riesz_transform — QUAT `riesz` op

• 数据种类:image2d → qimage

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

用法

图像的 2-D Riesz 变换,作为纯四元数场。→ (H, W, 4)。

> 以下的详细说明为原文 —— 摘要与标题已翻译。

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`.

详细使用指南

• quaternion_monogenic 族使用指南

参考(示例数据・文献)

• 示例数据目录(下载 URL / 许可证) —— 2-D 用 skimage.data(BSD/公有领域)加合成图,3-D 给出真实数据源(Stanford/PDS 等)的下载 URL。

• 算子来历与参考文献 —— 该算子族所依据的研究/方法出处。

• 算法的正典(作者・年份)与用途见上面的族使用指南。

可运行的示例(实际调用该算子并已验证的样例)

• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py

类型可衔接的下一个算子(可接受 `qimage` 作为输入)

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

同类别(`riesz`)

monogenic_signal · monogenic_amplitude · monogenic_phase · monogenic_orientation

*Provenance: quatimage.py — QUAT 算子登记表。本条目由 tools/opdocs.py md 自动生成(请勿手工编辑)。*

riesz_transform — QUAT riesz op

用法