quat_norm — QUAT convert op

• Data kinds: qimage → image2d

• Call: import quatimage; quatimage.quat_norm(qimage) -> 'np.ndarray' (or opsquat.get("quat_norm"))

Usage

Per-pixel quaternion modulus `|q| = sqrt(w^2+x^2+y^2+z^2)`. → (H, W).

Raw / unnormalised, following `complexops.cx_magnitude`: a modulus is a

metric quantity and routinely exceeds one (a QFT spectrum's DC term is huge).

For a colour quaternion it is the colour *magnitude* — the length of the RGB

vector, i.e. luminance in the L2 sense; for a monogenic signal it is the

local amplitude and :func:monogenic_amplitude is the name that says so.

Use `imgio.normalize` for a displayable view.

Detailed usage guide

• quaternion_monogenic family guide

References (sample data, literature)

• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).

• Operator provenance and references — the sources of the research/methods this op family came from.

• The canonical algorithm (author, year) and its uses are named in the family usage guide above.

Runnable examples (verified samples that actually call this op)

• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py

Ops the type connects to (they accept image2d as input)

riesz_transform · monogenic_signal

Same category (convert)

rgb_to_quaternion · quaternion_to_rgb

*Provenance: quatimage.py — QUAT operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

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