iqft2 — QUAT fourier op

• 資料種類:qimage → qimage

• 呼叫:import quatimage; quatimage.iqft2(spectrum, side, mu=None) -> 'np.ndarray'(或 opsquat.get("iqft2"))

用法

中心化頻譜的逆四元數傅立葉變換。→ (H, W, 4)。

> 以下的詳細說明為原文 —— 摘要與標題已翻譯。

The exact inverse of :func:qft2 for the same side and the same mu:

measured round-trip error `2.22e-15` for both sides on a standard-normal

`(32, 32, 4) field. The kernel is exp(+mu * 2*pi*(...))` applied on the

side named, and the `1/(H*W)` normalisation is carried here, as in

`numpy.fft.ifft2`.

Using the wrong side does not raise. `iqft2(qft2(q, "left"), "right")`

returns a finite, plausible quaternion image that is simply not `q`:

measured `max|err| = 1.113` on a random colour image whose own range is

`0.9994 (another seed: 1.063 against 1.0), and — the dangerous case — only 0.054` against a range of

`1.076` on a grey-axis-dominated one, which is small enough to survive a

look at the picture. The `side` argument is required at both ends for

exactly this reason, and the two calls must agree: nothing in the data

records which transform produced it, so nothing downstream can catch the

mismatch for you.

Raises `ValueError: *spectrum* is not a valid (H, W, 4)` field;

*side* is not `'left' / 'right'`; *mu* is not a finite non-zero

3-vector.

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(fourier)

qft2

*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)。*

© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.