riesz_transform — QUAT `riesz` op

• 資料種類:image2d → qimage

• 呼叫: import fullseye as fs; fs.ledger.riesz_transform(image) -> 'np.ndarray'(要直接呼叫實作,import quatimage; quatimage.riesz_transform(image) -> 'np.ndarray';從台帳取用則 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 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 monogenic_phase gives pi/2 everywhere, correctly but uselessly. Use 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 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