tb_iqft2 — 2D `typed` op

• Data kinds: qimage → qimage

• Call: fullseye.apply(img, "tb_iqft2", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])

*No figure: this op takes qimage as input. A Studio program starting from an image cannot reach that type — see the runnable examples below for how it is used.*

Usage

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.

Typed bridge of the quat op `iqft2 into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b` are unused.

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.

Runnable examples (verified samples that actually call this op)

• (none yet)

Ops the type connects to (they accept `qimage` as input)

identity · tb_quaternion_to_rgb · tb_quat_norm · tb_quat_conjugate_image · tb_quat_normalize_image · tb_monogenic_amplitude · tb_monogenic_phase · tb_monogenic_orientation

Same category (`typed`)

tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal

*Provenance: ops.py — 2D operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*

tb_iqft2 — 2D typed op