direction op• Data kinds: matrix × table → matrix
• Call: import fullseye as fs; fs.ledger.fly_t4t5_field(movie, lattice, dt_s, tau_s=0.25, k_e=5.0, k_d=5.0, k_s=10.0, dc=1.0, model='three_arm', tau_hr_s=0.05, reduce='mean') (to call the implementation directly, import flyvision; flyvision.fly_t4t5_field(movie, lattice, dt_s, tau_s=0.25, k_e=5.0, k_d=5.0, k_s=10.0, dc=1.0, model='three_arm', tau_hr_s=0.05, reduce='mean'); from the registry, opsflyvision.get("fly_t4t5_field"))
Direction-selective response over the whole eye, in the six hexagonal directions.
T4 (ON) and T5 (OFF) are the first direction-selective cells in the fly, and
two mechanisms make them so: *preferred-direction enhancement*, which is the
Hassenstein-Reichardt multiplication, and *null-direction suppression*, which
is the Barlow-Levick division. Haag et al. measured both in one cell and wrote
them as three arms reading three adjacent columns — an enhancing arm E one
column *before* the centre, the direct arm D, and a suppressing arm S one
column *after* it::
R = (dc + k_e * LP[E]) * (dc + k_d * D) / (dc + k_s * LP[S])
with first-order low-passes of time constant `tau_s` on E and S. This op
runs that, or either mechanism alone, at every ommatidium and in all six
lattice directions at once.
movie: `(T, n)` one polarity channel — the ON or the OFF half of
:func:fly_onoff_split, not both. lattice: a :func:fly_hex_lattice result
(a :func:fly_eye_merge result is refused: its coordinates repeat, so a
neighbour would be looked up in the wrong patch).
dt_s: sample interval, seconds.
model: one of four, the first three sharing the same resting value `dc` so
that their responses are directly comparable —
• `"three_arm"` — the whole model above (Haag et al., *eLife* 5:e17421,
2016);
• `"enhance" — the numerator alone, (dc + k_e LP[E])(dc + k_d D)/dc`:
preferred-direction *enhancement*, the Hassenstein-Reichardt
multiplication with no veto;
• `"suppress" — the denominator alone, `dc (dc + k_d D)/(dc + k_s
LP[S])``: null-direction *suppression*, the Barlow-Levick division with
no enhancement (Barlow & Levick, *J. Physiol.* 178:477, 1965);
• `"hr" — the classical opponent correlator LP[E]*D - E*LP[D]` with
its own time constant *tau_hr_s*, which is antisymmetric by construction
and so is direction-selective without either of the two mechanisms above
(Hassenstein & Reichardt, *Z. Naturforsch.* 11b:513, 1956). It is
:func:fly_emd_response run over the lattice instead of a pair.
tau_s / k_e / k_d / k_s / dc: the three-arm parameters. The defaults are the
paper's (tau = 250 ms, k = 5/5/10, DC = 1.0). tau_hr_s: the correlator time
constant, used by `model="hr"` only.
reduce: how the time course becomes one number per direction — `"mean"`
(the wide-field integration a tangential cell performs), `"last"` (the
value at the final sample, which is how a transient is read at a chosen
instant) or `"max"`.
Returns a `(6, n)` float64 matrix: row *k* is the response to motion in
hexagonal direction *k* (counter-clockwise from +azimuth, see
:data:HEX_STEPS), averaged over time, with the model's resting value
subtracted so that no stimulus reads exactly 0. It is the `(k, n)` shape
:func:fly_hs_readout and :func:fly_flow_from_directions take.
Ommatidia at the rim, which have no neighbour on one side, read exactly 0 in
that direction: a detector missing an arm has no motion to report, and
inventing one at the edge would put a ring of false flow around every eye.
Ground truth, and it is the paper's claim written as algebra: because the
three arms multiply, **the direction selectivity of the whole model is the
product of the selectivities of its two halves**. For any stimulus and any
pair of opposite directions,
ratio("three_arm") == ratio("enhance") * ratio("suppress")
exactly, where `ratio = R_preferred / R_null taken on R + dc`. Two
columns lit in turn, a step of amplitude 1 held for `tau`, with the paper's
constants, give `R + dc = (dc + k_e(1-1/e))(dc + k_d)/dc` = 24.96
preferred and `dc(dc + k_d)/(dc + k_s(1-1/e))` = 0.820 null: 4.16 from
enhancement, 7.32 from suppression, 30.46 together. The tests measure all
three and the identity between them.
Raises `ValueError`: a non-2-D / too-short / non-finite *movie*, a
column count that is not the lattice's ommatidium count, a non-positive
*dt_s* / *tau_s* / *tau_hr_s* / *dc*, a negative gain, an unknown *model*,
and any malformed *lattice*.
• 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_fly_optomotor_steering — py -3.11 examples/poc_fly_optomotor_steering.py
matrix as input)fly_lamina_filter · fly_onoff_split · fly_flow_from_directions · fly_egomotion_from_flow · fly_hs_readout
direction)*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.