riesz_transform — QUAT `riesz` op

• 資料種類:image2d → qimage

• 呼叫:import quatimage; quatimage.riesz_transform(image) -> 'np.ndarray'(或 opsquat.get("riesz_transform"))

用法

影像的 2-D Riesz 變換,作為純四元數場。→ (H, W, 4)。

> 以下的詳細說明為原文 —— 摘要與標題已翻譯。

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`.

詳細使用指南

• quaternion_monogenic 族使用指南

參考(範例資料・文獻)

• 範例資料目錄(下載 URL / 授權) —— 2-D 用 skimage.data(BSD/公有領域)加合成圖,3-D 給出真實資料源(Stanford/PDS 等)的下載 URL。

• 運算子來歷與參考文獻 —— 該運算子族所依據的研究/方法出處。

• 演算法的正典(作者・年份)與用途見上面的族使用指南。

可執行的範例(實際呼叫該運算子並已驗證的樣例)

• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py

型別可銜接的下一個運算子(可接受 `qimage` 作為輸入)

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

同類別(`riesz`)

monogenic_signal · monogenic_amplitude · monogenic_phase · monogenic_orientation

*Provenance: quatimage.py — QUAT 運算子登記表。本條目由 tools/opdocs.py md 自動產生(請勿手動編輯)。*

riesz_transform — QUAT riesz op

用法