selfmotion op• Data kinds: matrix × table → table
• Call: import fullseye as fs; fs.ledger.fly_egomotion_from_flow(flow, lattice, axes=None, weights=None) (to call the implementation directly, import flyvision; flyvision.fly_egomotion_from_flow(flow, lattice, axes=None, weights=None); from the registry, opsflyvision.get("fly_egomotion_from_flow"))
Least-squares rotation of the eye from its flow field — and how badly the eye's own shape conditions the answer.
Given the flow `f_i at known viewing directions d_i`, a pure rotation
`w predicts f_i = -(w x d_i)`, which is linear in w: projecting on
the tangent basis gives `f_az = -w . (d x e_az)` and
`f_el = -w . (d x e_el), so the estimate is one 2n x 3` least-squares
solve with no iteration and no starting guess (Franz et al.'s linear
egomotion estimate, *Biol. Cybern.* 2004).
The catch is not the algebra, it is the eye. A single patch of ommatidia sees
a small piece of the sphere, and over a small piece the flow of a yaw and the
flow of a sideways translation — or of a pitch — look nearly the same. This
op therefore returns the condition number of that solve next to the
answer, so that "the fit converged" and "the fit was identifiable" stay
separate claims.
flow: `(n, 2)` azimuth/elevation components per ommatidium
(:func:fly_flow_from_directions or :func:fly_matched_filter).
lattice: the eye they were measured on.
axes: `None to solve for the full 3-D rotation, or a (k, 3)` array of
axes to restrict the fit to (`[[0, 0, 1]]` = yaw only, the well-conditioned
question a forward-looking eye can actually answer).
weights: `None or (n,)` non-negative per-ommatidium weights — a
confidence, e.g. the local contrast, or zeros to drop the rim.
Returns a dict::
{"omega_rad_s": (3,), "yaw_rad_s": float, "pitch_rad_s": float,
"roll_rad_s": float, "residual_rms": float, "flow_rms": float,
"explained": float, "condition": float, "n_ommatidia": int}
with yaw about +z (left positive), pitch about +y, roll about +x, and
`explained = 1 - residual_rms/flow_rms` (1.0 = the flow is exactly a
rotation, 0.0 = the fit explains none of it).
Ground truth: handed a :func:fly_matched_filter template scaled by a known
rate, it returns that rate to machine precision and `explained = 1`; handed
a pure translation field it returns a small rate with a low `explained`; and
the condition number of a narrow forward eye is large (the tests measure it)
while the yaw-only fit is near 1.
Raises `ValueError: a *flow* that is not (n, 2)` for this lattice,
non-finite entries, a malformed *axes* / *weights*, all-zero weights, and a
lattice with fewer ommatidia than the fit has unknowns.
• 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
table as input)fly_t4t5_field · fly_flow_from_directions · fly_matched_filter · fly_eye_merge · fly_hex_resample · fly_hs_readout
selfmotion)fly_matched_filter · fly_eye_merge
*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.