riesz_transform — QUAT `riesz` op

• データ種: image2d → qimage

• 呼び出し: import quatimage; quatimage.riesz_transform(image) -> 'np.ndarray' (または opsquat.get("riesz_transform"))

使い方

The 2-D Riesz transform of an image, as a pure quaternion field. → (H, W, 4).

The isotropic generalisation of the Hilbert transform: a *pair* of filters

with frequency responses `-i*u/|w| and -i*v/|w|`, returned as the

quaternion `(0, R1 f, R2 f, 0)`. It is the 2-D object that has no complex

analogue — the 1-D analytic signal needs a direction to say which way "90

degrees later" is, and in 2-D there is no single direction, so the answer

needs two components and therefore an algebra with room for them.

Closed form, which is how this is tested rather than eyeballed

-------------------------------------------------------------

For a grating `cos(2*pi*(u0*x + v0*y))` sampled on the DFT grid,

`R1 = (u0/|w0|) * sin(2*pi*(u0*x + v0*y))`,

`R2 = (v0/|w0|) * sin(...)`

exactly. Measured over a table of eight grid-exact orientations from 0 to

159.4 degrees on a 64x64 frame, the largest absolute deviation from that

closed form is 6.1e-15, and the orientation recovered through

:func:monogenic_orientation matches the grating's to 3.6e-15 rad at

every one of them. There is no tolerance to choose.

Note the scalar component is 0, so this is the Riesz *transform* and not the

monogenic signal — feeding it to :func:monogenic_phase gives `pi/2`

everywhere, correctly but uselessly. Use :func:monogenic_signal, which

keeps the band-pass image in the scalar slot.

Raises `ValueError: *image* is not a finite real (H, W)` array with

`H, W >= 2, or exceeds :data:MAX_PIXELS`.

詳しい使い方ガイド

• quaternion_monogenic ファミリガイド

参考(サンプルデータ・文献)

• 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。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py

型が繋がる次の op(`qimage` を入力に取れる)

quaternion_to_rgb · quat_norm · quat_conjugate_image · quat_normalize_image · quat_image_multiply · monogenic_amplitude · monogenic_phase · monogenic_orientation

同カテゴリ(`riesz`)

monogenic_signal · monogenic_amplitude · monogenic_phase · monogenic_orientation

*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)。*

riesz_transform — QUAT riesz op

使い方