riesz op• Data kinds: qimage → image2d
• Call: import quatimage; quatimage.monogenic_phase(qimage, display: 'bool' = False) -> 'np.ndarray' (or opsquat.get("monogenic_phase"))
Local phase `atan2(|R|, f)` of a monogenic signal. → (H, W).
In `[0, pi]` — the monogenic phase is measured against the *magnitude* of
the Riesz vector, whose sign is carried by the orientation instead, so the
range is a half turn rather than a full one. That is the standard
convention (Felsberg & Sommer) and it is stated here because a caller
arriving from `complexops.cx_phase (whose raw range is (-pi, pi]`) will
otherwise assume a full turn and see a "wrapped" map that is not wrapped.
`display=True maps [0, pi] to [0, 1]` for viewing; the default is
`False — the **opposite** of cx_phase`'s default, deliberately,
because the consumers of this quantity in this module are numerical, and a
display scaling that arrives silently in a measurement is a factor of `pi`
that nothing announces.
Phase is the quantity a translation shifts linearly, which is why the whole
motion half of this module reads it. For an edge, phase 0 means the peak of
a bright line, `pi/2 a step edge and pi` the peak of a dark line — the
local *structure type*, independent of contrast.
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_orientation
*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.