riesz_transform — QUAT `riesz` op

• 数据种类:image2d → qimage

• 调用: import fullseye as fs; fs.ledger.riesz_transform(image) -> 'np.ndarray'(要直接调用实现,import quatimage; quatimage.riesz_transform(image) -> 'np.ndarray';从台账取用则 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 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.

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