riesz op• Datenarten: qimage → image2d
• Aufruf: import quatimage; quatimage.monogenic_orientation(qimage, display: 'bool' = False) -> 'np.ndarray' (oder opsquat.get("monogenic_orientation"))
Lokale Orientierung `atan2(R2, R1)` eines monogenen Signals. → (H, W).
> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.
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 :func: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 :func: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.
• Leitfaden zur Familie quaternion_monogenic
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
image2d als Eingabe)riesz_transform · monogenic_signal
riesz)riesz_transform · monogenic_signal · monogenic_amplitude · monogenic_phase
*Provenance: quatimage.py — QUAT Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.