riesz op• Data kinds: image2d → qimage
• Call: import fullseye as fs; fs.ledger.riesz_transform(image) -> 'np.ndarray' (implementation को सीधे call करना हो तो import quatimage; quatimage.riesz_transform(image) -> 'np.ndarray', registry से लेना हो तो opsquat.get("riesz_transform"))
image का 2-D Riesz transform, pure quaternion field के रूप में। → (H, W, 4)।
> नीचे का विस्तृत विवरण मूल text में है — सारांश और headings का अनुवाद हो चुका है।
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.
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.
• quaternion_monogenic family guide
• Sample data catalog (DL URL / license) — 2-D के लिए skimage.data (BSD/public) + synthetic, 3-D के लिए real data sources (Stanford/PDS आदि) के DL URL।
• Operators का स्रोत और संदर्भ — इस op family के मूल research/methods के स्रोत।
• Algorithm का मानक स्रोत (लेखक, वर्ष) और उपयोग ऊपर की family usage guide में दिए गए हैं।
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
qimage को input के रूप में लेते हैं)quaternion_to_rgb · quat_norm · quat_conjugate_image · quat_normalize_image · quat_image_multiply · monogenic_amplitude · monogenic_phase · monogenic_orientation
riesz)monogenic_signal · monogenic_amplitude · monogenic_phase · monogenic_orientation
*Provenance: quatimage.py — QUAT operator registry. यह per-op note tools/opdocs.py md से अपने-आप generate होता है (हाथ से edit न करें)।*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.