision.fly_expansion_readout(flow, lattice, axis=None, weights=None); from the registry, opsflyvision.get("fly_expansion_readout"))
Time-to-contact from the flow over the whole eye — and the aperture effect's 2x.
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.
• 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.
• poc_zebra_stripes_fly_eye — py -3.11 examples/poc_zebra_stripes_fly_eye.py
table as input)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. 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.