tb_quat_norm — 2D `typed` op

• Data kinds: qimage → image

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

tb_quat_norm: input → output

*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*

*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*

*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*

Stages (the ops that come before → this op, left to right):

▸ tb_quat_norm: stages (docs site)

On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):

▸ tb_quat_norm: other inputs (docs site)

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.

Typed bridge of the quat op `quat_norm 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.

Try it in Studio

The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.

img_to_rgb 0.50 0.50
tb_rgb_to_quaternion 0.50 0.50
tb_quat_norm 0.50 0.50

▸ Load this pipeline · Load & run

Runnable examples (verified samples that actually call this op)

The examples below call the underlying ledger op quat_norm. This bridge op is the same implementation adapted to the fn(v, a, b) convention, so the behaviour carries over unchanged (only the call form differs).

• quaternion_monogenic — py -3.11 examples/quaternion_monogenic.py

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

identity · gaussian · mean_box · bilateral · unsharp · median · min_filter · max_filter

Same category (`typed`)

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

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

tb_quat_norm — 2D typed op