fourier op• Data kinds: qimage → qimage
• Call: import quatimage; quatimage.iqft2(spectrum, side, mu=None) -> 'np.ndarray' (or opsquat.get("iqft2"))
Inverse quaternion Fourier transform of a centred spectrum. → (H, W, 4).
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.
• quaternion_monogenic family guide
• 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.
• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py
qimage as input)quaternion_to_rgb · quat_norm · quat_conjugate_image · quat_normalize_image · quat_image_multiply · monogenic_amplitude · monogenic_phase · monogenic_orientation
fourier)*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.