riesz op• Data kinds: qimage → image2d
• Call: import fullseye as fs; fs.ledger.monogenic_orientation(qimage, display: 'bool' = False) -> 'np.ndarray' (to call the implementation directly, import quatimage; quatimage.monogenic_orientation(qimage, display: 'bool' = False) -> 'np.ndarray'; from the registry, opsquat.get("monogenic_orientation"))
Local orientation atan2(R2, R1) of a monogenic signal. → (H, W).
Radians in [0, pi): an orientation is defined modulo pi (a grating at 10 degrees and one at 190 degrees are the same grating), and the value is folded into that range rather than left in (-pi, pi] where the same structure would read as two different numbers on either side of a contrast reversal. display=True maps it to [0, 1].
Continuous, not quantised — the angle is read directly from two filters, for any angle, where a steerable bank with K orientations interpolates between its K. Measured against eight grid-exact grating orientations the error is at most 3.6e-15 rad, including the obliques. (Whether that buys anything downstream is a separate question, and the measured answer is mostly *no* — see riesz_displacement.)
Where it is undefined, and the mask is not the one you expect. The orientation dies where the *Riesz vector* dies, which is at every even-symmetric point — local phase 0 or pi, the crest of a bright or dark line — and the amplitude is at full strength there. Measured on a 45-degree grating, the worst orientation error over the whole frame is 0.2764 rad, at a pixel where |R| = 6.8e-16 and monogenic_amplitude reads 1.0000. So masking on the amplitude does not protect you; mask on hypot(q[..., 1], q[..., 2]), the Riesz magnitude. With that mask the error over the same eight orientations is at most 3.6e-15 rad.
Where the Riesz vector is exactly zero, atan2(0, 0) = 0 is returned — a *value*, not a measurement.
Raises ValueError: the input is not a valid quaternion field, or its k component is non-zero; *display* is not a bool.
• quaternion_monogenic family guide
• 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.
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
image2d as input)riesz_transform · monogenic_signal
riesz)riesz_transform · monogenic_signal · monogenic_amplitude · monogenic_phase
*Provenance: quatimage.py — QUAT 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.