riesz op• データ種: qimage → image2d
• 呼び出し: import fullseye as fs; fs.ledger.monogenic_orientation(qimage, display: 'bool' = False) -> 'np.ndarray' (実装を直接呼ぶなら import quatimage; quatimage.monogenic_orientation(qimage, display: 'bool' = False) -> 'np.ndarray'、台帳から引くなら opsquat.get("monogenic_orientation"))
モノジェニック信号の局所方位 atan2(R2, R1)。→ (H, W)。
> 以下の詳細説明は原文のままです —— 要約と見出しは訳出済み。
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 ファミリ ガイド
• サンプルデータ カタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
• 演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
• アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
image2d を入力に取れる)riesz_transform · monogenic_signal
riesz)riesz_transform · monogenic_signal · monogenic_amplitude · monogenic_phase
*Provenance: quatimage.py — QUAT operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.